--- /dev/null
+CLASH, statistics insufficient
+4578: Facts:
+4578: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+4578: Id : 3, {_}:
+ multiply ?5 ?6 =?= multiply ?6 ?5
+ [6, 5] by commutativity_of_multiply ?5 ?6
+4578: Id : 4, {_}:
+ add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10)
+ [10, 9, 8] by distributivity1 ?8 ?9 ?10
+4578: Id : 5, {_}:
+ add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14)
+ [14, 13, 12] by distributivity2 ?12 ?13 ?14
+4578: Id : 6, {_}:
+ multiply (add ?16 ?17) ?18
+ =<=
+ add (multiply ?16 ?18) (multiply ?17 ?18)
+ [18, 17, 16] by distributivity3 ?16 ?17 ?18
+4578: Id : 7, {_}:
+ multiply ?20 (add ?21 ?22)
+ =<=
+ add (multiply ?20 ?21) (multiply ?20 ?22)
+ [22, 21, 20] by distributivity4 ?20 ?21 ?22
+4578: Id : 8, {_}:
+ add ?24 (inverse ?24) =>= multiplicative_identity
+ [24] by additive_inverse1 ?24
+4578: Id : 9, {_}:
+ add (inverse ?26) ?26 =>= multiplicative_identity
+ [26] by additive_inverse2 ?26
+4578: Id : 10, {_}:
+ multiply ?28 (inverse ?28) =>= additive_identity
+ [28] by multiplicative_inverse1 ?28
+4578: Id : 11, {_}:
+ multiply (inverse ?30) ?30 =>= additive_identity
+ [30] by multiplicative_inverse2 ?30
+4578: Id : 12, {_}:
+ multiply ?32 multiplicative_identity =>= ?32
+ [32] by multiplicative_id1 ?32
+4578: Id : 13, {_}:
+ multiply multiplicative_identity ?34 =>= ?34
+ [34] by multiplicative_id2 ?34
+4578: Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
+4578: Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
+4578: Goal:
+4578: Id : 1, {_}:
+ multiply a (multiply b c) =<= multiply (multiply a b) c
+ [] by prove_associativity
+4578: Order:
+4578: nrkbo
+4578: Leaf order:
+4578: additive_identity 4 0 0
+4578: multiplicative_identity 4 0 0
+4578: inverse 4 1 0
+4578: add 16 2 0 multiply
+4578: multiply 20 2 4 0,2add
+4578: c 2 0 2 2,2,2
+4578: b 2 0 2 1,2,2
+4578: a 2 0 2 1,2
+CLASH, statistics insufficient
+4579: Facts:
+4579: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+4579: Id : 3, {_}:
+ multiply ?5 ?6 =?= multiply ?6 ?5
+ [6, 5] by commutativity_of_multiply ?5 ?6
+4579: Id : 4, {_}:
+ add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10)
+ [10, 9, 8] by distributivity1 ?8 ?9 ?10
+4579: Id : 5, {_}:
+ add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14)
+ [14, 13, 12] by distributivity2 ?12 ?13 ?14
+4579: Id : 6, {_}:
+ multiply (add ?16 ?17) ?18
+ =<=
+ add (multiply ?16 ?18) (multiply ?17 ?18)
+ [18, 17, 16] by distributivity3 ?16 ?17 ?18
+4579: Id : 7, {_}:
+ multiply ?20 (add ?21 ?22)
+ =<=
+ add (multiply ?20 ?21) (multiply ?20 ?22)
+ [22, 21, 20] by distributivity4 ?20 ?21 ?22
+4579: Id : 8, {_}:
+ add ?24 (inverse ?24) =>= multiplicative_identity
+ [24] by additive_inverse1 ?24
+4579: Id : 9, {_}:
+ add (inverse ?26) ?26 =>= multiplicative_identity
+ [26] by additive_inverse2 ?26
+4579: Id : 10, {_}:
+ multiply ?28 (inverse ?28) =>= additive_identity
+ [28] by multiplicative_inverse1 ?28
+4579: Id : 11, {_}:
+ multiply (inverse ?30) ?30 =>= additive_identity
+ [30] by multiplicative_inverse2 ?30
+4579: Id : 12, {_}:
+ multiply ?32 multiplicative_identity =>= ?32
+ [32] by multiplicative_id1 ?32
+4579: Id : 13, {_}:
+ multiply multiplicative_identity ?34 =>= ?34
+ [34] by multiplicative_id2 ?34
+4579: Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
+4579: Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
+4579: Goal:
+4579: Id : 1, {_}:
+ multiply a (multiply b c) =<= multiply (multiply a b) c
+ [] by prove_associativity
+4579: Order:
+4579: kbo
+4579: Leaf order:
+4579: additive_identity 4 0 0
+4579: multiplicative_identity 4 0 0
+4579: inverse 4 1 0
+4579: add 16 2 0 multiply
+4579: multiply 20 2 4 0,2add
+4579: c 2 0 2 2,2,2
+4579: b 2 0 2 1,2,2
+4579: a 2 0 2 1,2
+CLASH, statistics insufficient
+4580: Facts:
+4580: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+4580: Id : 3, {_}:
+ multiply ?5 ?6 =?= multiply ?6 ?5
+ [6, 5] by commutativity_of_multiply ?5 ?6
+4580: Id : 4, {_}:
+ add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10)
+ [10, 9, 8] by distributivity1 ?8 ?9 ?10
+4580: Id : 5, {_}:
+ add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14)
+ [14, 13, 12] by distributivity2 ?12 ?13 ?14
+4580: Id : 6, {_}:
+ multiply (add ?16 ?17) ?18
+ =>=
+ add (multiply ?16 ?18) (multiply ?17 ?18)
+ [18, 17, 16] by distributivity3 ?16 ?17 ?18
+4580: Id : 7, {_}:
+ multiply ?20 (add ?21 ?22)
+ =>=
+ add (multiply ?20 ?21) (multiply ?20 ?22)
+ [22, 21, 20] by distributivity4 ?20 ?21 ?22
+4580: Id : 8, {_}:
+ add ?24 (inverse ?24) =>= multiplicative_identity
+ [24] by additive_inverse1 ?24
+4580: Id : 9, {_}:
+ add (inverse ?26) ?26 =>= multiplicative_identity
+ [26] by additive_inverse2 ?26
+4580: Id : 10, {_}:
+ multiply ?28 (inverse ?28) =>= additive_identity
+ [28] by multiplicative_inverse1 ?28
+4580: Id : 11, {_}:
+ multiply (inverse ?30) ?30 =>= additive_identity
+ [30] by multiplicative_inverse2 ?30
+4580: Id : 12, {_}:
+ multiply ?32 multiplicative_identity =>= ?32
+ [32] by multiplicative_id1 ?32
+4580: Id : 13, {_}:
+ multiply multiplicative_identity ?34 =>= ?34
+ [34] by multiplicative_id2 ?34
+4580: Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
+4580: Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
+4580: Goal:
+4580: Id : 1, {_}:
+ multiply a (multiply b c) =<= multiply (multiply a b) c
+ [] by prove_associativity
+4580: Order:
+4580: lpo
+4580: Leaf order:
+4580: additive_identity 4 0 0
+4580: multiplicative_identity 4 0 0
+4580: inverse 4 1 0
+4580: add 16 2 0 multiply
+4580: multiply 20 2 4 0,2add
+4580: c 2 0 2 2,2,2
+4580: b 2 0 2 1,2,2
+4580: a 2 0 2 1,2
+Statistics :
+Max weight : 22
+Found proof, 16.914436s
+% SZS status Unsatisfiable for BOO007-2.p
+% SZS output start CNFRefutation for BOO007-2.p
+Id : 12, {_}: multiply ?32 multiplicative_identity =>= ?32 [32] by multiplicative_id1 ?32
+Id : 7, {_}: multiply ?20 (add ?21 ?22) =<= add (multiply ?20 ?21) (multiply ?20 ?22) [22, 21, 20] by distributivity4 ?20 ?21 ?22
+Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
+Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
+Id : 10, {_}: multiply ?28 (inverse ?28) =>= additive_identity [28] by multiplicative_inverse1 ?28
+Id : 13, {_}: multiply multiplicative_identity ?34 =>= ?34 [34] by multiplicative_id2 ?34
+Id : 8, {_}: add ?24 (inverse ?24) =>= multiplicative_identity [24] by additive_inverse1 ?24
+Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+Id : 31, {_}: add (multiply ?78 ?79) ?80 =<= multiply (add ?78 ?80) (add ?79 ?80) [80, 79, 78] by distributivity1 ?78 ?79 ?80
+Id : 5, {_}: add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14) [14, 13, 12] by distributivity2 ?12 ?13 ?14
+Id : 3, {_}: multiply ?5 ?6 =?= multiply ?6 ?5 [6, 5] by commutativity_of_multiply ?5 ?6
+Id : 6, {_}: multiply (add ?16 ?17) ?18 =<= add (multiply ?16 ?18) (multiply ?17 ?18) [18, 17, 16] by distributivity3 ?16 ?17 ?18
+Id : 4, {_}: add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10) [10, 9, 8] by distributivity1 ?8 ?9 ?10
+Id : 65, {_}: add (multiply ?156 (multiply ?157 ?158)) (multiply ?159 ?158) =<= multiply (add ?156 (multiply ?159 ?158)) (multiply (add ?157 ?159) ?158) [159, 158, 157, 156] by Super 4 with 6 at 2,3
+Id : 46, {_}: multiply (add ?110 ?111) (add ?110 ?112) =>= add ?110 (multiply ?112 ?111) [112, 111, 110] by Super 3 with 5 at 3
+Id : 58, {_}: add ?110 (multiply ?111 ?112) =?= add ?110 (multiply ?112 ?111) [112, 111, 110] by Demod 46 with 5 at 2
+Id : 32, {_}: add (multiply ?82 ?83) ?84 =<= multiply (add ?82 ?84) (add ?84 ?83) [84, 83, 82] by Super 31 with 2 at 2,3
+Id : 121, {_}: add ?333 (multiply (inverse ?333) ?334) =>= multiply multiplicative_identity (add ?333 ?334) [334, 333] by Super 5 with 8 at 1,3
+Id : 2169, {_}: add ?2910 (multiply (inverse ?2910) ?2911) =>= add ?2910 ?2911 [2911, 2910] by Demod 121 with 13 at 3
+Id : 2179, {_}: add ?2938 additive_identity =<= add ?2938 (inverse (inverse ?2938)) [2938] by Super 2169 with 10 at 2,2
+Id : 2230, {_}: ?2938 =<= add ?2938 (inverse (inverse ?2938)) [2938] by Demod 2179 with 14 at 2
+Id : 2429, {_}: add (multiply ?3159 (inverse (inverse ?3160))) ?3160 =>= multiply (add ?3159 ?3160) ?3160 [3160, 3159] by Super 32 with 2230 at 2,3
+Id : 2455, {_}: add ?3160 (multiply ?3159 (inverse (inverse ?3160))) =>= multiply (add ?3159 ?3160) ?3160 [3159, 3160] by Demod 2429 with 2 at 2
+Id : 2456, {_}: add ?3160 (multiply ?3159 (inverse (inverse ?3160))) =>= multiply ?3160 (add ?3159 ?3160) [3159, 3160] by Demod 2455 with 3 at 3
+Id : 248, {_}: add (multiply additive_identity ?467) ?468 =<= multiply ?468 (add ?467 ?468) [468, 467] by Super 4 with 15 at 1,3
+Id : 2457, {_}: add ?3160 (multiply ?3159 (inverse (inverse ?3160))) =>= add (multiply additive_identity ?3159) ?3160 [3159, 3160] by Demod 2456 with 248 at 3
+Id : 120, {_}: add ?330 (multiply ?331 (inverse ?330)) =>= multiply (add ?330 ?331) multiplicative_identity [331, 330] by Super 5 with 8 at 2,3
+Id : 124, {_}: add ?330 (multiply ?331 (inverse ?330)) =>= multiply multiplicative_identity (add ?330 ?331) [331, 330] by Demod 120 with 3 at 3
+Id : 3170, {_}: add ?330 (multiply ?331 (inverse ?330)) =>= add ?330 ?331 [331, 330] by Demod 124 with 13 at 3
+Id : 144, {_}: multiply ?347 (add (inverse ?347) ?348) =>= add additive_identity (multiply ?347 ?348) [348, 347] by Super 7 with 10 at 1,3
+Id : 3378, {_}: multiply ?4138 (add (inverse ?4138) ?4139) =>= multiply ?4138 ?4139 [4139, 4138] by Demod 144 with 15 at 3
+Id : 3399, {_}: multiply ?4195 (inverse ?4195) =<= multiply ?4195 (inverse (inverse (inverse ?4195))) [4195] by Super 3378 with 2230 at 2,2
+Id : 3488, {_}: additive_identity =<= multiply ?4195 (inverse (inverse (inverse ?4195))) [4195] by Demod 3399 with 10 at 2
+Id : 3900, {_}: add (inverse (inverse ?4844)) additive_identity =?= add (inverse (inverse ?4844)) ?4844 [4844] by Super 3170 with 3488 at 2,2
+Id : 3924, {_}: add additive_identity (inverse (inverse ?4844)) =<= add (inverse (inverse ?4844)) ?4844 [4844] by Demod 3900 with 2 at 2
+Id : 3925, {_}: add additive_identity (inverse (inverse ?4844)) =?= add ?4844 (inverse (inverse ?4844)) [4844] by Demod 3924 with 2 at 3
+Id : 3926, {_}: inverse (inverse ?4844) =<= add ?4844 (inverse (inverse ?4844)) [4844] by Demod 3925 with 15 at 2
+Id : 3927, {_}: inverse (inverse ?4844) =>= ?4844 [4844] by Demod 3926 with 2230 at 3
+Id : 6845, {_}: add ?3160 (multiply ?3159 ?3160) =?= add (multiply additive_identity ?3159) ?3160 [3159, 3160] by Demod 2457 with 3927 at 2,2,2
+Id : 1130, {_}: add (multiply additive_identity ?1671) ?1672 =<= multiply ?1672 (add ?1671 ?1672) [1672, 1671] by Super 4 with 15 at 1,3
+Id : 1134, {_}: add (multiply additive_identity ?1683) (inverse ?1683) =>= multiply (inverse ?1683) multiplicative_identity [1683] by Super 1130 with 8 at 2,3
+Id : 1186, {_}: add (inverse ?1683) (multiply additive_identity ?1683) =>= multiply (inverse ?1683) multiplicative_identity [1683] by Demod 1134 with 2 at 2
+Id : 1187, {_}: add (inverse ?1683) (multiply additive_identity ?1683) =>= multiply multiplicative_identity (inverse ?1683) [1683] by Demod 1186 with 3 at 3
+Id : 1188, {_}: add (inverse ?1683) (multiply additive_identity ?1683) =>= inverse ?1683 [1683] by Demod 1187 with 13 at 3
+Id : 3360, {_}: multiply ?347 (add (inverse ?347) ?348) =>= multiply ?347 ?348 [348, 347] by Demod 144 with 15 at 3
+Id : 3364, {_}: add (inverse (add (inverse additive_identity) ?4095)) (multiply additive_identity ?4095) =>= inverse (add (inverse additive_identity) ?4095) [4095] by Super 1188 with 3360 at 2,2
+Id : 3442, {_}: add (multiply additive_identity ?4095) (inverse (add (inverse additive_identity) ?4095)) =>= inverse (add (inverse additive_identity) ?4095) [4095] by Demod 3364 with 2 at 2
+Id : 249, {_}: inverse additive_identity =>= multiplicative_identity [] by Super 8 with 15 at 2
+Id : 3443, {_}: add (multiply additive_identity ?4095) (inverse (add (inverse additive_identity) ?4095)) =>= inverse (add multiplicative_identity ?4095) [4095] by Demod 3442 with 249 at 1,1,3
+Id : 3444, {_}: add (multiply additive_identity ?4095) (inverse (add multiplicative_identity ?4095)) =>= inverse (add multiplicative_identity ?4095) [4095] by Demod 3443 with 249 at 1,1,2,2
+Id : 2180, {_}: add ?2940 (inverse ?2940) =>= add ?2940 multiplicative_identity [2940] by Super 2169 with 12 at 2,2
+Id : 2231, {_}: multiplicative_identity =<= add ?2940 multiplicative_identity [2940] by Demod 2180 with 8 at 2
+Id : 2263, {_}: add multiplicative_identity ?3015 =>= multiplicative_identity [3015] by Super 2 with 2231 at 3
+Id : 3445, {_}: add (multiply additive_identity ?4095) (inverse (add multiplicative_identity ?4095)) =>= inverse multiplicative_identity [4095] by Demod 3444 with 2263 at 1,3
+Id : 3446, {_}: add (multiply additive_identity ?4095) (inverse multiplicative_identity) =>= inverse multiplicative_identity [4095] by Demod 3445 with 2263 at 1,2,2
+Id : 191, {_}: inverse multiplicative_identity =>= additive_identity [] by Super 10 with 13 at 2
+Id : 3447, {_}: add (multiply additive_identity ?4095) (inverse multiplicative_identity) =>= additive_identity [4095] by Demod 3446 with 191 at 3
+Id : 3448, {_}: add (inverse multiplicative_identity) (multiply additive_identity ?4095) =>= additive_identity [4095] by Demod 3447 with 2 at 2
+Id : 3449, {_}: add additive_identity (multiply additive_identity ?4095) =>= additive_identity [4095] by Demod 3448 with 191 at 1,2
+Id : 3450, {_}: multiply additive_identity ?4095 =>= additive_identity [4095] by Demod 3449 with 15 at 2
+Id : 6846, {_}: add ?3160 (multiply ?3159 ?3160) =>= add additive_identity ?3160 [3159, 3160] by Demod 6845 with 3450 at 1,3
+Id : 6847, {_}: add ?3160 (multiply ?3159 ?3160) =>= ?3160 [3159, 3160] by Demod 6846 with 15 at 3
+Id : 6852, {_}: add ?8316 (multiply ?8316 ?8317) =>= ?8316 [8317, 8316] by Super 58 with 6847 at 3
+Id : 7003, {_}: add (multiply ?8541 (multiply ?8542 ?8543)) (multiply ?8541 ?8543) =>= multiply ?8541 (multiply (add ?8542 ?8541) ?8543) [8543, 8542, 8541] by Super 65 with 6852 at 1,3
+Id : 7114, {_}: add (multiply ?8541 ?8543) (multiply ?8541 (multiply ?8542 ?8543)) =>= multiply ?8541 (multiply (add ?8542 ?8541) ?8543) [8542, 8543, 8541] by Demod 7003 with 2 at 2
+Id : 7115, {_}: multiply ?8541 (add ?8543 (multiply ?8542 ?8543)) =?= multiply ?8541 (multiply (add ?8542 ?8541) ?8543) [8542, 8543, 8541] by Demod 7114 with 7 at 2
+Id : 21444, {_}: multiply ?30534 ?30535 =<= multiply ?30534 (multiply (add ?30536 ?30534) ?30535) [30536, 30535, 30534] by Demod 7115 with 6847 at 2,2
+Id : 21466, {_}: multiply (multiply ?30625 ?30626) ?30627 =<= multiply (multiply ?30625 ?30626) (multiply ?30626 ?30627) [30627, 30626, 30625] by Super 21444 with 6847 at 1,2,3
+Id : 147, {_}: multiply (add ?355 ?356) (inverse ?355) =>= add additive_identity (multiply ?356 (inverse ?355)) [356, 355] by Super 6 with 10 at 1,3
+Id : 152, {_}: multiply (inverse ?355) (add ?355 ?356) =>= add additive_identity (multiply ?356 (inverse ?355)) [356, 355] by Demod 147 with 3 at 2
+Id : 4375, {_}: multiply (inverse ?355) (add ?355 ?356) =>= multiply ?356 (inverse ?355) [356, 355] by Demod 152 with 15 at 3
+Id : 532, {_}: add (multiply ?866 ?867) ?868 =<= multiply (add ?866 ?868) (add ?868 ?867) [868, 867, 866] by Super 31 with 2 at 2,3
+Id : 547, {_}: add (multiply ?925 ?926) (inverse ?925) =?= multiply multiplicative_identity (add (inverse ?925) ?926) [926, 925] by Super 532 with 8 at 1,3
+Id : 583, {_}: add (inverse ?925) (multiply ?925 ?926) =?= multiply multiplicative_identity (add (inverse ?925) ?926) [926, 925] by Demod 547 with 2 at 2
+Id : 584, {_}: add (inverse ?925) (multiply ?925 ?926) =>= add (inverse ?925) ?926 [926, 925] by Demod 583 with 13 at 3
+Id : 4646, {_}: multiply (inverse (inverse ?5719)) (add (inverse ?5719) ?5720) =>= multiply (multiply ?5719 ?5720) (inverse (inverse ?5719)) [5720, 5719] by Super 4375 with 584 at 2,2
+Id : 4685, {_}: multiply ?5720 (inverse (inverse ?5719)) =<= multiply (multiply ?5719 ?5720) (inverse (inverse ?5719)) [5719, 5720] by Demod 4646 with 4375 at 2
+Id : 4686, {_}: multiply ?5720 (inverse (inverse ?5719)) =<= multiply (inverse (inverse ?5719)) (multiply ?5719 ?5720) [5719, 5720] by Demod 4685 with 3 at 3
+Id : 4687, {_}: multiply ?5720 ?5719 =<= multiply (inverse (inverse ?5719)) (multiply ?5719 ?5720) [5719, 5720] by Demod 4686 with 3927 at 2,2
+Id : 4688, {_}: multiply ?5720 ?5719 =<= multiply ?5719 (multiply ?5719 ?5720) [5719, 5720] by Demod 4687 with 3927 at 1,3
+Id : 21467, {_}: multiply (multiply ?30629 ?30630) ?30631 =<= multiply (multiply ?30629 ?30630) (multiply ?30629 ?30631) [30631, 30630, 30629] by Super 21444 with 6852 at 1,2,3
+Id : 36399, {_}: multiply (multiply ?58815 ?58816) (multiply ?58815 ?58817) =<= multiply (multiply ?58815 ?58817) (multiply (multiply ?58815 ?58817) ?58816) [58817, 58816, 58815] by Super 4688 with 21467 at 2,3
+Id : 36627, {_}: multiply (multiply ?58815 ?58816) ?58817 =<= multiply (multiply ?58815 ?58817) (multiply (multiply ?58815 ?58817) ?58816) [58817, 58816, 58815] by Demod 36399 with 21467 at 2
+Id : 36628, {_}: multiply (multiply ?58815 ?58816) ?58817 =>= multiply ?58816 (multiply ?58815 ?58817) [58817, 58816, 58815] by Demod 36627 with 4688 at 3
+Id : 36893, {_}: multiply ?30626 (multiply ?30625 ?30627) =<= multiply (multiply ?30625 ?30626) (multiply ?30626 ?30627) [30627, 30625, 30626] by Demod 21466 with 36628 at 2
+Id : 36894, {_}: multiply ?30626 (multiply ?30625 ?30627) =<= multiply ?30626 (multiply ?30625 (multiply ?30626 ?30627)) [30627, 30625, 30626] by Demod 36893 with 36628 at 3
+Id : 3522, {_}: add additive_identity ?468 =<= multiply ?468 (add ?467 ?468) [467, 468] by Demod 248 with 3450 at 1,2
+Id : 3543, {_}: ?468 =<= multiply ?468 (add ?467 ?468) [467, 468] by Demod 3522 with 15 at 2
+Id : 7020, {_}: add (multiply ?8599 (multiply ?8600 ?8601)) ?8600 =>= multiply (add ?8599 ?8600) ?8600 [8601, 8600, 8599] by Super 32 with 6852 at 2,3
+Id : 7087, {_}: add ?8600 (multiply ?8599 (multiply ?8600 ?8601)) =>= multiply (add ?8599 ?8600) ?8600 [8601, 8599, 8600] by Demod 7020 with 2 at 2
+Id : 7088, {_}: add ?8600 (multiply ?8599 (multiply ?8600 ?8601)) =>= multiply ?8600 (add ?8599 ?8600) [8601, 8599, 8600] by Demod 7087 with 3 at 3
+Id : 7089, {_}: add ?8600 (multiply ?8599 (multiply ?8600 ?8601)) =>= ?8600 [8601, 8599, 8600] by Demod 7088 with 3543 at 3
+Id : 20142, {_}: multiply ?27776 (multiply ?27777 ?27778) =<= multiply (multiply ?27776 (multiply ?27777 ?27778)) ?27777 [27778, 27777, 27776] by Super 3543 with 7089 at 2,3
+Id : 20329, {_}: multiply ?27776 (multiply ?27777 ?27778) =<= multiply ?27777 (multiply ?27776 (multiply ?27777 ?27778)) [27778, 27777, 27776] by Demod 20142 with 3 at 3
+Id : 36895, {_}: multiply ?30626 (multiply ?30625 ?30627) =?= multiply ?30625 (multiply ?30626 ?30627) [30627, 30625, 30626] by Demod 36894 with 20329 at 3
+Id : 34, {_}: add (multiply ?90 ?91) ?92 =<= multiply (add ?92 ?90) (add ?91 ?92) [92, 91, 90] by Super 31 with 2 at 1,3
+Id : 6868, {_}: add (multiply (multiply ?8366 ?8367) ?8368) ?8367 =>= multiply ?8367 (add ?8368 ?8367) [8368, 8367, 8366] by Super 34 with 6847 at 1,3
+Id : 6940, {_}: add ?8367 (multiply (multiply ?8366 ?8367) ?8368) =>= multiply ?8367 (add ?8368 ?8367) [8368, 8366, 8367] by Demod 6868 with 2 at 2
+Id : 6941, {_}: add ?8367 (multiply (multiply ?8366 ?8367) ?8368) =>= ?8367 [8368, 8366, 8367] by Demod 6940 with 3543 at 3
+Id : 19816, {_}: multiply (multiply ?27180 ?27181) ?27182 =<= multiply (multiply (multiply ?27180 ?27181) ?27182) ?27181 [27182, 27181, 27180] by Super 3543 with 6941 at 2,3
+Id : 19977, {_}: multiply (multiply ?27180 ?27181) ?27182 =<= multiply ?27181 (multiply (multiply ?27180 ?27181) ?27182) [27182, 27181, 27180] by Demod 19816 with 3 at 3
+Id : 36891, {_}: multiply ?27181 (multiply ?27180 ?27182) =<= multiply ?27181 (multiply (multiply ?27180 ?27181) ?27182) [27182, 27180, 27181] by Demod 19977 with 36628 at 2
+Id : 36892, {_}: multiply ?27181 (multiply ?27180 ?27182) =<= multiply ?27181 (multiply ?27181 (multiply ?27180 ?27182)) [27182, 27180, 27181] by Demod 36891 with 36628 at 2,3
+Id : 36900, {_}: multiply ?27181 (multiply ?27180 ?27182) =?= multiply (multiply ?27180 ?27182) ?27181 [27182, 27180, 27181] by Demod 36892 with 4688 at 3
+Id : 36901, {_}: multiply ?27181 (multiply ?27180 ?27182) =?= multiply ?27182 (multiply ?27180 ?27181) [27182, 27180, 27181] by Demod 36900 with 36628 at 3
+Id : 37364, {_}: multiply c (multiply b a) =?= multiply c (multiply b a) [] by Demod 37363 with 3 at 2,2
+Id : 37363, {_}: multiply c (multiply a b) =?= multiply c (multiply b a) [] by Demod 37362 with 3 at 2,3
+Id : 37362, {_}: multiply c (multiply a b) =?= multiply c (multiply a b) [] by Demod 37361 with 36901 at 2
+Id : 37361, {_}: multiply b (multiply a c) =>= multiply c (multiply a b) [] by Demod 37360 with 3 at 3
+Id : 37360, {_}: multiply b (multiply a c) =<= multiply (multiply a b) c [] by Demod 1 with 36895 at 2
+Id : 1, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
+% SZS output end CNFRefutation for BOO007-2.p
+4579: solved BOO007-2.p in 8.372523 using kbo
+4579: status Unsatisfiable for BOO007-2.p
+CLASH, statistics insufficient
+4588: Facts:
+4588: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+4588: Id : 3, {_}:
+ multiply ?5 ?6 =?= multiply ?6 ?5
+ [6, 5] by commutativity_of_multiply ?5 ?6
+4588: Id : 4, {_}:
+ add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10)
+ [10, 9, 8] by distributivity1 ?8 ?9 ?10
+4588: Id : 5, {_}:
+ multiply ?12 (add ?13 ?14)
+ =<=
+ add (multiply ?12 ?13) (multiply ?12 ?14)
+ [14, 13, 12] by distributivity2 ?12 ?13 ?14
+4588: Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
+4588: Id : 7, {_}:
+ multiply ?18 multiplicative_identity =>= ?18
+ [18] by multiplicative_id1 ?18
+4588: Id : 8, {_}:
+ add ?20 (inverse ?20) =>= multiplicative_identity
+ [20] by additive_inverse1 ?20
+4588: Id : 9, {_}:
+ multiply ?22 (inverse ?22) =>= additive_identity
+ [22] by multiplicative_inverse1 ?22
+4588: Goal:
+4588: Id : 1, {_}:
+ multiply a (multiply b c) =<= multiply (multiply a b) c
+ [] by prove_associativity
+4588: Order:
+4588: nrkbo
+4588: Leaf order:
+4588: inverse 2 1 0
+4588: multiplicative_identity 2 0 0
+4588: additive_identity 2 0 0
+4588: add 9 2 0 multiply
+4588: multiply 13 2 4 0,2add
+4588: c 2 0 2 2,2,2
+4588: b 2 0 2 1,2,2
+4588: a 2 0 2 1,2
+CLASH, statistics insufficient
+4589: Facts:
+4589: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+4589: Id : 3, {_}:
+ multiply ?5 ?6 =?= multiply ?6 ?5
+ [6, 5] by commutativity_of_multiply ?5 ?6
+4589: Id : 4, {_}:
+ add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10)
+ [10, 9, 8] by distributivity1 ?8 ?9 ?10
+4589: Id : 5, {_}:
+ multiply ?12 (add ?13 ?14)
+ =<=
+ add (multiply ?12 ?13) (multiply ?12 ?14)
+ [14, 13, 12] by distributivity2 ?12 ?13 ?14
+4589: Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
+4589: Id : 7, {_}:
+ multiply ?18 multiplicative_identity =>= ?18
+ [18] by multiplicative_id1 ?18
+4589: Id : 8, {_}:
+ add ?20 (inverse ?20) =>= multiplicative_identity
+ [20] by additive_inverse1 ?20
+4589: Id : 9, {_}:
+ multiply ?22 (inverse ?22) =>= additive_identity
+ [22] by multiplicative_inverse1 ?22
+4589: Goal:
+4589: Id : 1, {_}:
+ multiply a (multiply b c) =<= multiply (multiply a b) c
+ [] by prove_associativity
+4589: Order:
+4589: kbo
+4589: Leaf order:
+4589: inverse 2 1 0
+4589: multiplicative_identity 2 0 0
+4589: additive_identity 2 0 0
+4589: add 9 2 0 multiply
+4589: multiply 13 2 4 0,2add
+4589: c 2 0 2 2,2,2
+4589: b 2 0 2 1,2,2
+4589: a 2 0 2 1,2
+CLASH, statistics insufficient
+4590: Facts:
+4590: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+4590: Id : 3, {_}:
+ multiply ?5 ?6 =?= multiply ?6 ?5
+ [6, 5] by commutativity_of_multiply ?5 ?6
+4590: Id : 4, {_}:
+ add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10)
+ [10, 9, 8] by distributivity1 ?8 ?9 ?10
+4590: Id : 5, {_}:
+ multiply ?12 (add ?13 ?14)
+ =>=
+ add (multiply ?12 ?13) (multiply ?12 ?14)
+ [14, 13, 12] by distributivity2 ?12 ?13 ?14
+4590: Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
+4590: Id : 7, {_}:
+ multiply ?18 multiplicative_identity =>= ?18
+ [18] by multiplicative_id1 ?18
+4590: Id : 8, {_}:
+ add ?20 (inverse ?20) =>= multiplicative_identity
+ [20] by additive_inverse1 ?20
+4590: Id : 9, {_}:
+ multiply ?22 (inverse ?22) =>= additive_identity
+ [22] by multiplicative_inverse1 ?22
+4590: Goal:
+4590: Id : 1, {_}:
+ multiply a (multiply b c) =<= multiply (multiply a b) c
+ [] by prove_associativity
+4590: Order:
+4590: lpo
+4590: Leaf order:
+4590: inverse 2 1 0
+4590: multiplicative_identity 2 0 0
+4590: additive_identity 2 0 0
+4590: add 9 2 0 multiply
+4590: multiply 13 2 4 0,2add
+4590: c 2 0 2 2,2,2
+4590: b 2 0 2 1,2,2
+4590: a 2 0 2 1,2
+Statistics :
+Max weight : 25
+Found proof, 23.495904s
+% SZS status Unsatisfiable for BOO007-4.p
+% SZS output start CNFRefutation for BOO007-4.p
+Id : 44, {_}: multiply ?112 (add ?113 ?114) =<= add (multiply ?112 ?113) (multiply ?112 ?114) [114, 113, 112] by distributivity2 ?112 ?113 ?114
+Id : 4, {_}: add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10) [10, 9, 8] by distributivity1 ?8 ?9 ?10
+Id : 9, {_}: multiply ?22 (inverse ?22) =>= additive_identity [22] by multiplicative_inverse1 ?22
+Id : 5, {_}: multiply ?12 (add ?13 ?14) =<= add (multiply ?12 ?13) (multiply ?12 ?14) [14, 13, 12] by distributivity2 ?12 ?13 ?14
+Id : 7, {_}: multiply ?18 multiplicative_identity =>= ?18 [18] by multiplicative_id1 ?18
+Id : 3, {_}: multiply ?5 ?6 =?= multiply ?6 ?5 [6, 5] by commutativity_of_multiply ?5 ?6
+Id : 8, {_}: add ?20 (inverse ?20) =>= multiplicative_identity [20] by additive_inverse1 ?20
+Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
+Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+Id : 25, {_}: add ?62 (multiply ?63 ?64) =<= multiply (add ?62 ?63) (add ?62 ?64) [64, 63, 62] by distributivity1 ?62 ?63 ?64
+Id : 516, {_}: add ?742 (multiply ?743 ?744) =<= multiply (add ?742 ?743) (add ?744 ?742) [744, 743, 742] by Super 25 with 2 at 2,3
+Id : 530, {_}: add ?796 (multiply additive_identity ?797) =<= multiply ?796 (add ?797 ?796) [797, 796] by Super 516 with 6 at 1,3
+Id : 1019, {_}: add ?1448 (multiply additive_identity ?1449) =<= multiply ?1448 (add ?1449 ?1448) [1449, 1448] by Super 516 with 6 at 1,3
+Id : 1024, {_}: add (inverse ?1462) (multiply additive_identity ?1462) =>= multiply (inverse ?1462) multiplicative_identity [1462] by Super 1019 with 8 at 2,3
+Id : 1064, {_}: add (inverse ?1462) (multiply additive_identity ?1462) =>= multiply multiplicative_identity (inverse ?1462) [1462] by Demod 1024 with 3 at 3
+Id : 75, {_}: multiply multiplicative_identity ?178 =>= ?178 [178] by Super 3 with 7 at 3
+Id : 1065, {_}: add (inverse ?1462) (multiply additive_identity ?1462) =>= inverse ?1462 [1462] by Demod 1064 with 75 at 3
+Id : 97, {_}: multiply ?204 (add (inverse ?204) ?205) =>= add additive_identity (multiply ?204 ?205) [205, 204] by Super 5 with 9 at 1,3
+Id : 63, {_}: add additive_identity ?160 =>= ?160 [160] by Super 2 with 6 at 3
+Id : 2714, {_}: multiply ?204 (add (inverse ?204) ?205) =>= multiply ?204 ?205 [205, 204] by Demod 97 with 63 at 3
+Id : 2718, {_}: add (inverse (add (inverse additive_identity) ?3390)) (multiply additive_identity ?3390) =>= inverse (add (inverse additive_identity) ?3390) [3390] by Super 1065 with 2714 at 2,2
+Id : 2791, {_}: add (multiply additive_identity ?3390) (inverse (add (inverse additive_identity) ?3390)) =>= inverse (add (inverse additive_identity) ?3390) [3390] by Demod 2718 with 2 at 2
+Id : 184, {_}: inverse additive_identity =>= multiplicative_identity [] by Super 8 with 63 at 2
+Id : 2792, {_}: add (multiply additive_identity ?3390) (inverse (add (inverse additive_identity) ?3390)) =>= inverse (add multiplicative_identity ?3390) [3390] by Demod 2791 with 184 at 1,1,3
+Id : 2793, {_}: add (multiply additive_identity ?3390) (inverse (add multiplicative_identity ?3390)) =>= inverse (add multiplicative_identity ?3390) [3390] by Demod 2792 with 184 at 1,1,2,2
+Id : 86, {_}: add ?193 (multiply (inverse ?193) ?194) =>= multiply multiplicative_identity (add ?193 ?194) [194, 193] by Super 4 with 8 at 1,3
+Id : 1836, {_}: add ?2310 (multiply (inverse ?2310) ?2311) =>= add ?2310 ?2311 [2311, 2310] by Demod 86 with 75 at 3
+Id : 1846, {_}: add ?2338 (inverse ?2338) =>= add ?2338 multiplicative_identity [2338] by Super 1836 with 7 at 2,2
+Id : 1890, {_}: multiplicative_identity =<= add ?2338 multiplicative_identity [2338] by Demod 1846 with 8 at 2
+Id : 1917, {_}: add multiplicative_identity ?2407 =>= multiplicative_identity [2407] by Super 2 with 1890 at 3
+Id : 2794, {_}: add (multiply additive_identity ?3390) (inverse (add multiplicative_identity ?3390)) =>= inverse multiplicative_identity [3390] by Demod 2793 with 1917 at 1,3
+Id : 2795, {_}: add (multiply additive_identity ?3390) (inverse multiplicative_identity) =>= inverse multiplicative_identity [3390] by Demod 2794 with 1917 at 1,2,2
+Id : 476, {_}: inverse multiplicative_identity =>= additive_identity [] by Super 9 with 75 at 2
+Id : 2796, {_}: add (multiply additive_identity ?3390) (inverse multiplicative_identity) =>= additive_identity [3390] by Demod 2795 with 476 at 3
+Id : 2797, {_}: add (inverse multiplicative_identity) (multiply additive_identity ?3390) =>= additive_identity [3390] by Demod 2796 with 2 at 2
+Id : 2798, {_}: add additive_identity (multiply additive_identity ?3390) =>= additive_identity [3390] by Demod 2797 with 476 at 1,2
+Id : 2799, {_}: multiply additive_identity ?3390 =>= additive_identity [3390] by Demod 2798 with 63 at 2
+Id : 2854, {_}: add ?796 additive_identity =<= multiply ?796 (add ?797 ?796) [797, 796] by Demod 530 with 2799 at 2,2
+Id : 2870, {_}: ?796 =<= multiply ?796 (add ?797 ?796) [797, 796] by Demod 2854 with 6 at 2
+Id : 2113, {_}: add (multiply ?2595 ?2596) (multiply ?2597 (multiply ?2595 ?2598)) =<= multiply (add (multiply ?2595 ?2596) ?2597) (multiply ?2595 (add ?2596 ?2598)) [2598, 2597, 2596, 2595] by Super 4 with 5 at 2,3
+Id : 2126, {_}: add (multiply ?2655 multiplicative_identity) (multiply ?2656 (multiply ?2655 ?2657)) =?= multiply (add (multiply ?2655 multiplicative_identity) ?2656) (multiply ?2655 multiplicative_identity) [2657, 2656, 2655] by Super 2113 with 1917 at 2,2,3
+Id : 2201, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =?= multiply (add (multiply ?2655 multiplicative_identity) ?2656) (multiply ?2655 multiplicative_identity) [2657, 2656, 2655] by Demod 2126 with 7 at 1,2
+Id : 2202, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =?= multiply (multiply ?2655 multiplicative_identity) (add (multiply ?2655 multiplicative_identity) ?2656) [2657, 2656, 2655] by Demod 2201 with 3 at 3
+Id : 62, {_}: add ?157 (multiply additive_identity ?158) =<= multiply ?157 (add ?157 ?158) [158, 157] by Super 4 with 6 at 1,3
+Id : 2203, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =?= add (multiply ?2655 multiplicative_identity) (multiply additive_identity ?2656) [2657, 2656, 2655] by Demod 2202 with 62 at 3
+Id : 2204, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =>= add ?2655 (multiply additive_identity ?2656) [2657, 2656, 2655] by Demod 2203 with 7 at 1,3
+Id : 12654, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =>= add ?2655 additive_identity [2657, 2656, 2655] by Demod 2204 with 2799 at 2,3
+Id : 12655, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =>= ?2655 [2657, 2656, 2655] by Demod 12654 with 6 at 3
+Id : 12666, {_}: multiply ?15534 (multiply ?15535 ?15536) =<= multiply (multiply ?15534 (multiply ?15535 ?15536)) ?15535 [15536, 15535, 15534] by Super 2870 with 12655 at 2,3
+Id : 21339, {_}: multiply ?30912 (multiply ?30913 ?30914) =<= multiply ?30913 (multiply ?30912 (multiply ?30913 ?30914)) [30914, 30913, 30912] by Demod 12666 with 3 at 3
+Id : 21342, {_}: multiply ?30924 (multiply ?30925 ?30926) =<= multiply ?30925 (multiply ?30924 (multiply ?30926 ?30925)) [30926, 30925, 30924] by Super 21339 with 3 at 2,2,3
+Id : 28, {_}: add ?74 (multiply ?75 ?76) =<= multiply (add ?75 ?74) (add ?74 ?76) [76, 75, 74] by Super 25 with 2 at 1,3
+Id : 4808, {_}: multiply ?5796 (add ?5797 ?5798) =<= add (multiply ?5796 ?5797) (multiply ?5798 ?5796) [5798, 5797, 5796] by Super 44 with 3 at 2,3
+Id : 4837, {_}: multiply ?5913 (add multiplicative_identity ?5914) =?= add ?5913 (multiply ?5914 ?5913) [5914, 5913] by Super 4808 with 7 at 1,3
+Id : 4917, {_}: multiply ?5913 multiplicative_identity =<= add ?5913 (multiply ?5914 ?5913) [5914, 5913] by Demod 4837 with 1917 at 2,2
+Id : 4918, {_}: ?5913 =<= add ?5913 (multiply ?5914 ?5913) [5914, 5913] by Demod 4917 with 7 at 2
+Id : 5091, {_}: add ?6286 (multiply ?6287 (multiply ?6288 ?6286)) =>= multiply (add ?6287 ?6286) ?6286 [6288, 6287, 6286] by Super 28 with 4918 at 2,3
+Id : 5151, {_}: add ?6286 (multiply ?6287 (multiply ?6288 ?6286)) =>= multiply ?6286 (add ?6287 ?6286) [6288, 6287, 6286] by Demod 5091 with 3 at 3
+Id : 5152, {_}: add ?6286 (multiply ?6287 (multiply ?6288 ?6286)) =>= ?6286 [6288, 6287, 6286] by Demod 5151 with 2870 at 3
+Id : 19536, {_}: multiply ?27546 (multiply ?27547 ?27548) =<= multiply (multiply ?27546 (multiply ?27547 ?27548)) ?27548 [27548, 27547, 27546] by Super 2870 with 5152 at 2,3
+Id : 19689, {_}: multiply ?27546 (multiply ?27547 ?27548) =<= multiply ?27548 (multiply ?27546 (multiply ?27547 ?27548)) [27548, 27547, 27546] by Demod 19536 with 3 at 3
+Id : 31289, {_}: multiply ?30924 (multiply ?30925 ?30926) =?= multiply ?30924 (multiply ?30926 ?30925) [30926, 30925, 30924] by Demod 21342 with 19689 at 3
+Id : 521, {_}: add (inverse ?761) (multiply ?762 ?761) =?= multiply (add (inverse ?761) ?762) multiplicative_identity [762, 761] by Super 516 with 8 at 2,3
+Id : 550, {_}: add (inverse ?761) (multiply ?762 ?761) =?= multiply multiplicative_identity (add (inverse ?761) ?762) [762, 761] by Demod 521 with 3 at 3
+Id : 551, {_}: add (inverse ?761) (multiply ?762 ?761) =>= add (inverse ?761) ?762 [762, 761] by Demod 550 with 75 at 3
+Id : 3740, {_}: multiply ?4638 (add (inverse ?4638) ?4639) =>= multiply ?4638 (multiply ?4639 ?4638) [4639, 4638] by Super 2714 with 551 at 2,2
+Id : 3782, {_}: multiply ?4638 ?4639 =<= multiply ?4638 (multiply ?4639 ?4638) [4639, 4638] by Demod 3740 with 2714 at 2
+Id : 3863, {_}: multiply ?4768 (add ?4769 (multiply ?4770 ?4768)) =>= add (multiply ?4768 ?4769) (multiply ?4768 ?4770) [4770, 4769, 4768] by Super 5 with 3782 at 2,3
+Id : 15840, {_}: multiply ?20984 (add ?20985 (multiply ?20986 ?20984)) =>= multiply ?20984 (add ?20985 ?20986) [20986, 20985, 20984] by Demod 3863 with 5 at 3
+Id : 15903, {_}: multiply ?21234 (multiply ?21235 (add ?21236 ?21234)) =?= multiply ?21234 (add (multiply ?21235 ?21236) ?21235) [21236, 21235, 21234] by Super 15840 with 5 at 2,2
+Id : 16059, {_}: multiply ?21234 (multiply ?21235 (add ?21236 ?21234)) =?= multiply ?21234 (add ?21235 (multiply ?21235 ?21236)) [21236, 21235, 21234] by Demod 15903 with 2 at 2,3
+Id : 4814, {_}: multiply ?5818 (add ?5819 multiplicative_identity) =?= add (multiply ?5818 ?5819) ?5818 [5819, 5818] by Super 4808 with 75 at 2,3
+Id : 4891, {_}: multiply ?5818 multiplicative_identity =<= add (multiply ?5818 ?5819) ?5818 [5819, 5818] by Demod 4814 with 1890 at 2,2
+Id : 4892, {_}: multiply ?5818 multiplicative_identity =<= add ?5818 (multiply ?5818 ?5819) [5819, 5818] by Demod 4891 with 2 at 3
+Id : 4893, {_}: ?5818 =<= add ?5818 (multiply ?5818 ?5819) [5819, 5818] by Demod 4892 with 7 at 2
+Id : 26804, {_}: multiply ?40743 (multiply ?40744 (add ?40745 ?40743)) =>= multiply ?40743 ?40744 [40745, 40744, 40743] by Demod 16059 with 4893 at 2,3
+Id : 26854, {_}: multiply (multiply ?40962 ?40963) (multiply ?40964 ?40962) =>= multiply (multiply ?40962 ?40963) ?40964 [40964, 40963, 40962] by Super 26804 with 4893 at 2,2,2
+Id : 38294, {_}: multiply (multiply ?63621 ?63622) (multiply ?63621 ?63623) =>= multiply (multiply ?63621 ?63622) ?63623 [63623, 63622, 63621] by Super 31289 with 26854 at 3
+Id : 26855, {_}: multiply (multiply ?40966 ?40967) (multiply ?40968 ?40967) =>= multiply (multiply ?40966 ?40967) ?40968 [40968, 40967, 40966] by Super 26804 with 4918 at 2,2,2
+Id : 38958, {_}: multiply (multiply ?65058 ?65059) (multiply ?65059 ?65060) =>= multiply (multiply ?65058 ?65059) ?65060 [65060, 65059, 65058] by Super 31289 with 26855 at 3
+Id : 38330, {_}: multiply (multiply ?63784 ?63785) (multiply ?63785 ?63786) =>= multiply (multiply ?63785 ?63786) ?63784 [63786, 63785, 63784] by Super 3 with 26854 at 3
+Id : 46713, {_}: multiply (multiply ?65059 ?65060) ?65058 =?= multiply (multiply ?65058 ?65059) ?65060 [65058, 65060, 65059] by Demod 38958 with 38330 at 2
+Id : 46797, {_}: multiply ?81775 (multiply ?81776 ?81777) =<= multiply (multiply ?81775 ?81776) ?81777 [81777, 81776, 81775] by Super 3 with 46713 at 3
+Id : 47389, {_}: multiply ?63621 (multiply ?63622 (multiply ?63621 ?63623)) =>= multiply (multiply ?63621 ?63622) ?63623 [63623, 63622, 63621] by Demod 38294 with 46797 at 2
+Id : 47390, {_}: multiply ?63621 (multiply ?63622 (multiply ?63621 ?63623)) =>= multiply ?63621 (multiply ?63622 ?63623) [63623, 63622, 63621] by Demod 47389 with 46797 at 3
+Id : 12809, {_}: multiply ?15534 (multiply ?15535 ?15536) =<= multiply ?15535 (multiply ?15534 (multiply ?15535 ?15536)) [15536, 15535, 15534] by Demod 12666 with 3 at 3
+Id : 47391, {_}: multiply ?63622 (multiply ?63621 ?63623) =?= multiply ?63621 (multiply ?63622 ?63623) [63623, 63621, 63622] by Demod 47390 with 12809 at 2
+Id : 47371, {_}: multiply ?40962 (multiply ?40963 (multiply ?40964 ?40962)) =>= multiply (multiply ?40962 ?40963) ?40964 [40964, 40963, 40962] by Demod 26854 with 46797 at 2
+Id : 47372, {_}: multiply ?40962 (multiply ?40963 (multiply ?40964 ?40962)) =>= multiply ?40962 (multiply ?40963 ?40964) [40964, 40963, 40962] by Demod 47371 with 46797 at 3
