Preparing for 0.5.9 release.

[helm.git] / helm / software / components / binaries / matitaprover / benchmarks / log.090629-no-infer-on-closed-goals-10

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