+Id : 47409, {_}: multiply ?40963 (multiply ?40964 ?40962) =?= multiply ?40962 (multiply ?40963 ?40964) [40962, 40964, 40963] by Demod 47372 with 19689 at 2
+Id : 47847, {_}: multiply c (multiply b a) =?= multiply c (multiply b a) [] by Demod 47846 with 3 at 2,3
+Id : 47846, {_}: multiply c (multiply b a) =?= multiply c (multiply a b) [] by Demod 47845 with 47409 at 2
+Id : 47845, {_}: multiply b (multiply a c) =>= multiply c (multiply a b) [] by Demod 47844 with 3 at 3
+Id : 47844, {_}: multiply b (multiply a c) =<= multiply (multiply a b) c [] by Demod 1 with 47391 at 2
+Id : 1, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
+% SZS output end CNFRefutation for BOO007-4.p
+4589: solved BOO007-4.p in 11.664728 using kbo
+4589: status Unsatisfiable for BOO007-4.p
+CLASH, statistics insufficient
+4606: Facts:
+4606: Id : 2, {_}:
+ add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
+ =>=
+ multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
+ [4, 3, 2] by distributivity ?2 ?3 ?4
+4606: Id : 3, {_}:
+ add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
+ [8, 7, 6] by l1 ?6 ?7 ?8
+4606: Id : 4, {_}:
+ add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
+ [12, 11, 10] by l3 ?10 ?11 ?12
+4606: Id : 5, {_}:
+ multiply (add ?14 (inverse ?14)) ?15 =>= ?15
+ [15, 14] by property3 ?14 ?15
+4606: Id : 6, {_}:
+ multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17
+ [19, 18, 17] by l2 ?17 ?18 ?19
+4606: Id : 7, {_}:
+ multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22
+ [23, 22, 21] by l4 ?21 ?22 ?23
+4606: Id : 8, {_}:
+ add (multiply ?25 (inverse ?25)) ?26 =>= ?26
+ [26, 25] by property3_dual ?25 ?26
+4606: Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
+4606: Id : 10, {_}:
+ multiply ?30 (inverse ?30) =>= n0
+ [30] by multiplicative_inverse ?30
+4606: Id : 11, {_}:
+ add (add ?32 ?33) ?34 =?= add ?32 (add ?33 ?34)
+ [34, 33, 32] by associativity_of_add ?32 ?33 ?34
+4606: Id : 12, {_}:
+ multiply (multiply ?36 ?37) ?38 =?= multiply ?36 (multiply ?37 ?38)
+ [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
+4606: Goal:
+4606: Id : 1, {_}:
+ multiply a (add b c) =<= add (multiply b a) (multiply c a)
+ [] by prove_multiply_add_property
+4606: Order:
+4606: nrkbo
+4606: Leaf order:
+4606: n0 1 0 0
+4606: n1 1 0 0
+4606: inverse 4 1 0
+4606: multiply 22 2 3 0,2add
+4606: add 21 2 2 0,2,2multiply
+4606: c 2 0 2 2,2,2
+4606: b 2 0 2 1,2,2
+4606: a 3 0 3 1,2
+CLASH, statistics insufficient
+4607: Facts:
+4607: Id : 2, {_}:
+ add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
+ =>=
+ multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
+ [4, 3, 2] by distributivity ?2 ?3 ?4
+4607: Id : 3, {_}:
+ add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
+ [8, 7, 6] by l1 ?6 ?7 ?8
+4607: Id : 4, {_}:
+ add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
+ [12, 11, 10] by l3 ?10 ?11 ?12
+4607: Id : 5, {_}:
+ multiply (add ?14 (inverse ?14)) ?15 =>= ?15
+ [15, 14] by property3 ?14 ?15
+4607: Id : 6, {_}:
+ multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17
+ [19, 18, 17] by l2 ?17 ?18 ?19
+4607: Id : 7, {_}:
+ multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22
+ [23, 22, 21] by l4 ?21 ?22 ?23
+4607: Id : 8, {_}:
+ add (multiply ?25 (inverse ?25)) ?26 =>= ?26
+ [26, 25] by property3_dual ?25 ?26
+4607: Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
+4607: Id : 10, {_}:
+ multiply ?30 (inverse ?30) =>= n0
+ [30] by multiplicative_inverse ?30
+4607: Id : 11, {_}:
+ add (add ?32 ?33) ?34 =>= add ?32 (add ?33 ?34)
+ [34, 33, 32] by associativity_of_add ?32 ?33 ?34
+CLASH, statistics insufficient
+4608: Facts:
+4608: Id : 2, {_}:
+ add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
+ =>=
+ multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
+ [4, 3, 2] by distributivity ?2 ?3 ?4
+4608: Id : 3, {_}:
+ add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
+ [8, 7, 6] by l1 ?6 ?7 ?8
+4608: Id : 4, {_}:
+ add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
+ [12, 11, 10] by l3 ?10 ?11 ?12
+4608: Id : 5, {_}:
+ multiply (add ?14 (inverse ?14)) ?15 =>= ?15
+ [15, 14] by property3 ?14 ?15
+4608: Id : 6, {_}:
+ multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17
+ [19, 18, 17] by l2 ?17 ?18 ?19
+4608: Id : 7, {_}:
+ multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22
+ [23, 22, 21] by l4 ?21 ?22 ?23
+4608: Id : 8, {_}:
+ add (multiply ?25 (inverse ?25)) ?26 =>= ?26
+ [26, 25] by property3_dual ?25 ?26
+4608: Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
+4608: Id : 10, {_}:
+ multiply ?30 (inverse ?30) =>= n0
+ [30] by multiplicative_inverse ?30
+4608: Id : 11, {_}:
+ add (add ?32 ?33) ?34 =>= add ?32 (add ?33 ?34)
+ [34, 33, 32] by associativity_of_add ?32 ?33 ?34
+4607: Id : 12, {_}:
+ multiply (multiply ?36 ?37) ?38 =>= multiply ?36 (multiply ?37 ?38)
+ [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
+4607: Goal:
+4607: Id : 1, {_}:
+ multiply a (add b c) =<= add (multiply b a) (multiply c a)
+ [] by prove_multiply_add_property
+4607: Order:
+4607: kbo
+4607: Leaf order:
+4607: n0 1 0 0
+4607: n1 1 0 0
+4607: inverse 4 1 0
+4607: multiply 22 2 3 0,2add
+4607: add 21 2 2 0,2,2multiply
+4607: c 2 0 2 2,2,2
+4607: b 2 0 2 1,2,2
+4607: a 3 0 3 1,2
+4608: Id : 12, {_}:
+ multiply (multiply ?36 ?37) ?38 =>= multiply ?36 (multiply ?37 ?38)
+ [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
+4608: Goal:
+4608: Id : 1, {_}:
+ multiply a (add b c) =<= add (multiply b a) (multiply c a)
+ [] by prove_multiply_add_property
+4608: Order:
+4608: lpo
+4608: Leaf order:
+4608: n0 1 0 0
+4608: n1 1 0 0
+4608: inverse 4 1 0
+4608: multiply 22 2 3 0,2add
+4608: add 21 2 2 0,2,2multiply
+4608: c 2 0 2 2,2,2
+4608: b 2 0 2 1,2,2
+4608: a 3 0 3 1,2
+Statistics :
+Max weight : 29
+Found proof, 44.648027s
+% SZS status Unsatisfiable for BOO031-1.p
+% SZS output start CNFRefutation for BOO031-1.p
+Id : 7, {_}: multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22 [23, 22, 21] by l4 ?21 ?22 ?23
+Id : 10, {_}: multiply ?30 (inverse ?30) =>= n0 [30] by multiplicative_inverse ?30
+Id : 8, {_}: add (multiply ?25 (inverse ?25)) ?26 =>= ?26 [26, 25] by property3_dual ?25 ?26
+Id : 12, {_}: multiply (multiply ?36 ?37) ?38 =>= multiply ?36 (multiply ?37 ?38) [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
+Id : 52, {_}: multiply (multiply (add ?189 ?190) (add ?190 ?191)) ?190 =>= ?190 [191, 190, 189] by l4 ?189 ?190 ?191
+Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
+Id : 5, {_}: multiply (add ?14 (inverse ?14)) ?15 =>= ?15 [15, 14] by property3 ?14 ?15
+Id : 2, {_}: add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2)) =>= multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2)) [4, 3, 2] by distributivity ?2 ?3 ?4
+Id : 18, {_}: add (add (multiply ?58 ?59) (multiply ?59 ?60)) ?59 =>= ?59 [60, 59, 58] by l3 ?58 ?59 ?60
+Id : 11, {_}: add (add ?32 ?33) ?34 =>= add ?32 (add ?33 ?34) [34, 33, 32] by associativity_of_add ?32 ?33 ?34
+Id : 4, {_}: add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11 [12, 11, 10] by l3 ?10 ?11 ?12
+Id : 37, {_}: multiply ?128 (add ?129 (add ?128 ?130)) =>= ?128 [130, 129, 128] by l2 ?128 ?129 ?130
+Id : 6, {_}: multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17 [19, 18, 17] by l2 ?17 ?18 ?19
+Id : 3, {_}: add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6 [8, 7, 6] by l1 ?6 ?7 ?8
+Id : 35, {_}: add ?121 (multiply ?122 ?121) =>= ?121 [122, 121] by Super 3 with 6 at 2,2,2
+Id : 42, {_}: multiply ?149 (add ?149 ?150) =>= ?149 [150, 149] by Super 37 with 4 at 2,2
+Id : 1579, {_}: add (add ?2436 ?2437) ?2436 =>= add ?2436 ?2437 [2437, 2436] by Super 35 with 42 at 2,2
+Id : 1609, {_}: add ?2436 (add ?2437 ?2436) =>= add ?2436 ?2437 [2437, 2436] by Demod 1579 with 11 at 2
+Id : 19, {_}: add (multiply ?62 ?63) ?63 =>= ?63 [63, 62] by Super 18 with 3 at 1,2
+Id : 39, {_}: multiply ?137 (add ?138 ?137) =>= ?137 [138, 137] by Super 37 with 3 at 2,2,2
+Id : 1363, {_}: add ?2089 (add ?2090 ?2089) =>= add ?2090 ?2089 [2090, 2089] by Super 19 with 39 at 1,2
+Id : 2844, {_}: add ?2437 ?2436 =?= add ?2436 ?2437 [2436, 2437] by Demod 1609 with 1363 at 2
+Id : 32, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add (multiply ?109 ?107) ?107) =<= multiply (add (add ?106 (add ?107 ?108)) ?109) (multiply (add ?109 ?107) (add ?107 (add ?106 (add ?107 ?108)))) [109, 108, 107, 106] by Super 2 with 6 at 2,2,2
+Id : 5786, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add ?107 (multiply ?109 ?107)) =<= multiply (add (add ?106 (add ?107 ?108)) ?109) (multiply (add ?109 ?107) (add ?107 (add ?106 (add ?107 ?108)))) [109, 108, 107, 106] by Demod 32 with 2844 at 2,2
+Id : 5787, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add ?107 (multiply ?109 ?107)) =<= multiply (add ?106 (add (add ?107 ?108) ?109)) (multiply (add ?109 ?107) (add ?107 (add ?106 (add ?107 ?108)))) [109, 108, 107, 106] by Demod 5786 with 11 at 1,3
+Id : 1088, {_}: add (multiply ?1721 ?1722) ?1722 =>= ?1722 [1722, 1721] by Super 18 with 3 at 1,2
+Id : 1091, {_}: add ?1730 (add ?1731 (add ?1730 ?1732)) =>= add ?1731 (add ?1730 ?1732) [1732, 1731, 1730] by Super 1088 with 6 at 1,2
+Id : 5788, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add ?107 (multiply ?109 ?107)) =<= multiply (add ?106 (add (add ?107 ?108) ?109)) (multiply (add ?109 ?107) (add ?106 (add ?107 ?108))) [109, 108, 107, 106] by Demod 5787 with 1091 at 2,2,3
+Id : 5789, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) ?107 =<= multiply (add ?106 (add (add ?107 ?108) ?109)) (multiply (add ?109 ?107) (add ?106 (add ?107 ?108))) [109, 108, 107, 106] by Demod 5788 with 35 at 2,2
+Id : 5790, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) ?107 =<= multiply (add ?106 (add ?107 (add ?108 ?109))) (multiply (add ?109 ?107) (add ?106 (add ?107 ?108))) [109, 108, 107, 106] by Demod 5789 with 11 at 2,1,3
+Id : 5814, {_}: add ?7785 (multiply (add ?7786 (add ?7785 ?7787)) ?7788) =<= multiply (add ?7786 (add ?7785 (add ?7787 ?7788))) (multiply (add ?7788 ?7785) (add ?7786 (add ?7785 ?7787))) [7788, 7787, 7786, 7785] by Demod 5790 with 2844 at 2
+Id : 79, {_}: multiply n1 ?15 =>= ?15 [15] by Demod 5 with 9 at 1,2
+Id : 1095, {_}: add ?1743 ?1743 =>= ?1743 [1743] by Super 1088 with 79 at 1,2
+Id : 5853, {_}: add ?7982 (multiply (add (add ?7982 ?7983) (add ?7982 ?7983)) ?7984) =<= multiply (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) (multiply (add ?7984 ?7982) (add ?7982 ?7983)) [7984, 7983, 7982] by Super 5814 with 1095 at 2,2,3
+Id : 6183, {_}: add ?7982 (multiply (add ?7982 (add ?7983 (add ?7982 ?7983))) ?7984) =<= multiply (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) (multiply (add ?7984 ?7982) (add ?7982 ?7983)) [7984, 7983, 7982] by Demod 5853 with 11 at 1,2,2
+Id : 1663, {_}: multiply (add ?2570 ?2571) ?2571 =>= ?2571 [2571, 2570] by Super 52 with 6 at 1,2
+Id : 1673, {_}: multiply ?2601 (multiply ?2602 ?2601) =>= multiply ?2602 ?2601 [2602, 2601] by Super 1663 with 35 at 1,2
+Id : 1365, {_}: multiply ?2095 (add ?2096 ?2095) =>= ?2095 [2096, 2095] by Super 37 with 3 at 2,2,2
+Id : 22, {_}: add ?71 (multiply ?71 ?72) =>= ?71 [72, 71] by Super 3 with 5 at 2,2
+Id : 1374, {_}: multiply (multiply ?2123 ?2124) ?2123 =>= multiply ?2123 ?2124 [2124, 2123] by Super 1365 with 22 at 2,2
+Id : 1408, {_}: multiply ?2123 (multiply ?2124 ?2123) =>= multiply ?2123 ?2124 [2124, 2123] by Demod 1374 with 12 at 2
+Id : 2987, {_}: multiply ?2601 ?2602 =?= multiply ?2602 ?2601 [2602, 2601] by Demod 1673 with 1408 at 2
+Id : 6184, {_}: add ?7982 (multiply (add ?7982 (add ?7983 (add ?7982 ?7983))) ?7984) =<= multiply (multiply (add ?7984 ?7982) (add ?7982 ?7983)) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) [7984, 7983, 7982] by Demod 6183 with 2987 at 3
+Id : 6185, {_}: add ?7982 (multiply (add ?7983 (add ?7982 ?7983)) ?7984) =<= multiply (multiply (add ?7984 ?7982) (add ?7982 ?7983)) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) [7984, 7983, 7982] by Demod 6184 with 1091 at 1,2,2
+Id : 6186, {_}: add ?7982 (multiply (add ?7983 (add ?7982 ?7983)) ?7984) =<= multiply (add ?7984 ?7982) (multiply (add ?7982 ?7983) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984)))) [7984, 7983, 7982] by Demod 6185 with 12 at 3
+Id : 6187, {_}: add ?7982 (multiply (add ?7982 ?7983) ?7984) =<= multiply (add ?7984 ?7982) (multiply (add ?7982 ?7983) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984)))) [7984, 7983, 7982] by Demod 6186 with 1363 at 1,2,2
+Id : 13074, {_}: add ?18195 (multiply (add ?18195 ?18196) ?18197) =>= multiply (add ?18197 ?18195) (add ?18195 ?18196) [18197, 18196, 18195] by Demod 6187 with 42 at 2,3
+Id : 16401, {_}: add ?22734 (multiply (add ?22735 ?22734) ?22736) =>= multiply (add ?22736 ?22734) (add ?22734 ?22735) [22736, 22735, 22734] by Super 13074 with 2844 at 1,2,2
+Id : 18162, {_}: add ?24925 (multiply ?24926 (add ?24927 ?24925)) =>= multiply (add ?24926 ?24925) (add ?24925 ?24927) [24927, 24926, 24925] by Super 16401 with 2987 at 2,2
+Id : 18171, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =<= multiply (add ?24965 (multiply ?24963 ?24964)) (add (multiply ?24963 ?24964) ?24964) [24965, 24964, 24963] by Super 18162 with 35 at 2,2,2
+Id : 18379, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =<= multiply (add ?24965 (multiply ?24963 ?24964)) (add ?24964 (multiply ?24963 ?24964)) [24965, 24964, 24963] by Demod 18171 with 2844 at 2,3
+Id : 18380, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =>= multiply (add ?24965 (multiply ?24963 ?24964)) ?24964 [24965, 24964, 24963] by Demod 18379 with 35 at 2,3
+Id : 18381, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =>= multiply ?24964 (add ?24965 (multiply ?24963 ?24964)) [24965, 24964, 24963] by Demod 18380 with 2987 at 3
+Id : 1575, {_}: multiply ?2421 ?2422 =<= multiply ?2421 (multiply (add ?2421 ?2423) ?2422) [2423, 2422, 2421] by Super 12 with 42 at 1,2
+Id : 16456, {_}: add ?22968 (multiply ?22969 (add ?22970 ?22968)) =>= multiply (add ?22969 ?22968) (add ?22968 ?22970) [22970, 22969, 22968] by Super 16401 with 2987 at 2,2
+Id : 1247, {_}: add ?1879 ?1880 =<= add ?1879 (add (multiply ?1879 ?1881) ?1880) [1881, 1880, 1879] by Super 11 with 22 at 1,2
+Id : 6619, {_}: multiply (multiply ?8607 ?8608) (add ?8607 ?8609) =>= multiply ?8607 ?8608 [8609, 8608, 8607] by Super 6 with 1247 at 2,2
+Id : 6763, {_}: multiply ?8607 (multiply ?8608 (add ?8607 ?8609)) =>= multiply ?8607 ?8608 [8609, 8608, 8607] by Demod 6619 with 12 at 2
+Id : 65, {_}: add (multiply ?237 ?238) (multiply (inverse ?238) ?237) =<= multiply (add ?237 ?238) (multiply (add ?238 (inverse ?238)) (add (inverse ?238) ?237)) [238, 237] by Super 2 with 8 at 2,2
+Id : 76, {_}: add (multiply ?237 ?238) (multiply (inverse ?238) ?237) =>= multiply (add ?237 ?238) (add (inverse ?238) ?237) [238, 237] by Demod 65 with 5 at 2,3
+Id : 18170, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =<= multiply (add ?24961 (multiply ?24959 ?24960)) (add (multiply ?24959 ?24960) ?24959) [24961, 24960, 24959] by Super 18162 with 22 at 2,2,2
+Id : 18376, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =<= multiply (add ?24961 (multiply ?24959 ?24960)) (add ?24959 (multiply ?24959 ?24960)) [24961, 24960, 24959] by Demod 18170 with 2844 at 2,3
+Id : 18377, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =>= multiply (add ?24961 (multiply ?24959 ?24960)) ?24959 [24961, 24960, 24959] by Demod 18376 with 22 at 2,3
+Id : 18378, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =>= multiply ?24959 (add ?24961 (multiply ?24959 ?24960)) [24961, 24960, 24959] by Demod 18377 with 2987 at 3
+Id : 22657, {_}: multiply ?237 (add (inverse ?238) (multiply ?237 ?238)) =<= multiply (add ?237 ?238) (add (inverse ?238) ?237) [238, 237] by Demod 76 with 18378 at 2
+Id : 22699, {_}: multiply (inverse ?30910) (multiply ?30911 (add (inverse ?30910) (multiply ?30911 ?30910))) =>= multiply (inverse ?30910) (add ?30911 ?30910) [30911, 30910] by Super 6763 with 22657 at 2,2
+Id : 22814, {_}: multiply (inverse ?30910) ?30911 =<= multiply (inverse ?30910) (add ?30911 ?30910) [30911, 30910] by Demod 22699 with 6763 at 2
+Id : 23609, {_}: add ?31619 (multiply (inverse ?31619) ?31620) =<= multiply (add (inverse ?31619) ?31619) (add ?31619 ?31620) [31620, 31619] by Super 16456 with 22814 at 2,2
+Id : 23775, {_}: add ?31619 (multiply (inverse ?31619) ?31620) =<= multiply (add ?31619 (inverse ?31619)) (add ?31619 ?31620) [31620, 31619] by Demod 23609 with 2844 at 1,3
+Id : 23776, {_}: add ?31619 (multiply (inverse ?31619) ?31620) =>= multiply n1 (add ?31619 ?31620) [31620, 31619] by Demod 23775 with 9 at 1,3
+Id : 24286, {_}: add ?32553 (multiply (inverse ?32553) ?32554) =>= add ?32553 ?32554 [32554, 32553] by Demod 23776 with 79 at 3
+Id : 13130, {_}: add ?18432 (multiply ?18433 (add ?18432 ?18434)) =>= multiply (add ?18433 ?18432) (add ?18432 ?18434) [18434, 18433, 18432] by Super 13074 with 2987 at 2,2
+Id : 22705, {_}: multiply ?30931 (add (inverse ?30932) (multiply ?30931 ?30932)) =<= multiply (add ?30931 ?30932) (add (inverse ?30932) ?30931) [30932, 30931] by Demod 76 with 18378 at 2
+Id : 22751, {_}: multiply ?31084 (add (inverse (inverse ?31084)) (multiply ?31084 (inverse ?31084))) =>= multiply n1 (add (inverse (inverse ?31084)) ?31084) [31084] by Super 22705 with 9 at 1,3
+Id : 23065, {_}: multiply ?31084 (add (inverse (inverse ?31084)) n0) =?= multiply n1 (add (inverse (inverse ?31084)) ?31084) [31084] by Demod 22751 with 10 at 2,2,2
+Id : 23066, {_}: multiply ?31084 (add (inverse (inverse ?31084)) n0) =>= add (inverse (inverse ?31084)) ?31084 [31084] by Demod 23065 with 79 at 3
+Id : 130, {_}: multiply (add ?21 ?22) (multiply (add ?22 ?23) ?22) =>= ?22 [23, 22, 21] by Demod 7 with 12 at 2
+Id : 89, {_}: n0 =<= inverse n1 [] by Super 79 with 10 at 2
+Id : 360, {_}: add n1 n0 =>= n1 [] by Super 9 with 89 at 2,2
+Id : 382, {_}: multiply n1 (multiply (add n0 ?765) n0) =>= n0 [765] by Super 130 with 360 at 1,2
+Id : 422, {_}: multiply (add n0 ?765) n0 =>= n0 [765] by Demod 382 with 79 at 2
+Id : 88, {_}: add n0 ?26 =>= ?26 [26] by Demod 8 with 10 at 1,2
+Id : 423, {_}: multiply ?765 n0 =>= n0 [765] by Demod 422 with 88 at 1,2
+Id : 831, {_}: add ?1448 (multiply ?1449 n0) =>= ?1448 [1449, 1448] by Super 3 with 423 at 2,2,2
+Id : 867, {_}: add ?1448 n0 =>= ?1448 [1448] by Demod 831 with 423 at 2,2
+Id : 23067, {_}: multiply ?31084 (inverse (inverse ?31084)) =<= add (inverse (inverse ?31084)) ?31084 [31084] by Demod 23066 with 867 at 2,2
+Id : 23068, {_}: multiply ?31084 (inverse (inverse ?31084)) =<= add ?31084 (inverse (inverse ?31084)) [31084] by Demod 23067 with 2844 at 3
+Id : 23215, {_}: add ?31334 (multiply ?31335 (multiply ?31334 (inverse (inverse ?31334)))) =>= multiply (add ?31335 ?31334) (add ?31334 (inverse (inverse ?31334))) [31335, 31334] by Super 13130 with 23068 at 2,2,2
+Id : 23280, {_}: ?31334 =<= multiply (add ?31335 ?31334) (add ?31334 (inverse (inverse ?31334))) [31335, 31334] by Demod 23215 with 3 at 2
+Id : 23281, {_}: ?31334 =<= multiply (add ?31335 ?31334) (multiply ?31334 (inverse (inverse ?31334))) [31335, 31334] by Demod 23280 with 23068 at 2,3
+Id : 2547, {_}: multiply (multiply ?3698 ?3699) ?3700 =<= multiply ?3698 (multiply (multiply ?3699 ?3698) ?3700) [3700, 3699, 3698] by Super 12 with 1408 at 1,2
+Id : 2578, {_}: multiply ?3698 (multiply ?3699 ?3700) =<= multiply ?3698 (multiply (multiply ?3699 ?3698) ?3700) [3700, 3699, 3698] by Demod 2547 with 12 at 2
+Id : 2579, {_}: multiply ?3698 (multiply ?3699 ?3700) =<= multiply ?3698 (multiply ?3699 (multiply ?3698 ?3700)) [3700, 3699, 3698] by Demod 2578 with 12 at 2,3
+Id : 1667, {_}: multiply ?2583 (multiply ?2584 (multiply ?2583 ?2585)) =>= multiply ?2584 (multiply ?2583 ?2585) [2585, 2584, 2583] by Super 1663 with 3 at 1,2
+Id : 12236, {_}: multiply ?3698 (multiply ?3699 ?3700) =?= multiply ?3699 (multiply ?3698 ?3700) [3700, 3699, 3698] by Demod 2579 with 1667 at 3
+Id : 23282, {_}: ?31334 =<= multiply ?31334 (multiply (add ?31335 ?31334) (inverse (inverse ?31334))) [31335, 31334] by Demod 23281 with 12236 at 3
+Id : 1360, {_}: multiply ?2077 ?2078 =<= multiply ?2077 (multiply (add ?2079 ?2077) ?2078) [2079, 2078, 2077] by Super 12 with 39 at 1,2
+Id : 23283, {_}: ?31334 =<= multiply ?31334 (inverse (inverse ?31334)) [31334] by Demod 23282 with 1360 at 3
+Id : 23386, {_}: add (inverse (inverse ?31435)) ?31435 =>= inverse (inverse ?31435) [31435] by Super 35 with 23283 at 2,2
+Id : 23494, {_}: add ?31435 (inverse (inverse ?31435)) =>= inverse (inverse ?31435) [31435] by Demod 23386 with 2844 at 2
+Id : 23374, {_}: ?31084 =<= add ?31084 (inverse (inverse ?31084)) [31084] by Demod 23068 with 23283 at 2
+Id : 23495, {_}: ?31435 =<= inverse (inverse ?31435) [31435] by Demod 23494 with 23374 at 2
+Id : 24293, {_}: add (inverse ?32572) (multiply ?32572 ?32573) =>= add (inverse ?32572) ?32573 [32573, 32572] by Super 24286 with 23495 at 1,2,2
+Id : 23619, {_}: multiply (multiply (inverse ?31653) ?31654) ?31655 =<= multiply (inverse ?31653) (multiply (add ?31654 ?31653) ?31655) [31655, 31654, 31653] by Super 12 with 22814 at 1,2
+Id : 23754, {_}: multiply (inverse ?31653) (multiply ?31654 ?31655) =<= multiply (inverse ?31653) (multiply (add ?31654 ?31653) ?31655) [31655, 31654, 31653] by Demod 23619 with 12 at 2
+Id : 77768, {_}: add (inverse (inverse ?103133)) (multiply (inverse ?103133) (multiply ?103134 ?103135)) =>= add (inverse (inverse ?103133)) (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Super 24293 with 23754 at 2,2
+Id : 78028, {_}: add (inverse (inverse ?103133)) (multiply ?103134 ?103135) =<= add (inverse (inverse ?103133)) (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Demod 77768 with 24293 at 2
+Id : 78029, {_}: add (inverse (inverse ?103133)) (multiply ?103134 ?103135) =?= add ?103133 (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Demod 78028 with 23495 at 1,3
+Id : 78030, {_}: add ?103133 (multiply ?103134 ?103135) =<= add ?103133 (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Demod 78029 with 23495 at 1,2
+Id : 13094, {_}: add ?18275 (multiply (add ?18276 ?18275) ?18277) =>= multiply (add ?18277 ?18275) (add ?18275 ?18276) [18277, 18276, 18275] by Super 13074 with 2844 at 1,2,2
+Id : 78031, {_}: add ?103133 (multiply ?103134 ?103135) =<= multiply (add ?103135 ?103133) (add ?103133 ?103134) [103135, 103134, 103133] by Demod 78030 with 13094 at 3
+Id : 78812, {_}: multiply ?104288 (add ?104289 ?104290) =<= multiply ?104288 (add ?104289 (multiply ?104290 ?104288)) [104290, 104289, 104288] by Super 1575 with 78031 at 2,3
+Id : 80954, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =>= multiply ?24964 (add ?24965 ?24963) [24965, 24964, 24963] by Demod 18381 with 78812 at 3
+Id : 81595, {_}: multiply a (add c b) =?= multiply a (add c b) [] by Demod 81594 with 2844 at 2,3
+Id : 81594, {_}: multiply a (add c b) =?= multiply a (add b c) [] by Demod 81593 with 80954 at 3
+Id : 81593, {_}: multiply a (add c b) =<= add (multiply c a) (multiply b a) [] by Demod 81592 with 2844 at 3
+Id : 81592, {_}: multiply a (add c b) =<= add (multiply b a) (multiply c a) [] by Demod 1 with 2844 at 2,2
+Id : 1, {_}: multiply a (add b c) =<= add (multiply b a) (multiply c a) [] by prove_multiply_add_property
+% SZS output end CNFRefutation for BOO031-1.p
+4607: solved BOO031-1.p in 22.309393 using kbo
+4607: status Unsatisfiable for BOO031-1.p
+NO CLASH, using fixed ground order
+4619: Facts:
+4619: Id : 2, {_}:
+ inverse
+ (add (inverse (add (inverse (add ?2 ?3)) ?4))
+ (inverse
+ (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
+4619: Goal:
+4619: Id : 1, {_}: add b a =>= add a b [] by huntinton_1
+4619: Order:
+4619: nrkbo
+4619: Leaf order:
+4619: inverse 7 1 0
+4619: add 8 2 2 0,2
+4619: a 2 0 2 2,2
+4619: b 2 0 2 1,2
+NO CLASH, using fixed ground order
+4620: Facts:
+4620: Id : 2, {_}:
+ inverse
+ (add (inverse (add (inverse (add ?2 ?3)) ?4))
+ (inverse
+ (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
+4620: Goal:
+4620: Id : 1, {_}: add b a =>= add a b [] by huntinton_1
+4620: Order:
+4620: kbo
+4620: Leaf order:
+4620: inverse 7 1 0
+4620: add 8 2 2 0,2
+4620: a 2 0 2 2,2
+4620: b 2 0 2 1,2
+NO CLASH, using fixed ground order
+4621: Facts:
+4621: Id : 2, {_}:
+ inverse
+ (add (inverse (add (inverse (add ?2 ?3)) ?4))
+ (inverse
+ (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
+4621: Goal:
+4621: Id : 1, {_}: add b a =>= add a b [] by huntinton_1
+4621: Order:
+4621: lpo
+4621: Leaf order:
+4621: inverse 7 1 0
+4621: add 8 2 2 0,2
+4621: a 2 0 2 2,2
+4621: b 2 0 2 1,2
+Statistics :
+Max weight : 70
+Found proof, 56.468020s
+% SZS status Unsatisfiable for BOO072-1.p
+% SZS output start CNFRefutation for BOO072-1.p
+Id : 3, {_}: inverse (add (inverse (add (inverse (add ?7 ?8)) ?9)) (inverse (add ?7 (inverse (add (inverse ?9) (inverse (add ?9 ?10))))))) =>= ?9 [10, 9, 8, 7] by dn1 ?7 ?8 ?9 ?10
+Id : 2, {_}: inverse (add (inverse (add (inverse (add ?2 ?3)) ?4)) (inverse (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) =>= ?4 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
+Id : 15, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?74)) ?75)) ?74)) ?76)) (inverse ?74))) ?74) =>= inverse ?74 [76, 75, 74] by Super 3 with 2 at 2,1,2
+Id : 20, {_}: inverse (add (inverse (add ?104 (inverse ?104))) ?104) =>= inverse ?104 [104] by Super 15 with 2 at 1,1,1,1,2
+Id : 99, {_}: inverse (add (inverse ?355) (inverse (add ?355 (inverse (add (inverse ?355) (inverse (add ?355 ?356))))))) =>= ?355 [356, 355] by Super 2 with 20 at 1,1,2
+Id : 136, {_}: inverse (add (inverse (add (inverse (add ?450 ?451)) ?452)) (inverse (add ?450 ?452))) =>= ?452 [452, 451, 450] by Super 2 with 99 at 2,1,2,1,2
+Id : 536, {_}: inverse (add (inverse (add (inverse (add ?1808 ?1809)) ?1810)) (inverse (add ?1808 ?1810))) =>= ?1810 [1810, 1809, 1808] by Super 2 with 99 at 2,1,2,1,2
+Id : 550, {_}: inverse (add (inverse (add ?1882 ?1883)) (inverse (add (inverse ?1882) ?1883))) =>= ?1883 [1883, 1882] by Super 536 with 99 at 1,1,1,1,2
+Id : 724, {_}: inverse (add ?2517 (inverse (add ?2518 (inverse (add (inverse ?2518) ?2517))))) =>= inverse (add (inverse ?2518) ?2517) [2518, 2517] by Super 136 with 550 at 1,1,2
+Id : 1584, {_}: inverse (add (inverse ?4978) (inverse (add ?4978 (inverse (add (inverse ?4978) (inverse ?4978)))))) =>= ?4978 [4978] by Super 99 with 724 at 2,1,2,1,2
+Id : 1652, {_}: inverse (add (inverse ?4978) (inverse ?4978)) =>= ?4978 [4978] by Demod 1584 with 724 at 2
+Id : 763, {_}: inverse (add (inverse (add ?2736 ?2737)) (inverse (add (inverse ?2736) ?2737))) =>= ?2737 [2737, 2736] by Super 536 with 99 at 1,1,1,1,2
+Id : 144, {_}: inverse (add (inverse ?482) (inverse (add ?482 (inverse (add (inverse ?482) (inverse (add ?482 ?483))))))) =>= ?482 [483, 482] by Super 2 with 20 at 1,1,2
+Id : 155, {_}: inverse (add (inverse ?528) (inverse (add ?528 ?528))) =>= ?528 [528] by Super 144 with 99 at 2,1,2,1,2
+Id : 782, {_}: inverse (add (inverse (add ?2830 (inverse (add ?2830 ?2830)))) ?2830) =>= inverse (add ?2830 ?2830) [2830] by Super 763 with 155 at 2,1,2
+Id : 871, {_}: inverse (add (inverse (add ?3076 ?3076)) (inverse (add ?3076 ?3076))) =>= ?3076 [3076] by Super 136 with 782 at 1,1,2
+Id : 1724, {_}: add ?3076 ?3076 =>= ?3076 [3076] by Demod 871 with 1652 at 2
+Id : 1754, {_}: inverse (inverse ?5284) =>= ?5284 [5284] by Demod 1652 with 1724 at 1,2
+Id : 1761, {_}: inverse ?5314 =<= add (inverse (add ?5315 ?5314)) (inverse (add (inverse ?5315) ?5314)) [5315, 5314] by Super 1754 with 550 at 1,2
+Id : 1733, {_}: inverse (inverse ?4978) =>= ?4978 [4978] by Demod 1652 with 1724 at 1,2
+Id : 6, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?26)) ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Super 3 with 2 at 2,1,2
+Id : 1734, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add ?26 ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Demod 6 with 1733 at 1,1,1,1,1,1,1,1,1,1,2
+Id : 921, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse (add ?3102 ?3102))))) =>= inverse (add ?3102 ?3102) [3102] by Super 136 with 871 at 1,1,2
+Id : 1725, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse (add ?3102 ?3102) [3102] by Demod 921 with 1724 at 1,2,1,2,1,2
+Id : 1726, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse ?3102 [3102] by Demod 1725 with 1724 at 1,3
+Id : 1763, {_}: inverse (inverse ?5320) =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Super 1754 with 1726 at 1,2
+Id : 1786, {_}: ?5320 =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Demod 1763 with 1733 at 2
+Id : 2715, {_}: inverse (add (inverse (add (inverse ?7389) (inverse (inverse ?7389)))) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Super 724 with 1786 at 1,2,1,2,1,2
+Id : 2755, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2715 with 1733 at 2,1,1,1,2
+Id : 2756, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =?= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2755 with 1733 at 2,1,2,1,2
+Id : 2757, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =>= inverse (inverse ?7389) [7389] by Demod 2756 with 1786 at 1,3
+Id : 2758, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= inverse (inverse ?7389) [7389] by Demod 2757 with 1724 at 1,2,1,2
+Id : 2759, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= ?7389 [7389] by Demod 2758 with 1733 at 3
+Id : 2920, {_}: inverse ?7714 =<= add (inverse (add (inverse ?7714) ?7714)) (inverse ?7714) [7714] by Super 1733 with 2759 at 1,2
+Id : 3142, {_}: inverse (add (inverse (add (inverse (add (inverse (inverse ?8118)) ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Super 1734 with 2920 at 1,1,1,1,1,1,1,2
+Id : 3172, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3142 with 1733 at 1,1,1,1,1,1,2
+Id : 3173, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) ?8118)) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3172 with 1733 at 2,1,1,1,2
+Id : 8100, {_}: inverse (add (inverse (add (inverse (add ?15581 ?15582)) ?15581)) (inverse ?15581)) =>= ?15581 [15582, 15581] by Demod 3173 with 1733 at 3
+Id : 8144, {_}: inverse (add ?15759 (inverse (inverse (add ?15760 ?15759)))) =>= inverse (add ?15760 ?15759) [15760, 15759] by Super 8100 with 136 at 1,1,2
+Id : 8459, {_}: inverse (add ?16264 (add ?16265 ?16264)) =>= inverse (add ?16265 ?16264) [16265, 16264] by Demod 8144 with 1733 at 2,1,2
+Id : 1749, {_}: inverse (add (inverse (add (inverse ?5262) ?5263)) (inverse (add ?5262 ?5263))) =>= ?5263 [5263, 5262] by Super 550 with 1733 at 1,1,2,1,2
+Id : 5602, {_}: inverse ?11750 =<= add (inverse (add (inverse ?11751) ?11750)) (inverse (add ?11751 ?11750)) [11751, 11750] by Super 1733 with 1749 at 1,2
+Id : 8468, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =<= inverse (add (inverse (add (inverse ?16285) ?16286)) (inverse (add ?16285 ?16286))) [16286, 16285] by Super 8459 with 5602 at 2,1,2
+Id : 8598, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= inverse (inverse ?16286) [16286, 16285] by Demod 8468 with 5602 at 1,3
+Id : 8599, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= ?16286 [16286, 16285] by Demod 8598 with 1733 at 3
+Id : 8791, {_}: inverse ?16774 =<= add (inverse (add ?16775 ?16774)) (inverse ?16774) [16775, 16774] by Super 1733 with 8599 at 1,2
+Id : 10568, {_}: inverse (add (inverse (inverse ?20566)) (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Super 136 with 8791 at 1,1,1,2
+Id : 10805, {_}: inverse (add ?20566 (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Demod 10568 with 1733 at 1,1,2
+Id : 11153, {_}: inverse (inverse ?21486) =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Super 1733 with 10805 at 1,2
+Id : 11260, {_}: ?21486 =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Demod 11153 with 1733 at 2
+Id : 12127, {_}: inverse (inverse (add ?22871 (inverse (inverse ?22872)))) =<= add (inverse (add ?22872 (inverse (add ?22871 (inverse (inverse ?22872)))))) (inverse (inverse ?22872)) [22872, 22871] by Super 1761 with 11260 at 1,2,3
+Id : 12312, {_}: add ?22871 (inverse (inverse ?22872)) =<= add (inverse (add ?22872 (inverse (add ?22871 (inverse (inverse ?22872)))))) (inverse (inverse ?22872)) [22872, 22871] by Demod 12127 with 1733 at 2
+Id : 12313, {_}: add ?22871 (inverse (inverse ?22872)) =<= add (inverse (add ?22872 (inverse (add ?22871 ?22872)))) (inverse (inverse ?22872)) [22872, 22871] by Demod 12312 with 1733 at 2,1,2,1,1,3
+Id : 12314, {_}: add ?22871 (inverse (inverse ?22872)) =<= add (inverse (add ?22872 (inverse (add ?22871 ?22872)))) ?22872 [22872, 22871] by Demod 12313 with 1733 at 2,3
+Id : 12315, {_}: add ?22871 ?22872 =<= add (inverse (add ?22872 (inverse (add ?22871 ?22872)))) ?22872 [22872, 22871] by Demod 12314 with 1733 at 2,2
+Id : 12, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Super 2 with 6 at 2,1,2
+Id : 3710, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 12 with 1733 at 1,1,1,1,1,1,1,1,1,1,1,1,1,1,2
+Id : 3711, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3710 with 1733 at 2,1,1,1,1,1,1,1,2
+Id : 3712, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (add (inverse ?57) (inverse (add ?57 ?58)))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3711 with 1733 at 2,1,2
+Id : 10590, {_}: inverse (add (inverse (inverse ?20667)) (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Super 3712 with 8791 at 1,1,1,2
+Id : 10753, {_}: inverse (add ?20667 (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10590 with 1733 at 1,1,2
+Id : 10754, {_}: inverse (add ?20667 (add ?20667 (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10753 with 1733 at 1,2,1,2
+Id : 15430, {_}: inverse (inverse ?28103) =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Super 1733 with 10754 at 1,2
+Id : 15735, {_}: ?28103 =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Demod 15430 with 1733 at 2
+Id : 1762, {_}: inverse (inverse (add (inverse ?5317) ?5318)) =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Super 1754 with 724 at 1,2
+Id : 1785, {_}: add (inverse ?5317) ?5318 =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Demod 1762 with 1733 at 2
+Id : 11176, {_}: inverse (add ?21600 (inverse (add ?21601 (inverse ?21600)))) =>= inverse ?21600 [21601, 21600] by Demod 10568 with 1733 at 1,1,2
+Id : 11183, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= inverse (inverse ?21642) [21643, 21642] by Super 11176 with 1733 at 2,1,2,1,2
+Id : 11564, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= ?21642 [21643, 21642] by Demod 11183 with 1733 at 3
+Id : 13294, {_}: inverse ?24726 =<= add (inverse ?24726) (inverse (add ?24727 ?24726)) [24727, 24726] by Super 1733 with 11564 at 1,2
+Id : 13313, {_}: inverse (add (inverse ?24792) (inverse (add ?24792 ?24793))) =<= add (inverse (add (inverse ?24792) (inverse (add ?24792 ?24793)))) ?24792 [24793, 24792] by Super 13294 with 3712 at 2,3
+Id : 16466, {_}: add (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) ?29660 =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Super 1785 with 13313 at 1,2,1,2,3
+Id : 16829, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Demod 16466 with 13313 at 2
+Id : 16830, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (add (inverse ?29660) (inverse (add ?29660 ?29661))))) [29661, 29660] by Demod 16829 with 1733 at 2,1,2,3
+Id : 16831, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) [29661, 29660] by Demod 16830 with 1724 at 1,2,3
+Id : 17624, {_}: ?31105 =<= add ?31105 (inverse (add (inverse ?31105) (inverse (add ?31105 ?31106)))) [31106, 31105] by Super 15735 with 16831 at 2,3
+Id : 17680, {_}: ?31105 =<= inverse (add (inverse ?31105) (inverse (add ?31105 ?31106))) [31106, 31105] by Demod 17624 with 16831 at 3
+Id : 18257, {_}: add ?31431 ?31432 =<= add (add ?31431 ?31432) ?31431 [31432, 31431] by Super 11260 with 17680 at 2,3
+Id : 18514, {_}: add (add ?31834 ?31835) ?31834 =<= add (inverse (add ?31834 (inverse (add ?31834 ?31835)))) ?31834 [31835, 31834] by Super 12315 with 18257 at 1,2,1,1,3
+Id : 19938, {_}: add ?34185 ?34186 =<= add (inverse (add ?34185 (inverse (add ?34185 ?34186)))) ?34185 [34186, 34185] by Demod 18514 with 18257 at 2
+Id : 8365, {_}: inverse (add ?15759 (add ?15760 ?15759)) =>= inverse (add ?15760 ?15759) [15760, 15759] by Demod 8144 with 1733 at 2,1,2
+Id : 8391, {_}: inverse (inverse (add ?15887 ?15888)) =<= add ?15888 (add ?15887 ?15888) [15888, 15887] by Super 1733 with 8365 at 1,2
+Id : 8543, {_}: add ?15887 ?15888 =<= add ?15888 (add ?15887 ?15888) [15888, 15887] by Demod 8391 with 1733 at 2
+Id : 15853, {_}: add ?28715 (add ?28715 (inverse (add (inverse ?28715) ?28716))) =?= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Super 8543 with 15735 at 2,3
+Id : 16108, {_}: ?28715 =<= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Demod 15853 with 15735 at 2
+Id : 18478, {_}: ?28715 =<= add ?28715 (inverse (add (inverse ?28715) ?28716)) [28716, 28715] by Demod 16108 with 18257 at 3
+Id : 18480, {_}: add (inverse ?5317) ?5318 =?= add ?5318 (inverse ?5317) [5318, 5317] by Demod 1785 with 18478 at 1,2,3
+Id : 20385, {_}: add ?34911 ?34912 =<= add (inverse (add (inverse (add ?34911 ?34912)) ?34911)) ?34911 [34912, 34911] by Super 19938 with 18480 at 1,1,3
+Id : 20390, {_}: add ?34925 (add ?34926 ?34925) =<= add (inverse (add (inverse (add ?34926 ?34925)) ?34925)) ?34925 [34926, 34925] by Super 20385 with 8543 at 1,1,1,1,3
+Id : 20500, {_}: add ?34926 ?34925 =<= add (inverse (add (inverse (add ?34926 ?34925)) ?34925)) ?34925 [34925, 34926] by Demod 20390 with 8543 at 2
+Id : 5906, {_}: inverse (add (inverse (inverse ?12265)) (inverse (add (inverse ?12266) (inverse (add ?12266 ?12265))))) =>= inverse (add ?12266 ?12265) [12266, 12265] by Super 136 with 5602 at 1,1,1,2
+Id : 6067, {_}: inverse (add ?12265 (inverse (add (inverse ?12266) (inverse (add ?12266 ?12265))))) =>= inverse (add ?12266 ?12265) [12266, 12265] by Demod 5906 with 1733 at 1,1,2
+Id : 15857, {_}: add (inverse ?28730) (add (inverse ?28730) (inverse (add (inverse (inverse ?28730)) ?28731))) =<= add (add (inverse ?28730) (inverse (add (inverse (inverse ?28730)) ?28731))) (inverse (add ?28730 (inverse (inverse ?28730)))) [28731, 28730] by Super 1785 with 15735 at 1,2,1,2,3
+Id : 16100, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add (inverse (inverse ?28730)) ?28731))) (inverse (add ?28730 (inverse (inverse ?28730)))) [28731, 28730] by Demod 15857 with 15735 at 2
+Id : 16101, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add ?28730 ?28731))) (inverse (add ?28730 (inverse (inverse ?28730)))) [28731, 28730] by Demod 16100 with 1733 at 1,1,2,1,3
+Id : 16102, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add ?28730 ?28731))) (inverse (add ?28730 ?28730)) [28731, 28730] by Demod 16101 with 1733 at 2,1,2,3
+Id : 16103, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add ?28730 ?28731))) (inverse ?28730) [28731, 28730] by Demod 16102 with 1724 at 1,2,3
+Id : 18477, {_}: inverse ?28730 =<= add (inverse ?28730) (inverse (add ?28730 ?28731)) [28731, 28730] by Demod 16103 with 18257 at 3
+Id : 21222, {_}: inverse (add ?12265 (inverse (inverse ?12266))) =>= inverse (add ?12266 ?12265) [12266, 12265] by Demod 6067 with 18477 at 1,2,1,2
+Id : 21223, {_}: inverse (add ?12265 ?12266) =?= inverse (add ?12266 ?12265) [12266, 12265] by Demod 21222 with 1733 at 2,1,2
+Id : 21386, {_}: add ?36951 ?36952 =<= add (inverse (add (inverse (add ?36952 ?36951)) ?36952)) ?36952 [36952, 36951] by Super 20500 with 21223 at 1,1,1,3
+Id : 19969, {_}: add ?34289 ?34290 =<= add (inverse (add (inverse (add ?34289 ?34290)) ?34289)) ?34289 [34290, 34289] by Super 19938 with 18480 at 1,1,3
+Id : 21454, {_}: add ?36951 ?36952 =?= add ?36952 ?36951 [36952, 36951] by Demod 21386 with 19969 at 3
+Id : 21981, {_}: add a b === add a b [] by Demod 1 with 21454 at 2
+Id : 1, {_}: add b a =>= add a b [] by huntinton_1
+% SZS output end CNFRefutation for BOO072-1.p
+4619: solved BOO072-1.p in 9.46059 using nrkbo
+4619: status Unsatisfiable for BOO072-1.p
+NO CLASH, using fixed ground order
+4637: Facts:
+4637: Id : 2, {_}:
+ inverse
+ (add (inverse (add (inverse (add ?2 ?3)) ?4))
+ (inverse
+ (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
+4637: Goal:
+4637: Id : 1, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2
+4637: Order:
+4637: nrkbo
+4637: Leaf order:
+4637: inverse 7 1 0
+4637: c 2 0 2 2,2
+4637: add 10 2 4 0,2
+4637: b 2 0 2 2,1,2
+4637: a 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+4638: Facts:
+4638: Id : 2, {_}:
+ inverse
+ (add (inverse (add (inverse (add ?2 ?3)) ?4))
+ (inverse
+ (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
+4638: Goal:
+4638: Id : 1, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2
+4638: Order:
+4638: kbo
+4638: Leaf order:
+4638: inverse 7 1 0
+4638: c 2 0 2 2,2
+4638: add 10 2 4 0,2
+4638: b 2 0 2 2,1,2
+4638: a 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+4639: Facts:
+4639: Id : 2, {_}:
+ inverse
+ (add (inverse (add (inverse (add ?2 ?3)) ?4))
+ (inverse
+ (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
+4639: Goal:
+4639: Id : 1, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2
+4639: Order:
+4639: lpo
+4639: Leaf order:
+4639: inverse 7 1 0
+4639: c 2 0 2 2,2
+4639: add 10 2 4 0,2
+4639: b 2 0 2 2,1,2
+4639: a 2 0 2 1,1,2
+% SZS status Timeout for BOO073-1.p
+NO CLASH, using fixed ground order
+4666: Facts:
+4666: Id : 2, {_}:
+ inverse
+ (add (inverse (add (inverse (add ?2 ?3)) ?4))
+ (inverse
+ (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
+4666: Goal:
+4666: Id : 1, {_}:
+ add (inverse (add (inverse a) b))
+ (inverse (add (inverse a) (inverse b)))
+ =>=
+ a
+ [] by huntinton_3
+4666: Order:
+4666: nrkbo
+4666: Leaf order:
+4666: add 9 2 3 0,2
+4666: b 2 0 2 2,1,1,2
+4666: inverse 12 1 5 0,1,2
+4666: a 3 0 3 1,1,1,1,2
+NO CLASH, using fixed ground order
+4667: Facts:
+4667: Id : 2, {_}:
+ inverse
+ (add (inverse (add (inverse (add ?2 ?3)) ?4))
+ (inverse
+ (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
+4667: Goal:
+4667: Id : 1, {_}:
+ add (inverse (add (inverse a) b))
+ (inverse (add (inverse a) (inverse b)))
+ =>=
+ a
+ [] by huntinton_3
+4667: Order:
+4667: kbo
+4667: Leaf order:
+4667: add 9 2 3 0,2
+4667: b 2 0 2 2,1,1,2
+4667: inverse 12 1 5 0,1,2
+4667: a 3 0 3 1,1,1,1,2
+NO CLASH, using fixed ground order
+4668: Facts:
+4668: Id : 2, {_}:
+ inverse
+ (add (inverse (add (inverse (add ?2 ?3)) ?4))
+ (inverse
+ (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
+4668: Goal:
+4668: Id : 1, {_}:
+ add (inverse (add (inverse a) b))
+ (inverse (add (inverse a) (inverse b)))
+ =>=
+ a
+ [] by huntinton_3
+4668: Order:
+4668: lpo
+4668: Leaf order:
+4668: add 9 2 3 0,2
+4668: b 2 0 2 2,1,1,2
+4668: inverse 12 1 5 0,1,2
+4668: a 3 0 3 1,1,1,1,2
+Statistics :
+Max weight : 70
+Found proof, 17.395929s
+% SZS status Unsatisfiable for BOO074-1.p
+% SZS output start CNFRefutation for BOO074-1.p
+Id : 3, {_}: inverse (add (inverse (add (inverse (add ?7 ?8)) ?9)) (inverse (add ?7 (inverse (add (inverse ?9) (inverse (add ?9 ?10))))))) =>= ?9 [10, 9, 8, 7] by dn1 ?7 ?8 ?9 ?10
+Id : 2, {_}: inverse (add (inverse (add (inverse (add ?2 ?3)) ?4)) (inverse (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) =>= ?4 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
+Id : 15, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?74)) ?75)) ?74)) ?76)) (inverse ?74))) ?74) =>= inverse ?74 [76, 75, 74] by Super 3 with 2 at 2,1,2
+Id : 20, {_}: inverse (add (inverse (add ?104 (inverse ?104))) ?104) =>= inverse ?104 [104] by Super 15 with 2 at 1,1,1,1,2
+Id : 99, {_}: inverse (add (inverse ?355) (inverse (add ?355 (inverse (add (inverse ?355) (inverse (add ?355 ?356))))))) =>= ?355 [356, 355] by Super 2 with 20 at 1,1,2
+Id : 136, {_}: inverse (add (inverse (add (inverse (add ?450 ?451)) ?452)) (inverse (add ?450 ?452))) =>= ?452 [452, 451, 450] by Super 2 with 99 at 2,1,2,1,2
+Id : 536, {_}: inverse (add (inverse (add (inverse (add ?1808 ?1809)) ?1810)) (inverse (add ?1808 ?1810))) =>= ?1810 [1810, 1809, 1808] by Super 2 with 99 at 2,1,2,1,2
+Id : 550, {_}: inverse (add (inverse (add ?1882 ?1883)) (inverse (add (inverse ?1882) ?1883))) =>= ?1883 [1883, 1882] by Super 536 with 99 at 1,1,1,1,2
+Id : 724, {_}: inverse (add ?2517 (inverse (add ?2518 (inverse (add (inverse ?2518) ?2517))))) =>= inverse (add (inverse ?2518) ?2517) [2518, 2517] by Super 136 with 550 at 1,1,2
+Id : 1584, {_}: inverse (add (inverse ?4978) (inverse (add ?4978 (inverse (add (inverse ?4978) (inverse ?4978)))))) =>= ?4978 [4978] by Super 99 with 724 at 2,1,2,1,2
+Id : 1652, {_}: inverse (add (inverse ?4978) (inverse ?4978)) =>= ?4978 [4978] by Demod 1584 with 724 at 2
+Id : 763, {_}: inverse (add (inverse (add ?2736 ?2737)) (inverse (add (inverse ?2736) ?2737))) =>= ?2737 [2737, 2736] by Super 536 with 99 at 1,1,1,1,2
+Id : 144, {_}: inverse (add (inverse ?482) (inverse (add ?482 (inverse (add (inverse ?482) (inverse (add ?482 ?483))))))) =>= ?482 [483, 482] by Super 2 with 20 at 1,1,2
+Id : 155, {_}: inverse (add (inverse ?528) (inverse (add ?528 ?528))) =>= ?528 [528] by Super 144 with 99 at 2,1,2,1,2
+Id : 782, {_}: inverse (add (inverse (add ?2830 (inverse (add ?2830 ?2830)))) ?2830) =>= inverse (add ?2830 ?2830) [2830] by Super 763 with 155 at 2,1,2
+Id : 871, {_}: inverse (add (inverse (add ?3076 ?3076)) (inverse (add ?3076 ?3076))) =>= ?3076 [3076] by Super 136 with 782 at 1,1,2
+Id : 1724, {_}: add ?3076 ?3076 =>= ?3076 [3076] by Demod 871 with 1652 at 2
+Id : 1754, {_}: inverse (inverse ?5284) =>= ?5284 [5284] by Demod 1652 with 1724 at 1,2
+Id : 1762, {_}: inverse (inverse (add (inverse ?5317) ?5318)) =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Super 1754 with 724 at 1,2
+Id : 1733, {_}: inverse (inverse ?4978) =>= ?4978 [4978] by Demod 1652 with 1724 at 1,2
+Id : 1785, {_}: add (inverse ?5317) ?5318 =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Demod 1762 with 1733 at 2
+Id : 6, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?26)) ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Super 3 with 2 at 2,1,2
+Id : 1734, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add ?26 ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Demod 6 with 1733 at 1,1,1,1,1,1,1,1,1,1,2
+Id : 921, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse (add ?3102 ?3102))))) =>= inverse (add ?3102 ?3102) [3102] by Super 136 with 871 at 1,1,2
+Id : 1725, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse (add ?3102 ?3102) [3102] by Demod 921 with 1724 at 1,2,1,2,1,2
+Id : 1726, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse ?3102 [3102] by Demod 1725 with 1724 at 1,3
+Id : 1763, {_}: inverse (inverse ?5320) =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Super 1754 with 1726 at 1,2
+Id : 1786, {_}: ?5320 =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Demod 1763 with 1733 at 2
+Id : 2715, {_}: inverse (add (inverse (add (inverse ?7389) (inverse (inverse ?7389)))) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Super 724 with 1786 at 1,2,1,2,1,2
+Id : 2755, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2715 with 1733 at 2,1,1,1,2
+Id : 2756, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =?= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2755 with 1733 at 2,1,2,1,2
+Id : 2757, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =>= inverse (inverse ?7389) [7389] by Demod 2756 with 1786 at 1,3
+Id : 2758, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= inverse (inverse ?7389) [7389] by Demod 2757 with 1724 at 1,2,1,2
+Id : 2759, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= ?7389 [7389] by Demod 2758 with 1733 at 3
+Id : 2920, {_}: inverse ?7714 =<= add (inverse (add (inverse ?7714) ?7714)) (inverse ?7714) [7714] by Super 1733 with 2759 at 1,2
+Id : 3142, {_}: inverse (add (inverse (add (inverse (add (inverse (inverse ?8118)) ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Super 1734 with 2920 at 1,1,1,1,1,1,1,2
+Id : 3172, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3142 with 1733 at 1,1,1,1,1,1,2
+Id : 3173, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) ?8118)) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3172 with 1733 at 2,1,1,1,2
+Id : 8100, {_}: inverse (add (inverse (add (inverse (add ?15581 ?15582)) ?15581)) (inverse ?15581)) =>= ?15581 [15582, 15581] by Demod 3173 with 1733 at 3
+Id : 8144, {_}: inverse (add ?15759 (inverse (inverse (add ?15760 ?15759)))) =>= inverse (add ?15760 ?15759) [15760, 15759] by Super 8100 with 136 at 1,1,2
+Id : 8365, {_}: inverse (add ?15759 (add ?15760 ?15759)) =>= inverse (add ?15760 ?15759) [15760, 15759] by Demod 8144 with 1733 at 2,1,2
+Id : 8391, {_}: inverse (inverse (add ?15887 ?15888)) =?= add ?15888 (add ?15887 ?15888) [15888, 15887] by Super 1733 with 8365 at 1,2
+Id : 8543, {_}: add ?15887 ?15888 =<= add ?15888 (add ?15887 ?15888) [15888, 15887] by Demod 8391 with 1733 at 2
+Id : 12, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Super 2 with 6 at 2,1,2
+Id : 3710, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 12 with 1733 at 1,1,1,1,1,1,1,1,1,1,1,1,1,1,2
+Id : 3711, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3710 with 1733 at 2,1,1,1,1,1,1,1,2
+Id : 3712, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (add (inverse ?57) (inverse (add ?57 ?58)))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3711 with 1733 at 2,1,2
+Id : 8459, {_}: inverse (add ?16264 (add ?16265 ?16264)) =>= inverse (add ?16265 ?16264) [16265, 16264] by Demod 8144 with 1733 at 2,1,2
+Id : 1749, {_}: inverse (add (inverse (add (inverse ?5262) ?5263)) (inverse (add ?5262 ?5263))) =>= ?5263 [5263, 5262] by Super 550 with 1733 at 1,1,2,1,2
+Id : 5602, {_}: inverse ?11750 =<= add (inverse (add (inverse ?11751) ?11750)) (inverse (add ?11751 ?11750)) [11751, 11750] by Super 1733 with 1749 at 1,2
+Id : 8468, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =<= inverse (add (inverse (add (inverse ?16285) ?16286)) (inverse (add ?16285 ?16286))) [16286, 16285] by Super 8459 with 5602 at 2,1,2
+Id : 8598, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= inverse (inverse ?16286) [16286, 16285] by Demod 8468 with 5602 at 1,3
+Id : 8599, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= ?16286 [16286, 16285] by Demod 8598 with 1733 at 3
+Id : 8791, {_}: inverse ?16774 =<= add (inverse (add ?16775 ?16774)) (inverse ?16774) [16775, 16774] by Super 1733 with 8599 at 1,2
+Id : 10590, {_}: inverse (add (inverse (inverse ?20667)) (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Super 3712 with 8791 at 1,1,1,2
+Id : 10753, {_}: inverse (add ?20667 (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10590 with 1733 at 1,1,2
+Id : 10754, {_}: inverse (add ?20667 (add ?20667 (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10753 with 1733 at 1,2,1,2
+Id : 15430, {_}: inverse (inverse ?28103) =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Super 1733 with 10754 at 1,2
+Id : 15735, {_}: ?28103 =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Demod 15430 with 1733 at 2
+Id : 15853, {_}: add ?28715 (add ?28715 (inverse (add (inverse ?28715) ?28716))) =?= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Super 8543 with 15735 at 2,3
+Id : 16108, {_}: ?28715 =<= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Demod 15853 with 15735 at 2
+Id : 10568, {_}: inverse (add (inverse (inverse ?20566)) (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Super 136 with 8791 at 1,1,1,2
+Id : 10805, {_}: inverse (add ?20566 (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Demod 10568 with 1733 at 1,1,2
+Id : 11153, {_}: inverse (inverse ?21486) =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Super 1733 with 10805 at 1,2
+Id : 11260, {_}: ?21486 =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Demod 11153 with 1733 at 2
+Id : 11176, {_}: inverse (add ?21600 (inverse (add ?21601 (inverse ?21600)))) =>= inverse ?21600 [21601, 21600] by Demod 10568 with 1733 at 1,1,2
+Id : 11183, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= inverse (inverse ?21642) [21643, 21642] by Super 11176 with 1733 at 2,1,2,1,2
+Id : 11564, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= ?21642 [21643, 21642] by Demod 11183 with 1733 at 3
+Id : 13294, {_}: inverse ?24726 =<= add (inverse ?24726) (inverse (add ?24727 ?24726)) [24727, 24726] by Super 1733 with 11564 at 1,2
+Id : 13313, {_}: inverse (add (inverse ?24792) (inverse (add ?24792 ?24793))) =<= add (inverse (add (inverse ?24792) (inverse (add ?24792 ?24793)))) ?24792 [24793, 24792] by Super 13294 with 3712 at 2,3
+Id : 16466, {_}: add (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) ?29660 =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Super 1785 with 13313 at 1,2,1,2,3
+Id : 16829, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Demod 16466 with 13313 at 2
+Id : 16830, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (add (inverse ?29660) (inverse (add ?29660 ?29661))))) [29661, 29660] by Demod 16829 with 1733 at 2,1,2,3
+Id : 16831, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) [29661, 29660] by Demod 16830 with 1724 at 1,2,3
+Id : 17624, {_}: ?31105 =<= add ?31105 (inverse (add (inverse ?31105) (inverse (add ?31105 ?31106)))) [31106, 31105] by Super 15735 with 16831 at 2,3
+Id : 17680, {_}: ?31105 =<= inverse (add (inverse ?31105) (inverse (add ?31105 ?31106))) [31106, 31105] by Demod 17624 with 16831 at 3
+Id : 18257, {_}: add ?31431 ?31432 =<= add (add ?31431 ?31432) ?31431 [31432, 31431] by Super 11260 with 17680 at 2,3
+Id : 18478, {_}: ?28715 =<= add ?28715 (inverse (add (inverse ?28715) ?28716)) [28716, 28715] by Demod 16108 with 18257 at 3
+Id : 18480, {_}: add (inverse ?5317) ?5318 =?= add ?5318 (inverse ?5317) [5318, 5317] by Demod 1785 with 18478 at 1,2,3
+Id : 1761, {_}: inverse ?5314 =<= add (inverse (add ?5315 ?5314)) (inverse (add (inverse ?5315) ?5314)) [5315, 5314] by Super 1754 with 550 at 1,2
+Id : 18644, {_}: a === a [] by Demod 18643 with 1733 at 2
+Id : 18643, {_}: inverse (inverse a) =>= a [] by Demod 18642 with 1761 at 2
+Id : 18642, {_}: add (inverse (add b (inverse a))) (inverse (add (inverse b) (inverse a))) =>= a [] by Demod 18641 with 18480 at 1,2,2
+Id : 18641, {_}: add (inverse (add b (inverse a))) (inverse (add (inverse a) (inverse b))) =>= a [] by Demod 1 with 18480 at 1,1,2
+Id : 1, {_}: add (inverse (add (inverse a) b)) (inverse (add (inverse a) (inverse b))) =>= a [] by huntinton_3
+% SZS output end CNFRefutation for BOO074-1.p
+4666: solved BOO074-1.p in 8.672542 using nrkbo
+4666: status Unsatisfiable for BOO074-1.p
+NO CLASH, using fixed ground order
+4673: Facts:
+4673: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+4673: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+4673: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b))
+ [] by strong_fixed_point
+4673: Goal:
+4673: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+4673: Order:
+4673: nrkbo
+4673: Leaf order:
+4673: w 4 0 0
+4673: b 6 0 0
+4673: apply 19 2 3 0,2
+4673: fixed_pt 3 0 3 2,2
+4673: strong_fixed_point 3 0 2 1,2
+NO CLASH, using fixed ground order
+4674: Facts:
+4674: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+4674: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+4674: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b))
+ [] by strong_fixed_point
+4674: Goal:
+4674: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+4674: Order:
+4674: kbo
+4674: Leaf order:
+4674: w 4 0 0
+4674: b 6 0 0
+4674: apply 19 2 3 0,2
+4674: fixed_pt 3 0 3 2,2
+4674: strong_fixed_point 3 0 2 1,2
+NO CLASH, using fixed ground order
+4675: Facts:
+4675: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+4675: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+4675: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b))
+ [] by strong_fixed_point
+4675: Goal:
+4675: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+4675: Order:
+4675: lpo
+4675: Leaf order:
+4675: w 4 0 0
+4675: b 6 0 0
+4675: apply 19 2 3 0,2
+4675: fixed_pt 3 0 3 2,2
+4675: strong_fixed_point 3 0 2 1,2
+% SZS status Timeout for COL003-12.p
+NO CLASH, using fixed ground order
+4697: Facts:
+4697: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+4697: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+4697: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply (apply b (apply (apply b (apply w w)) (apply b w))) b)) b
+ [] by strong_fixed_point
+4697: Goal:
+4697: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+4697: Order:
+4697: nrkbo
+4697: Leaf order:
+4697: w 4 0 0
+4697: b 7 0 0
+4697: apply 20 2 3 0,2
+4697: fixed_pt 3 0 3 2,2
+4697: strong_fixed_point 3 0 2 1,2
+NO CLASH, using fixed ground order
+4698: Facts:
+4698: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+4698: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+4698: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply (apply b (apply (apply b (apply w w)) (apply b w))) b)) b
+ [] by strong_fixed_point
+4698: Goal:
+4698: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+4698: Order:
+4698: kbo
+4698: Leaf order:
+4698: w 4 0 0
+4698: b 7 0 0
+4698: apply 20 2 3 0,2
+4698: fixed_pt 3 0 3 2,2
+4698: strong_fixed_point 3 0 2 1,2
+NO CLASH, using fixed ground order
+4699: Facts:
+4699: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+4699: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+4699: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply (apply b (apply (apply b (apply w w)) (apply b w))) b)) b
+ [] by strong_fixed_point
+4699: Goal:
+4699: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+4699: Order:
+4699: lpo
+4699: Leaf order:
+4699: w 4 0 0
+4699: b 7 0 0
+4699: apply 20 2 3 0,2
+4699: fixed_pt 3 0 3 2,2
+4699: strong_fixed_point 3 0 2 1,2
+% SZS status Timeout for COL003-17.p
+NO CLASH, using fixed ground order
+4971: Facts:
+4971: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+4971: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+4971: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply (apply b (apply (apply b (apply w w)) (apply b w)))
+ (apply (apply b b) b)
+ [] by strong_fixed_point
+4971: Goal:
+4971: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+4971: Order:
+4971: nrkbo
+4971: Leaf order:
+4971: w 4 0 0
+4971: b 7 0 0
+4971: apply 20 2 3 0,2
+4971: fixed_pt 3 0 3 2,2
+4971: strong_fixed_point 3 0 2 1,2
+NO CLASH, using fixed ground order
+4972: Facts:
+4972: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+4972: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+4972: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply (apply b (apply (apply b (apply w w)) (apply b w)))
+ (apply (apply b b) b)
+ [] by strong_fixed_point
+4972: Goal:
+4972: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+4972: Order:
+4972: kbo
+4972: Leaf order:
+4972: w 4 0 0
+4972: b 7 0 0
+4972: apply 20 2 3 0,2
+4972: fixed_pt 3 0 3 2,2
+4972: strong_fixed_point 3 0 2 1,2
+NO CLASH, using fixed ground order
+4973: Facts:
+4973: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+4973: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+4973: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply (apply b (apply (apply b (apply w w)) (apply b w)))
+ (apply (apply b b) b)
+ [] by strong_fixed_point
+4973: Goal:
+4973: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+4973: Order:
+4973: lpo
+4973: Leaf order:
+4973: w 4 0 0
+4973: b 7 0 0
+4973: apply 20 2 3 0,2
+4973: fixed_pt 3 0 3 2,2
+4973: strong_fixed_point 3 0 2 1,2
+% SZS status Timeout for COL003-18.p
+NO CLASH, using fixed ground order
+7458: Facts:
+7458: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+7458: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+7458: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply (apply b (apply w w)) (apply (apply b (apply b w)) b))) b
+ [] by strong_fixed_point
+7458: Goal:
+7458: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+7458: Order:
+7458: nrkbo
+7458: Leaf order:
+7458: w 4 0 0
+7458: b 7 0 0
+7458: apply 20 2 3 0,2
+7458: fixed_pt 3 0 3 2,2
+7458: strong_fixed_point 3 0 2 1,2
+NO CLASH, using fixed ground order
+7459: Facts:
+7459: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+7459: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+7459: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply (apply b (apply w w)) (apply (apply b (apply b w)) b))) b
+ [] by strong_fixed_point
+7459: Goal:
+7459: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+7459: Order:
+7459: kbo
+7459: Leaf order:
+7459: w 4 0 0
+7459: b 7 0 0
+7459: apply 20 2 3 0,2
+7459: fixed_pt 3 0 3 2,2
+7459: strong_fixed_point 3 0 2 1,2
+NO CLASH, using fixed ground order
+7460: Facts:
+7460: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+7460: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+7460: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply (apply b (apply w w)) (apply (apply b (apply b w)) b))) b
+ [] by strong_fixed_point
+7460: Goal:
+7460: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+7460: Order:
+7460: lpo
+7460: Leaf order:
+7460: w 4 0 0
+7460: b 7 0 0
+7460: apply 20 2 3 0,2
+7460: fixed_pt 3 0 3 2,2
+7460: strong_fixed_point 3 0 2 1,2
+% SZS status Timeout for COL003-19.p
+CLASH, statistics insufficient
+9903: Facts:
+9903: Id : 2, {_}:
+ apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4)
+ [4, 3] by o_definition ?3 ?4
+9903: Id : 3, {_}:
+ apply (apply (apply q1 ?6) ?7) ?8 =>= apply ?6 (apply ?8 ?7)
+ [8, 7, 6] by q1_definition ?6 ?7 ?8
+9903: Goal:
+9903: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
+9903: Order:
+9903: nrkbo
+9903: Leaf order:
+9903: q1 1 0 0
+9903: o 1 0 0
+9903: apply 10 2 1 0,3
+9903: combinator 1 0 1 1,3
+CLASH, statistics insufficient
+9904: Facts:
+9904: Id : 2, {_}:
+ apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4)
+ [4, 3] by o_definition ?3 ?4
+9904: Id : 3, {_}:
+ apply (apply (apply q1 ?6) ?7) ?8 =>= apply ?6 (apply ?8 ?7)
+ [8, 7, 6] by q1_definition ?6 ?7 ?8
+9904: Goal:
+9904: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
+9904: Order:
+9904: kbo
+9904: Leaf order:
+9904: q1 1 0 0
+9904: o 1 0 0
+9904: apply 10 2 1 0,3
+9904: combinator 1 0 1 1,3
+CLASH, statistics insufficient
+9905: Facts:
+9905: Id : 2, {_}:
+ apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4)
+ [4, 3] by o_definition ?3 ?4
+9905: Id : 3, {_}:
+ apply (apply (apply q1 ?6) ?7) ?8 =?= apply ?6 (apply ?8 ?7)
+ [8, 7, 6] by q1_definition ?6 ?7 ?8
+9905: Goal:
+9905: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
+9905: Order:
+9905: lpo
+9905: Leaf order:
+9905: q1 1 0 0
+9905: o 1 0 0
+9905: apply 10 2 1 0,3
+9905: combinator 1 0 1 1,3
+% SZS status Timeout for COL011-1.p
+CLASH, statistics insufficient
+9926: Facts:
+9926: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+9926: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
+9926: Id : 4, {_}:
+ apply (apply t ?9) ?10 =>= apply ?10 ?9
+ [10, 9] by t_definition ?9 ?10
+9926: Goal:
+9926: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+9926: Order:
+9926: nrkbo
+9926: Leaf order:
+9926: t 1 0 0
+9926: m 1 0 0
+9926: b 1 0 0
+9926: apply 13 2 3 0,2
+9926: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+9927: Facts:
+9927: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+9927: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
+9927: Id : 4, {_}:
+ apply (apply t ?9) ?10 =>= apply ?10 ?9
+ [10, 9] by t_definition ?9 ?10
+9927: Goal:
+9927: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+9927: Order:
+9927: kbo
+9927: Leaf order:
+9927: t 1 0 0
+9927: m 1 0 0
+9927: b 1 0 0
+9927: apply 13 2 3 0,2
+9927: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+9928: Facts:
+9928: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+9928: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
+9928: Id : 4, {_}:
+ apply (apply t ?9) ?10 =?= apply ?10 ?9
+ [10, 9] by t_definition ?9 ?10
+9928: Goal:
+9928: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+9928: Order:
+9928: lpo
+9928: Leaf order:
+9928: t 1 0 0
+9928: m 1 0 0
+9928: b 1 0 0
+9928: apply 13 2 3 0,2
+9928: f 3 1 3 0,2,2
+Goal subsumed
+Statistics :
+Max weight : 62
+Found proof, 1.513358s
+% SZS status Unsatisfiable for COL034-1.p
+% SZS output start CNFRefutation for COL034-1.p
+Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
+Id : 4, {_}: apply (apply t ?9) ?10 =>= apply ?10 ?9 [10, 9] by t_definition ?9 ?10
+Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
+Id : 11, {_}: apply m (apply (apply b ?29) ?30) =<= apply ?29 (apply ?30 (apply (apply b ?29) ?30)) [30, 29] by Super 2 with 3 at 2
+Id : 2545, {_}: apply (f (apply (apply b m) (apply (apply b (apply t m)) b))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply b (apply t m)) b)))) m)) === apply (f (apply (apply b m) (apply (apply b (apply t m)) b))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply b (apply t m)) b)))) m)) [] by Super 2544 with 11 at 2
+Id : 2544, {_}: apply ?1974 (apply (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976)))) ?1975) =<= apply (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976))) (apply ?1974 (apply (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976)))) ?1975)) [1975, 1976, 1974] by Demod 2294 with 4 at 2,2
+Id : 2294, {_}: apply ?1974 (apply (apply t ?1975) (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976))))) =<= apply (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976))) (apply ?1974 (apply (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976)))) ?1975)) [1976, 1975, 1974] by Super 53 with 4 at 2,2,3
+Id : 53, {_}: apply ?78 (apply ?79 (apply ?80 (f (apply (apply b ?78) (apply (apply b ?79) ?80))))) =<= apply (f (apply (apply b ?78) (apply (apply b ?79) ?80))) (apply ?78 (apply ?79 (apply ?80 (f (apply (apply b ?78) (apply (apply b ?79) ?80)))))) [80, 79, 78] by Demod 39 with 2 at 2,2
+Id : 39, {_}: apply ?78 (apply (apply (apply b ?79) ?80) (f (apply (apply b ?78) (apply (apply b ?79) ?80)))) =<= apply (f (apply (apply b ?78) (apply (apply b ?79) ?80))) (apply ?78 (apply ?79 (apply ?80 (f (apply (apply b ?78) (apply (apply b ?79) ?80)))))) [80, 79, 78] by Super 8 with 2 at 2,2,3
+Id : 8, {_}: apply ?20 (apply ?21 (f (apply (apply b ?20) ?21))) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Demod 7 with 2 at 2
+Id : 7, {_}: apply (apply (apply b ?20) ?21) (f (apply (apply b ?20) ?21)) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Super 1 with 2 at 2,3
+Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1
+% SZS output end CNFRefutation for COL034-1.p
+9926: solved COL034-1.p in 0.528032 using nrkbo
+9926: status Unsatisfiable for COL034-1.p
+CLASH, statistics insufficient
+9933: Facts:
+9933: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+9933: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+9933: Id : 4, {_}:
+ apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
+ [13, 12, 11] by c_definition ?11 ?12 ?13
+9933: Goal:
+9933: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+9933: Order:
+9933: nrkbo
+9933: Leaf order:
+9933: c 1 0 0
+9933: b 1 0 0
+9933: s 1 0 0
+9933: apply 19 2 3 0,2
+9933: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+9934: Facts:
+9934: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+9934: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+9934: Id : 4, {_}:
+ apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
+ [13, 12, 11] by c_definition ?11 ?12 ?13
+9934: Goal:
+9934: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+9934: Order:
+9934: kbo
+9934: Leaf order:
+9934: c 1 0 0
+9934: b 1 0 0
+9934: s 1 0 0
+9934: apply 19 2 3 0,2
+9934: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+9935: Facts:
+9935: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+9935: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+9935: Id : 4, {_}:
+ apply (apply (apply c ?11) ?12) ?13 =?= apply (apply ?11 ?13) ?12
+ [13, 12, 11] by c_definition ?11 ?12 ?13
+9935: Goal:
+9935: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+9935: Order:
+9935: lpo
+9935: Leaf order:
+9935: c 1 0 0
+9935: b 1 0 0
+9935: s 1 0 0
+9935: apply 19 2 3 0,2
+9935: f 3 1 3 0,2,2
+% SZS status Timeout for COL037-1.p
+CLASH, statistics insufficient
+9973: Facts:
+9973: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+9973: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
+9973: Id : 4, {_}:
+ apply (apply (apply c ?9) ?10) ?11 =>= apply (apply ?9 ?11) ?10
+ [11, 10, 9] by c_definition ?9 ?10 ?11
+9973: Goal:
+9973: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+9973: Order:
+9973: nrkbo
+9973: Leaf order:
+9973: c 1 0 0
+9973: m 1 0 0
+9973: b 1 0 0
+9973: apply 15 2 3 0,2
+9973: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+9974: Facts:
+9974: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+9974: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
+9974: Id : 4, {_}:
+ apply (apply (apply c ?9) ?10) ?11 =>= apply (apply ?9 ?11) ?10
+ [11, 10, 9] by c_definition ?9 ?10 ?11
+9974: Goal:
+9974: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+9974: Order:
+9974: kbo
+9974: Leaf order:
+9974: c 1 0 0
+9974: m 1 0 0
+9974: b 1 0 0
+9974: apply 15 2 3 0,2
+9974: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+9975: Facts:
+9975: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+9975: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
+9975: Id : 4, {_}:
+ apply (apply (apply c ?9) ?10) ?11 =?= apply (apply ?9 ?11) ?10
+ [11, 10, 9] by c_definition ?9 ?10 ?11
+9975: Goal:
+9975: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+9975: Order:
+9975: lpo
+9975: Leaf order:
+9975: c 1 0 0
+9975: m 1 0 0
+9975: b 1 0 0
+9975: apply 15 2 3 0,2
+9975: f 3 1 3 0,2,2
+Goal subsumed
+Statistics :
+Max weight : 54
+Found proof, 2.234152s
+% SZS status Unsatisfiable for COL041-1.p
+% SZS output start CNFRefutation for COL041-1.p
+Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
+Id : 4, {_}: apply (apply (apply c ?9) ?10) ?11 =>= apply (apply ?9 ?11) ?10 [11, 10, 9] by c_definition ?9 ?10 ?11
+Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
+Id : 11, {_}: apply m (apply (apply b ?30) ?31) =<= apply ?30 (apply ?31 (apply (apply b ?30) ?31)) [31, 30] by Super 2 with 3 at 2
+Id : 4380, {_}: apply (f (apply (apply b m) (apply (apply c b) m))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply c b) m)))) m)) === apply (f (apply (apply b m) (apply (apply c b) m))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply c b) m)))) m)) [] by Super 53 with 11 at 2
+Id : 53, {_}: apply ?91 (apply (apply ?92 (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) ?93) =<= apply (f (apply (apply b ?91) (apply (apply c ?92) ?93))) (apply ?91 (apply (apply ?92 (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) ?93)) [93, 92, 91] by Demod 39 with 4 at 2,2
+Id : 39, {_}: apply ?91 (apply (apply (apply c ?92) ?93) (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) =<= apply (f (apply (apply b ?91) (apply (apply c ?92) ?93))) (apply ?91 (apply (apply ?92 (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) ?93)) [93, 92, 91] by Super 8 with 4 at 2,2,3
+Id : 8, {_}: apply ?21 (apply ?22 (f (apply (apply b ?21) ?22))) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Demod 7 with 2 at 2
+Id : 7, {_}: apply (apply (apply b ?21) ?22) (f (apply (apply b ?21) ?22)) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Super 1 with 2 at 2,3
+Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1
+% SZS output end CNFRefutation for COL041-1.p
+9973: solved COL041-1.p in 1.13607 using nrkbo
+9973: status Unsatisfiable for COL041-1.p
+CLASH, statistics insufficient
+9980: Facts:
+9980: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+9980: Id : 3, {_}:
+ apply (apply (apply n ?7) ?8) ?9
+ =?=
+ apply (apply (apply ?7 ?9) ?8) ?9
+ [9, 8, 7] by n_definition ?7 ?8 ?9
+9980: Goal:
+9980: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+9980: Order:
+9980: nrkbo
+9980: Leaf order:
+9980: n 1 0 0
+9980: b 1 0 0
+9980: apply 14 2 3 0,2
+9980: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+9981: Facts:
+9981: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+9981: Id : 3, {_}:
+ apply (apply (apply n ?7) ?8) ?9
+ =?=
+ apply (apply (apply ?7 ?9) ?8) ?9
+ [9, 8, 7] by n_definition ?7 ?8 ?9
+9981: Goal:
+9981: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+9981: Order:
+9981: kbo
+9981: Leaf order:
+9981: n 1 0 0
+9981: b 1 0 0
+9981: apply 14 2 3 0,2
+9981: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+9982: Facts:
+9982: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+9982: Id : 3, {_}:
+ apply (apply (apply n ?7) ?8) ?9
+ =?=
+ apply (apply (apply ?7 ?9) ?8) ?9
+ [9, 8, 7] by n_definition ?7 ?8 ?9
+9982: Goal:
+9982: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+9982: Order:
+9982: lpo
+9982: Leaf order:
+9982: n 1 0 0
+9982: b 1 0 0
+9982: apply 14 2 3 0,2
+9982: f 3 1 3 0,2,2
+Goal subsumed
+Statistics :
+Max weight : 88
+Found proof, 76.191737s
+% SZS status Unsatisfiable for COL044-1.p
+% SZS output start CNFRefutation for COL044-1.p
+Id : 4, {_}: apply (apply (apply b ?11) ?12) ?13 =>= apply ?11 (apply ?12 ?13) [13, 12, 11] by b_definition ?11 ?12 ?13
+Id : 3, {_}: apply (apply (apply n ?7) ?8) ?9 =?= apply (apply (apply ?7 ?9) ?8) ?9 [9, 8, 7] by n_definition ?7 ?8 ?9
+Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
+Id : 8, {_}: apply (apply (apply n b) ?22) ?23 =?= apply ?23 (apply ?22 ?23) [23, 22] by Super 2 with 3 at 2
+Id : 5, {_}: apply ?15 (apply ?16 ?17) =?= apply ?15 (apply ?16 ?17) [17, 16, 15] by Super 4 with 2 at 2
+Id : 83, {_}: apply (apply (apply (apply n b) ?260) (apply b ?261)) ?262 =?= apply ?261 (apply (apply ?260 (apply b ?261)) ?262) [262, 261, 260] by Super 2 with 8 at 1,2
+Id : 24939, {_}: apply (apply (apply n b) (apply (apply (apply n (apply n b)) (apply b (apply n b))) (apply n (apply n b)))) (f (apply (apply (apply (apply n b) (apply n (apply n b))) (apply b (apply n b))) (apply n (apply n b)))) =?= apply (apply (apply n b) (apply (apply (apply n (apply n b)) (apply b (apply n b))) (apply n (apply n b)))) (f (apply (apply (apply (apply n b) (apply n (apply n b))) (apply b (apply n b))) (apply n (apply n b)))) [] by Super 24245 with 83 at 1,2
+Id : 24245, {_}: apply (apply (apply (apply ?35313 ?35314) ?35315) ?35314) (f (apply (apply (apply ?35313 ?35314) ?35315) ?35314)) =?= apply (apply (apply n b) (apply (apply (apply n ?35313) ?35315) ?35314)) (f (apply (apply (apply ?35313 ?35314) ?35315) ?35314)) [35315, 35314, 35313] by Super 153 with 3 at 2,1,3
+Id : 153, {_}: apply (apply ?460 ?461) (f (apply ?460 ?461)) =<= apply (apply (apply n b) (apply ?460 ?461)) (f (apply ?460 ?461)) [461, 460] by Super 115 with 5 at 1,3
+Id : 115, {_}: apply ?375 (f ?375) =<= apply (apply (apply n b) ?375) (f ?375) [375] by Super 1 with 8 at 3
+Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1
+% SZS output end CNFRefutation for COL044-1.p
+9981: solved COL044-1.p in 12.724795 using kbo
+9981: status Unsatisfiable for COL044-1.p
+CLASH, statistics insufficient
+9998: Facts:
+9998: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+9998: Id : 3, {_}:
+ apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
+ [8, 7] by w_definition ?7 ?8
+9998: Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
+9998: Goal:
+9998: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_strong_fixed_point ?1
+9998: Order:
+9998: nrkbo
+9998: Leaf order:
+9998: m 1 0 0
+9998: w 1 0 0
+9998: b 1 0 0
+9998: apply 14 2 3 0,2
+9998: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+9999: Facts:
+9999: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+9999: Id : 3, {_}:
+ apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
+ [8, 7] by w_definition ?7 ?8
+9999: Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
+9999: Goal:
+9999: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_strong_fixed_point ?1
+9999: Order:
+9999: kbo
+9999: Leaf order:
+9999: m 1 0 0
+9999: w 1 0 0
+9999: b 1 0 0
+9999: apply 14 2 3 0,2
+9999: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+10000: Facts:
+10000: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+10000: Id : 3, {_}:
+ apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
+ [8, 7] by w_definition ?7 ?8
+10000: Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
+10000: Goal:
+10000: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_strong_fixed_point ?1
+10000: Order:
+10000: lpo
+10000: Leaf order:
+10000: m 1 0 0
+10000: w 1 0 0
+10000: b 1 0 0
+10000: apply 14 2 3 0,2
+10000: f 3 1 3 0,2,2
+Goal subsumed
+Statistics :
+Max weight : 54
+Found proof, 12.856628s
+% SZS status Unsatisfiable for COL049-1.p
+% SZS output start CNFRefutation for COL049-1.p
+Id : 3, {_}: apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 [8, 7] by w_definition ?7 ?8
+Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
+Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
+Id : 226, {_}: apply (apply w (apply b ?378)) ?379 =?= apply ?378 (apply ?379 ?379) [379, 378] by Super 2 with 3 at 2
+Id : 231, {_}: apply (apply w (apply b ?393)) ?394 =>= apply ?393 (apply m ?394) [394, 393] by Super 226 with 4 at 2,3
+Id : 289, {_}: apply m (apply w (apply b ?503)) =<= apply ?503 (apply m (apply w (apply b ?503))) [503] by Super 4 with 231 at 3
+Id : 15983, {_}: apply (f (apply (apply b m) (apply (apply b w) b))) (apply m (apply w (apply b (f (apply (apply b m) (apply (apply b w) b)))))) === apply (f (apply (apply b m) (apply (apply b w) b))) (apply m (apply w (apply b (f (apply (apply b m) (apply (apply b w) b)))))) [] by Super 72 with 289 at 2
+Id : 72, {_}: apply ?123 (apply ?124 (apply ?125 (f (apply (apply b ?123) (apply (apply b ?124) ?125))))) =<= apply (f (apply (apply b ?123) (apply (apply b ?124) ?125))) (apply ?123 (apply ?124 (apply ?125 (f (apply (apply b ?123) (apply (apply b ?124) ?125)))))) [125, 124, 123] by Demod 59 with 2 at 2,2
+Id : 59, {_}: apply ?123 (apply (apply (apply b ?124) ?125) (f (apply (apply b ?123) (apply (apply b ?124) ?125)))) =<= apply (f (apply (apply b ?123) (apply (apply b ?124) ?125))) (apply ?123 (apply ?124 (apply ?125 (f (apply (apply b ?123) (apply (apply b ?124) ?125)))))) [125, 124, 123] by Super 8 with 2 at 2,2,3
+Id : 8, {_}: apply ?20 (apply ?21 (f (apply (apply b ?20) ?21))) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Demod 7 with 2 at 2
+Id : 7, {_}: apply (apply (apply b ?20) ?21) (f (apply (apply b ?20) ?21)) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Super 1 with 2 at 2,3
+Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_strong_fixed_point ?1
+% SZS output end CNFRefutation for COL049-1.p
+9998: solved COL049-1.p in 6.372397 using nrkbo
+9998: status Unsatisfiable for COL049-1.p
+CLASH, statistics insufficient
+10010: Facts:
+10010: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+10010: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+10010: Id : 4, {_}:
+ apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
+ [13, 12, 11] by c_definition ?11 ?12 ?13
+10010: Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
+10010: Goal:
+10010: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_strong_fixed_point ?1
+10010: Order:
+10010: nrkbo
+10010: Leaf order:
+10010: i 1 0 0
+10010: c 1 0 0
+10010: b 1 0 0
+10010: s 1 0 0
+10010: apply 20 2 3 0,2
+10010: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+10011: Facts:
+10011: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+10011: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+10011: Id : 4, {_}:
+ apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
+ [13, 12, 11] by c_definition ?11 ?12 ?13
+10011: Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
+10011: Goal:
+10011: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_strong_fixed_point ?1
+10011: Order:
+10011: kbo
+10011: Leaf order:
+10011: i 1 0 0
+10011: c 1 0 0
+10011: b 1 0 0
+10011: s 1 0 0
+10011: apply 20 2 3 0,2
+10011: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+10012: Facts:
+10012: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+10012: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+10012: Id : 4, {_}:
+ apply (apply (apply c ?11) ?12) ?13 =?= apply (apply ?11 ?13) ?12
+ [13, 12, 11] by c_definition ?11 ?12 ?13
+10012: Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
+10012: Goal:
+10012: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_strong_fixed_point ?1
+10012: Order:
+10012: lpo
+10012: Leaf order:
+10012: i 1 0 0
+10012: c 1 0 0
+10012: b 1 0 0
+10012: s 1 0 0
+10012: apply 20 2 3 0,2
+10012: f 3 1 3 0,2,2
+Goal subsumed
+Statistics :
+Max weight : 84
+Found proof, 12.629405s
+% SZS status Unsatisfiable for COL057-1.p
+% SZS output start CNFRefutation for COL057-1.p
+Id : 3, {_}: apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) [9, 8, 7] by b_definition ?7 ?8 ?9
+Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
+Id : 2, {_}: apply (apply (apply s ?3) ?4) ?5 =?= apply (apply ?3 ?5) (apply ?4 ?5) [5, 4, 3] by s_definition ?3 ?4 ?5
+Id : 37, {_}: apply (apply (apply s i) ?141) ?142 =?= apply ?142 (apply ?141 ?142) [142, 141] by Super 2 with 5 at 1,3
+Id : 16, {_}: apply (apply (apply s (apply b ?64)) ?65) ?66 =?= apply ?64 (apply ?66 (apply ?65 ?66)) [66, 65, 64] by Super 2 with 3 at 3
+Id : 9068, {_}: apply (apply (apply (apply s (apply b (apply s i))) i) (apply (apply s (apply b (apply s i))) i)) (f (apply (apply (apply s (apply b (apply s i))) i) (apply i (apply (apply s (apply b (apply s i))) i)))) === apply (apply (apply (apply s (apply b (apply s i))) i) (apply (apply s (apply b (apply s i))) i)) (f (apply (apply (apply s (apply b (apply s i))) i) (apply i (apply (apply s (apply b (apply s i))) i)))) [] by Super 9059 with 5 at 2,1,2
+Id : 9059, {_}: apply (apply ?16932 (apply ?16933 ?16932)) (f (apply ?16932 (apply ?16933 ?16932))) =?= apply (apply (apply (apply s (apply b (apply s i))) ?16933) ?16932) (f (apply ?16932 (apply ?16933 ?16932))) [16933, 16932] by Super 9058 with 16 at 1,3
+Id : 9058, {_}: apply ?16930 (f ?16930) =<= apply (apply (apply s i) ?16930) (f ?16930) [16930] by Super 1 with 37 at 3
+Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_strong_fixed_point ?1
+% SZS output end CNFRefutation for COL057-1.p
+10010: solved COL057-1.p in 2.124132 using nrkbo
+10010: status Unsatisfiable for COL057-1.p
+NO CLASH, using fixed ground order
+10025: Facts:
+10025: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply
+ (multiply
+ (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
+ ?5) (inverse (multiply ?3 ?5))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
+10025: Goal:
+10025: Id : 1, {_}:
+ multiply a (multiply b c) =<= multiply (multiply a b) c
+ [] by prove_associativity
+10025: Order:
+10025: nrkbo
+10025: Leaf order:
+10025: inverse 5 1 0
+10025: multiply 10 2 4 0,2
+10025: c 2 0 2 2,2,2
+10025: b 2 0 2 1,2,2
+10025: a 2 0 2 1,2
+NO CLASH, using fixed ground order
+10026: Facts:
+10026: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply
+ (multiply
+ (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
+ ?5) (inverse (multiply ?3 ?5))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
+10026: Goal:
+10026: Id : 1, {_}:
+ multiply a (multiply b c) =<= multiply (multiply a b) c
+ [] by prove_associativity
+10026: Order:
+10026: kbo
+10026: Leaf order:
+10026: inverse 5 1 0
+10026: multiply 10 2 4 0,2
+10026: c 2 0 2 2,2,2
+10026: b 2 0 2 1,2,2
+10026: a 2 0 2 1,2
+NO CLASH, using fixed ground order
+10027: Facts:
+10027: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply
+ (multiply
+ (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
+ ?5) (inverse (multiply ?3 ?5))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
+10027: Goal:
+10027: Id : 1, {_}:
+ multiply a (multiply b c) =<= multiply (multiply a b) c
+ [] by prove_associativity
+10027: Order:
+10027: lpo
+10027: Leaf order:
+10027: inverse 5 1 0
+10027: multiply 10 2 4 0,2
+10027: c 2 0 2 2,2,2
+10027: b 2 0 2 1,2,2
+10027: a 2 0 2 1,2
+Statistics :
+Max weight : 62
+Found proof, 20.319552s
+% SZS status Unsatisfiable for GRP014-1.p
+% SZS output start CNFRefutation for GRP014-1.p
+Id : 2, {_}: multiply ?2 (inverse (multiply (multiply (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) ?5) (inverse (multiply ?3 ?5)))) =>= ?4 [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
+Id : 3, {_}: multiply ?7 (inverse (multiply (multiply (inverse (multiply (inverse ?8) (multiply (inverse ?7) ?9))) ?10) (inverse (multiply ?8 ?10)))) =>= ?9 [10, 9, 8, 7] by group_axiom ?7 ?8 ?9 ?10
+Id : 6, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (inverse (multiply (inverse ?29) (multiply (inverse (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?27))) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 30, 29, 28, 27, 26] by Super 3 with 2 at 1,1,2,2
+Id : 5, {_}: multiply ?19 (inverse (multiply (multiply (inverse (multiply (inverse ?20) ?21)) ?22) (inverse (multiply ?20 ?22)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24) (inverse (multiply ?23 ?24))) [24, 23, 22, 21, 20, 19] by Super 3 with 2 at 2,1,1,1,1,2,2
+Id : 28, {_}: multiply (inverse ?215) (multiply ?215 (inverse (multiply (multiply (inverse (multiply (inverse ?216) ?217)) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 217, 216, 215] by Super 2 with 5 at 2,2
+Id : 29, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?220) (multiply (inverse (inverse ?221)) (multiply (inverse ?221) ?222)))) ?223) (inverse (multiply ?220 ?223))) =>= ?222 [223, 222, 221, 220] by Super 2 with 5 at 2
+Id : 287, {_}: multiply (inverse ?2293) (multiply ?2293 ?2294) =?= multiply (inverse (inverse ?2295)) (multiply (inverse ?2295) ?2294) [2295, 2294, 2293] by Super 28 with 29 at 2,2,2
+Id : 136, {_}: multiply (inverse ?1148) (multiply ?1148 ?1149) =?= multiply (inverse (inverse ?1150)) (multiply (inverse ?1150) ?1149) [1150, 1149, 1148] by Super 28 with 29 at 2,2,2
+Id : 301, {_}: multiply (inverse ?2384) (multiply ?2384 ?2385) =?= multiply (inverse ?2386) (multiply ?2386 ?2385) [2386, 2385, 2384] by Super 287 with 136 at 3
+Id : 356, {_}: multiply (inverse ?2583) (multiply ?2583 (inverse (multiply (multiply (inverse (multiply (inverse ?2584) (multiply ?2584 ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585, 2584, 2583] by Super 28 with 301 at 1,1,1,1,2,2,2
+Id : 679, {_}: multiply ?5168 (inverse (multiply (multiply (inverse (multiply (inverse ?5169) (multiply ?5169 ?5170))) ?5171) (inverse (multiply (inverse ?5168) ?5171)))) =>= ?5170 [5171, 5170, 5169, 5168] by Super 2 with 301 at 1,1,1,1,2,2
+Id : 2910, {_}: multiply ?23936 (inverse (multiply (multiply (inverse (multiply (inverse ?23937) (multiply ?23937 ?23938))) (multiply ?23936 ?23939)) (inverse (multiply (inverse ?23940) (multiply ?23940 ?23939))))) =>= ?23938 [23940, 23939, 23938, 23937, 23936] by Super 679 with 301 at 1,2,1,2,2
+Id : 2996, {_}: multiply (multiply (inverse ?24702) (multiply ?24702 ?24703)) (inverse (multiply ?24704 (inverse (multiply (inverse ?24705) (multiply ?24705 (inverse (multiply (multiply (inverse (multiply (inverse ?24706) ?24704)) ?24707) (inverse (multiply ?24706 ?24707))))))))) =>= ?24703 [24707, 24706, 24705, 24704, 24703, 24702] by Super 2910 with 28 at 1,1,2,2
+Id : 3034, {_}: multiply (multiply (inverse ?24702) (multiply ?24702 ?24703)) (inverse (multiply ?24704 (inverse ?24704))) =>= ?24703 [24704, 24703, 24702] by Demod 2996 with 28 at 1,2,1,2,2
+Id : 3426, {_}: multiply (inverse (multiply (inverse ?29536) (multiply ?29536 ?29537))) ?29537 =?= multiply (inverse (multiply (inverse ?29538) (multiply ?29538 ?29539))) ?29539 [29539, 29538, 29537, 29536] by Super 356 with 3034 at 2,2
+Id : 3726, {_}: multiply (inverse (inverse (multiply (inverse ?31745) (multiply ?31745 (inverse (multiply (multiply (inverse (multiply (inverse ?31746) ?31747)) ?31748) (inverse (multiply ?31746 ?31748)))))))) (multiply (inverse (multiply (inverse ?31749) (multiply ?31749 ?31750))) ?31750) =>= ?31747 [31750, 31749, 31748, 31747, 31746, 31745] by Super 28 with 3426 at 2,2
+Id : 3919, {_}: multiply (inverse (inverse ?31747)) (multiply (inverse (multiply (inverse ?31749) (multiply ?31749 ?31750))) ?31750) =>= ?31747 [31750, 31749, 31747] by Demod 3726 with 28 at 1,1,1,2
+Id : 91, {_}: multiply (inverse ?821) (multiply ?821 (inverse (multiply (multiply (inverse (multiply (inverse ?822) ?823)) ?824) (inverse (multiply ?822 ?824))))) =>= ?823 [824, 823, 822, 821] by Super 2 with 5 at 2,2
+Id : 107, {_}: multiply (inverse ?949) (multiply ?949 (multiply ?950 (inverse (multiply (multiply (inverse (multiply (inverse ?951) ?952)) ?953) (inverse (multiply ?951 ?953)))))) =>= multiply (inverse (inverse ?950)) ?952 [953, 952, 951, 950, 949] by Super 91 with 5 at 2,2,2
+Id : 3966, {_}: multiply (inverse (inverse (inverse ?33635))) ?33635 =?= multiply (inverse (inverse (inverse (multiply (inverse ?33636) (multiply ?33636 (inverse (multiply (multiply (inverse (multiply (inverse ?33637) ?33638)) ?33639) (inverse (multiply ?33637 ?33639))))))))) ?33638 [33639, 33638, 33637, 33636, 33635] by Super 107 with 3919 at 2,2
+Id : 4117, {_}: multiply (inverse (inverse (inverse ?33635))) ?33635 =?= multiply (inverse (inverse (inverse ?33638))) ?33638 [33638, 33635] by Demod 3966 with 28 at 1,1,1,1,3
+Id : 4346, {_}: multiply (inverse (inverse ?35898)) (multiply (inverse (multiply (inverse (inverse (inverse (inverse ?35899)))) (multiply (inverse (inverse (inverse ?35900))) ?35900))) ?35899) =>= ?35898 [35900, 35899, 35898] by Super 3919 with 4117 at 2,1,1,2,2
+Id : 3965, {_}: multiply (inverse ?33628) (multiply ?33628 (multiply ?33629 (inverse (multiply (multiply (inverse ?33630) ?33631) (inverse (multiply (inverse ?33630) ?33631)))))) =?= multiply (inverse (inverse ?33629)) (multiply (inverse (multiply (inverse ?33632) (multiply ?33632 ?33633))) ?33633) [33633, 33632, 33631, 33630, 33629, 33628] by Super 107 with 3919 at 1,1,1,1,2,2,2,2
+Id : 6632, {_}: multiply (inverse ?52916) (multiply ?52916 (multiply ?52917 (inverse (multiply (multiply (inverse ?52918) ?52919) (inverse (multiply (inverse ?52918) ?52919)))))) =>= ?52917 [52919, 52918, 52917, 52916] by Demod 3965 with 3919 at 3
+Id : 6641, {_}: multiply (inverse ?52992) (multiply ?52992 (multiply ?52993 (inverse (multiply (multiply (inverse ?52994) (inverse (multiply (multiply (inverse (multiply (inverse ?52995) (multiply (inverse (inverse ?52994)) ?52996))) ?52997) (inverse (multiply ?52995 ?52997))))) (inverse ?52996))))) =>= ?52993 [52997, 52996, 52995, 52994, 52993, 52992] by Super 6632 with 2 at 1,2,1,2,2,2,2
+Id : 6773, {_}: multiply (inverse ?52992) (multiply ?52992 (multiply ?52993 (inverse (multiply ?52996 (inverse ?52996))))) =>= ?52993 [52996, 52993, 52992] by Demod 6641 with 2 at 1,1,2,2,2,2
+Id : 6832, {_}: multiply (inverse (inverse ?53817)) (multiply (inverse ?53818) (multiply ?53818 (inverse (multiply ?53819 (inverse ?53819))))) =>= ?53817 [53819, 53818, 53817] by Super 4346 with 6773 at 1,1,2,2
+Id : 4, {_}: multiply ?12 (inverse (multiply (multiply (inverse (multiply (inverse ?13) (multiply (inverse ?12) ?14))) (inverse (multiply (multiply (inverse (multiply (inverse ?15) (multiply (inverse ?13) ?16))) ?17) (inverse (multiply ?15 ?17))))) (inverse ?16))) =>= ?14 [17, 16, 15, 14, 13, 12] by Super 3 with 2 at 1,2,1,2,2
+Id : 9, {_}: multiply ?44 (inverse (multiply (multiply (inverse (multiply (inverse ?45) ?46)) ?47) (inverse (multiply ?45 ?47)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?48) (multiply (inverse (inverse ?44)) ?46))) (inverse (multiply (multiply (inverse (multiply (inverse ?49) (multiply (inverse ?48) ?50))) ?51) (inverse (multiply ?49 ?51))))) (inverse ?50)) [51, 50, 49, 48, 47, 46, 45, 44] by Super 2 with 4 at 2,1,1,1,1,2,2
+Id : 7754, {_}: multiply ?63171 (inverse (multiply (multiply (inverse (multiply (inverse ?63172) (multiply (inverse ?63171) (inverse (multiply ?63173 (inverse ?63173)))))) ?63174) (inverse (multiply ?63172 ?63174)))) =?= inverse (multiply (multiply (inverse ?63175) (inverse (multiply (multiply (inverse (multiply (inverse ?63176) (multiply (inverse (inverse ?63175)) ?63177))) ?63178) (inverse (multiply ?63176 ?63178))))) (inverse ?63177)) [63178, 63177, 63176, 63175, 63174, 63173, 63172, 63171] by Super 9 with 6832 at 1,1,1,1,3
+Id : 7872, {_}: inverse (multiply ?63173 (inverse ?63173)) =?= inverse (multiply (multiply (inverse ?63175) (inverse (multiply (multiply (inverse (multiply (inverse ?63176) (multiply (inverse (inverse ?63175)) ?63177))) ?63178) (inverse (multiply ?63176 ?63178))))) (inverse ?63177)) [63178, 63177, 63176, 63175, 63173] by Demod 7754 with 2 at 2
+Id : 7873, {_}: inverse (multiply ?63173 (inverse ?63173)) =?= inverse (multiply ?63177 (inverse ?63177)) [63177, 63173] by Demod 7872 with 2 at 1,1,3
+Id : 8249, {_}: multiply (inverse (inverse (multiply ?66459 (inverse ?66459)))) (multiply (inverse ?66460) (multiply ?66460 (inverse (multiply ?66461 (inverse ?66461))))) =?= multiply ?66462 (inverse ?66462) [66462, 66461, 66460, 66459] by Super 6832 with 7873 at 1,1,2
+Id : 8282, {_}: multiply ?66459 (inverse ?66459) =?= multiply ?66462 (inverse ?66462) [66462, 66459] by Demod 8249 with 6832 at 2
+Id : 8520, {_}: multiply (multiply (inverse ?67970) (multiply ?67971 (inverse ?67971))) (inverse (multiply ?67972 (inverse ?67972))) =>= inverse ?67970 [67972, 67971, 67970] by Super 3034 with 8282 at 2,1,2
+Id : 380, {_}: multiply ?2743 (inverse (multiply (multiply (inverse ?2744) (multiply ?2744 ?2745)) (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745))))) =>= ?2747 [2747, 2746, 2745, 2744, 2743] by Super 2 with 301 at 1,1,2,2
+Id : 8912, {_}: multiply ?70596 (inverse (multiply (multiply (inverse ?70597) (multiply ?70597 (inverse (multiply ?70598 (inverse ?70598))))) (inverse (multiply ?70599 (inverse ?70599))))) =>= inverse (inverse ?70596) [70599, 70598, 70597, 70596] by Super 380 with 8520 at 2,1,2,1,2,2
+Id : 9021, {_}: multiply ?70596 (inverse (inverse (multiply ?70598 (inverse ?70598)))) =>= inverse (inverse ?70596) [70598, 70596] by Demod 8912 with 3034 at 1,2,2
+Id : 9165, {_}: multiply (inverse (inverse ?72171)) (multiply (inverse (multiply (inverse ?72172) (inverse (inverse ?72172)))) (inverse (inverse (multiply ?72173 (inverse ?72173))))) =>= ?72171 [72173, 72172, 72171] by Super 3919 with 9021 at 2,1,1,2,2
+Id : 10068, {_}: multiply (inverse (inverse ?76580)) (inverse (inverse (inverse (multiply (inverse ?76581) (inverse (inverse ?76581)))))) =>= ?76580 [76581, 76580] by Demod 9165 with 9021 at 2,2
+Id : 9180, {_}: multiply ?72234 (inverse ?72234) =?= inverse (inverse (inverse (multiply ?72235 (inverse ?72235)))) [72235, 72234] by Super 8282 with 9021 at 3
+Id : 10100, {_}: multiply (inverse (inverse ?76745)) (multiply ?76746 (inverse ?76746)) =>= ?76745 [76746, 76745] by Super 10068 with 9180 at 2,2
+Id : 10663, {_}: multiply ?82289 (inverse (multiply ?82290 (inverse ?82290))) =>= inverse (inverse ?82289) [82290, 82289] by Super 8520 with 10100 at 1,2
+Id : 10913, {_}: multiply (inverse (inverse ?83563)) (inverse (inverse (inverse (multiply (inverse ?83564) (multiply ?83564 (inverse (multiply ?83565 (inverse ?83565)))))))) =>= ?83563 [83565, 83564, 83563] by Super 3919 with 10663 at 2,2
+Id : 10892, {_}: inverse (inverse (multiply (inverse ?24702) (multiply ?24702 ?24703))) =>= ?24703 [24703, 24702] by Demod 3034 with 10663 at 2
+Id : 11238, {_}: multiply (inverse (inverse ?83563)) (inverse (inverse (multiply ?83565 (inverse ?83565)))) =>= ?83563 [83565, 83563] by Demod 10913 with 10892 at 1,2,2
+Id : 11239, {_}: inverse (inverse (inverse (inverse ?83563))) =>= ?83563 [83563] by Demod 11238 with 9021 at 2
+Id : 138, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1160) (multiply (inverse (inverse ?1161)) (multiply (inverse ?1161) ?1162)))) ?1163) (inverse (multiply ?1160 ?1163))) =>= ?1162 [1163, 1162, 1161, 1160] by Super 2 with 5 at 2
+Id : 145, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1213) (multiply (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?1214) (multiply (inverse (inverse ?1215)) (multiply (inverse ?1215) ?1216)))) ?1217) (inverse (multiply ?1214 ?1217))))) (multiply ?1216 ?1218)))) ?1219) (inverse (multiply ?1213 ?1219))) =>= ?1218 [1219, 1218, 1217, 1216, 1215, 1214, 1213] by Super 138 with 29 at 1,2,2,1,1,1,1,2
+Id : 168, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1213) (multiply (inverse ?1216) (multiply ?1216 ?1218)))) ?1219) (inverse (multiply ?1213 ?1219))) =>= ?1218 [1219, 1218, 1216, 1213] by Demod 145 with 29 at 1,1,2,1,1,1,1,2
+Id : 777, {_}: multiply (inverse ?5891) (multiply ?5891 (multiply ?5892 (inverse (multiply (multiply (inverse (multiply (inverse ?5893) ?5894)) ?5895) (inverse (multiply ?5893 ?5895)))))) =>= multiply (inverse (inverse ?5892)) ?5894 [5895, 5894, 5893, 5892, 5891] by Super 91 with 5 at 2,2,2
+Id : 813, {_}: multiply (inverse ?6211) (multiply ?6211 (multiply ?6212 ?6213)) =?= multiply (inverse (inverse ?6212)) (multiply (inverse ?6214) (multiply ?6214 ?6213)) [6214, 6213, 6212, 6211] by Super 777 with 168 at 2,2,2,2
+Id : 1401, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?11491) (multiply ?11491 (multiply ?11492 ?11493)))) ?11494) (inverse (multiply (inverse ?11492) ?11494))) =>= ?11493 [11494, 11493, 11492, 11491] by Super 168 with 813 at 1,1,1,1,2
+Id : 1427, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?11709) (multiply ?11709 (multiply (inverse ?11710) (multiply ?11710 ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711, 11710, 11709] by Super 1401 with 301 at 2,2,1,1,1,1,2
+Id : 10889, {_}: multiply (inverse ?52992) (multiply ?52992 (inverse (inverse ?52993))) =>= ?52993 [52993, 52992] by Demod 6773 with 10663 at 2,2,2
+Id : 11440, {_}: multiply (inverse ?85947) (multiply ?85947 ?85948) =>= inverse (inverse ?85948) [85948, 85947] by Super 10889 with 11239 at 2,2,2
+Id : 12070, {_}: inverse (multiply (multiply (inverse (inverse (inverse (multiply (inverse ?11710) (multiply ?11710 ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711, 11710] by Demod 1427 with 11440 at 1,1,1,1,2
+Id : 12071, {_}: inverse (multiply (multiply (inverse (inverse (inverse (inverse (inverse ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711] by Demod 12070 with 11440 at 1,1,1,1,1,1,2
+Id : 12086, {_}: inverse (multiply (multiply (inverse ?11711) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711] by Demod 12071 with 11239 at 1,1,1,2
+Id : 11284, {_}: multiply ?84907 (inverse (multiply (inverse (inverse (inverse ?84908))) ?84908)) =>= inverse (inverse ?84907) [84908, 84907] by Super 10663 with 11239 at 2,1,2,2
+Id : 12456, {_}: inverse (inverse (inverse (multiply (inverse ?89511) ?89512))) =>= multiply (inverse ?89512) ?89511 [89512, 89511] by Super 12086 with 11284 at 1,2
+Id : 12807, {_}: inverse (multiply (inverse ?89891) ?89892) =>= multiply (inverse ?89892) ?89891 [89892, 89891] by Super 11239 with 12456 at 1,2
+Id : 13084, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (inverse (multiply (inverse (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?27)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 6 with 12807 at 1,1,1,2,1,2,1,2,2
+Id : 13085, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13084 with 12807 at 1,1,1,1,2,1,2,1,2,2
+Id : 13086, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (inverse (multiply (inverse ?26) ?30)) ?28)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13085 with 12807 at 2,1,1,1,1,2,1,2,1,2,2
+Id : 13087, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13086 with 12807 at 1,2,1,1,1,1,2,1,2,1,2,2
+Id : 12072, {_}: multiply ?2743 (inverse (multiply (inverse (inverse ?2745)) (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745))))) =>= ?2747 [2747, 2746, 2745, 2743] by Demod 380 with 11440 at 1,1,2,2
+Id : 13068, {_}: multiply ?2743 (multiply (inverse (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745)))) (inverse ?2745)) =>= ?2747 [2745, 2747, 2746, 2743] by Demod 12072 with 12807 at 2,2
+Id : 358, {_}: multiply (inverse ?2595) (multiply ?2595 (inverse (multiply (multiply (inverse ?2596) (multiply ?2596 ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597, 2596, 2595] by Super 28 with 301 at 1,1,2,2,2
+Id : 12055, {_}: inverse (inverse (inverse (multiply (multiply (inverse ?2596) (multiply ?2596 ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597, 2596] by Demod 358 with 11440 at 2
+Id : 12056, {_}: inverse (inverse (inverse (multiply (inverse (inverse ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597] by Demod 12055 with 11440 at 1,1,1,1,2
+Id : 12778, {_}: multiply (inverse (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))) (inverse ?2597) =>= ?2599 [2597, 2599, 2598] by Demod 12056 with 12456 at 2
+Id : 13130, {_}: multiply ?2743 (multiply (inverse ?2743) ?2747) =>= ?2747 [2747, 2743] by Demod 13068 with 12778 at 2,2
+Id : 12068, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?2584) (multiply ?2584 ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585, 2584] by Demod 356 with 11440 at 2
+Id : 12069, {_}: inverse (inverse (inverse (multiply (multiply (inverse (inverse (inverse ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 12068 with 11440 at 1,1,1,1,1,1,2
+Id : 12343, {_}: inverse (inverse (inverse (inverse (inverse (multiply (inverse (inverse (inverse ?88665))) ?88666))))) =>= multiply (inverse (inverse (inverse ?88666))) ?88665 [88666, 88665] by Super 12069 with 11284 at 1,1,1,2
+Id : 12705, {_}: inverse (multiply (inverse (inverse (inverse ?88665))) ?88666) =>= multiply (inverse (inverse (inverse ?88666))) ?88665 [88666, 88665] by Demod 12343 with 11239 at 2
+Id : 13398, {_}: multiply (inverse ?88666) (inverse (inverse ?88665)) =?= multiply (inverse (inverse (inverse ?88666))) ?88665 [88665, 88666] by Demod 12705 with 12807 at 2
+Id : 13591, {_}: multiply (inverse ?93455) (inverse (inverse (multiply (inverse (inverse (inverse (inverse ?93455)))) ?93456))) =>= ?93456 [93456, 93455] by Super 13130 with 13398 at 2
+Id : 13688, {_}: multiply (inverse ?93455) (inverse (multiply (inverse ?93456) (inverse (inverse (inverse ?93455))))) =>= ?93456 [93456, 93455] by Demod 13591 with 12807 at 1,2,2
+Id : 13689, {_}: multiply (inverse ?93455) (multiply (inverse (inverse (inverse (inverse ?93455)))) ?93456) =>= ?93456 [93456, 93455] by Demod 13688 with 12807 at 2,2
+Id : 13690, {_}: multiply (inverse ?93455) (multiply ?93455 ?93456) =>= ?93456 [93456, 93455] by Demod 13689 with 11239 at 1,2,2
+Id : 13691, {_}: inverse (inverse ?93456) =>= ?93456 [93456] by Demod 13690 with 11440 at 2
+Id : 14259, {_}: inverse (multiply ?94937 ?94938) =<= multiply (inverse ?94938) (inverse ?94937) [94938, 94937] by Super 12807 with 13691 at 1,1,2
+Id : 14272, {_}: inverse (multiply ?94994 (inverse ?94995)) =>= multiply ?94995 (inverse ?94994) [94995, 94994] by Super 14259 with 13691 at 1,3
+Id : 15113, {_}: multiply ?26 (multiply (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31) (inverse (multiply ?29 ?31))))) (inverse ?27)) =>= ?30 [31, 29, 30, 27, 28, 26] by Demod 13087 with 14272 at 2,2
+Id : 15114, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31)))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 15113 with 14272 at 2,1,2,2
+Id : 14099, {_}: inverse (multiply ?94283 ?94284) =<= multiply (inverse ?94284) (inverse ?94283) [94284, 94283] by Super 12807 with 13691 at 1,1,2
+Id : 15376, {_}: multiply ?101449 (inverse (multiply ?101450 ?101449)) =>= inverse ?101450 [101450, 101449] by Super 13130 with 14099 at 2,2
+Id : 14196, {_}: multiply ?94524 (inverse (multiply ?94525 ?94524)) =>= inverse ?94525 [94525, 94524] by Super 13130 with 14099 at 2,2
+Id : 15386, {_}: multiply (inverse (multiply ?101486 ?101487)) (inverse (inverse ?101486)) =>= inverse ?101487 [101487, 101486] by Super 15376 with 14196 at 1,2,2
+Id : 15574, {_}: inverse (multiply (inverse ?101486) (multiply ?101486 ?101487)) =>= inverse ?101487 [101487, 101486] by Demod 15386 with 14099 at 2
+Id : 16040, {_}: multiply (inverse (multiply ?103094 ?103095)) ?103094 =>= inverse ?103095 [103095, 103094] by Demod 15574 with 12807 at 2
+Id : 12061, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?216) ?217)) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 217, 216] by Demod 28 with 11440 at 2
+Id : 13066, {_}: inverse (inverse (inverse (multiply (multiply (multiply (inverse ?217) ?216) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 216, 217] by Demod 12061 with 12807 at 1,1,1,1,1,2
+Id : 14035, {_}: inverse (multiply (multiply (multiply (inverse ?217) ?216) ?218) (inverse (multiply ?216 ?218))) =>= ?217 [218, 216, 217] by Demod 13066 with 13691 at 2
+Id : 15129, {_}: multiply (multiply ?216 ?218) (inverse (multiply (multiply (inverse ?217) ?216) ?218)) =>= ?217 [217, 218, 216] by Demod 14035 with 14272 at 2
+Id : 16059, {_}: multiply (inverse ?103200) (multiply ?103201 ?103202) =<= inverse (inverse (multiply (multiply (inverse ?103200) ?103201) ?103202)) [103202, 103201, 103200] by Super 16040 with 15129 at 1,1,2
+Id : 16156, {_}: multiply (inverse ?103200) (multiply ?103201 ?103202) =<= multiply (multiply (inverse ?103200) ?103201) ?103202 [103202, 103201, 103200] by Demod 16059 with 13691 at 3
+Id : 17066, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?30) ?26) ?28) ?29)) ?31)))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 15114 with 16156 at 1,1,2,2,1,2,2
+Id : 17067, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (multiply (inverse ?30) ?26) ?28) ?29) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17066 with 16156 at 1,2,2,1,2,2
+Id : 17068, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?30) (multiply ?26 ?28)) ?29) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17067 with 16156 at 1,1,2,1,2,2,1,2,2
+Id : 17069, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (inverse ?30) (multiply (multiply ?26 ?28) ?29)) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17068 with 16156 at 1,2,1,2,2,1,2,2
+Id : 17070, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (inverse ?30) (multiply (multiply (multiply ?26 ?28) ?29) ?31)))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17069 with 16156 at 2,1,2,2,1,2,2
+Id : 17075, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (inverse (multiply (inverse ?30) (multiply (multiply (multiply ?26 ?28) ?29) ?31))) ?27))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17070 with 12807 at 2,2,1,2,2
+Id : 17076, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (multiply (inverse (multiply (multiply (multiply ?26 ?28) ?29) ?31)) ?30) ?27))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17075 with 12807 at 1,2,2,1,2,2
+Id : 17077, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (inverse (multiply (multiply (multiply ?26 ?28) ?29) ?31)) (multiply ?30 ?27)))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17076 with 16156 at 2,2,1,2,2
+Id : 14023, {_}: multiply (inverse ?33635) ?33635 =?= multiply (inverse (inverse (inverse ?33638))) ?33638 [33638, 33635] by Demod 4117 with 13691 at 1,2
+Id : 14024, {_}: multiply (inverse ?33635) ?33635 =?= multiply (inverse ?33638) ?33638 [33638, 33635] by Demod 14023 with 13691 at 1,3
+Id : 14053, {_}: multiply (inverse ?93965) ?93965 =?= multiply ?93966 (inverse ?93966) [93966, 93965] by Super 14024 with 13691 at 1,3
+Id : 19206, {_}: multiply ?108859 (multiply (multiply ?108860 (multiply (multiply ?108861 ?108862) (multiply ?108863 (inverse ?108863)))) (inverse ?108862)) =>= multiply (multiply ?108859 ?108860) ?108861 [108863, 108862, 108861, 108860, 108859] by Super 17077 with 14053 at 2,2,1,2,2
+Id : 14021, {_}: multiply ?70596 (multiply ?70598 (inverse ?70598)) =>= inverse (inverse ?70596) [70598, 70596] by Demod 9021 with 13691 at 2,2
+Id : 14022, {_}: multiply ?70596 (multiply ?70598 (inverse ?70598)) =>= ?70596 [70598, 70596] by Demod 14021 with 13691 at 3
+Id : 19669, {_}: multiply ?108859 (multiply (multiply ?108860 (multiply ?108861 ?108862)) (inverse ?108862)) =>= multiply (multiply ?108859 ?108860) ?108861 [108862, 108861, 108860, 108859] by Demod 19206 with 14022 at 2,1,2,2
+Id : 14028, {_}: inverse (multiply (multiply (inverse (inverse (inverse ?2585))) ?2586) (inverse (multiply ?2587 ?2586))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 12069 with 13691 at 2
+Id : 14029, {_}: inverse (multiply (multiply (inverse ?2585) ?2586) (inverse (multiply ?2587 ?2586))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 14028 with 13691 at 1,1,1,2
+Id : 15108, {_}: multiply (multiply ?2587 ?2586) (inverse (multiply (inverse ?2585) ?2586)) =>= multiply ?2587 ?2585 [2585, 2586, 2587] by Demod 14029 with 14272 at 2
+Id : 15134, {_}: multiply (multiply ?2587 ?2586) (multiply (inverse ?2586) ?2585) =>= multiply ?2587 ?2585 [2585, 2586, 2587] by Demod 15108 with 12807 at 2,2
+Id : 15575, {_}: multiply (inverse (multiply ?101486 ?101487)) ?101486 =>= inverse ?101487 [101487, 101486] by Demod 15574 with 12807 at 2
+Id : 16032, {_}: multiply (multiply ?103052 (multiply ?103053 ?103054)) (inverse ?103054) =>= multiply ?103052 ?103053 [103054, 103053, 103052] by Super 15134 with 15575 at 2,2
+Id : 32860, {_}: multiply ?108859 (multiply ?108860 ?108861) =?= multiply (multiply ?108859 ?108860) ?108861 [108861, 108860, 108859] by Demod 19669 with 16032 at 2,2
+Id : 33337, {_}: multiply a (multiply b c) === multiply a (multiply b c) [] by Demod 1 with 32860 at 3
+Id : 1, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
+% SZS output end CNFRefutation for GRP014-1.p
+10025: solved GRP014-1.p in 10.216638 using nrkbo
+10025: status Unsatisfiable for GRP014-1.p
+CLASH, statistics insufficient
+10036: Facts:
+10036: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10036: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+10036: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+10036: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+10036: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+10036: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+10036: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+10036: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+10036: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+10036: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+10036: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+10036: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+10036: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+10036: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+10036: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+10036: Id : 17, {_}:
+ positive_part ?50 =<= least_upper_bound ?50 identity
+ [50] by lat4_1 ?50
+10036: Id : 18, {_}:
+ negative_part ?52 =<= greatest_lower_bound ?52 identity
+ [52] by lat4_2 ?52
+10036: Id : 19, {_}:
+ least_upper_bound ?54 (greatest_lower_bound ?55 ?56)
+ =<=
+ greatest_lower_bound (least_upper_bound ?54 ?55)
+ (least_upper_bound ?54 ?56)
+ [56, 55, 54] by lat4_3 ?54 ?55 ?56
+10036: Id : 20, {_}:
+ greatest_lower_bound ?58 (least_upper_bound ?59 ?60)
+ =<=
+ least_upper_bound (greatest_lower_bound ?58 ?59)
+ (greatest_lower_bound ?58 ?60)
+ [60, 59, 58] by lat4_4 ?58 ?59 ?60
+10036: Goal:
+10036: Id : 1, {_}:
+ a =<= multiply (positive_part a) (negative_part a)
+ [] by prove_lat4
+10036: Order:
+10036: nrkbo
+10036: Leaf order:
+10036: least_upper_bound 19 2 0
+10036: greatest_lower_bound 19 2 0
+10036: inverse 1 1 0
+10036: identity 4 0 0
+10036: multiply 19 2 1 0,3
+10036: negative_part 2 1 1 0,2,3
+10036: positive_part 2 1 1 0,1,3
+10036: a 3 0 3 2
+CLASH, statistics insufficient
+10037: Facts:
+10037: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10037: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+10037: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+10037: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+10037: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+10037: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+10037: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+10037: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+10037: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+10037: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+10037: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+10037: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+10037: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+10037: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+10037: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+10037: Id : 17, {_}:
+ positive_part ?50 =<= least_upper_bound ?50 identity
+ [50] by lat4_1 ?50
+10037: Id : 18, {_}:
+ negative_part ?52 =<= greatest_lower_bound ?52 identity
+ [52] by lat4_2 ?52
+10037: Id : 19, {_}:
+ least_upper_bound ?54 (greatest_lower_bound ?55 ?56)
+ =<=
+ greatest_lower_bound (least_upper_bound ?54 ?55)
+ (least_upper_bound ?54 ?56)
+ [56, 55, 54] by lat4_3 ?54 ?55 ?56
+10037: Id : 20, {_}:
+ greatest_lower_bound ?58 (least_upper_bound ?59 ?60)
+ =<=
+ least_upper_bound (greatest_lower_bound ?58 ?59)
+ (greatest_lower_bound ?58 ?60)
+ [60, 59, 58] by lat4_4 ?58 ?59 ?60
+10037: Goal:
+10037: Id : 1, {_}:
+ a =<= multiply (positive_part a) (negative_part a)
+ [] by prove_lat4
+10037: Order:
+10037: kbo
+10037: Leaf order:
+10037: least_upper_bound 19 2 0
+10037: greatest_lower_bound 19 2 0
+10037: inverse 1 1 0
+10037: identity 4 0 0
+10037: multiply 19 2 1 0,3
+10037: negative_part 2 1 1 0,2,3
+10037: positive_part 2 1 1 0,1,3
+10037: a 3 0 3 2
+CLASH, statistics insufficient
+10038: Facts:
+10038: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10038: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+10038: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+10038: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+10038: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+10038: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+10038: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+10038: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+10038: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+10038: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+10038: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+10038: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+10038: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+10038: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+10038: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+10038: Id : 17, {_}:
+ positive_part ?50 =>= least_upper_bound ?50 identity
+ [50] by lat4_1 ?50
+10038: Id : 18, {_}:
+ negative_part ?52 =>= greatest_lower_bound ?52 identity
+ [52] by lat4_2 ?52
+10038: Id : 19, {_}:
+ least_upper_bound ?54 (greatest_lower_bound ?55 ?56)
+ =<=
+ greatest_lower_bound (least_upper_bound ?54 ?55)
+ (least_upper_bound ?54 ?56)
+ [56, 55, 54] by lat4_3 ?54 ?55 ?56
+10038: Id : 20, {_}:
+ greatest_lower_bound ?58 (least_upper_bound ?59 ?60)
+ =>=
+ least_upper_bound (greatest_lower_bound ?58 ?59)
+ (greatest_lower_bound ?58 ?60)
+ [60, 59, 58] by lat4_4 ?58 ?59 ?60
+10038: Goal:
+10038: Id : 1, {_}:
+ a =<= multiply (positive_part a) (negative_part a)
+ [] by prove_lat4
+10038: Order:
+10038: lpo
+10038: Leaf order:
+10038: least_upper_bound 19 2 0
+10038: greatest_lower_bound 19 2 0
+10038: inverse 1 1 0
+10038: identity 4 0 0
+10038: multiply 19 2 1 0,3
+10038: negative_part 2 1 1 0,2,3
+10038: positive_part 2 1 1 0,1,3
+10038: a 3 0 3 2
+Statistics :
+Max weight : 19
+Found proof, 19.804581s
+% SZS status Unsatisfiable for GRP167-1.p
+% SZS output start CNFRefutation for GRP167-1.p
+Id : 11, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
+Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+Id : 134, {_}: multiply ?322 (least_upper_bound ?323 ?324) =<= least_upper_bound (multiply ?322 ?323) (multiply ?322 ?324) [324, 323, 322] by monotony_lub1 ?322 ?323 ?324
+Id : 12, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
+Id : 7, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =<= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+Id : 16, {_}: multiply (greatest_lower_bound ?46 ?47) ?48 =<= greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+Id : 20, {_}: greatest_lower_bound ?58 (least_upper_bound ?59 ?60) =<= least_upper_bound (greatest_lower_bound ?58 ?59) (greatest_lower_bound ?58 ?60) [60, 59, 58] by lat4_4 ?58 ?59 ?60
+Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
+Id : 17, {_}: positive_part ?50 =<= least_upper_bound ?50 identity [50] by lat4_1 ?50
+Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =<= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+Id : 18, {_}: negative_part ?52 =<= greatest_lower_bound ?52 identity [52] by lat4_2 ?52
+Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
+Id : 237, {_}: multiply (greatest_lower_bound ?514 ?515) ?516 =<= greatest_lower_bound (multiply ?514 ?516) (multiply ?515 ?516) [516, 515, 514] by monotony_glb2 ?514 ?515 ?516
+Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+Id : 25, {_}: multiply (multiply ?69 ?70) ?71 =>= multiply ?69 (multiply ?70 ?71) [71, 70, 69] by associativity ?69 ?70 ?71
+Id : 27, {_}: multiply identity ?76 =<= multiply (inverse ?77) (multiply ?77 ?76) [77, 76] by Super 25 with 3 at 1,2
+Id : 31, {_}: ?76 =<= multiply (inverse ?77) (multiply ?77 ?76) [77, 76] by Demod 27 with 2 at 2
+Id : 242, {_}: multiply (greatest_lower_bound (inverse ?532) ?533) ?532 =>= greatest_lower_bound identity (multiply ?533 ?532) [533, 532] by Super 237 with 3 at 1,3
+Id : 278, {_}: greatest_lower_bound identity ?584 =>= negative_part ?584 [584] by Super 5 with 18 at 3
+Id : 15662, {_}: multiply (greatest_lower_bound (inverse ?19569) ?19570) ?19569 =>= negative_part (multiply ?19570 ?19569) [19570, 19569] by Demod 242 with 278 at 3
+Id : 15688, {_}: multiply (negative_part (inverse ?19646)) ?19646 =>= negative_part (multiply identity ?19646) [19646] by Super 15662 with 18 at 1,2
+Id : 15740, {_}: multiply (negative_part (inverse ?19646)) ?19646 =>= negative_part ?19646 [19646] by Demod 15688 with 2 at 1,3
+Id : 15765, {_}: ?19710 =<= multiply (inverse (negative_part (inverse ?19710))) (negative_part ?19710) [19710] by Super 31 with 15740 at 2,3
+Id : 778, {_}: ?1461 =<= multiply (inverse ?1462) (multiply ?1462 ?1461) [1462, 1461] by Demod 27 with 2 at 2
+Id : 782, {_}: ?1472 =<= multiply (inverse (inverse ?1472)) identity [1472] by Super 778 with 3 at 2,3
+Id : 1371, {_}: multiply (inverse (inverse ?2316)) (least_upper_bound ?2317 identity) =?= least_upper_bound (multiply (inverse (inverse ?2316)) ?2317) ?2316 [2317, 2316] by Super 13 with 782 at 2,3
+Id : 1392, {_}: multiply (inverse (inverse ?2316)) (positive_part ?2317) =<= least_upper_bound (multiply (inverse (inverse ?2316)) ?2317) ?2316 [2317, 2316] by Demod 1371 with 17 at 2,2
+Id : 1393, {_}: multiply (inverse (inverse ?2316)) (positive_part ?2317) =<= least_upper_bound ?2316 (multiply (inverse (inverse ?2316)) ?2317) [2317, 2316] by Demod 1392 with 6 at 3
+Id : 786, {_}: multiply ?1484 ?1485 =<= multiply (inverse (inverse ?1484)) ?1485 [1485, 1484] by Super 778 with 31 at 2,3
+Id : 2137, {_}: ?1472 =<= multiply ?1472 identity [1472] by Demod 782 with 786 at 3
+Id : 2138, {_}: inverse (inverse ?3405) =<= multiply ?3405 identity [3405] by Super 2137 with 786 at 3
+Id : 2189, {_}: inverse (inverse ?3405) =>= ?3405 [3405] by Demod 2138 with 2137 at 3
+Id : 49575, {_}: multiply ?2316 (positive_part ?2317) =<= least_upper_bound ?2316 (multiply (inverse (inverse ?2316)) ?2317) [2317, 2316] by Demod 1393 with 2189 at 1,2
+Id : 49621, {_}: multiply ?54979 (positive_part ?54980) =<= least_upper_bound ?54979 (multiply ?54979 ?54980) [54980, 54979] by Demod 49575 with 2189 at 1,2,3
+Id : 15768, {_}: multiply (negative_part (inverse ?19715)) ?19715 =>= negative_part ?19715 [19715] by Demod 15688 with 2 at 1,3
+Id : 15773, {_}: multiply (negative_part ?19724) (inverse ?19724) =>= negative_part (inverse ?19724) [19724] by Super 15768 with 2189 at 1,1,2
+Id : 49652, {_}: multiply (negative_part ?55064) (positive_part (inverse ?55064)) =>= least_upper_bound (negative_part ?55064) (negative_part (inverse ?55064)) [55064] by Super 49621 with 15773 at 2,3
+Id : 865, {_}: greatest_lower_bound identity (least_upper_bound ?1569 ?1570) =<= least_upper_bound (greatest_lower_bound identity ?1569) (negative_part ?1570) [1570, 1569] by Super 20 with 278 at 2,3
+Id : 880, {_}: negative_part (least_upper_bound ?1569 ?1570) =<= least_upper_bound (greatest_lower_bound identity ?1569) (negative_part ?1570) [1570, 1569] by Demod 865 with 278 at 2
+Id : 881, {_}: negative_part (least_upper_bound ?1569 ?1570) =<= least_upper_bound (negative_part ?1569) (negative_part ?1570) [1570, 1569] by Demod 880 with 278 at 1,3
+Id : 49776, {_}: multiply (negative_part ?55064) (positive_part (inverse ?55064)) =>= negative_part (least_upper_bound ?55064 (inverse ?55064)) [55064] by Demod 49652 with 881 at 3
+Id : 15757, {_}: multiply (greatest_lower_bound (negative_part (inverse ?19686)) ?19687) ?19686 =>= greatest_lower_bound (negative_part ?19686) (multiply ?19687 ?19686) [19687, 19686] by Super 16 with 15740 at 1,3
+Id : 859, {_}: greatest_lower_bound identity (greatest_lower_bound ?1558 ?1559) =>= greatest_lower_bound (negative_part ?1558) ?1559 [1559, 1558] by Super 7 with 278 at 1,3
+Id : 890, {_}: negative_part (greatest_lower_bound ?1558 ?1559) =>= greatest_lower_bound (negative_part ?1558) ?1559 [1559, 1558] by Demod 859 with 278 at 2
+Id : 281, {_}: greatest_lower_bound ?591 (greatest_lower_bound ?592 identity) =>= negative_part (greatest_lower_bound ?591 ?592) [592, 591] by Super 7 with 18 at 3
+Id : 289, {_}: greatest_lower_bound ?591 (negative_part ?592) =<= negative_part (greatest_lower_bound ?591 ?592) [592, 591] by Demod 281 with 18 at 2,2
+Id : 1628, {_}: greatest_lower_bound ?1558 (negative_part ?1559) =<= greatest_lower_bound (negative_part ?1558) ?1559 [1559, 1558] by Demod 890 with 289 at 2
+Id : 15802, {_}: multiply (greatest_lower_bound (inverse ?19686) (negative_part ?19687)) ?19686 =>= greatest_lower_bound (negative_part ?19686) (multiply ?19687 ?19686) [19687, 19686] by Demod 15757 with 1628 at 1,2
+Id : 15803, {_}: multiply (greatest_lower_bound (inverse ?19686) (negative_part ?19687)) ?19686 =>= greatest_lower_bound ?19686 (negative_part (multiply ?19687 ?19686)) [19687, 19686] by Demod 15802 with 1628 at 3
+Id : 15650, {_}: multiply (greatest_lower_bound (inverse ?532) ?533) ?532 =>= negative_part (multiply ?533 ?532) [533, 532] by Demod 242 with 278 at 3
+Id : 15804, {_}: negative_part (multiply (negative_part ?19687) ?19686) =<= greatest_lower_bound ?19686 (negative_part (multiply ?19687 ?19686)) [19686, 19687] by Demod 15803 with 15650 at 2
+Id : 49651, {_}: multiply (negative_part (inverse ?55062)) (positive_part ?55062) =>= least_upper_bound (negative_part (inverse ?55062)) (negative_part ?55062) [55062] by Super 49621 with 15740 at 2,3
+Id : 49774, {_}: multiply (negative_part (inverse ?55062)) (positive_part ?55062) =>= least_upper_bound (negative_part ?55062) (negative_part (inverse ?55062)) [55062] by Demod 49651 with 6 at 3
+Id : 49775, {_}: multiply (negative_part (inverse ?55062)) (positive_part ?55062) =>= negative_part (least_upper_bound ?55062 (inverse ?55062)) [55062] by Demod 49774 with 881 at 3
+Id : 49840, {_}: negative_part (multiply (negative_part (negative_part (inverse ?55170))) (positive_part ?55170)) =<= greatest_lower_bound (positive_part ?55170) (negative_part (negative_part (least_upper_bound ?55170 (inverse ?55170)))) [55170] by Super 15804 with 49775 at 1,2,3
+Id : 268, {_}: greatest_lower_bound ?569 (positive_part ?569) =>= ?569 [569] by Super 12 with 17 at 2,2
+Id : 139, {_}: multiply (inverse ?340) (least_upper_bound ?340 ?341) =>= least_upper_bound identity (multiply (inverse ?340) ?341) [341, 340] by Super 134 with 3 at 1,3
+Id : 264, {_}: least_upper_bound identity ?559 =>= positive_part ?559 [559] by Super 6 with 17 at 3
+Id : 4901, {_}: multiply (inverse ?7380) (least_upper_bound ?7380 ?7381) =>= positive_part (multiply (inverse ?7380) ?7381) [7381, 7380] by Demod 139 with 264 at 3
+Id : 4921, {_}: multiply (inverse ?7441) (positive_part ?7441) =?= positive_part (multiply (inverse ?7441) identity) [7441] by Super 4901 with 17 at 2,2
+Id : 4985, {_}: multiply (inverse ?7525) (positive_part ?7525) =>= positive_part (inverse ?7525) [7525] by Demod 4921 with 2137 at 1,3
+Id : 267, {_}: least_upper_bound ?566 (least_upper_bound ?567 identity) =>= positive_part (least_upper_bound ?566 ?567) [567, 566] by Super 8 with 17 at 3
+Id : 1187, {_}: least_upper_bound ?2080 (positive_part ?2081) =<= positive_part (least_upper_bound ?2080 ?2081) [2081, 2080] by Demod 267 with 17 at 2,2
+Id : 1199, {_}: least_upper_bound ?2117 (positive_part identity) =>= positive_part (positive_part ?2117) [2117] by Super 1187 with 17 at 1,3
+Id : 263, {_}: positive_part identity =>= identity [] by Super 9 with 17 at 2
+Id : 1218, {_}: least_upper_bound ?2117 identity =<= positive_part (positive_part ?2117) [2117] by Demod 1199 with 263 at 2,2
+Id : 1219, {_}: positive_part ?2117 =<= positive_part (positive_part ?2117) [2117] by Demod 1218 with 17 at 2
+Id : 4997, {_}: multiply (inverse (positive_part ?7553)) (positive_part ?7553) =>= positive_part (inverse (positive_part ?7553)) [7553] by Super 4985 with 1219 at 2,2
+Id : 5031, {_}: identity =<= positive_part (inverse (positive_part ?7553)) [7553] by Demod 4997 with 3 at 2
+Id : 5129, {_}: greatest_lower_bound (inverse (positive_part ?7677)) identity =>= inverse (positive_part ?7677) [7677] by Super 268 with 5031 at 2,2
+Id : 5176, {_}: greatest_lower_bound identity (inverse (positive_part ?7677)) =>= inverse (positive_part ?7677) [7677] by Demod 5129 with 5 at 2
+Id : 5177, {_}: negative_part (inverse (positive_part ?7677)) =>= inverse (positive_part ?7677) [7677] by Demod 5176 with 278 at 2
+Id : 5325, {_}: greatest_lower_bound (inverse (positive_part ?7851)) (negative_part ?7852) =>= greatest_lower_bound (inverse (positive_part ?7851)) ?7852 [7852, 7851] by Super 1628 with 5177 at 1,3
+Id : 15685, {_}: multiply (greatest_lower_bound (inverse (positive_part ?19637)) ?19638) (positive_part ?19637) =>= negative_part (multiply (negative_part ?19638) (positive_part ?19637)) [19638, 19637] by Super 15662 with 5325 at 1,2
+Id : 15737, {_}: negative_part (multiply ?19638 (positive_part ?19637)) =<= negative_part (multiply (negative_part ?19638) (positive_part ?19637)) [19637, 19638] by Demod 15685 with 15650 at 2
+Id : 49928, {_}: negative_part (multiply (negative_part (inverse ?55170)) (positive_part ?55170)) =<= greatest_lower_bound (positive_part ?55170) (negative_part (negative_part (least_upper_bound ?55170 (inverse ?55170)))) [55170] by Demod 49840 with 15737 at 2
+Id : 1648, {_}: greatest_lower_bound ?2900 (negative_part ?2901) =<= greatest_lower_bound (negative_part ?2900) ?2901 [2901, 2900] by Demod 890 with 289 at 2
+Id : 863, {_}: negative_part (least_upper_bound identity ?1566) =>= identity [1566] by Super 12 with 278 at 2
+Id : 886, {_}: negative_part (positive_part ?1566) =>= identity [1566] by Demod 863 with 264 at 1,2
+Id : 1653, {_}: greatest_lower_bound (positive_part ?2914) (negative_part ?2915) =>= greatest_lower_bound identity ?2915 [2915, 2914] by Super 1648 with 886 at 1,3
+Id : 1710, {_}: greatest_lower_bound (positive_part ?2914) (negative_part ?2915) =>= negative_part ?2915 [2915, 2914] by Demod 1653 with 278 at 3
+Id : 49929, {_}: negative_part (multiply (negative_part (inverse ?55170)) (positive_part ?55170)) =>= negative_part (negative_part (least_upper_bound ?55170 (inverse ?55170))) [55170] by Demod 49928 with 1710 at 3
+Id : 49930, {_}: negative_part (multiply (inverse ?55170) (positive_part ?55170)) =<= negative_part (negative_part (least_upper_bound ?55170 (inverse ?55170))) [55170] by Demod 49929 with 15737 at 2
+Id : 1014, {_}: greatest_lower_bound ?1717 (positive_part ?1717) =>= ?1717 [1717] by Super 12 with 17 at 2,2
+Id : 858, {_}: least_upper_bound identity (negative_part ?1556) =>= identity [1556] by Super 11 with 278 at 2,2
+Id : 891, {_}: positive_part (negative_part ?1556) =>= identity [1556] by Demod 858 with 264 at 2
+Id : 1019, {_}: greatest_lower_bound (negative_part ?1726) identity =>= negative_part ?1726 [1726] by Super 1014 with 891 at 2,2
+Id : 1039, {_}: greatest_lower_bound identity (negative_part ?1726) =>= negative_part ?1726 [1726] by Demod 1019 with 5 at 2
+Id : 1040, {_}: negative_part (negative_part ?1726) =>= negative_part ?1726 [1726] by Demod 1039 with 278 at 2
+Id : 49931, {_}: negative_part (multiply (inverse ?55170) (positive_part ?55170)) =>= negative_part (least_upper_bound ?55170 (inverse ?55170)) [55170] by Demod 49930 with 1040 at 3
+Id : 4960, {_}: multiply (inverse ?7441) (positive_part ?7441) =>= positive_part (inverse ?7441) [7441] by Demod 4921 with 2137 at 1,3
+Id : 49932, {_}: negative_part (positive_part (inverse ?55170)) =<= negative_part (least_upper_bound ?55170 (inverse ?55170)) [55170] by Demod 49931 with 4960 at 1,2
+Id : 49933, {_}: identity =<= negative_part (least_upper_bound ?55170 (inverse ?55170)) [55170] by Demod 49932 with 886 at 2
+Id : 53516, {_}: multiply (negative_part ?55064) (positive_part (inverse ?55064)) =>= identity [55064] by Demod 49776 with 49933 at 3
+Id : 53529, {_}: positive_part (inverse ?58317) =<= multiply (inverse (negative_part ?58317)) identity [58317] by Super 31 with 53516 at 2,3
+Id : 53947, {_}: positive_part (inverse ?58761) =>= inverse (negative_part ?58761) [58761] by Demod 53529 with 2137 at 3
+Id : 53952, {_}: positive_part ?58770 =<= inverse (negative_part (inverse ?58770)) [58770] by Super 53947 with 2189 at 1,2
+Id : 54151, {_}: ?19710 =<= multiply (positive_part ?19710) (negative_part ?19710) [19710] by Demod 15765 with 53952 at 1,3
+Id : 54473, {_}: a =?= a [] by Demod 1 with 54151 at 3
+Id : 1, {_}: a =<= multiply (positive_part a) (negative_part a) [] by prove_lat4
+% SZS output end CNFRefutation for GRP167-1.p
+10037: solved GRP167-1.p in 9.872616 using kbo
+10037: status Unsatisfiable for GRP167-1.p
+CLASH, statistics insufficient
+10051: Facts:
+10051: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10051: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+10051: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+10051: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+10051: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+10051: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+10051: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+10051: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+10051: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+10051: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+10051: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+10051: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+10051: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+10051: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+10051: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+10051: Id : 17, {_}: inverse identity =>= identity [] by lat4_1
+10051: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51
+10051: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by lat4_3 ?53 ?54
+10051: Id : 20, {_}:
+ positive_part ?56 =<= least_upper_bound ?56 identity
+ [56] by lat4_4 ?56
+10051: Id : 21, {_}:
+ negative_part ?58 =<= greatest_lower_bound ?58 identity
+ [58] by lat4_5 ?58
+10051: Id : 22, {_}:
+ least_upper_bound ?60 (greatest_lower_bound ?61 ?62)
+ =<=
+ greatest_lower_bound (least_upper_bound ?60 ?61)
+ (least_upper_bound ?60 ?62)
+ [62, 61, 60] by lat4_6 ?60 ?61 ?62
+10051: Id : 23, {_}:
+ greatest_lower_bound ?64 (least_upper_bound ?65 ?66)
+ =<=
+ least_upper_bound (greatest_lower_bound ?64 ?65)
+ (greatest_lower_bound ?64 ?66)
+ [66, 65, 64] by lat4_7 ?64 ?65 ?66
+10051: Goal:
+10051: Id : 1, {_}:
+ a =<= multiply (positive_part a) (negative_part a)
+ [] by prove_lat4
+10051: Order:
+10051: nrkbo
+10051: Leaf order:
+10051: least_upper_bound 19 2 0
+10051: greatest_lower_bound 19 2 0
+10051: inverse 7 1 0
+10051: identity 6 0 0
+10051: multiply 21 2 1 0,3
+10051: negative_part 2 1 1 0,2,3
+10051: positive_part 2 1 1 0,1,3
+10051: a 3 0 3 2
+CLASH, statistics insufficient
+10052: Facts:
+10052: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10052: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+10052: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+10052: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+10052: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+10052: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+10052: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+10052: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+10052: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+10052: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+10052: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+10052: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+10052: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+10052: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+10052: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+10052: Id : 17, {_}: inverse identity =>= identity [] by lat4_1
+10052: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51
+10052: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by lat4_3 ?53 ?54
+10052: Id : 20, {_}:
+ positive_part ?56 =<= least_upper_bound ?56 identity
+ [56] by lat4_4 ?56
+10052: Id : 21, {_}:
+ negative_part ?58 =<= greatest_lower_bound ?58 identity
+ [58] by lat4_5 ?58
+10052: Id : 22, {_}:
+ least_upper_bound ?60 (greatest_lower_bound ?61 ?62)
+ =<=
+ greatest_lower_bound (least_upper_bound ?60 ?61)
+ (least_upper_bound ?60 ?62)
+ [62, 61, 60] by lat4_6 ?60 ?61 ?62
+10052: Id : 23, {_}:
+ greatest_lower_bound ?64 (least_upper_bound ?65 ?66)
+ =<=
+ least_upper_bound (greatest_lower_bound ?64 ?65)
+ (greatest_lower_bound ?64 ?66)
+ [66, 65, 64] by lat4_7 ?64 ?65 ?66
+10052: Goal:
+10052: Id : 1, {_}:
+ a =<= multiply (positive_part a) (negative_part a)
+ [] by prove_lat4
+10052: Order:
+10052: kbo
+10052: Leaf order:
+10052: least_upper_bound 19 2 0
+10052: greatest_lower_bound 19 2 0
+10052: inverse 7 1 0
+10052: identity 6 0 0
+10052: multiply 21 2 1 0,3
+10052: negative_part 2 1 1 0,2,3
+10052: positive_part 2 1 1 0,1,3
+10052: a 3 0 3 2
+CLASH, statistics insufficient
+10053: Facts:
+10053: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10053: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+10053: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+10053: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+10053: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+10053: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+10053: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+10053: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+10053: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+10053: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+10053: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+10053: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+10053: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+10053: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+10053: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+10053: Id : 17, {_}: inverse identity =>= identity [] by lat4_1
+10053: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51
+10053: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by lat4_3 ?53 ?54
+10053: Id : 20, {_}:
+ positive_part ?56 =>= least_upper_bound ?56 identity
+ [56] by lat4_4 ?56
+10053: Id : 21, {_}:
+ negative_part ?58 =>= greatest_lower_bound ?58 identity
+ [58] by lat4_5 ?58
+10053: Id : 22, {_}:
+ least_upper_bound ?60 (greatest_lower_bound ?61 ?62)
+ =<=
+ greatest_lower_bound (least_upper_bound ?60 ?61)
+ (least_upper_bound ?60 ?62)
+ [62, 61, 60] by lat4_6 ?60 ?61 ?62
+10053: Id : 23, {_}:
+ greatest_lower_bound ?64 (least_upper_bound ?65 ?66)
+ =>=
+ least_upper_bound (greatest_lower_bound ?64 ?65)
+ (greatest_lower_bound ?64 ?66)
+ [66, 65, 64] by lat4_7 ?64 ?65 ?66
+10053: Goal:
+10053: Id : 1, {_}:
+ a =<= multiply (positive_part a) (negative_part a)
+ [] by prove_lat4
+10053: Order:
+10053: lpo
+10053: Leaf order:
+10053: least_upper_bound 19 2 0
+10053: greatest_lower_bound 19 2 0
+10053: inverse 7 1 0
+10053: identity 6 0 0
+10053: multiply 21 2 1 0,3
+10053: negative_part 2 1 1 0,2,3
+10053: positive_part 2 1 1 0,1,3
+10053: a 3 0 3 2
+Statistics :
+Max weight : 15
+Found proof, 6.844655s
+% SZS status Unsatisfiable for GRP167-2.p
+% SZS output start CNFRefutation for GRP167-2.p
+Id : 19, {_}: inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) [54, 53] by lat4_3 ?53 ?54
+Id : 7, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =<= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+Id : 12, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
+Id : 11, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
+Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+Id : 22, {_}: least_upper_bound ?60 (greatest_lower_bound ?61 ?62) =<= greatest_lower_bound (least_upper_bound ?60 ?61) (least_upper_bound ?60 ?62) [62, 61, 60] by lat4_6 ?60 ?61 ?62
+Id : 210, {_}: multiply (least_upper_bound ?453 ?454) ?455 =<= least_upper_bound (multiply ?453 ?455) (multiply ?454 ?455) [455, 454, 453] by monotony_lub2 ?453 ?454 ?455
+Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
+Id : 21, {_}: negative_part ?58 =<= greatest_lower_bound ?58 identity [58] by lat4_5 ?58
+Id : 14, {_}: multiply ?38 (greatest_lower_bound ?39 ?40) =<= greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
+Id : 20, {_}: positive_part ?56 =<= least_upper_bound ?56 identity [56] by lat4_4 ?56
+Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =<= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+Id : 286, {_}: inverse (multiply ?614 ?615) =<= multiply (inverse ?615) (inverse ?614) [615, 614] by lat4_3 ?614 ?615
+Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+Id : 28, {_}: multiply (multiply ?75 ?76) ?77 =>= multiply ?75 (multiply ?76 ?77) [77, 76, 75] by associativity ?75 ?76 ?77
+Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51
+Id : 30, {_}: multiply identity ?82 =<= multiply (inverse ?83) (multiply ?83 ?82) [83, 82] by Super 28 with 3 at 1,2
+Id : 34, {_}: ?82 =<= multiply (inverse ?83) (multiply ?83 ?82) [83, 82] by Demod 30 with 2 at 2
+Id : 288, {_}: inverse (multiply (inverse ?619) ?620) =>= multiply (inverse ?620) ?619 [620, 619] by Super 286 with 18 at 2,3
+Id : 997, {_}: ?1719 =<= multiply (inverse ?1720) (multiply ?1720 ?1719) [1720, 1719] by Demod 30 with 2 at 2
+Id : 1001, {_}: ?1730 =<= multiply (inverse (inverse ?1730)) identity [1730] by Super 997 with 3 at 2,3
+Id : 1026, {_}: ?1730 =<= multiply ?1730 identity [1730] by Demod 1001 with 18 at 1,3
+Id : 1045, {_}: multiply ?1785 (least_upper_bound ?1786 identity) =?= least_upper_bound (multiply ?1785 ?1786) ?1785 [1786, 1785] by Super 13 with 1026 at 2,3
+Id : 1078, {_}: multiply ?1785 (positive_part ?1786) =<= least_upper_bound (multiply ?1785 ?1786) ?1785 [1786, 1785] by Demod 1045 with 20 at 2,2
+Id : 5086, {_}: multiply ?7297 (positive_part ?7298) =<= least_upper_bound ?7297 (multiply ?7297 ?7298) [7298, 7297] by Demod 1078 with 6 at 3
+Id : 5090, {_}: multiply (inverse ?7308) (positive_part ?7308) =>= least_upper_bound (inverse ?7308) identity [7308] by Super 5086 with 3 at 2,3
+Id : 5133, {_}: multiply (inverse ?7308) (positive_part ?7308) =>= least_upper_bound identity (inverse ?7308) [7308] by Demod 5090 with 6 at 3
+Id : 298, {_}: least_upper_bound identity ?640 =>= positive_part ?640 [640] by Super 6 with 20 at 3
+Id : 5134, {_}: multiply (inverse ?7308) (positive_part ?7308) =>= positive_part (inverse ?7308) [7308] by Demod 5133 with 298 at 3
+Id : 5356, {_}: inverse (positive_part (inverse ?7872)) =<= multiply (inverse (positive_part ?7872)) ?7872 [7872] by Super 288 with 5134 at 1,2
+Id : 1051, {_}: multiply ?1799 (greatest_lower_bound ?1800 identity) =?= greatest_lower_bound (multiply ?1799 ?1800) ?1799 [1800, 1799] by Super 14 with 1026 at 2,3
+Id : 1072, {_}: multiply ?1799 (negative_part ?1800) =<= greatest_lower_bound (multiply ?1799 ?1800) ?1799 [1800, 1799] by Demod 1051 with 21 at 2,2
+Id : 4381, {_}: multiply ?6565 (negative_part ?6566) =<= greatest_lower_bound ?6565 (multiply ?6565 ?6566) [6566, 6565] by Demod 1072 with 5 at 3
+Id : 270, {_}: multiply ?567 (inverse ?567) =>= identity [567] by Super 3 with 18 at 1,2
+Id : 4388, {_}: multiply ?6585 (negative_part (inverse ?6585)) =>= greatest_lower_bound ?6585 identity [6585] by Super 4381 with 270 at 2,3
+Id : 4428, {_}: multiply ?6585 (negative_part (inverse ?6585)) =>= negative_part ?6585 [6585] by Demod 4388 with 21 at 3
+Id : 1073, {_}: multiply ?1799 (negative_part ?1800) =<= greatest_lower_bound ?1799 (multiply ?1799 ?1800) [1800, 1799] by Demod 1072 with 5 at 3
+Id : 215, {_}: multiply (least_upper_bound (inverse ?471) ?472) ?471 =>= least_upper_bound identity (multiply ?472 ?471) [472, 471] by Super 210 with 3 at 1,3
+Id : 11818, {_}: multiply (least_upper_bound (inverse ?15728) ?15729) ?15728 =>= positive_part (multiply ?15729 ?15728) [15729, 15728] by Demod 215 with 298 at 3
+Id : 11845, {_}: multiply (positive_part (inverse ?15810)) ?15810 =>= positive_part (multiply identity ?15810) [15810] by Super 11818 with 20 at 1,2
+Id : 12179, {_}: multiply (positive_part (inverse ?16312)) ?16312 =>= positive_part ?16312 [16312] by Demod 11845 with 2 at 1,3
+Id : 12183, {_}: multiply (positive_part ?16319) (inverse ?16319) =>= positive_part (inverse ?16319) [16319] by Super 12179 with 18 at 1,1,2
+Id : 12264, {_}: multiply (positive_part ?16391) (negative_part (inverse ?16391)) =>= greatest_lower_bound (positive_part ?16391) (positive_part (inverse ?16391)) [16391] by Super 1073 with 12183 at 2,3
+Id : 849, {_}: least_upper_bound identity (greatest_lower_bound ?1555 ?1556) =<= greatest_lower_bound (least_upper_bound identity ?1555) (positive_part ?1556) [1556, 1555] by Super 22 with 298 at 2,3
+Id : 877, {_}: positive_part (greatest_lower_bound ?1555 ?1556) =<= greatest_lower_bound (least_upper_bound identity ?1555) (positive_part ?1556) [1556, 1555] by Demod 849 with 298 at 2
+Id : 878, {_}: positive_part (greatest_lower_bound ?1555 ?1556) =<= greatest_lower_bound (positive_part ?1555) (positive_part ?1556) [1556, 1555] by Demod 877 with 298 at 1,3
+Id : 12306, {_}: multiply (positive_part ?16391) (negative_part (inverse ?16391)) =>= positive_part (greatest_lower_bound ?16391 (inverse ?16391)) [16391] by Demod 12264 with 878 at 3
+Id : 853, {_}: least_upper_bound identity (least_upper_bound ?1564 ?1565) =>= least_upper_bound (positive_part ?1564) ?1565 [1565, 1564] by Super 8 with 298 at 1,3
+Id : 874, {_}: positive_part (least_upper_bound ?1564 ?1565) =>= least_upper_bound (positive_part ?1564) ?1565 [1565, 1564] by Demod 853 with 298 at 2
+Id : 297, {_}: least_upper_bound ?637 (least_upper_bound ?638 identity) =>= positive_part (least_upper_bound ?637 ?638) [638, 637] by Super 8 with 20 at 3
+Id : 307, {_}: least_upper_bound ?637 (positive_part ?638) =<= positive_part (least_upper_bound ?637 ?638) [638, 637] by Demod 297 with 20 at 2,2
+Id : 1518, {_}: least_upper_bound ?1564 (positive_part ?1565) =<= least_upper_bound (positive_part ?1564) ?1565 [1565, 1564] by Demod 874 with 307 at 2
+Id : 309, {_}: least_upper_bound ?657 (negative_part ?657) =>= ?657 [657] by Super 11 with 21 at 2,2
+Id : 4385, {_}: multiply (inverse ?6576) (negative_part ?6576) =>= greatest_lower_bound (inverse ?6576) identity [6576] by Super 4381 with 3 at 2,3
+Id : 4422, {_}: multiply (inverse ?6576) (negative_part ?6576) =>= greatest_lower_bound identity (inverse ?6576) [6576] by Demod 4385 with 5 at 3
+Id : 312, {_}: greatest_lower_bound identity ?665 =>= negative_part ?665 [665] by Super 5 with 21 at 3
+Id : 4454, {_}: multiply (inverse ?6658) (negative_part ?6658) =>= negative_part (inverse ?6658) [6658] by Demod 4422 with 312 at 3
+Id : 1166, {_}: greatest_lower_bound ?1914 (positive_part ?1914) =>= ?1914 [1914] by Super 12 with 20 at 2,2
+Id : 898, {_}: least_upper_bound identity (negative_part ?1605) =>= identity [1605] by Super 11 with 312 at 2,2
+Id : 922, {_}: positive_part (negative_part ?1605) =>= identity [1605] by Demod 898 with 298 at 2
+Id : 1171, {_}: greatest_lower_bound (negative_part ?1923) identity =>= negative_part ?1923 [1923] by Super 1166 with 922 at 2,2
+Id : 1191, {_}: greatest_lower_bound identity (negative_part ?1923) =>= negative_part ?1923 [1923] by Demod 1171 with 5 at 2
+Id : 1192, {_}: negative_part (negative_part ?1923) =>= negative_part ?1923 [1923] by Demod 1191 with 312 at 2
+Id : 4460, {_}: multiply (inverse (negative_part ?6669)) (negative_part ?6669) =>= negative_part (inverse (negative_part ?6669)) [6669] by Super 4454 with 1192 at 2,2
+Id : 4502, {_}: identity =<= negative_part (inverse (negative_part ?6669)) [6669] by Demod 4460 with 3 at 2
+Id : 4607, {_}: least_upper_bound (inverse (negative_part ?6821)) identity =>= inverse (negative_part ?6821) [6821] by Super 309 with 4502 at 2,2
+Id : 4660, {_}: least_upper_bound identity (inverse (negative_part ?6821)) =>= inverse (negative_part ?6821) [6821] by Demod 4607 with 6 at 2
+Id : 4661, {_}: positive_part (inverse (negative_part ?6821)) =>= inverse (negative_part ?6821) [6821] by Demod 4660 with 298 at 2
+Id : 4799, {_}: least_upper_bound (inverse (negative_part ?6984)) (positive_part ?6985) =>= least_upper_bound (inverse (negative_part ?6984)) ?6985 [6985, 6984] by Super 1518 with 4661 at 1,3
+Id : 11842, {_}: multiply (least_upper_bound (inverse (negative_part ?15801)) ?15802) (negative_part ?15801) =>= positive_part (multiply (positive_part ?15802) (negative_part ?15801)) [15802, 15801] by Super 11818 with 4799 at 1,2
+Id : 11803, {_}: multiply (least_upper_bound (inverse ?471) ?472) ?471 =>= positive_part (multiply ?472 ?471) [472, 471] by Demod 215 with 298 at 3
+Id : 11889, {_}: positive_part (multiply ?15802 (negative_part ?15801)) =<= positive_part (multiply (positive_part ?15802) (negative_part ?15801)) [15801, 15802] by Demod 11842 with 11803 at 2
+Id : 11892, {_}: multiply (positive_part (inverse ?15810)) ?15810 =>= positive_part ?15810 [15810] by Demod 11845 with 2 at 1,3
+Id : 12165, {_}: multiply (positive_part (inverse ?16276)) (negative_part ?16276) =>= greatest_lower_bound (positive_part (inverse ?16276)) (positive_part ?16276) [16276] by Super 1073 with 11892 at 2,3
+Id : 12217, {_}: multiply (positive_part (inverse ?16276)) (negative_part ?16276) =>= greatest_lower_bound (positive_part ?16276) (positive_part (inverse ?16276)) [16276] by Demod 12165 with 5 at 3
+Id : 12218, {_}: multiply (positive_part (inverse ?16276)) (negative_part ?16276) =>= positive_part (greatest_lower_bound ?16276 (inverse ?16276)) [16276] by Demod 12217 with 878 at 3
+Id : 12981, {_}: positive_part (multiply (inverse ?17147) (negative_part ?17147)) =<= positive_part (positive_part (greatest_lower_bound ?17147 (inverse ?17147))) [17147] by Super 11889 with 12218 at 1,3
+Id : 4423, {_}: multiply (inverse ?6576) (negative_part ?6576) =>= negative_part (inverse ?6576) [6576] by Demod 4422 with 312 at 3
+Id : 13027, {_}: positive_part (negative_part (inverse ?17147)) =<= positive_part (positive_part (greatest_lower_bound ?17147 (inverse ?17147))) [17147] by Demod 12981 with 4423 at 1,2
+Id : 1230, {_}: least_upper_bound ?1974 (positive_part ?1975) =<= positive_part (least_upper_bound ?1974 ?1975) [1975, 1974] by Demod 297 with 20 at 2,2
+Id : 1242, {_}: least_upper_bound ?2011 (positive_part identity) =>= positive_part (positive_part ?2011) [2011] by Super 1230 with 20 at 1,3
+Id : 300, {_}: positive_part identity =>= identity [] by Super 9 with 20 at 2
+Id : 1261, {_}: least_upper_bound ?2011 identity =<= positive_part (positive_part ?2011) [2011] by Demod 1242 with 300 at 2,2
+Id : 1262, {_}: positive_part ?2011 =<= positive_part (positive_part ?2011) [2011] by Demod 1261 with 20 at 2
+Id : 13028, {_}: positive_part (negative_part (inverse ?17147)) =<= positive_part (greatest_lower_bound ?17147 (inverse ?17147)) [17147] by Demod 13027 with 1262 at 3
+Id : 13029, {_}: identity =<= positive_part (greatest_lower_bound ?17147 (inverse ?17147)) [17147] by Demod 13028 with 922 at 2
+Id : 14199, {_}: multiply (positive_part ?16391) (negative_part (inverse ?16391)) =>= identity [16391] by Demod 12306 with 13029 at 3
+Id : 14209, {_}: negative_part (inverse ?18032) =<= multiply (inverse (positive_part ?18032)) identity [18032] by Super 34 with 14199 at 2,3
+Id : 14275, {_}: negative_part (inverse ?18032) =>= inverse (positive_part ?18032) [18032] by Demod 14209 with 1026 at 3
+Id : 14351, {_}: multiply ?6585 (inverse (positive_part ?6585)) =>= negative_part ?6585 [6585] by Demod 4428 with 14275 at 2,2
+Id : 290, {_}: inverse (multiply ?624 (inverse ?625)) =>= multiply ?625 (inverse ?624) [625, 624] by Super 286 with 18 at 1,3
+Id : 12177, {_}: inverse (positive_part (inverse ?16308)) =<= multiply ?16308 (inverse (positive_part (inverse (inverse ?16308)))) [16308] by Super 290 with 11892 at 1,2
+Id : 12203, {_}: inverse (positive_part (inverse ?16308)) =<= multiply ?16308 (inverse (positive_part ?16308)) [16308] by Demod 12177 with 18 at 1,1,2,3
+Id : 14356, {_}: inverse (positive_part (inverse ?6585)) =>= negative_part ?6585 [6585] by Demod 14351 with 12203 at 2
+Id : 14357, {_}: negative_part ?7872 =<= multiply (inverse (positive_part ?7872)) ?7872 [7872] by Demod 5356 with 14356 at 2
+Id : 13168, {_}: multiply (inverse (greatest_lower_bound ?17321 (inverse ?17321))) identity =>= positive_part (inverse (greatest_lower_bound ?17321 (inverse ?17321))) [17321] by Super 5134 with 13029 at 2,2
+Id : 15132, {_}: inverse (greatest_lower_bound ?18904 (inverse ?18904)) =<= positive_part (inverse (greatest_lower_bound ?18904 (inverse ?18904))) [18904] by Demod 13168 with 1026 at 2
+Id : 15140, {_}: inverse (greatest_lower_bound (positive_part (inverse ?18921)) (inverse (positive_part (inverse ?18921)))) =>= positive_part (inverse (greatest_lower_bound (positive_part (inverse ?18921)) (negative_part ?18921))) [18921] by Super 15132 with 14356 at 2,1,1,3
+Id : 899, {_}: greatest_lower_bound identity (greatest_lower_bound ?1607 ?1608) =>= greatest_lower_bound (negative_part ?1607) ?1608 [1608, 1607] by Super 7 with 312 at 1,3
+Id : 921, {_}: negative_part (greatest_lower_bound ?1607 ?1608) =>= greatest_lower_bound (negative_part ?1607) ?1608 [1608, 1607] by Demod 899 with 312 at 2
+Id : 311, {_}: greatest_lower_bound ?662 (greatest_lower_bound ?663 identity) =>= negative_part (greatest_lower_bound ?662 ?663) [663, 662] by Super 7 with 21 at 3
+Id : 321, {_}: greatest_lower_bound ?662 (negative_part ?663) =<= negative_part (greatest_lower_bound ?662 ?663) [663, 662] by Demod 311 with 21 at 2,2
+Id : 1610, {_}: greatest_lower_bound ?2637 (negative_part ?2638) =<= greatest_lower_bound (negative_part ?2637) ?2638 [2638, 2637] by Demod 921 with 321 at 2
+Id : 903, {_}: negative_part (least_upper_bound identity ?1615) =>= identity [1615] by Super 12 with 312 at 2
+Id : 917, {_}: negative_part (positive_part ?1615) =>= identity [1615] by Demod 903 with 298 at 1,2
+Id : 1615, {_}: greatest_lower_bound (positive_part ?2651) (negative_part ?2652) =>= greatest_lower_bound identity ?2652 [2652, 2651] by Super 1610 with 917 at 1,3
+Id : 1662, {_}: greatest_lower_bound (positive_part ?2651) (negative_part ?2652) =>= negative_part ?2652 [2652, 2651] by Demod 1615 with 312 at 3
+Id : 4459, {_}: multiply (inverse (positive_part ?6667)) identity =>= negative_part (inverse (positive_part ?6667)) [6667] by Super 4454 with 917 at 2,2
+Id : 4501, {_}: inverse (positive_part ?6667) =<= negative_part (inverse (positive_part ?6667)) [6667] by Demod 4459 with 1026 at 2
+Id : 4523, {_}: greatest_lower_bound (positive_part ?6721) (inverse (positive_part ?6722)) =>= negative_part (inverse (positive_part ?6722)) [6722, 6721] by Super 1662 with 4501 at 2,2
+Id : 4568, {_}: greatest_lower_bound (positive_part ?6721) (inverse (positive_part ?6722)) =>= inverse (positive_part ?6722) [6722, 6721] by Demod 4523 with 4501 at 3
+Id : 15267, {_}: inverse (inverse (positive_part (inverse ?18921))) =<= positive_part (inverse (greatest_lower_bound (positive_part (inverse ?18921)) (negative_part ?18921))) [18921] by Demod 15140 with 4568 at 1,2
+Id : 4810, {_}: positive_part (inverse (negative_part ?7011)) =>= inverse (negative_part ?7011) [7011] by Demod 4660 with 298 at 2
+Id : 4822, {_}: positive_part (inverse (greatest_lower_bound ?7038 (negative_part ?7039))) =>= inverse (negative_part (greatest_lower_bound ?7038 ?7039)) [7039, 7038] by Super 4810 with 321 at 1,1,2
+Id : 4871, {_}: positive_part (inverse (greatest_lower_bound ?7038 (negative_part ?7039))) =>= inverse (greatest_lower_bound ?7038 (negative_part ?7039)) [7039, 7038] by Demod 4822 with 321 at 1,3
+Id : 15268, {_}: inverse (inverse (positive_part (inverse ?18921))) =<= inverse (greatest_lower_bound (positive_part (inverse ?18921)) (negative_part ?18921)) [18921] by Demod 15267 with 4871 at 3
+Id : 15269, {_}: positive_part (inverse ?18921) =<= inverse (greatest_lower_bound (positive_part (inverse ?18921)) (negative_part ?18921)) [18921] by Demod 15268 with 18 at 2
+Id : 15270, {_}: positive_part (inverse ?18921) =<= inverse (greatest_lower_bound (negative_part ?18921) (positive_part (inverse ?18921))) [18921] by Demod 15269 with 5 at 1,3
+Id : 1594, {_}: greatest_lower_bound ?1607 (negative_part ?1608) =<= greatest_lower_bound (negative_part ?1607) ?1608 [1608, 1607] by Demod 921 with 321 at 2
+Id : 15271, {_}: positive_part (inverse ?18921) =<= inverse (greatest_lower_bound ?18921 (negative_part (positive_part (inverse ?18921)))) [18921] by Demod 15270 with 1594 at 1,3
+Id : 15272, {_}: positive_part (inverse ?18921) =<= inverse (greatest_lower_bound ?18921 identity) [18921] by Demod 15271 with 917 at 2,1,3
+Id : 15273, {_}: positive_part (inverse ?18921) =>= inverse (negative_part ?18921) [18921] by Demod 15272 with 21 at 1,3
+Id : 15393, {_}: negative_part (inverse ?19045) =<= multiply (inverse (inverse (negative_part ?19045))) (inverse ?19045) [19045] by Super 14357 with 15273 at 1,1,3
+Id : 15435, {_}: inverse (positive_part ?19045) =<= multiply (inverse (inverse (negative_part ?19045))) (inverse ?19045) [19045] by Demod 15393 with 14275 at 2
+Id : 15436, {_}: inverse (positive_part ?19045) =<= inverse (multiply ?19045 (inverse (negative_part ?19045))) [19045] by Demod 15435 with 19 at 3
+Id : 15437, {_}: inverse (positive_part ?19045) =<= multiply (negative_part ?19045) (inverse ?19045) [19045] by Demod 15436 with 290 at 3
+Id : 15800, {_}: inverse ?19405 =<= multiply (inverse (negative_part ?19405)) (inverse (positive_part ?19405)) [19405] by Super 34 with 15437 at 2,3
+Id : 15843, {_}: inverse ?19405 =<= inverse (multiply (positive_part ?19405) (negative_part ?19405)) [19405] by Demod 15800 with 19 at 3
+Id : 20580, {_}: inverse (inverse ?23723) =<= multiply (positive_part ?23723) (negative_part ?23723) [23723] by Super 18 with 15843 at 1,2
+Id : 20668, {_}: ?23723 =<= multiply (positive_part ?23723) (negative_part ?23723) [23723] by Demod 20580 with 18 at 2
+Id : 20964, {_}: a =?= a [] by Demod 1 with 20668 at 3
+Id : 1, {_}: a =<= multiply (positive_part a) (negative_part a) [] by prove_lat4
+% SZS output end CNFRefutation for GRP167-2.p
+10052: solved GRP167-2.p in 3.352209 using kbo
+10052: status Unsatisfiable for GRP167-2.p
+NO CLASH, using fixed ground order
+10058: Facts:
+10058: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10058: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+10058: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+10058: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+10058: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+10058: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+10058: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+10058: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+10058: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+10058: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+10058: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+10058: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+10058: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+10058: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+10058: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+10058: Id : 17, {_}: least_upper_bound identity a =>= a [] by p09a_1
+10058: Id : 18, {_}: least_upper_bound identity b =>= b [] by p09a_2
+10058: Id : 19, {_}: least_upper_bound identity c =>= c [] by p09a_3
+10058: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09a_4
+10058: Goal:
+10058: Id : 1, {_}:
+ greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
+ [] by prove_p09a
+10058: Order:
+10058: nrkbo
+10058: Leaf order:
+10058: least_upper_bound 16 2 0
+10058: inverse 1 1 0
+10058: identity 6 0 0
+10058: greatest_lower_bound 16 2 2 0,2
+10058: multiply 19 2 1 0,2,2
+10058: c 4 0 2 2,2,2
+10058: b 4 0 1 1,2,2
+10058: a 5 0 2 1,2
+NO CLASH, using fixed ground order
+10059: Facts:
+10059: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10059: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+10059: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+10059: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+10059: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+10059: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+10059: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+NO CLASH, using fixed ground order
+10060: Facts:
+10060: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10060: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+10060: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+10060: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+10060: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+10060: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+10059: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+10059: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+10059: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+10059: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+10059: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+10059: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+10059: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+10059: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+10059: Id : 17, {_}: least_upper_bound identity a =>= a [] by p09a_1
+10059: Id : 18, {_}: least_upper_bound identity b =>= b [] by p09a_2
+10059: Id : 19, {_}: least_upper_bound identity c =>= c [] by p09a_3
+10059: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09a_4
+10059: Goal:
+10059: Id : 1, {_}:
+ greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
+ [] by prove_p09a
+10059: Order:
+10059: kbo
+10059: Leaf order:
+10059: least_upper_bound 16 2 0
+10059: inverse 1 1 0
+10059: identity 6 0 0
+10059: greatest_lower_bound 16 2 2 0,2
+10059: multiply 19 2 1 0,2,2
+10059: c 4 0 2 2,2,2
+10059: b 4 0 1 1,2,2
+10059: a 5 0 2 1,2
+10060: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+10060: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+10060: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+10060: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+10060: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+10060: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+10060: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+10060: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+10060: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+10060: Id : 17, {_}: least_upper_bound identity a =>= a [] by p09a_1
+10060: Id : 18, {_}: least_upper_bound identity b =>= b [] by p09a_2
+10060: Id : 19, {_}: least_upper_bound identity c =>= c [] by p09a_3
+10060: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09a_4
+10060: Goal:
+10060: Id : 1, {_}:
+ greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
+ [] by prove_p09a
+10060: Order:
+10060: lpo
+10060: Leaf order:
+10060: least_upper_bound 16 2 0
+10060: inverse 1 1 0
+10060: identity 6 0 0
+10060: greatest_lower_bound 16 2 2 0,2
+10060: multiply 19 2 1 0,2,2
+10060: c 4 0 2 2,2,2
+10060: b 4 0 1 1,2,2
+10060: a 5 0 2 1,2
+% SZS status Timeout for GRP178-1.p
+NO CLASH, using fixed ground order
+10102: Facts:
+10102: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10102: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+10102: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+10102: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+10102: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+10102: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+10102: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+10102: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+10102: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+10102: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+10102: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+10102: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+10102: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+10102: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+10102: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+10102: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1
+10102: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2
+10102: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3
+10102: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09b_4
+10102: Goal:
+10102: Id : 1, {_}:
+ greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
+ [] by prove_p09b
+10102: Order:
+10102: nrkbo
+10102: Leaf order:
+10102: least_upper_bound 13 2 0
+10102: inverse 1 1 0
+10102: identity 9 0 0
+10102: greatest_lower_bound 19 2 2 0,2
+10102: multiply 19 2 1 0,2,2
+10102: c 3 0 2 2,2,2
+10102: b 3 0 1 1,2,2
+10102: a 4 0 2 1,2
+NO CLASH, using fixed ground order
+10103: Facts:
+10103: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10103: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+10103: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+10103: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+10103: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+10103: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+10103: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+10103: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+10103: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+10103: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+10103: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+10103: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+10103: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+10103: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+10103: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+10103: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1
+10103: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2
+10103: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3
+10103: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09b_4
+10103: Goal:
+10103: Id : 1, {_}:
+ greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
+ [] by prove_p09b
+10103: Order:
+10103: kbo
+10103: Leaf order:
+10103: least_upper_bound 13 2 0
+10103: inverse 1 1 0
+10103: identity 9 0 0
+10103: greatest_lower_bound 19 2 2 0,2
+10103: multiply 19 2 1 0,2,2
+10103: c 3 0 2 2,2,2
+10103: b 3 0 1 1,2,2
+10103: a 4 0 2 1,2
+NO CLASH, using fixed ground order
+10104: Facts:
+10104: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10104: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+10104: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+10104: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+10104: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+10104: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+10104: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+10104: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+10104: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+10104: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+10104: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+10104: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+10104: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+10104: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+10104: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+10104: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1
+10104: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2
+10104: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3
+10104: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09b_4
+10104: Goal:
+10104: Id : 1, {_}:
+ greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
+ [] by prove_p09b
+10104: Order:
+10104: lpo
+10104: Leaf order:
+10104: least_upper_bound 13 2 0
+10104: inverse 1 1 0
+10104: identity 9 0 0
+10104: greatest_lower_bound 19 2 2 0,2
+10104: multiply 19 2 1 0,2,2
+10104: c 3 0 2 2,2,2
+10104: b 3 0 1 1,2,2
+10104: a 4 0 2 1,2
+% SZS status Timeout for GRP178-2.p
+CLASH, statistics insufficient
+10125: Facts:
+10125: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10125: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+10125: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+10125: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+10125: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+10125: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+10125: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+10125: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+10125: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+10125: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+10125: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+10125: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+10125: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+10125: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+10125: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+10125: Id : 17, {_}:
+ greatest_lower_bound a c =>= greatest_lower_bound b c
+ [] by p12x_1
+10125: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_2
+10125: Id : 19, {_}:
+ inverse (greatest_lower_bound ?52 ?53)
+ =<=
+ least_upper_bound (inverse ?52) (inverse ?53)
+ [53, 52] by p12x_3 ?52 ?53
+10125: Id : 20, {_}:
+ inverse (least_upper_bound ?55 ?56)
+ =<=
+ greatest_lower_bound (inverse ?55) (inverse ?56)
+ [56, 55] by p12x_4 ?55 ?56
+10125: Goal:
+10125: Id : 1, {_}: a =>= b [] by prove_p12x
+10125: Order:
+10125: nrkbo
+10125: Leaf order:
+10125: c 4 0 0
+10125: least_upper_bound 17 2 0
+10125: greatest_lower_bound 17 2 0
+10125: inverse 7 1 0
+10125: multiply 18 2 0
+10125: identity 2 0 0
+10125: b 3 0 1 3
+10125: a 3 0 1 2
+CLASH, statistics insufficient
+10126: Facts:
+10126: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10126: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+10126: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+10126: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+10126: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+10126: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+10126: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+10126: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+10126: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+10126: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+10126: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+10126: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+10126: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+10126: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+10126: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+10126: Id : 17, {_}:
+ greatest_lower_bound a c =>= greatest_lower_bound b c
+ [] by p12x_1
+10126: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_2
+10126: Id : 19, {_}:
+ inverse (greatest_lower_bound ?52 ?53)
+ =<=
+ least_upper_bound (inverse ?52) (inverse ?53)
+ [53, 52] by p12x_3 ?52 ?53
+10126: Id : 20, {_}:
+ inverse (least_upper_bound ?55 ?56)
+ =<=
+ greatest_lower_bound (inverse ?55) (inverse ?56)
+ [56, 55] by p12x_4 ?55 ?56
+10126: Goal:
+10126: Id : 1, {_}: a =>= b [] by prove_p12x
+10126: Order:
+10126: kbo
+10126: Leaf order:
+10126: c 4 0 0
+10126: least_upper_bound 17 2 0
+10126: greatest_lower_bound 17 2 0
+10126: inverse 7 1 0
+10126: multiply 18 2 0
+10126: identity 2 0 0
+10126: b 3 0 1 3
+10126: a 3 0 1 2
+CLASH, statistics insufficient
+10127: Facts:
+10127: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10127: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+10127: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+10127: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+10127: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+10127: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+10127: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+10127: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+10127: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+10127: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+10127: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+10127: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+10127: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+10127: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+10127: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+10127: Id : 17, {_}:
+ greatest_lower_bound a c =>= greatest_lower_bound b c
+ [] by p12x_1
+10127: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_2
+10127: Id : 19, {_}:
+ inverse (greatest_lower_bound ?52 ?53)
+ =>=
+ least_upper_bound (inverse ?52) (inverse ?53)
+ [53, 52] by p12x_3 ?52 ?53
+10127: Id : 20, {_}:
+ inverse (least_upper_bound ?55 ?56)
+ =>=
+ greatest_lower_bound (inverse ?55) (inverse ?56)
+ [56, 55] by p12x_4 ?55 ?56
+10127: Goal:
+10127: Id : 1, {_}: a =>= b [] by prove_p12x
+10127: Order:
+10127: lpo
+10127: Leaf order:
+10127: c 4 0 0
+10127: least_upper_bound 17 2 0
+10127: greatest_lower_bound 17 2 0
+10127: inverse 7 1 0
+10127: multiply 18 2 0
+10127: identity 2 0 0
+10127: b 3 0 1 3
+10127: a 3 0 1 2
+% SZS status Timeout for GRP181-3.p
+NO CLASH, using fixed ground order
+10150: Facts:
+10150: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10150: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+10150: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+10150: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+10150: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+10150: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+10150: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+10150: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+10150: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+10150: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+10150: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+10150: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+10150: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+10150: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+10150: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+10150: Id : 17, {_}: inverse identity =>= identity [] by p21_1
+10150: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p21_2 ?51
+10150: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p21_3 ?53 ?54
+10150: Goal:
+10150: Id : 1, {_}:
+ multiply (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =>=
+ multiply (inverse (greatest_lower_bound a identity))
+ (least_upper_bound a identity)
+ [] by prove_p21
+10150: Order:
+10150: nrkbo
+10150: Leaf order:
+10150: multiply 22 2 2 0,2
+10150: inverse 9 1 2 0,2,2
+10150: greatest_lower_bound 15 2 2 0,1,2,2
+10150: least_upper_bound 15 2 2 0,1,2
+10150: identity 8 0 4 2,1,2
+10150: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+10151: Facts:
+10151: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10151: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+10151: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+10151: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+10151: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+10151: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+10151: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+10151: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+10151: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+10151: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+10151: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+10151: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+10151: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+10151: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+10151: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+10151: Id : 17, {_}: inverse identity =>= identity [] by p21_1
+10151: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p21_2 ?51
+10151: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p21_3 ?53 ?54
+10151: Goal:
+10151: Id : 1, {_}:
+ multiply (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =<=
+ multiply (inverse (greatest_lower_bound a identity))
+ (least_upper_bound a identity)
+ [] by prove_p21
+10151: Order:
+10151: kbo
+10151: Leaf order:
+10151: multiply 22 2 2 0,2
+10151: inverse 9 1 2 0,2,2
+10151: greatest_lower_bound 15 2 2 0,1,2,2
+10151: least_upper_bound 15 2 2 0,1,2
+10151: identity 8 0 4 2,1,2
+10151: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+10152: Facts:
+10152: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10152: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+10152: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+10152: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+10152: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+10152: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+10152: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+10152: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+10152: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+10152: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+10152: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+10152: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+10152: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+10152: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+10152: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+10152: Id : 17, {_}: inverse identity =>= identity [] by p21_1
+10152: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p21_2 ?51
+10152: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =>= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p21_3 ?53 ?54
+10152: Goal:
+10152: Id : 1, {_}:
+ multiply (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =>=
+ multiply (inverse (greatest_lower_bound a identity))
+ (least_upper_bound a identity)
+ [] by prove_p21
+10152: Order:
+10152: lpo
+10152: Leaf order:
+10152: multiply 22 2 2 0,2
+10152: inverse 9 1 2 0,2,2
+10152: greatest_lower_bound 15 2 2 0,1,2,2
+10152: least_upper_bound 15 2 2 0,1,2
+10152: identity 8 0 4 2,1,2
+10152: a 4 0 4 1,1,2
+% SZS status Timeout for GRP184-2.p
+NO CLASH, using fixed ground order
+10174: Facts:
+10174: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10174: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+10174: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+10174: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+10174: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+10174: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+10174: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+10174: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+10174: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+10174: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+10174: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+10174: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+10174: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+10174: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+10174: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+10174: Goal:
+10174: Id : 1, {_}:
+ least_upper_bound (least_upper_bound (multiply a b) identity)
+ (multiply (least_upper_bound a identity)
+ (least_upper_bound b identity))
+ =>=
+ multiply (least_upper_bound a identity)
+ (least_upper_bound b identity)
+ [] by prove_p22a
+10174: Order:
+10174: nrkbo
+10174: Leaf order:
+10174: greatest_lower_bound 13 2 0
+10174: inverse 1 1 0
+10174: least_upper_bound 19 2 6 0,2
+10174: identity 7 0 5 2,1,2
+10174: multiply 21 2 3 0,1,1,2
+10174: b 3 0 3 2,1,1,2
+10174: a 3 0 3 1,1,1,2
+NO CLASH, using fixed ground order
+10175: Facts:
+10175: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10175: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+10175: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+10175: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+10175: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+10175: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+10175: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+10175: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+10175: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+10175: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+10175: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+10175: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+10175: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+10175: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+10175: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+10175: Goal:
+10175: Id : 1, {_}:
+ least_upper_bound (least_upper_bound (multiply a b) identity)
+ (multiply (least_upper_bound a identity)
+ (least_upper_bound b identity))
+ =>=
+ multiply (least_upper_bound a identity)
+ (least_upper_bound b identity)
+ [] by prove_p22a
+10175: Order:
+10175: kbo
+10175: Leaf order:
+10175: greatest_lower_bound 13 2 0
+10175: inverse 1 1 0
+10175: least_upper_bound 19 2 6 0,2
+10175: identity 7 0 5 2,1,2
+10175: multiply 21 2 3 0,1,1,2
+10175: b 3 0 3 2,1,1,2
+10175: a 3 0 3 1,1,1,2
+NO CLASH, using fixed ground order
+10176: Facts:
+10176: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10176: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+10176: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+10176: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+10176: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+10176: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+10176: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+10176: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+10176: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+10176: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+10176: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+10176: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+10176: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+10176: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+10176: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+10176: Goal:
+10176: Id : 1, {_}:
+ least_upper_bound (least_upper_bound (multiply a b) identity)
+ (multiply (least_upper_bound a identity)
+ (least_upper_bound b identity))
+ =>=
+ multiply (least_upper_bound a identity)
+ (least_upper_bound b identity)
+ [] by prove_p22a
+10176: Order:
+10176: lpo
+10176: Leaf order:
+10176: greatest_lower_bound 13 2 0
+10176: inverse 1 1 0
+10176: least_upper_bound 19 2 6 0,2
+10176: identity 7 0 5 2,1,2
+10176: multiply 21 2 3 0,1,1,2
+10176: b 3 0 3 2,1,1,2
+10176: a 3 0 3 1,1,1,2
+Statistics :
+Max weight : 21
+Found proof, 4.014671s
+% SZS status Unsatisfiable for GRP185-1.p
+% SZS output start CNFRefutation for GRP185-1.p
+Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+Id : 21, {_}: multiply (multiply ?57 ?58) ?59 =>= multiply ?57 (multiply ?58 ?59) [59, 58, 57] by associativity ?57 ?58 ?59
+Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+Id : 67, {_}: least_upper_bound ?151 (least_upper_bound ?152 ?153) =<= least_upper_bound (least_upper_bound ?151 ?152) ?153 [153, 152, 151] by associativity_of_lub ?151 ?152 ?153
+Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
+Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+Id : 68, {_}: least_upper_bound ?155 (least_upper_bound ?156 ?157) =<= least_upper_bound (least_upper_bound ?156 ?155) ?157 [157, 156, 155] by Super 67 with 6 at 1,3
+Id : 74, {_}: least_upper_bound ?155 (least_upper_bound ?156 ?157) =?= least_upper_bound ?156 (least_upper_bound ?155 ?157) [157, 156, 155] by Demod 68 with 8 at 3
+Id : 23, {_}: multiply identity ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Super 21 with 3 at 1,2
+Id : 562, {_}: ?594 =<= multiply (inverse ?595) (multiply ?595 ?594) [595, 594] by Demod 23 with 2 at 2
+Id : 564, {_}: ?599 =<= multiply (inverse (inverse ?599)) identity [599] by Super 562 with 3 at 2,3
+Id : 27, {_}: ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Demod 23 with 2 at 2
+Id : 570, {_}: multiply ?621 ?622 =<= multiply (inverse (inverse ?621)) ?622 [622, 621] by Super 562 with 27 at 2,3
+Id : 855, {_}: ?599 =<= multiply ?599 identity [599] by Demod 564 with 570 at 3
+Id : 65, {_}: least_upper_bound ?143 (least_upper_bound ?144 ?145) =?= least_upper_bound ?144 (least_upper_bound ?145 ?143) [145, 144, 143] by Super 6 with 8 at 3
+Id : 85, {_}: least_upper_bound ?180 (least_upper_bound ?180 ?181) =>= least_upper_bound ?180 ?181 [181, 180] by Super 8 with 9 at 1,3
+Id : 5149, {_}: least_upper_bound identity (least_upper_bound b (least_upper_bound a (multiply a b))) === least_upper_bound identity (least_upper_bound b (least_upper_bound a (multiply a b))) [] by Demod 5148 with 74 at 2,2
+Id : 5148, {_}: least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) =>= least_upper_bound identity (least_upper_bound b (least_upper_bound a (multiply a b))) [] by Demod 5147 with 9 at 2,2,2,2
+Id : 5147, {_}: least_upper_bound identity (least_upper_bound a (least_upper_bound b (least_upper_bound (multiply a b) (multiply a b)))) =>= least_upper_bound identity (least_upper_bound b (least_upper_bound a (multiply a b))) [] by Demod 5146 with 2 at 1,2,2,2
+Id : 5146, {_}: least_upper_bound identity (least_upper_bound a (least_upper_bound (multiply identity b) (least_upper_bound (multiply a b) (multiply a b)))) =>= least_upper_bound identity (least_upper_bound b (least_upper_bound a (multiply a b))) [] by Demod 5145 with 85 at 2
+Id : 5145, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound a (least_upper_bound (multiply identity b) (least_upper_bound (multiply a b) (multiply a b))))) =>= least_upper_bound identity (least_upper_bound b (least_upper_bound a (multiply a b))) [] by Demod 5144 with 74 at 3
+Id : 5144, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound a (least_upper_bound (multiply identity b) (least_upper_bound (multiply a b) (multiply a b))))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound a (multiply a b))) [] by Demod 5143 with 65 at 2,2,2,2
+Id : 5143, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound a (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b))))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound a (multiply a b))) [] by Demod 5142 with 855 at 1,2,2,2
+Id : 5142, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound (multiply a identity) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b))))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound a (multiply a b))) [] by Demod 5141 with 2 at 1,2,2
+Id : 5141, {_}: least_upper_bound identity (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b))))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound a (multiply a b))) [] by Demod 5140 with 855 at 1,2,2,3
+Id : 5140, {_}: least_upper_bound identity (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b))))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a identity) (multiply a b))) [] by Demod 5139 with 2 at 1,2,3
+Id : 5139, {_}: least_upper_bound identity (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b))))) =>= least_upper_bound b (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (multiply a b))) [] by Demod 5138 with 8 at 2,2
+Id : 5138, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound b (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (multiply a b))) [] by Demod 5137 with 8 at 2,3
+Id : 5137, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound b (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply a b)) [] by Demod 5136 with 2 at 1,3
+Id : 5136, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound (multiply identity b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply a b)) [] by Demod 5135 with 74 at 2,2
+Id : 5135, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound (multiply identity b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply a b)) [] by Demod 5134 with 74 at 3
+Id : 5134, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)) [] by Demod 5133 with 15 at 2,2,2,2
+Id : 5133, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)) [] by Demod 5132 with 15 at 1,2,2,2
+Id : 5132, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)) [] by Demod 5131 with 15 at 2,3
+Id : 5131, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply (least_upper_bound identity a) b) [] by Demod 5130 with 15 at 1,3
+Id : 5130, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b) [] by Demod 237 with 74 at 2
+Id : 237, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b) [] by Demod 236 with 6 at 1,2,2,2,2
+Id : 236, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound a identity) b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b) [] by Demod 235 with 6 at 1,1,2,2,2
+Id : 235, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b) [] by Demod 234 with 6 at 1,2,3
+Id : 234, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound a identity) b) [] by Demod 233 with 6 at 1,1,3
+Id : 233, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b))) =>= least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b) [] by Demod 232 with 6 at 2,2,2
+Id : 232, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b) [] by Demod 231 with 6 at 3
+Id : 231, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity) [] by Demod 230 with 13 at 2,2,2
+Id : 230, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (multiply (least_upper_bound a identity) (least_upper_bound b identity))) =>= least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity) [] by Demod 229 with 13 at 3
+Id : 229, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (multiply (least_upper_bound a identity) (least_upper_bound b identity))) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 1 with 8 at 2
+Id : 1, {_}: least_upper_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by prove_p22a
+% SZS output end CNFRefutation for GRP185-1.p
+10176: solved GRP185-1.p in 1.916119 using lpo
+10176: status Unsatisfiable for GRP185-1.p
+NO CLASH, using fixed ground order
+10187: Facts:
+10187: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10187: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+10187: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+10187: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+10187: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+10187: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+10187: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+10187: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+10187: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+10187: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+10187: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+10187: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+10187: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+10187: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+10187: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+10187: Id : 17, {_}: inverse identity =>= identity [] by p22a_1
+10187: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
+10187: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p22a_3 ?53 ?54
+10187: Goal:
+10187: Id : 1, {_}:
+ least_upper_bound (least_upper_bound (multiply a b) identity)
+ (multiply (least_upper_bound a identity)
+ (least_upper_bound b identity))
+ =>=
+ multiply (least_upper_bound a identity)
+ (least_upper_bound b identity)
+ [] by prove_p22a
+10187: Order:
+10187: nrkbo
+10187: Leaf order:
+10187: greatest_lower_bound 13 2 0
+10187: inverse 7 1 0
+10187: least_upper_bound 19 2 6 0,2
+10187: identity 9 0 5 2,1,2
+10187: multiply 23 2 3 0,1,1,2
+10187: b 3 0 3 2,1,1,2
+10187: a 3 0 3 1,1,1,2
+NO CLASH, using fixed ground order
+10188: Facts:
+10188: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10188: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+10188: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+10188: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+10188: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+10188: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+10188: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+10188: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+10188: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+10188: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+10188: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+10188: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+10188: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+10188: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+10188: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+10188: Id : 17, {_}: inverse identity =>= identity [] by p22a_1
+10188: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
+10188: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p22a_3 ?53 ?54
+10188: Goal:
+10188: Id : 1, {_}:
+ least_upper_bound (least_upper_bound (multiply a b) identity)
+ (multiply (least_upper_bound a identity)
+ (least_upper_bound b identity))
+ =>=
+ multiply (least_upper_bound a identity)
+ (least_upper_bound b identity)
+ [] by prove_p22a
+10188: Order:
+10188: kbo
+10188: Leaf order:
+10188: greatest_lower_bound 13 2 0
+10188: inverse 7 1 0
+10188: least_upper_bound 19 2 6 0,2
+10188: identity 9 0 5 2,1,2
+10188: multiply 23 2 3 0,1,1,2
+10188: b 3 0 3 2,1,1,2
+10188: a 3 0 3 1,1,1,2
+NO CLASH, using fixed ground order
+10189: Facts:
+10189: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10189: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+10189: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+10189: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+10189: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+10189: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+10189: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+10189: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+10189: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+10189: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+10189: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+10189: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+10189: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+10189: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+10189: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+10189: Id : 17, {_}: inverse identity =>= identity [] by p22a_1
+10189: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
+10189: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p22a_3 ?53 ?54
+10189: Goal:
+10189: Id : 1, {_}:
+ least_upper_bound (least_upper_bound (multiply a b) identity)
+ (multiply (least_upper_bound a identity)
+ (least_upper_bound b identity))
+ =>=
+ multiply (least_upper_bound a identity)
+ (least_upper_bound b identity)
+ [] by prove_p22a
+10189: Order:
+10189: lpo
+10189: Leaf order:
+10189: greatest_lower_bound 13 2 0
+10189: inverse 7 1 0
+10189: least_upper_bound 19 2 6 0,2
+10189: identity 9 0 5 2,1,2
+10189: multiply 23 2 3 0,1,1,2
+10189: b 3 0 3 2,1,1,2
+10189: a 3 0 3 1,1,1,2
+Statistics :
+Max weight : 21
+Found proof, 5.587205s
+% SZS status Unsatisfiable for GRP185-2.p
+% SZS output start CNFRefutation for GRP185-2.p
+Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
+Id : 17, {_}: inverse identity =>= identity [] by p22a_1
+Id : 506, {_}: inverse (multiply ?520 ?521) =?= multiply (inverse ?521) (inverse ?520) [521, 520] by p22a_3 ?520 ?521
+Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
+Id : 782, {_}: least_upper_bound ?667 (least_upper_bound ?667 ?668) =>= least_upper_bound ?667 ?668 [668, 667] by Super 8 with 9 at 1,3
+Id : 1203, {_}: least_upper_bound ?943 (least_upper_bound ?944 ?943) =>= least_upper_bound ?943 ?944 [944, 943] by Super 782 with 6 at 2,2
+Id : 1211, {_}: least_upper_bound ?966 (least_upper_bound ?967 (least_upper_bound ?968 ?966)) =>= least_upper_bound ?966 (least_upper_bound ?967 ?968) [968, 967, 966] by Super 1203 with 8 at 2,2
+Id : 507, {_}: inverse (multiply identity ?523) =<= multiply (inverse ?523) identity [523] by Super 506 with 17 at 2,3
+Id : 571, {_}: inverse ?569 =<= multiply (inverse ?569) identity [569] by Demod 507 with 2 at 1,2
+Id : 573, {_}: inverse (inverse ?572) =<= multiply ?572 identity [572] by Super 571 with 18 at 1,3
+Id : 581, {_}: ?572 =<= multiply ?572 identity [572] by Demod 573 with 18 at 2
+Id : 88, {_}: least_upper_bound ?186 (least_upper_bound ?186 ?187) =>= least_upper_bound ?186 ?187 [187, 186] by Super 8 with 9 at 1,3
+Id : 3310, {_}: least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) === least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3309 with 88 at 2
+Id : 3309, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b)))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3308 with 2 at 1,2,2,2,2
+Id : 3308, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound a (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3307 with 581 at 1,2,2,2
+Id : 3307, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3306 with 2 at 1,2,2
+Id : 3306, {_}: least_upper_bound identity (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3305 with 8 at 2,2
+Id : 3305, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3304 with 8 at 2,2
+Id : 3304, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply identity b)) (multiply a b)) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3303 with 6 at 2,2
+Id : 3303, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply identity b))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3302 with 2 at 1,2,2,3
+Id : 3302, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply identity b))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound (multiply identity b) (multiply a b))) [] by Demod 3301 with 581 at 1,2,3
+Id : 3301, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply identity b))) =>= least_upper_bound identity (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity b) (multiply a b))) [] by Demod 3300 with 2 at 1,3
+Id : 3300, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply identity b))) =>= least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity b) (multiply a b))) [] by Demod 3299 with 1211 at 2,2
+Id : 3299, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity b) (multiply a b))) [] by Demod 3298 with 8 at 3
+Id : 3298, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)) [] by Demod 3297 with 15 at 2,2,2,2
+Id : 3297, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)) [] by Demod 3296 with 15 at 1,2,2,2
+Id : 3296, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)) [] by Demod 3295 with 15 at 2,3
+Id : 3295, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply (least_upper_bound identity a) b) [] by Demod 3294 with 15 at 1,3
+Id : 3294, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b) [] by Demod 3293 with 13 at 2,2,2
+Id : 3293, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (multiply (least_upper_bound identity a) (least_upper_bound identity b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b) [] by Demod 3292 with 13 at 3
+Id : 3292, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (multiply (least_upper_bound identity a) (least_upper_bound identity b))) =>= multiply (least_upper_bound identity a) (least_upper_bound identity b) [] by Demod 67 with 8 at 2
+Id : 67, {_}: least_upper_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound identity a) (least_upper_bound identity b)) =>= multiply (least_upper_bound identity a) (least_upper_bound identity b) [] by Demod 66 with 6 at 2,3
+Id : 66, {_}: least_upper_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound identity a) (least_upper_bound identity b)) =<= multiply (least_upper_bound identity a) (least_upper_bound b identity) [] by Demod 65 with 6 at 1,3
+Id : 65, {_}: least_upper_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound identity a) (least_upper_bound identity b)) =<= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 64 with 6 at 2,2,2
+Id : 64, {_}: least_upper_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound identity a) (least_upper_bound b identity)) =<= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 63 with 6 at 1,2,2
+Id : 63, {_}: least_upper_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 1 with 6 at 1,2
+Id : 1, {_}: least_upper_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by prove_p22a
+% SZS output end CNFRefutation for GRP185-2.p
+10189: solved GRP185-2.p in 0.988061 using lpo
+10189: status Unsatisfiable for GRP185-2.p
+CLASH, statistics insufficient
+10194: Facts:
+10194: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10194: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+10194: Id : 4, {_}:
+ multiply ?6 (left_division ?6 ?7) =>= ?7
+ [7, 6] by multiply_left_division ?6 ?7
+10194: Id : 5, {_}:
+ left_division ?9 (multiply ?9 ?10) =>= ?10
+ [10, 9] by left_division_multiply ?9 ?10
+10194: Id : 6, {_}:
+ multiply (right_division ?12 ?13) ?13 =>= ?12
+ [13, 12] by multiply_right_division ?12 ?13
+10194: Id : 7, {_}:
+ right_division (multiply ?15 ?16) ?16 =>= ?15
+ [16, 15] by right_division_multiply ?15 ?16
+10194: Id : 8, {_}:
+ multiply ?18 (right_inverse ?18) =>= identity
+ [18] by right_inverse ?18
+10194: Id : 9, {_}:
+ multiply (left_inverse ?20) ?20 =>= identity
+ [20] by left_inverse ?20
+10194: Id : 10, {_}:
+ multiply (multiply ?22 (multiply ?23 ?24)) ?22
+ =?=
+ multiply (multiply ?22 ?23) (multiply ?24 ?22)
+ [24, 23, 22] by moufang1 ?22 ?23 ?24
+10194: Goal:
+10194: Id : 1, {_}:
+ multiply (multiply (multiply a b) c) b
+ =>=
+ multiply a (multiply b (multiply c b))
+ [] by prove_moufang2
+10194: Order:
+10194: nrkbo
+10194: Leaf order:
+10194: left_inverse 1 1 0
+10194: right_inverse 1 1 0
+10194: right_division 2 2 0
+10194: left_division 2 2 0
+10194: identity 4 0 0
+10194: c 2 0 2 2,1,2
+10194: multiply 20 2 6 0,2
+10194: b 4 0 4 2,1,1,2
+10194: a 2 0 2 1,1,1,2
+CLASH, statistics insufficient
+10195: Facts:
+10195: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10195: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+10195: Id : 4, {_}:
+ multiply ?6 (left_division ?6 ?7) =>= ?7
+ [7, 6] by multiply_left_division ?6 ?7
+10195: Id : 5, {_}:
+ left_division ?9 (multiply ?9 ?10) =>= ?10
+ [10, 9] by left_division_multiply ?9 ?10
+10195: Id : 6, {_}:
+ multiply (right_division ?12 ?13) ?13 =>= ?12
+ [13, 12] by multiply_right_division ?12 ?13
+10195: Id : 7, {_}:
+ right_division (multiply ?15 ?16) ?16 =>= ?15
+ [16, 15] by right_division_multiply ?15 ?16
+10195: Id : 8, {_}:
+ multiply ?18 (right_inverse ?18) =>= identity
+ [18] by right_inverse ?18
+10195: Id : 9, {_}:
+ multiply (left_inverse ?20) ?20 =>= identity
+ [20] by left_inverse ?20
+10195: Id : 10, {_}:
+ multiply (multiply ?22 (multiply ?23 ?24)) ?22
+ =>=
+ multiply (multiply ?22 ?23) (multiply ?24 ?22)
+ [24, 23, 22] by moufang1 ?22 ?23 ?24
+10195: Goal:
+10195: Id : 1, {_}:
+ multiply (multiply (multiply a b) c) b
+ =>=
+ multiply a (multiply b (multiply c b))
+ [] by prove_moufang2
+10195: Order:
+10195: kbo
+10195: Leaf order:
+10195: left_inverse 1 1 0
+10195: right_inverse 1 1 0
+10195: right_division 2 2 0
+10195: left_division 2 2 0
+10195: identity 4 0 0
+10195: c 2 0 2 2,1,2
+10195: multiply 20 2 6 0,2
+10195: b 4 0 4 2,1,1,2
+10195: a 2 0 2 1,1,1,2
+CLASH, statistics insufficient
+10196: Facts:
+10196: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10196: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+10196: Id : 4, {_}:
+ multiply ?6 (left_division ?6 ?7) =>= ?7
+ [7, 6] by multiply_left_division ?6 ?7
+10196: Id : 5, {_}:
+ left_division ?9 (multiply ?9 ?10) =>= ?10
+ [10, 9] by left_division_multiply ?9 ?10
+10196: Id : 6, {_}:
+ multiply (right_division ?12 ?13) ?13 =>= ?12
+ [13, 12] by multiply_right_division ?12 ?13
+10196: Id : 7, {_}:
+ right_division (multiply ?15 ?16) ?16 =>= ?15
+ [16, 15] by right_division_multiply ?15 ?16
+10196: Id : 8, {_}:
+ multiply ?18 (right_inverse ?18) =>= identity
+ [18] by right_inverse ?18
+10196: Id : 9, {_}:
+ multiply (left_inverse ?20) ?20 =>= identity
+ [20] by left_inverse ?20
+10196: Id : 10, {_}:
+ multiply (multiply ?22 (multiply ?23 ?24)) ?22
+ =>=
+ multiply (multiply ?22 ?23) (multiply ?24 ?22)
+ [24, 23, 22] by moufang1 ?22 ?23 ?24
+10196: Goal:
+10196: Id : 1, {_}:
+ multiply (multiply (multiply a b) c) b
+ =>=
+ multiply a (multiply b (multiply c b))
+ [] by prove_moufang2
+10196: Order:
+10196: lpo
+10196: Leaf order:
+10196: left_inverse 1 1 0
+10196: right_inverse 1 1 0
+10196: right_division 2 2 0
+10196: left_division 2 2 0
+10196: identity 4 0 0
+10196: c 2 0 2 2,1,2
+10196: multiply 20 2 6 0,2
+10196: b 4 0 4 2,1,1,2
+10196: a 2 0 2 1,1,1,2
+% SZS status Timeout for GRP200-1.p
+CLASH, statistics insufficient
+10959: Facts:
+10959: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10959: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+10959: Id : 4, {_}:
+ multiply ?6 (left_division ?6 ?7) =>= ?7
+ [7, 6] by multiply_left_division ?6 ?7
+10959: Id : 5, {_}:
+ left_division ?9 (multiply ?9 ?10) =>= ?10
+ [10, 9] by left_division_multiply ?9 ?10
+10959: Id : 6, {_}:
+ multiply (right_division ?12 ?13) ?13 =>= ?12
+ [13, 12] by multiply_right_division ?12 ?13
+10959: Id : 7, {_}:
+ right_division (multiply ?15 ?16) ?16 =>= ?15
+ [16, 15] by right_division_multiply ?15 ?16
+10959: Id : 8, {_}:
+ multiply ?18 (right_inverse ?18) =>= identity
+ [18] by right_inverse ?18
+10959: Id : 9, {_}:
+ multiply (left_inverse ?20) ?20 =>= identity
+ [20] by left_inverse ?20
+10959: Id : 10, {_}:
+ multiply (multiply (multiply ?22 ?23) ?24) ?23
+ =?=
+ multiply ?22 (multiply ?23 (multiply ?24 ?23))
+ [24, 23, 22] by moufang2 ?22 ?23 ?24
+10959: Goal:
+10959: Id : 1, {_}:
+ multiply (multiply (multiply a b) a) c
+ =>=
+ multiply a (multiply b (multiply a c))
+ [] by prove_moufang3
+10959: Order:
+10959: nrkbo
+10959: Leaf order:
+10959: left_inverse 1 1 0
+10959: right_inverse 1 1 0
+10959: right_division 2 2 0
+10959: left_division 2 2 0
+10959: identity 4 0 0
+10959: c 2 0 2 2,2
+10959: multiply 20 2 6 0,2
+10959: b 2 0 2 2,1,1,2
+10959: a 4 0 4 1,1,1,2
+CLASH, statistics insufficient
+10960: Facts:
+10960: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10960: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+10960: Id : 4, {_}:
+ multiply ?6 (left_division ?6 ?7) =>= ?7
+ [7, 6] by multiply_left_division ?6 ?7
+10960: Id : 5, {_}:
+ left_division ?9 (multiply ?9 ?10) =>= ?10
+ [10, 9] by left_division_multiply ?9 ?10
+10960: Id : 6, {_}:
+ multiply (right_division ?12 ?13) ?13 =>= ?12
+ [13, 12] by multiply_right_division ?12 ?13
+10960: Id : 7, {_}:
+ right_division (multiply ?15 ?16) ?16 =>= ?15
+ [16, 15] by right_division_multiply ?15 ?16
+10960: Id : 8, {_}:
+ multiply ?18 (right_inverse ?18) =>= identity
+ [18] by right_inverse ?18
+10960: Id : 9, {_}:
+ multiply (left_inverse ?20) ?20 =>= identity
+ [20] by left_inverse ?20
+10960: Id : 10, {_}:
+ multiply (multiply (multiply ?22 ?23) ?24) ?23
+ =>=
+ multiply ?22 (multiply ?23 (multiply ?24 ?23))
+ [24, 23, 22] by moufang2 ?22 ?23 ?24
+10960: Goal:
+10960: Id : 1, {_}:
+ multiply (multiply (multiply a b) a) c
+ =>=
+ multiply a (multiply b (multiply a c))
+ [] by prove_moufang3
+10960: Order:
+10960: kbo
+10960: Leaf order:
+10960: left_inverse 1 1 0
+10960: right_inverse 1 1 0
+10960: right_division 2 2 0
+10960: left_division 2 2 0
+10960: identity 4 0 0
+10960: c 2 0 2 2,2
+10960: multiply 20 2 6 0,2
+10960: b 2 0 2 2,1,1,2
+10960: a 4 0 4 1,1,1,2
+CLASH, statistics insufficient
+10961: Facts:
+10961: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10961: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+10961: Id : 4, {_}:
+ multiply ?6 (left_division ?6 ?7) =>= ?7
+ [7, 6] by multiply_left_division ?6 ?7
+10961: Id : 5, {_}:
+ left_division ?9 (multiply ?9 ?10) =>= ?10
+ [10, 9] by left_division_multiply ?9 ?10
+10961: Id : 6, {_}:
+ multiply (right_division ?12 ?13) ?13 =>= ?12
+ [13, 12] by multiply_right_division ?12 ?13
+10961: Id : 7, {_}:
+ right_division (multiply ?15 ?16) ?16 =>= ?15
+ [16, 15] by right_division_multiply ?15 ?16
+10961: Id : 8, {_}:
+ multiply ?18 (right_inverse ?18) =>= identity
+ [18] by right_inverse ?18
+10961: Id : 9, {_}:
+ multiply (left_inverse ?20) ?20 =>= identity
+ [20] by left_inverse ?20
+10961: Id : 10, {_}:
+ multiply (multiply (multiply ?22 ?23) ?24) ?23
+ =>=
+ multiply ?22 (multiply ?23 (multiply ?24 ?23))
+ [24, 23, 22] by moufang2 ?22 ?23 ?24
+10961: Goal:
+10961: Id : 1, {_}:
+ multiply (multiply (multiply a b) a) c
+ =>=
+ multiply a (multiply b (multiply a c))
+ [] by prove_moufang3
+10961: Order:
+10961: lpo
+10961: Leaf order:
+10961: left_inverse 1 1 0
+10961: right_inverse 1 1 0
+10961: right_division 2 2 0
+10961: left_division 2 2 0
+10961: identity 4 0 0
+10961: c 2 0 2 2,2
+10961: multiply 20 2 6 0,2
+10961: b 2 0 2 2,1,1,2
+10961: a 4 0 4 1,1,1,2
+Statistics :
+Max weight : 15
+Found proof, 24.390962s
+% SZS status Unsatisfiable for GRP201-1.p
+% SZS output start CNFRefutation for GRP201-1.p
+Id : 22, {_}: left_division ?48 (multiply ?48 ?49) =>= ?49 [49, 48] by left_division_multiply ?48 ?49
+Id : 8, {_}: multiply ?18 (right_inverse ?18) =>= identity [18] by right_inverse ?18
+Id : 6, {_}: multiply (right_division ?12 ?13) ?13 =>= ?12 [13, 12] by multiply_right_division ?12 ?13
+Id : 4, {_}: multiply ?6 (left_division ?6 ?7) =>= ?7 [7, 6] by multiply_left_division ?6 ?7
+Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+Id : 9, {_}: multiply (left_inverse ?20) ?20 =>= identity [20] by left_inverse ?20
+Id : 10, {_}: multiply (multiply (multiply ?22 ?23) ?24) ?23 =>= multiply ?22 (multiply ?23 (multiply ?24 ?23)) [24, 23, 22] by moufang2 ?22 ?23 ?24
+Id : 7, {_}: right_division (multiply ?15 ?16) ?16 =>= ?15 [16, 15] by right_division_multiply ?15 ?16
+Id : 5, {_}: left_division ?9 (multiply ?9 ?10) =>= ?10 [10, 9] by left_division_multiply ?9 ?10
+Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+Id : 54, {_}: multiply (multiply (multiply ?119 ?120) ?121) ?120 =>= multiply ?119 (multiply ?120 (multiply ?121 ?120)) [121, 120, 119] by moufang2 ?119 ?120 ?121
+Id : 55, {_}: multiply (multiply ?123 ?124) ?123 =<= multiply identity (multiply ?123 (multiply ?124 ?123)) [124, 123] by Super 54 with 2 at 1,1,2
+Id : 71, {_}: multiply (multiply ?123 ?124) ?123 =>= multiply ?123 (multiply ?124 ?123) [124, 123] by Demod 55 with 2 at 3
+Id : 897, {_}: right_division (multiply ?1221 (multiply ?1222 (multiply ?1223 ?1222))) ?1222 =>= multiply (multiply ?1221 ?1222) ?1223 [1223, 1222, 1221] by Super 7 with 10 at 1,2
+Id : 904, {_}: right_division (multiply ?1247 (multiply ?1248 identity)) ?1248 =>= multiply (multiply ?1247 ?1248) (left_inverse ?1248) [1248, 1247] by Super 897 with 9 at 2,2,1,2
+Id : 944, {_}: right_division (multiply ?1247 ?1248) ?1248 =<= multiply (multiply ?1247 ?1248) (left_inverse ?1248) [1248, 1247] by Demod 904 with 3 at 2,1,2
+Id : 945, {_}: ?1247 =<= multiply (multiply ?1247 ?1248) (left_inverse ?1248) [1248, 1247] by Demod 944 with 7 at 2
+Id : 1320, {_}: left_division (multiply ?1774 ?1775) ?1774 =>= left_inverse ?1775 [1775, 1774] by Super 5 with 945 at 2,2
+Id : 1325, {_}: left_division ?1787 ?1788 =<= left_inverse (left_division ?1788 ?1787) [1788, 1787] by Super 1320 with 4 at 1,2
+Id : 1124, {_}: ?1512 =<= multiply (multiply ?1512 ?1513) (left_inverse ?1513) [1513, 1512] by Demod 944 with 7 at 2
+Id : 1136, {_}: right_division ?1545 ?1546 =<= multiply ?1545 (left_inverse ?1546) [1546, 1545] by Super 1124 with 6 at 1,3
+Id : 1239, {_}: right_division (multiply (left_inverse ?1664) ?1665) ?1664 =<= multiply (left_inverse ?1664) (multiply ?1665 (left_inverse ?1664)) [1665, 1664] by Super 71 with 1136 at 2
+Id : 1291, {_}: right_division (multiply (left_inverse ?1664) ?1665) ?1664 =<= multiply (left_inverse ?1664) (right_division ?1665 ?1664) [1665, 1664] by Demod 1239 with 1136 at 2,3
+Id : 621, {_}: right_division (multiply ?874 (multiply ?875 ?874)) ?874 =>= multiply ?874 ?875 [875, 874] by Super 7 with 71 at 1,2
+Id : 2721, {_}: right_division (multiply (left_inverse ?3427) (multiply ?3427 (multiply ?3428 ?3427))) ?3427 =>= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3428, 3427] by Super 1291 with 621 at 2,3
+Id : 53, {_}: right_division (multiply ?115 (multiply ?116 (multiply ?117 ?116))) ?116 =>= multiply (multiply ?115 ?116) ?117 [117, 116, 115] by Super 7 with 10 at 1,2
+Id : 2757, {_}: multiply (multiply (left_inverse ?3427) ?3427) ?3428 =>= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3428, 3427] by Demod 2721 with 53 at 2
+Id : 2758, {_}: multiply identity ?3428 =<= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3427, 3428] by Demod 2757 with 9 at 1,2
+Id : 2759, {_}: ?3428 =<= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3427, 3428] by Demod 2758 with 2 at 2
+Id : 3344, {_}: left_division (left_inverse ?4254) ?4255 =>= multiply ?4254 ?4255 [4255, 4254] by Super 5 with 2759 at 2,2
+Id : 46, {_}: left_division (left_inverse ?101) identity =>= ?101 [101] by Super 5 with 9 at 2,2
+Id : 40, {_}: left_division ?91 identity =>= right_inverse ?91 [91] by Super 5 with 8 at 2,2
+Id : 425, {_}: right_inverse (left_inverse ?101) =>= ?101 [101] by Demod 46 with 40 at 2
+Id : 626, {_}: multiply (multiply ?892 ?893) ?892 =>= multiply ?892 (multiply ?893 ?892) [893, 892] by Demod 55 with 2 at 3
+Id : 633, {_}: multiply identity ?911 =<= multiply ?911 (multiply (right_inverse ?911) ?911) [911] by Super 626 with 8 at 1,2
+Id : 654, {_}: ?911 =<= multiply ?911 (multiply (right_inverse ?911) ?911) [911] by Demod 633 with 2 at 2
+Id : 727, {_}: left_division ?1053 ?1053 =<= multiply (right_inverse ?1053) ?1053 [1053] by Super 5 with 654 at 2,2
+Id : 24, {_}: left_division ?53 ?53 =>= identity [53] by Super 22 with 3 at 2,2
+Id : 754, {_}: identity =<= multiply (right_inverse ?1053) ?1053 [1053] by Demod 727 with 24 at 2
+Id : 784, {_}: right_division identity ?1115 =>= right_inverse ?1115 [1115] by Super 7 with 754 at 1,2
+Id : 45, {_}: right_division identity ?99 =>= left_inverse ?99 [99] by Super 7 with 9 at 1,2
+Id : 808, {_}: left_inverse ?1115 =<= right_inverse ?1115 [1115] by Demod 784 with 45 at 2
+Id : 829, {_}: left_inverse (left_inverse ?101) =>= ?101 [101] by Demod 425 with 808 at 2
+Id : 3348, {_}: left_division ?4266 ?4267 =<= multiply (left_inverse ?4266) ?4267 [4267, 4266] by Super 3344 with 829 at 1,2
+Id : 3417, {_}: multiply (multiply (left_division ?4342 ?4343) ?4344) ?4343 =<= multiply (left_inverse ?4342) (multiply ?4343 (multiply ?4344 ?4343)) [4344, 4343, 4342] by Super 10 with 3348 at 1,1,2
+Id : 3495, {_}: multiply (multiply (left_division ?4342 ?4343) ?4344) ?4343 =>= left_division ?4342 (multiply ?4343 (multiply ?4344 ?4343)) [4344, 4343, 4342] by Demod 3417 with 3348 at 3
+Id : 3351, {_}: left_division (left_division ?4274 ?4275) ?4276 =<= multiply (left_division ?4275 ?4274) ?4276 [4276, 4275, 4274] by Super 3344 with 1325 at 1,2
+Id : 9541, {_}: multiply (left_division (left_division ?4343 ?4342) ?4344) ?4343 =>= left_division ?4342 (multiply ?4343 (multiply ?4344 ?4343)) [4344, 4342, 4343] by Demod 3495 with 3351 at 1,2
+Id : 9542, {_}: left_division (left_division ?4344 (left_division ?4343 ?4342)) ?4343 =>= left_division ?4342 (multiply ?4343 (multiply ?4344 ?4343)) [4342, 4343, 4344] by Demod 9541 with 3351 at 2
+Id : 9554, {_}: left_division ?10951 (left_division ?10952 (left_division ?10951 ?10953)) =<= left_inverse (left_division ?10953 (multiply ?10951 (multiply ?10952 ?10951))) [10953, 10952, 10951] by Super 1325 with 9542 at 1,3
+Id : 27037, {_}: left_division ?28025 (left_division ?28026 (left_division ?28025 ?28027)) =<= left_division (multiply ?28025 (multiply ?28026 ?28025)) ?28027 [28027, 28026, 28025] by Demod 9554 with 1325 at 3
+Id : 27055, {_}: left_division (left_inverse ?28099) (left_division ?28100 (left_division (left_inverse ?28099) ?28101)) =>= left_division (multiply (left_inverse ?28099) (right_division ?28100 ?28099)) ?28101 [28101, 28100, 28099] by Super 27037 with 1136 at 2,1,3
+Id : 3143, {_}: left_division (left_inverse ?4011) ?4012 =>= multiply ?4011 ?4012 [4012, 4011] by Super 5 with 2759 at 2,2
+Id : 27191, {_}: multiply ?28099 (left_division ?28100 (left_division (left_inverse ?28099) ?28101)) =>= left_division (multiply (left_inverse ?28099) (right_division ?28100 ?28099)) ?28101 [28101, 28100, 28099] by Demod 27055 with 3143 at 2
+Id : 27192, {_}: multiply ?28099 (left_division ?28100 (left_division (left_inverse ?28099) ?28101)) =>= left_division (left_division ?28099 (right_division ?28100 ?28099)) ?28101 [28101, 28100, 28099] by Demod 27191 with 3348 at 1,3
+Id : 1117, {_}: right_division ?1491 (left_inverse ?1492) =>= multiply ?1491 ?1492 [1492, 1491] by Super 7 with 945 at 1,2
+Id : 1524, {_}: right_division ?2086 (left_division ?2087 ?2088) =<= multiply ?2086 (left_division ?2088 ?2087) [2088, 2087, 2086] by Super 1117 with 1325 at 2,2
+Id : 27193, {_}: right_division ?28099 (left_division (left_division (left_inverse ?28099) ?28101) ?28100) =>= left_division (left_division ?28099 (right_division ?28100 ?28099)) ?28101 [28100, 28101, 28099] by Demod 27192 with 1524 at 2
+Id : 3400, {_}: right_division (left_division ?1664 ?1665) ?1664 =<= multiply (left_inverse ?1664) (right_division ?1665 ?1664) [1665, 1664] by Demod 1291 with 3348 at 1,2
+Id : 3401, {_}: right_division (left_division ?1664 ?1665) ?1664 =<= left_division ?1664 (right_division ?1665 ?1664) [1665, 1664] by Demod 3400 with 3348 at 3
+Id : 27194, {_}: right_division ?28099 (left_division (left_division (left_inverse ?28099) ?28101) ?28100) =>= left_division (right_division (left_division ?28099 ?28100) ?28099) ?28101 [28100, 28101, 28099] by Demod 27193 with 3401 at 1,3
+Id : 40132, {_}: right_division ?42719 (left_division (multiply ?42719 ?42720) ?42721) =<= left_division (right_division (left_division ?42719 ?42721) ?42719) ?42720 [42721, 42720, 42719] by Demod 27194 with 3143 at 1,2,2
+Id : 1118, {_}: left_division (multiply ?1494 ?1495) ?1494 =>= left_inverse ?1495 [1495, 1494] by Super 5 with 945 at 2,2
+Id : 3133, {_}: left_division ?3978 (left_inverse ?3979) =>= left_inverse (multiply ?3979 ?3978) [3979, 3978] by Super 1118 with 2759 at 1,2
+Id : 40144, {_}: right_division ?42768 (left_division (multiply ?42768 ?42769) (left_inverse ?42770)) =<= left_division (right_division (left_inverse (multiply ?42770 ?42768)) ?42768) ?42769 [42770, 42769, 42768] by Super 40132 with 3133 at 1,1,3
+Id : 40468, {_}: right_division ?42768 (left_inverse (multiply ?42770 (multiply ?42768 ?42769))) =<= left_division (right_division (left_inverse (multiply ?42770 ?42768)) ?42768) ?42769 [42769, 42770, 42768] by Demod 40144 with 3133 at 2,2
+Id : 3414, {_}: right_division (left_inverse ?4334) ?4335 =<= left_division ?4334 (left_inverse ?4335) [4335, 4334] by Super 1136 with 3348 at 3
+Id : 3502, {_}: right_division (left_inverse ?4334) ?4335 =>= left_inverse (multiply ?4335 ?4334) [4335, 4334] by Demod 3414 with 3133 at 3
+Id : 40469, {_}: right_division ?42768 (left_inverse (multiply ?42770 (multiply ?42768 ?42769))) =<= left_division (left_inverse (multiply ?42768 (multiply ?42770 ?42768))) ?42769 [42769, 42770, 42768] by Demod 40468 with 3502 at 1,3
+Id : 40470, {_}: multiply ?42768 (multiply ?42770 (multiply ?42768 ?42769)) =<= left_division (left_inverse (multiply ?42768 (multiply ?42770 ?42768))) ?42769 [42769, 42770, 42768] by Demod 40469 with 1117 at 2
+Id : 40471, {_}: multiply ?42768 (multiply ?42770 (multiply ?42768 ?42769)) =<= multiply (multiply ?42768 (multiply ?42770 ?42768)) ?42769 [42769, 42770, 42768] by Demod 40470 with 3143 at 3
+Id : 50862, {_}: multiply a (multiply b (multiply a c)) =?= multiply a (multiply b (multiply a c)) [] by Demod 50861 with 40471 at 2
+Id : 50861, {_}: multiply (multiply a (multiply b a)) c =>= multiply a (multiply b (multiply a c)) [] by Demod 1 with 71 at 1,2
+Id : 1, {_}: multiply (multiply (multiply a b) a) c =>= multiply a (multiply b (multiply a c)) [] by prove_moufang3
+% SZS output end CNFRefutation for GRP201-1.p
+10960: solved GRP201-1.p in 12.208762 using kbo
+10960: status Unsatisfiable for GRP201-1.p
+CLASH, statistics insufficient
+10977: Facts:
+10977: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10977: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+10977: Id : 4, {_}:
+ multiply ?6 (left_division ?6 ?7) =>= ?7
+ [7, 6] by multiply_left_division ?6 ?7
+10977: Id : 5, {_}:
+ left_division ?9 (multiply ?9 ?10) =>= ?10
+ [10, 9] by left_division_multiply ?9 ?10
+10977: Id : 6, {_}:
+ multiply (right_division ?12 ?13) ?13 =>= ?12
+ [13, 12] by multiply_right_division ?12 ?13
+10977: Id : 7, {_}:
+ right_division (multiply ?15 ?16) ?16 =>= ?15
+ [16, 15] by right_division_multiply ?15 ?16
+10977: Id : 8, {_}:
+ multiply ?18 (right_inverse ?18) =>= identity
+ [18] by right_inverse ?18
+10977: Id : 9, {_}:
+ multiply (left_inverse ?20) ?20 =>= identity
+ [20] by left_inverse ?20
+10977: Id : 10, {_}:
+ multiply (multiply (multiply ?22 ?23) ?22) ?24
+ =?=
+ multiply ?22 (multiply ?23 (multiply ?22 ?24))
+ [24, 23, 22] by moufang3 ?22 ?23 ?24
+10977: Goal:
+10977: Id : 1, {_}:
+ multiply (multiply a (multiply b c)) a
+ =>=
+ multiply (multiply a b) (multiply c a)
+ [] by prove_moufang1
+10977: Order:
+10977: nrkbo
+10977: Leaf order:
+10977: left_inverse 1 1 0
+10977: right_inverse 1 1 0
+10977: right_division 2 2 0
+10977: left_division 2 2 0
+10977: identity 4 0 0
+10977: multiply 20 2 6 0,2
+10977: c 2 0 2 2,2,1,2
+10977: b 2 0 2 1,2,1,2
+10977: a 4 0 4 1,1,2
+CLASH, statistics insufficient
+10978: Facts:
+10978: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10978: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+10978: Id : 4, {_}:
+ multiply ?6 (left_division ?6 ?7) =>= ?7
+ [7, 6] by multiply_left_division ?6 ?7
+10978: Id : 5, {_}:
+ left_division ?9 (multiply ?9 ?10) =>= ?10
+ [10, 9] by left_division_multiply ?9 ?10
+10978: Id : 6, {_}:
+ multiply (right_division ?12 ?13) ?13 =>= ?12
+ [13, 12] by multiply_right_division ?12 ?13
+10978: Id : 7, {_}:
+ right_division (multiply ?15 ?16) ?16 =>= ?15
+ [16, 15] by right_division_multiply ?15 ?16
+10978: Id : 8, {_}:
+ multiply ?18 (right_inverse ?18) =>= identity
+ [18] by right_inverse ?18
+10978: Id : 9, {_}:
+ multiply (left_inverse ?20) ?20 =>= identity
+ [20] by left_inverse ?20
+10978: Id : 10, {_}:
+ multiply (multiply (multiply ?22 ?23) ?22) ?24
+ =>=
+ multiply ?22 (multiply ?23 (multiply ?22 ?24))
+ [24, 23, 22] by moufang3 ?22 ?23 ?24
+10978: Goal:
+10978: Id : 1, {_}:
+ multiply (multiply a (multiply b c)) a
+ =>=
+ multiply (multiply a b) (multiply c a)
+ [] by prove_moufang1
+10978: Order:
+10978: kbo
+10978: Leaf order:
+10978: left_inverse 1 1 0
+10978: right_inverse 1 1 0
+10978: right_division 2 2 0
+10978: left_division 2 2 0
+10978: identity 4 0 0
+10978: multiply 20 2 6 0,2
+10978: c 2 0 2 2,2,1,2
+10978: b 2 0 2 1,2,1,2
+10978: a 4 0 4 1,1,2
+CLASH, statistics insufficient
+10979: Facts:
+10979: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+10979: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+10979: Id : 4, {_}:
+ multiply ?6 (left_division ?6 ?7) =>= ?7
+ [7, 6] by multiply_left_division ?6 ?7
+10979: Id : 5, {_}:
+ left_division ?9 (multiply ?9 ?10) =>= ?10
+ [10, 9] by left_division_multiply ?9 ?10
+10979: Id : 6, {_}:
+ multiply (right_division ?12 ?13) ?13 =>= ?12
+ [13, 12] by multiply_right_division ?12 ?13
+10979: Id : 7, {_}:
+ right_division (multiply ?15 ?16) ?16 =>= ?15
+ [16, 15] by right_division_multiply ?15 ?16
+10979: Id : 8, {_}:
+ multiply ?18 (right_inverse ?18) =>= identity
+ [18] by right_inverse ?18
+10979: Id : 9, {_}:
+ multiply (left_inverse ?20) ?20 =>= identity
+ [20] by left_inverse ?20
+10979: Id : 10, {_}:
+ multiply (multiply (multiply ?22 ?23) ?22) ?24
+ =>=
+ multiply ?22 (multiply ?23 (multiply ?22 ?24))
+ [24, 23, 22] by moufang3 ?22 ?23 ?24
+10979: Goal:
+10979: Id : 1, {_}:
+ multiply (multiply a (multiply b c)) a
+ =>=
+ multiply (multiply a b) (multiply c a)
+ [] by prove_moufang1
+10979: Order:
+10979: lpo
+10979: Leaf order:
+10979: left_inverse 1 1 0
+10979: right_inverse 1 1 0
+10979: right_division 2 2 0
+10979: left_division 2 2 0
+10979: identity 4 0 0
+10979: multiply 20 2 6 0,2
+10979: c 2 0 2 2,2,1,2
+10979: b 2 0 2 1,2,1,2
+10979: a 4 0 4 1,1,2
+Statistics :
+Max weight : 20
+Found proof, 29.848585s
+% SZS status Unsatisfiable for GRP202-1.p
+% SZS output start CNFRefutation for GRP202-1.p
+Id : 56, {_}: multiply (multiply (multiply ?126 ?127) ?126) ?128 =>= multiply ?126 (multiply ?127 (multiply ?126 ?128)) [128, 127, 126] by moufang3 ?126 ?127 ?128
+Id : 4, {_}: multiply ?6 (left_division ?6 ?7) =>= ?7 [7, 6] by multiply_left_division ?6 ?7
+Id : 9, {_}: multiply (left_inverse ?20) ?20 =>= identity [20] by left_inverse ?20
+Id : 22, {_}: left_division ?48 (multiply ?48 ?49) =>= ?49 [49, 48] by left_division_multiply ?48 ?49
+Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+Id : 5, {_}: left_division ?9 (multiply ?9 ?10) =>= ?10 [10, 9] by left_division_multiply ?9 ?10
+Id : 8, {_}: multiply ?18 (right_inverse ?18) =>= identity [18] by right_inverse ?18
+Id : 6, {_}: multiply (right_division ?12 ?13) ?13 =>= ?12 [13, 12] by multiply_right_division ?12 ?13
+Id : 7, {_}: right_division (multiply ?15 ?16) ?16 =>= ?15 [16, 15] by right_division_multiply ?15 ?16
+Id : 10, {_}: multiply (multiply (multiply ?22 ?23) ?22) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by moufang3 ?22 ?23 ?24
+Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+Id : 53, {_}: multiply ?115 (multiply ?116 (multiply ?115 identity)) =>= multiply (multiply ?115 ?116) ?115 [116, 115] by Super 3 with 10 at 2
+Id : 70, {_}: multiply ?115 (multiply ?116 ?115) =<= multiply (multiply ?115 ?116) ?115 [116, 115] by Demod 53 with 3 at 2,2,2
+Id : 894, {_}: right_division (multiply ?1099 (multiply ?1100 ?1099)) ?1099 =>= multiply ?1099 ?1100 [1100, 1099] by Super 7 with 70 at 1,2
+Id : 900, {_}: right_division (multiply ?1115 ?1116) ?1115 =<= multiply ?1115 (right_division ?1116 ?1115) [1116, 1115] by Super 894 with 6 at 2,1,2
+Id : 55, {_}: right_division (multiply ?122 (multiply ?123 (multiply ?122 ?124))) ?124 =>= multiply (multiply ?122 ?123) ?122 [124, 123, 122] by Super 7 with 10 at 1,2
+Id : 2577, {_}: right_division (multiply ?3478 (multiply ?3479 (multiply ?3478 ?3480))) ?3480 =>= multiply ?3478 (multiply ?3479 ?3478) [3480, 3479, 3478] by Demod 55 with 70 at 3
+Id : 647, {_}: multiply ?831 (multiply ?832 ?831) =<= multiply (multiply ?831 ?832) ?831 [832, 831] by Demod 53 with 3 at 2,2,2
+Id : 654, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= multiply identity ?850 [850] by Super 647 with 8 at 1,3
+Id : 677, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= ?850 [850] by Demod 654 with 2 at 3
+Id : 765, {_}: left_division ?991 ?991 =<= multiply (right_inverse ?991) ?991 [991] by Super 5 with 677 at 2,2
+Id : 24, {_}: left_division ?53 ?53 =>= identity [53] by Super 22 with 3 at 2,2
+Id : 791, {_}: identity =<= multiply (right_inverse ?991) ?991 [991] by Demod 765 with 24 at 2
+Id : 819, {_}: right_division identity ?1047 =>= right_inverse ?1047 [1047] by Super 7 with 791 at 1,2
+Id : 45, {_}: right_division identity ?99 =>= left_inverse ?99 [99] by Super 7 with 9 at 1,2
+Id : 846, {_}: left_inverse ?1047 =<= right_inverse ?1047 [1047] by Demod 819 with 45 at 2
+Id : 861, {_}: multiply ?18 (left_inverse ?18) =>= identity [18] by Demod 8 with 846 at 2,2
+Id : 2586, {_}: right_division (multiply ?3513 (multiply ?3514 identity)) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Super 2577 with 861 at 2,2,1,2
+Id : 2645, {_}: right_division (multiply ?3513 ?3514) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Demod 2586 with 3 at 2,1,2
+Id : 2833, {_}: right_division (multiply (left_inverse ?3781) (multiply ?3781 ?3782)) (left_inverse ?3781) =>= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Super 900 with 2645 at 2,3
+Id : 52, {_}: multiply ?111 (multiply ?112 (multiply ?111 (left_division (multiply (multiply ?111 ?112) ?111) ?113))) =>= ?113 [113, 112, 111] by Super 4 with 10 at 2
+Id : 969, {_}: multiply ?1216 (multiply ?1217 (multiply ?1216 (left_division (multiply ?1216 (multiply ?1217 ?1216)) ?1218))) =>= ?1218 [1218, 1217, 1216] by Demod 52 with 70 at 1,2,2,2,2
+Id : 976, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division (multiply ?1242 identity) ?1243))) =>= ?1243 [1243, 1242] by Super 969 with 9 at 2,1,2,2,2,2
+Id : 1036, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division ?1242 ?1243))) =>= ?1243 [1243, 1242] by Demod 976 with 3 at 1,2,2,2,2
+Id : 1037, {_}: multiply ?1242 (multiply (left_inverse ?1242) ?1243) =>= ?1243 [1243, 1242] by Demod 1036 with 4 at 2,2,2
+Id : 1172, {_}: left_division ?1548 ?1549 =<= multiply (left_inverse ?1548) ?1549 [1549, 1548] by Super 5 with 1037 at 2,2
+Id : 2879, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =<= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2833 with 1172 at 1,2
+Id : 2880, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =>= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2879 with 1172 at 3
+Id : 2881, {_}: right_division ?3782 (left_inverse ?3781) =<= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3781, 3782] by Demod 2880 with 5 at 1,2
+Id : 2882, {_}: right_division ?3782 (left_inverse ?3781) =>= multiply ?3782 ?3781 [3781, 3782] by Demod 2881 with 5 at 3
+Id : 1389, {_}: right_division (left_division ?1827 ?1828) ?1828 =>= left_inverse ?1827 [1828, 1827] by Super 7 with 1172 at 1,2
+Id : 28, {_}: left_division (right_division ?62 ?63) ?62 =>= ?63 [63, 62] by Super 5 with 6 at 2,2
+Id : 1395, {_}: right_division ?1844 ?1845 =<= left_inverse (right_division ?1845 ?1844) [1845, 1844] by Super 1389 with 28 at 1,2
+Id : 3679, {_}: multiply (multiply ?4879 ?4880) ?4881 =<= multiply ?4880 (multiply (left_division ?4880 ?4879) (multiply ?4880 ?4881)) [4881, 4880, 4879] by Super 56 with 4 at 1,1,2
+Id : 3684, {_}: multiply (multiply ?4897 ?4898) (left_division ?4898 ?4899) =>= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Super 3679 with 4 at 2,2,3
+Id : 2950, {_}: right_division (left_inverse ?3910) ?3911 =>= left_inverse (multiply ?3911 ?3910) [3911, 3910] by Super 1395 with 2882 at 1,3
+Id : 3037, {_}: left_inverse (multiply (left_inverse ?4021) ?4022) =>= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Super 2882 with 2950 at 2
+Id : 3056, {_}: left_inverse (left_division ?4021 ?4022) =<= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Demod 3037 with 1172 at 1,2
+Id : 3057, {_}: left_inverse (left_division ?4021 ?4022) =>= left_division ?4022 ?4021 [4022, 4021] by Demod 3056 with 1172 at 3
+Id : 3222, {_}: right_division ?4224 (left_division ?4225 ?4226) =<= multiply ?4224 (left_division ?4226 ?4225) [4226, 4225, 4224] by Super 2882 with 3057 at 2,2
+Id : 8079, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Demod 3684 with 3222 at 2
+Id : 3218, {_}: left_division (left_division ?4210 ?4211) ?4212 =<= multiply (left_division ?4211 ?4210) ?4212 [4212, 4211, 4210] by Super 1172 with 3057 at 1,3
+Id : 8080, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (left_division (left_division ?4897 ?4898) ?4899) [4899, 4898, 4897] by Demod 8079 with 3218 at 2,3
+Id : 8081, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =>= right_division ?4898 (left_division ?4899 (left_division ?4897 ?4898)) [4899, 4898, 4897] by Demod 8080 with 3222 at 3
+Id : 8094, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= left_inverse (right_division ?9767 (left_division ?9766 (left_division ?9768 ?9767))) [9768, 9767, 9766] by Super 1395 with 8081 at 1,3
+Id : 8159, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= right_division (left_division ?9766 (left_division ?9768 ?9767)) ?9767 [9768, 9767, 9766] by Demod 8094 with 1395 at 3
+Id : 23778, {_}: right_division (left_division ?25246 (left_inverse ?25247)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25247, 25246] by Super 2882 with 8159 at 2
+Id : 2960, {_}: right_division ?3937 (left_inverse ?3938) =>= multiply ?3937 ?3938 [3938, 3937] by Demod 2881 with 5 at 3
+Id : 46, {_}: left_division (left_inverse ?101) identity =>= ?101 [101] by Super 5 with 9 at 2,2
+Id : 40, {_}: left_division ?91 identity =>= right_inverse ?91 [91] by Super 5 with 8 at 2,2
+Id : 426, {_}: right_inverse (left_inverse ?101) =>= ?101 [101] by Demod 46 with 40 at 2
+Id : 864, {_}: left_inverse (left_inverse ?101) =>= ?101 [101] by Demod 426 with 846 at 2
+Id : 2964, {_}: right_division ?3949 ?3950 =<= multiply ?3949 (left_inverse ?3950) [3950, 3949] by Super 2960 with 864 at 2,2
+Id : 3107, {_}: left_division ?4125 (left_inverse ?4126) =>= right_division (left_inverse ?4125) ?4126 [4126, 4125] by Super 1172 with 2964 at 3
+Id : 3145, {_}: left_division ?4125 (left_inverse ?4126) =>= left_inverse (multiply ?4126 ?4125) [4126, 4125] by Demod 3107 with 2950 at 3
+Id : 23925, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23778 with 3145 at 1,2
+Id : 23926, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23925 with 2964 at 2,2
+Id : 23927, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25248, 25246, 25247] by Demod 23926 with 3218 at 3
+Id : 23928, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23927 with 2950 at 2
+Id : 23929, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23928 with 3145 at 1,1,3
+Id : 1175, {_}: multiply ?1556 (multiply (left_inverse ?1556) ?1557) =>= ?1557 [1557, 1556] by Demod 1036 with 4 at 2,2,2
+Id : 1185, {_}: multiply ?1584 ?1585 =<= left_division (left_inverse ?1584) ?1585 [1585, 1584] by Super 1175 with 4 at 2,2
+Id : 1426, {_}: multiply (right_division ?1873 ?1874) ?1875 =>= left_division (right_division ?1874 ?1873) ?1875 [1875, 1874, 1873] by Super 1185 with 1395 at 1,3
+Id : 23930, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25248, 25247] by Demod 23929 with 1426 at 1,2
+Id : 23931, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =>= left_division (multiply (multiply ?25247 ?25248) ?25246) ?25247 [25246, 25248, 25247] by Demod 23930 with 1185 at 1,3
+Id : 37380, {_}: left_division (multiply ?37773 ?37774) (right_division ?37773 ?37775) =<= left_division (multiply (multiply ?37773 ?37775) ?37774) ?37773 [37775, 37774, 37773] by Demod 23931 with 3057 at 2
+Id : 37397, {_}: left_division (multiply ?37844 ?37845) (right_division ?37844 (left_inverse ?37846)) =>= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Super 37380 with 2964 at 1,1,3
+Id : 37604, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Demod 37397 with 2882 at 2,2
+Id : 37605, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (left_division (right_division ?37846 ?37844) ?37845) ?37844 [37846, 37845, 37844] by Demod 37604 with 1426 at 1,3
+Id : 8101, {_}: right_division (multiply ?9794 ?9795) (left_division ?9796 ?9795) =>= right_division ?9795 (left_division ?9796 (left_division ?9794 ?9795)) [9796, 9795, 9794] by Demod 8080 with 3222 at 3
+Id : 8114, {_}: right_division (multiply ?9845 (left_inverse ?9846)) (left_inverse (multiply ?9846 ?9847)) =>= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Super 8101 with 3145 at 2,2
+Id : 8186, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Demod 8114 with 2882 at 2
+Id : 8187, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8186 with 2950 at 3
+Id : 8188, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8187 with 2964 at 1,2
+Id : 8189, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9846, 9845] by Demod 8188 with 3218 at 1,3
+Id : 8190, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9845, 9846] by Demod 8189 with 1426 at 2
+Id : 8191, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) [9847, 9845, 9846] by Demod 8190 with 3057 at 3
+Id : 8192, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_inverse (multiply ?9846 ?9845)) ?9847) [9847, 9845, 9846] by Demod 8191 with 3145 at 1,2,3
+Id : 24138, {_}: left_division (right_division ?25824 ?25825) (multiply ?25824 ?25826) =>= left_division ?25824 (multiply (multiply ?25824 ?25825) ?25826) [25826, 25825, 25824] by Demod 8192 with 1185 at 2,3
+Id : 24175, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =<= left_division ?25977 (multiply (multiply ?25977 (left_inverse ?25978)) ?25979) [25979, 25978, 25977] by Super 24138 with 2882 at 1,2
+Id : 24394, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (multiply (right_division ?25977 ?25978) ?25979) [25979, 25978, 25977] by Demod 24175 with 2964 at 1,2,3
+Id : 24395, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (left_division (right_division ?25978 ?25977) ?25979) [25979, 25978, 25977] by Demod 24394 with 1426 at 2,3
+Id : 47972, {_}: left_division ?49234 (left_division (right_division ?49235 ?49234) ?49236) =<= left_division (left_division (right_division ?49236 ?49234) ?49235) ?49234 [49236, 49235, 49234] by Demod 37605 with 24395 at 2
+Id : 1255, {_}: multiply (left_inverse ?1641) (multiply ?1642 (left_inverse ?1641)) =>= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Super 70 with 1172 at 1,3
+Id : 1319, {_}: left_division ?1641 (multiply ?1642 (left_inverse ?1641)) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1255 with 1172 at 2
+Id : 3086, {_}: left_division ?1641 (right_division ?1642 ?1641) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1319 with 2964 at 2,2
+Id : 3087, {_}: left_division ?1641 (right_division ?1642 ?1641) =>= right_division (left_division ?1641 ?1642) ?1641 [1642, 1641] by Demod 3086 with 2964 at 3
+Id : 48040, {_}: left_division ?49524 (left_division (right_division (right_division ?49525 (right_division ?49526 ?49524)) ?49524) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Super 47972 with 3087 at 1,3
+Id : 59, {_}: multiply (multiply ?136 ?137) ?138 =<= multiply ?137 (multiply (left_division ?137 ?136) (multiply ?137 ?138)) [138, 137, 136] by Super 56 with 4 at 1,1,2
+Id : 3668, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= multiply (left_division ?4830 ?4831) (multiply ?4830 ?4832) [4832, 4831, 4830] by Super 5 with 59 at 2,2
+Id : 7892, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= left_division (left_division ?4831 ?4830) (multiply ?4830 ?4832) [4832, 4831, 4830] by Demod 3668 with 3218 at 3
+Id : 7900, {_}: left_inverse (left_division ?9488 (multiply (multiply ?9489 ?9488) ?9490)) =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9489, 9488] by Super 3057 with 7892 at 1,2
+Id : 7969, {_}: left_division (multiply (multiply ?9489 ?9488) ?9490) ?9488 =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9488, 9489] by Demod 7900 with 3057 at 2
+Id : 22647, {_}: left_division (multiply (left_inverse ?23598) ?23599) (left_division ?23600 (left_inverse ?23598)) =>= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Super 3145 with 7969 at 2
+Id : 22730, {_}: left_division (left_division ?23598 ?23599) (left_division ?23600 (left_inverse ?23598)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22647 with 1172 at 1,2
+Id : 22731, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22730 with 3145 at 2,2
+Id : 22732, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23600, 23599, 23598] by Demod 22731 with 2964 at 1,2,1,3
+Id : 22733, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23599, 23600, 23598] by Demod 22732 with 3145 at 2
+Id : 22734, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22733 with 1426 at 2,1,3
+Id : 22735, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =<= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22734 with 3222 at 1,2
+Id : 22736, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =>= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23599, 23600, 23598] by Demod 22735 with 3222 at 1,3
+Id : 22737, {_}: right_division (left_division ?23599 ?23598) (multiply ?23598 ?23600) =<= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23600, 23598, 23599] by Demod 22736 with 1395 at 2
+Id : 33406, {_}: right_division (left_division ?33402 ?33403) (multiply ?33403 ?33404) =<= right_division (left_division ?33402 (right_division ?33403 ?33404)) ?33403 [33404, 33403, 33402] by Demod 22737 with 1395 at 3
+Id : 33487, {_}: right_division (left_division (left_inverse ?33737) ?33738) (multiply ?33738 ?33739) =>= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Super 33406 with 1185 at 1,3
+Id : 33773, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Demod 33487 with 1185 at 1,2
+Id : 2967, {_}: right_division ?3957 (right_division ?3958 ?3959) =<= multiply ?3957 (right_division ?3959 ?3958) [3959, 3958, 3957] by Super 2960 with 1395 at 2,2
+Id : 33774, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (right_division ?33737 (right_division ?33739 ?33738)) ?33738 [33739, 33738, 33737] by Demod 33773 with 2967 at 1,3
+Id : 48410, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Demod 48040 with 33774 at 1,2,2
+Id : 640, {_}: multiply (multiply ?22 (multiply ?23 ?22)) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by Demod 10 with 70 at 1,2
+Id : 1260, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =<= multiply ?1655 (multiply (left_inverse ?1656) (multiply ?1655 ?1657)) [1657, 1656, 1655] by Super 640 with 1172 at 2,1,2
+Id : 1315, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1260 with 1172 at 2,3
+Id : 5054, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1315 with 3222 at 1,2
+Id : 5055, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5054 with 3222 at 3
+Id : 5056, {_}: left_division (right_division (left_division ?1655 ?1656) ?1655) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5055 with 1426 at 2
+Id : 48411, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49526, 49525, 49524] by Demod 48410 with 5056 at 3
+Id : 3100, {_}: multiply (multiply (left_inverse ?4103) (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Super 640 with 2964 at 2,1,2
+Id : 3156, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3100 with 1172 at 1,2
+Id : 3157, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3156 with 1172 at 3
+Id : 3158, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3157 with 3087 at 1,2
+Id : 3159, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3158 with 1172 at 2,2,3
+Id : 3160, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3159 with 1426 at 2
+Id : 7103, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (right_division ?4104 (left_division ?4105 ?4103)) [4105, 4104, 4103] by Demod 3160 with 3222 at 2,3
+Id : 7119, {_}: left_division ?8435 (right_division ?8436 (left_division (left_inverse ?8437) ?8435)) =>= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Super 3145 with 7103 at 2
+Id : 7221, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Demod 7119 with 1185 at 2,2,2
+Id : 7222, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (right_division ?8437 (right_division (left_division ?8435 ?8436) ?8435)) [8437, 8436, 8435] by Demod 7221 with 2967 at 1,3
+Id : 7223, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =>= right_division (right_division (left_division ?8435 ?8436) ?8435) ?8437 [8437, 8436, 8435] by Demod 7222 with 1395 at 3
+Id : 21525, {_}: left_inverse (right_division (right_division (left_division ?22100 ?22101) ?22100) ?22102) =>= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22102, 22101, 22100] by Super 3057 with 7223 at 1,2
+Id : 21646, {_}: right_division ?22102 (right_division (left_division ?22100 ?22101) ?22100) =<= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22101, 22100, 22102] by Demod 21525 with 1395 at 2
+Id : 48412, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49525, 49526, 49524] by Demod 48411 with 21646 at 2,2
+Id : 48413, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49525, 49526, 49524] by Demod 48412 with 1426 at 1,2,3
+Id : 3103, {_}: left_division ?4114 (right_division ?4114 ?4115) =>= left_inverse ?4115 [4115, 4114] by Super 5 with 2964 at 2,2
+Id : 48414, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =<= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49524, 49525, 49526] by Demod 48413 with 3103 at 2
+Id : 48415, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48414 with 28 at 1,2,3
+Id : 48416, {_}: right_division ?49526 (left_division ?49526 (multiply ?49525 ?49524)) =<= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48415 with 1395 at 2
+Id : 52586, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= left_inverse (right_division ?54688 (left_division ?54688 (multiply ?54689 ?54690))) [54690, 54689, 54688] by Super 1395 with 48416 at 1,3
+Id : 52816, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= right_division (left_division ?54688 (multiply ?54689 ?54690)) ?54688 [54690, 54689, 54688] by Demod 52586 with 1395 at 3
+Id : 55129, {_}: right_division (left_division (left_inverse ?57654) ?57655) (right_division (left_inverse ?57654) ?57656) =>= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Super 2882 with 52816 at 2
+Id : 55322, {_}: right_division (multiply ?57654 ?57655) (right_division (left_inverse ?57654) ?57656) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55129 with 1185 at 1,2
+Id : 55323, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55322 with 2950 at 2,2
+Id : 55324, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55323 with 3218 at 3
+Id : 55325, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55324 with 2882 at 2
+Id : 55326, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_inverse (multiply ?57654 (multiply ?57655 ?57656))) ?57654 [57656, 57655, 57654] by Demod 55325 with 3145 at 1,3
+Id : 55327, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= multiply (multiply ?57654 (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55326 with 1185 at 3
+Id : 55328, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =>= multiply ?57654 (multiply (multiply ?57655 ?57656) ?57654) [57656, 57655, 57654] by Demod 55327 with 70 at 3
+Id : 57081, {_}: multiply a (multiply (multiply b c) a) =?= multiply a (multiply (multiply b c) a) [] by Demod 57080 with 55328 at 3
+Id : 57080, {_}: multiply a (multiply (multiply b c) a) =<= multiply (multiply a b) (multiply c a) [] by Demod 1 with 70 at 2
+Id : 1, {_}: multiply (multiply a (multiply b c)) a =>= multiply (multiply a b) (multiply c a) [] by prove_moufang1
+% SZS output end CNFRefutation for GRP202-1.p
+10978: solved GRP202-1.p in 14.864928 using kbo
+10978: status Unsatisfiable for GRP202-1.p
+NO CLASH, using fixed ground order
+10984: Facts:
+10984: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
+ (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
+ =>=
+ ?4
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+10984: Goal:
+10984: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+10984: Order:
+10984: nrkbo
+10984: Leaf order:
+10984: a2 2 0 2 2,2
+10984: multiply 8 2 2 0,2
+10984: inverse 6 1 1 0,1,1,2
+10984: b2 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+10985: Facts:
+10985: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
+ (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
+ =>=
+ ?4
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+10985: Goal:
+10985: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+10985: Order:
+10985: kbo
+10985: Leaf order:
+10985: a2 2 0 2 2,2
+10985: multiply 8 2 2 0,2
+10985: inverse 6 1 1 0,1,1,2
+10985: b2 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+10986: Facts:
+10986: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
+ (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
+ =>=
+ ?4
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+10986: Goal:
+10986: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+10986: Order:
+10986: lpo
+10986: Leaf order:
+10986: a2 2 0 2 2,2
+10986: multiply 8 2 2 0,2
+10986: inverse 6 1 1 0,1,1,2
+10986: b2 2 0 2 1,1,1,2
+% SZS status Timeout for GRP404-1.p
+NO CLASH, using fixed ground order
+11033: Facts:
+11033: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
+ (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
+ =>=
+ ?4
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+11033: Goal:
+11033: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+11033: Order:
+11033: nrkbo
+11033: Leaf order:
+11033: inverse 5 1 0
+11033: c3 2 0 2 2,2
+11033: multiply 10 2 4 0,2
+11033: b3 2 0 2 2,1,2
+11033: a3 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+11034: Facts:
+11034: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
+ (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
+ =>=
+ ?4
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+11034: Goal:
+11034: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+11034: Order:
+11034: kbo
+11034: Leaf order:
+11034: inverse 5 1 0
+11034: c3 2 0 2 2,2
+11034: multiply 10 2 4 0,2
+11034: b3 2 0 2 2,1,2
+11034: a3 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+11035: Facts:
+11035: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
+ (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
+ =>=
+ ?4
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+11035: Goal:
+11035: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+11035: Order:
+11035: lpo
+11035: Leaf order:
+11035: inverse 5 1 0
+11035: c3 2 0 2 2,2
+11035: multiply 10 2 4 0,2
+11035: b3 2 0 2 2,1,2
+11035: a3 2 0 2 1,1,2
+% SZS status Timeout for GRP405-1.p
+NO CLASH, using fixed ground order
+11052: Facts:
+11052: Id : 2, {_}:
+ multiply
+ (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
+ (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+11052: Goal:
+11052: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+11052: Order:
+11052: nrkbo
+11052: Leaf order:
+11052: a2 2 0 2 2,2
+11052: multiply 8 2 2 0,2
+11052: inverse 6 1 1 0,1,1,2
+11052: b2 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+11053: Facts:
+11053: Id : 2, {_}:
+ multiply
+ (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
+ (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+11053: Goal:
+11053: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+11053: Order:
+11053: kbo
+11053: Leaf order:
+11053: a2 2 0 2 2,2
+11053: multiply 8 2 2 0,2
+11053: inverse 6 1 1 0,1,1,2
+11053: b2 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+11054: Facts:
+11054: Id : 2, {_}:
+ multiply
+ (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
+ (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+11054: Goal:
+11054: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+11054: Order:
+11054: lpo
+11054: Leaf order:
+11054: a2 2 0 2 2,2
+11054: multiply 8 2 2 0,2
+11054: inverse 6 1 1 0,1,1,2
+11054: b2 2 0 2 1,1,1,2
+% SZS status Timeout for GRP410-1.p
+NO CLASH, using fixed ground order
+11087: Facts:
+11087: Id : 2, {_}:
+ multiply
+ (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
+ (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+11087: Goal:
+11087: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+11087: Order:
+11087: nrkbo
+11087: Leaf order:
+11087: inverse 5 1 0
+11087: c3 2 0 2 2,2
+11087: multiply 10 2 4 0,2
+11087: b3 2 0 2 2,1,2
+11087: a3 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+11088: Facts:
+11088: Id : 2, {_}:
+ multiply
+ (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
+ (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+11088: Goal:
+11088: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+11088: Order:
+11088: kbo
+11088: Leaf order:
+11088: inverse 5 1 0
+11088: c3 2 0 2 2,2
+11088: multiply 10 2 4 0,2
+11088: b3 2 0 2 2,1,2
+11088: a3 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+11089: Facts:
+11089: Id : 2, {_}:
+ multiply
+ (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
+ (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+11089: Goal:
+11089: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+11089: Order:
+11089: lpo
+11089: Leaf order:
+11089: inverse 5 1 0
+11089: c3 2 0 2 2,2
+11089: multiply 10 2 4 0,2
+11089: b3 2 0 2 2,1,2
+11089: a3 2 0 2 1,1,2
+% SZS status Timeout for GRP411-1.p
+NO CLASH, using fixed ground order
+11106: Facts:
+11106: Id : 2, {_}:
+ inverse
+ (multiply
+ (inverse
+ (multiply ?2
+ (inverse
+ (multiply (inverse ?3)
+ (inverse
+ (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
+ (multiply ?2 ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+11106: Goal:
+11106: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+11106: Order:
+11106: nrkbo
+11106: Leaf order:
+11106: a2 2 0 2 2,2
+11106: multiply 8 2 2 0,2
+11106: inverse 8 1 1 0,1,1,2
+11106: b2 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+11107: Facts:
+11107: Id : 2, {_}:
+ inverse
+ (multiply
+ (inverse
+ (multiply ?2
+ (inverse
+ (multiply (inverse ?3)
+ (inverse
+ (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
+ (multiply ?2 ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+11107: Goal:
+11107: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+11107: Order:
+11107: kbo
+11107: Leaf order:
+11107: a2 2 0 2 2,2
+11107: multiply 8 2 2 0,2
+11107: inverse 8 1 1 0,1,1,2
+11107: b2 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+11108: Facts:
+11108: Id : 2, {_}:
+ inverse
+ (multiply
+ (inverse
+ (multiply ?2
+ (inverse
+ (multiply (inverse ?3)
+ (inverse
+ (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
+ (multiply ?2 ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+11108: Goal:
+11108: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+11108: Order:
+11108: lpo
+11108: Leaf order:
+11108: a2 2 0 2 2,2
+11108: multiply 8 2 2 0,2
+11108: inverse 8 1 1 0,1,1,2
+11108: b2 2 0 2 1,1,1,2
+% SZS status Timeout for GRP419-1.p
+NO CLASH, using fixed ground order
+11140: Facts:
+11140: Id : 2, {_}:
+ inverse
+ (multiply
+ (inverse
+ (multiply ?2
+ (inverse
+ (multiply (inverse ?3)
+ (multiply (inverse ?4)
+ (inverse (multiply (inverse ?4) ?4)))))))
+ (multiply ?2 ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+11140: Goal:
+11140: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+11140: Order:
+11140: nrkbo
+11140: Leaf order:
+11140: a2 2 0 2 2,2
+11140: multiply 8 2 2 0,2
+11140: inverse 8 1 1 0,1,1,2
+11140: b2 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+11141: Facts:
+11141: Id : 2, {_}:
+ inverse
+ (multiply
+ (inverse
+ (multiply ?2
+ (inverse
+ (multiply (inverse ?3)
+ (multiply (inverse ?4)
+ (inverse (multiply (inverse ?4) ?4)))))))
+ (multiply ?2 ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+11141: Goal:
+11141: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+11141: Order:
+11141: kbo
+11141: Leaf order:
+11141: a2 2 0 2 2,2
+11141: multiply 8 2 2 0,2
+11141: inverse 8 1 1 0,1,1,2
+11141: b2 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+11142: Facts:
+11142: Id : 2, {_}:
+ inverse
+ (multiply
+ (inverse
+ (multiply ?2
+ (inverse
+ (multiply (inverse ?3)
+ (multiply (inverse ?4)
+ (inverse (multiply (inverse ?4) ?4)))))))
+ (multiply ?2 ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+11142: Goal:
+11142: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+11142: Order:
+11142: lpo
+11142: Leaf order:
+11142: a2 2 0 2 2,2
+11142: multiply 8 2 2 0,2
+11142: inverse 8 1 1 0,1,1,2
+11142: b2 2 0 2 1,1,1,2
+% SZS status Timeout for GRP422-1.p
+NO CLASH, using fixed ground order
+11162: Facts:
+NO CLASH, using fixed ground order
+11164: Facts:
+11164: Id : 2, {_}:
+ inverse
+ (multiply
+ (inverse
+ (multiply ?2
+ (inverse
+ (multiply (inverse ?3)
+ (multiply (inverse ?4)
+ (inverse (multiply (inverse ?4) ?4)))))))
+ (multiply ?2 ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+11164: Goal:
+11164: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+11164: Order:
+11164: lpo
+11164: Leaf order:
+11164: inverse 7 1 0
+11164: c3 2 0 2 2,2
+11164: multiply 10 2 4 0,2
+11164: b3 2 0 2 2,1,2
+11164: a3 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+11163: Facts:
+11163: Id : 2, {_}:
+ inverse
+ (multiply
+ (inverse
+ (multiply ?2
+ (inverse
+ (multiply (inverse ?3)
+ (multiply (inverse ?4)
+ (inverse (multiply (inverse ?4) ?4)))))))
+ (multiply ?2 ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+11163: Goal:
+11163: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+11163: Order:
+11163: kbo
+11163: Leaf order:
+11163: inverse 7 1 0
+11163: c3 2 0 2 2,2
+11163: multiply 10 2 4 0,2
+11163: b3 2 0 2 2,1,2
+11163: a3 2 0 2 1,1,2
+11162: Id : 2, {_}:
+ inverse
+ (multiply
+ (inverse
+ (multiply ?2
+ (inverse
+ (multiply (inverse ?3)
+ (multiply (inverse ?4)
+ (inverse (multiply (inverse ?4) ?4)))))))
+ (multiply ?2 ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+11162: Goal:
+11162: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+11162: Order:
+11162: nrkbo
+11162: Leaf order:
+11162: inverse 7 1 0
+11162: c3 2 0 2 2,2
+11162: multiply 10 2 4 0,2
+11162: b3 2 0 2 2,1,2
+11162: a3 2 0 2 1,1,2
+% SZS status Timeout for GRP423-1.p
+NO CLASH, using fixed ground order
+11197: Facts:
+11197: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply
+ (multiply
+ (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
+ ?5) (inverse (multiply ?3 ?5))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11197: Goal:
+11197: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+11197: Order:
+11197: kbo
+11197: Leaf order:
+11197: inverse 5 1 0
+11197: c3 2 0 2 2,2
+11197: multiply 10 2 4 0,2
+11197: b3 2 0 2 2,1,2
+11197: a3 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+11198: Facts:
+11198: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply
+ (multiply
+ (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
+ ?5) (inverse (multiply ?3 ?5))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11198: Goal:
+11198: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+11198: Order:
+11198: lpo
+11198: Leaf order:
+11198: inverse 5 1 0
+11198: c3 2 0 2 2,2
+11198: multiply 10 2 4 0,2
+11198: b3 2 0 2 2,1,2
+11198: a3 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+11196: Facts:
+11196: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply
+ (multiply
+ (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
+ ?5) (inverse (multiply ?3 ?5))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11196: Goal:
+11196: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+11196: Order:
+11196: nrkbo
+11196: Leaf order:
+11196: inverse 5 1 0
+11196: c3 2 0 2 2,2
+11196: multiply 10 2 4 0,2
+11196: b3 2 0 2 2,1,2
+11196: a3 2 0 2 1,1,2
+Statistics :
+Max weight : 62
+Found proof, 60.632898s
+% SZS status Unsatisfiable for GRP429-1.p
+% SZS output start CNFRefutation for GRP429-1.p
+Id : 3, {_}: multiply ?7 (inverse (multiply (multiply (inverse (multiply (inverse ?8) (multiply (inverse ?7) ?9))) ?10) (inverse (multiply ?8 ?10)))) =>= ?9 [10, 9, 8, 7] by single_axiom ?7 ?8 ?9 ?10
+Id : 2, {_}: multiply ?2 (inverse (multiply (multiply (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) ?5) (inverse (multiply ?3 ?5)))) =>= ?4 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+Id : 5, {_}: multiply ?19 (inverse (multiply (multiply (inverse (multiply (inverse ?20) ?21)) ?22) (inverse (multiply ?20 ?22)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24) (inverse (multiply ?23 ?24))) [24, 23, 22, 21, 20, 19] by Super 3 with 2 at 2,1,1,1,1,2,2
+Id : 1086, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?5854) (multiply (inverse (inverse ?5855)) (multiply (inverse ?5855) ?5856)))) ?5857) (inverse (multiply ?5854 ?5857))) =>= ?5856 [5857, 5856, 5855, 5854] by Super 2 with 5 at 2
+Id : 473, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1916) (multiply (inverse (inverse ?1917)) (multiply (inverse ?1917) ?1918)))) ?1919) (inverse (multiply ?1916 ?1919))) =>= ?1918 [1919, 1918, 1917, 1916] by Super 2 with 5 at 2
+Id : 1106, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?5982) (multiply (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?5983) (multiply (inverse (inverse ?5984)) (multiply (inverse ?5984) ?5985)))) ?5986) (inverse (multiply ?5983 ?5986))))) (multiply ?5985 ?5987)))) ?5988) (inverse (multiply ?5982 ?5988))) =>= ?5987 [5988, 5987, 5986, 5985, 5984, 5983, 5982] by Super 1086 with 473 at 1,2,2,1,1,1,1,2
+Id : 2050, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?13160) (multiply (inverse ?13161) (multiply ?13161 ?13162)))) ?13163) (inverse (multiply ?13160 ?13163))) =>= ?13162 [13163, 13162, 13161, 13160] by Demod 1106 with 473 at 1,1,2,1,1,1,1,2
+Id : 472, {_}: multiply (inverse ?1911) (multiply ?1911 (inverse (multiply (multiply (inverse (multiply (inverse ?1912) ?1913)) ?1914) (inverse (multiply ?1912 ?1914))))) =>= ?1913 [1914, 1913, 1912, 1911] by Super 2 with 5 at 2,2
+Id : 1697, {_}: multiply (inverse ?11063) (multiply ?11063 ?11064) =?= multiply (inverse (inverse ?11065)) (multiply (inverse ?11065) ?11064) [11065, 11064, 11063] by Super 472 with 473 at 2,2,2
+Id : 1084, {_}: multiply (inverse ?5842) (multiply ?5842 ?5843) =?= multiply (inverse (inverse ?5844)) (multiply (inverse ?5844) ?5843) [5844, 5843, 5842] by Super 472 with 473 at 2,2,2
+Id : 1735, {_}: multiply (inverse ?11276) (multiply ?11276 ?11277) =?= multiply (inverse ?11278) (multiply ?11278 ?11277) [11278, 11277, 11276] by Super 1697 with 1084 at 3
+Id : 2837, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?18056) (multiply ?18056 (multiply ?18057 ?18058)))) ?18059) (inverse (multiply (inverse ?18057) ?18059))) =>= ?18058 [18059, 18058, 18057, 18056] by Super 2050 with 1735 at 1,1,1,1,2
+Id : 2876, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?18341) (multiply ?18341 (multiply (inverse ?18342) (multiply ?18342 ?18343))))) ?18344) (inverse (multiply (inverse (inverse ?18345)) ?18344))) =>= multiply ?18345 ?18343 [18345, 18344, 18343, 18342, 18341] by Super 2837 with 1735 at 2,2,1,1,1,1,2
+Id : 930, {_}: multiply (inverse ?5077) (multiply ?5077 (inverse (multiply (multiply (inverse (multiply (inverse ?5078) ?5079)) ?5080) (inverse (multiply ?5078 ?5080))))) =>= ?5079 [5080, 5079, 5078, 5077] by Super 2 with 5 at 2,2
+Id : 983, {_}: multiply (inverse ?5420) (multiply ?5420 (multiply ?5421 (inverse (multiply (multiply (inverse (multiply (inverse ?5422) ?5423)) ?5424) (inverse (multiply ?5422 ?5424)))))) =>= multiply (inverse (inverse ?5421)) ?5423 [5424, 5423, 5422, 5421, 5420] by Super 930 with 5 at 2,2,2
+Id : 1838, {_}: multiply (inverse ?11737) (multiply ?11737 (inverse (multiply (multiply (inverse (multiply (inverse ?11738) (multiply ?11738 ?11739))) ?11740) (inverse (multiply ?11741 ?11740))))) =>= multiply ?11741 ?11739 [11741, 11740, 11739, 11738, 11737] by Super 472 with 1735 at 1,1,1,1,2,2,2
+Id : 2618, {_}: multiply ?16805 (inverse (multiply (multiply (inverse (multiply (inverse ?16806) (multiply ?16806 ?16807))) ?16808) (inverse (multiply (inverse ?16805) ?16808)))) =>= ?16807 [16808, 16807, 16806, 16805] by Super 2 with 1735 at 1,1,1,1,2,2
+Id : 7049, {_}: multiply ?47447 (inverse (multiply (multiply (inverse (multiply (inverse ?47448) (multiply ?47448 ?47449))) (multiply ?47447 ?47450)) (inverse (multiply (inverse ?47451) (multiply ?47451 ?47450))))) =>= ?47449 [47451, 47450, 47449, 47448, 47447] by Super 2618 with 1735 at 1,2,1,2,2
+Id : 7182, {_}: multiply (multiply (inverse ?48545) (multiply ?48545 ?48546)) (inverse (multiply ?48547 (inverse (multiply (inverse ?48548) (multiply ?48548 (inverse (multiply (multiply (inverse (multiply (inverse ?48549) ?48547)) ?48550) (inverse (multiply ?48549 ?48550))))))))) =>= ?48546 [48550, 48549, 48548, 48547, 48546, 48545] by Super 7049 with 472 at 1,1,2,2
+Id : 7272, {_}: multiply (multiply (inverse ?48545) (multiply ?48545 ?48546)) (inverse (multiply ?48547 (inverse ?48547))) =>= ?48546 [48547, 48546, 48545] by Demod 7182 with 472 at 1,2,1,2,2
+Id : 7322, {_}: multiply (inverse (multiply (inverse ?48938) (multiply ?48938 ?48939))) ?48939 =?= multiply (inverse (multiply (inverse ?48940) (multiply ?48940 ?48941))) ?48941 [48941, 48940, 48939, 48938] by Super 1838 with 7272 at 2,2
+Id : 9244, {_}: multiply (inverse (inverse (multiply (inverse ?63609) (multiply ?63609 (inverse (multiply (multiply (inverse (multiply (inverse ?63610) ?63611)) ?63612) (inverse (multiply ?63610 ?63612)))))))) (multiply (inverse (multiply (inverse ?63613) (multiply ?63613 ?63614))) ?63614) =>= ?63611 [63614, 63613, 63612, 63611, 63610, 63609] by Super 472 with 7322 at 2,2
+Id : 9553, {_}: multiply (inverse (inverse ?63611)) (multiply (inverse (multiply (inverse ?63613) (multiply ?63613 ?63614))) ?63614) =>= ?63611 [63614, 63613, 63611] by Demod 9244 with 472 at 1,1,1,2
+Id : 9607, {_}: multiply (inverse ?66347) (multiply ?66347 (multiply ?66348 (inverse (multiply (multiply (inverse ?66349) ?66350) (inverse (multiply (inverse ?66349) ?66350)))))) =?= multiply (inverse (inverse ?66348)) (multiply (inverse (multiply (inverse ?66351) (multiply ?66351 ?66352))) ?66352) [66352, 66351, 66350, 66349, 66348, 66347] by Super 983 with 9553 at 1,1,1,1,2,2,2,2
+Id : 13028, {_}: multiply (inverse ?88877) (multiply ?88877 (multiply ?88878 (inverse (multiply (multiply (inverse ?88879) ?88880) (inverse (multiply (inverse ?88879) ?88880)))))) =>= ?88878 [88880, 88879, 88878, 88877] by Demod 9607 with 9553 at 3
+Id : 2125, {_}: inverse (multiply (multiply (inverse ?13666) (multiply ?13666 ?13667)) (inverse (multiply ?13668 (multiply (multiply (inverse ?13668) (multiply (inverse ?13669) (multiply ?13669 ?13670))) ?13667)))) =>= ?13670 [13670, 13669, 13668, 13667, 13666] by Super 2050 with 1735 at 1,1,2
+Id : 7292, {_}: inverse (multiply (multiply (inverse ?48720) (multiply ?48720 (inverse (multiply ?48721 (inverse ?48721))))) (inverse (multiply (inverse ?48722) (multiply ?48722 ?48723)))) =>= ?48723 [48723, 48722, 48721, 48720] by Super 2125 with 7272 at 2,1,2,1,2
+Id : 13145, {_}: multiply (inverse ?89741) (multiply ?89741 (multiply ?89742 (inverse (multiply ?89743 (inverse ?89743))))) =>= ?89742 [89743, 89742, 89741] by Super 13028 with 7292 at 2,2,2,2
+Id : 1878, {_}: multiply ?12021 (inverse (multiply (multiply (inverse ?12022) (multiply ?12022 ?12023)) (inverse (multiply ?12024 (multiply (multiply (inverse ?12024) (multiply (inverse ?12021) ?12025)) ?12023))))) =>= ?12025 [12025, 12024, 12023, 12022, 12021] by Super 2 with 1735 at 1,1,2,2
+Id : 13510, {_}: multiply (inverse (inverse ?91449)) (multiply (inverse ?91450) (multiply ?91450 (inverse (multiply ?91451 (inverse ?91451))))) =>= ?91449 [91451, 91450, 91449] by Super 9553 with 13145 at 1,1,2,2
+Id : 4, {_}: multiply ?12 (inverse (multiply (multiply (inverse (multiply (inverse ?13) (multiply (inverse ?12) ?14))) (inverse (multiply (multiply (inverse (multiply (inverse ?15) (multiply (inverse ?13) ?16))) ?17) (inverse (multiply ?15 ?17))))) (inverse ?16))) =>= ?14 [17, 16, 15, 14, 13, 12] by Super 3 with 2 at 1,2,1,2,2
+Id : 98, {_}: multiply ?266 (inverse (multiply (multiply (inverse (multiply (inverse ?267) ?268)) ?269) (inverse (multiply ?267 ?269)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?270) (multiply (inverse (inverse ?266)) ?268))) (inverse (multiply (multiply (inverse (multiply (inverse ?271) (multiply (inverse ?270) ?272))) ?273) (inverse (multiply ?271 ?273))))) (inverse ?272)) [273, 272, 271, 270, 269, 268, 267, 266] by Super 2 with 4 at 2,1,1,1,1,2,2
+Id : 13781, {_}: multiply ?92573 (inverse (multiply (multiply (inverse (multiply (inverse ?92574) (multiply (inverse ?92573) (inverse (multiply ?92575 (inverse ?92575)))))) ?92576) (inverse (multiply ?92574 ?92576)))) =?= inverse (multiply (multiply (inverse ?92577) (inverse (multiply (multiply (inverse (multiply (inverse ?92578) (multiply (inverse (inverse ?92577)) ?92579))) ?92580) (inverse (multiply ?92578 ?92580))))) (inverse ?92579)) [92580, 92579, 92578, 92577, 92576, 92575, 92574, 92573] by Super 98 with 13510 at 1,1,1,1,3
+Id : 13970, {_}: inverse (multiply ?92575 (inverse ?92575)) =?= inverse (multiply (multiply (inverse ?92577) (inverse (multiply (multiply (inverse (multiply (inverse ?92578) (multiply (inverse (inverse ?92577)) ?92579))) ?92580) (inverse (multiply ?92578 ?92580))))) (inverse ?92579)) [92580, 92579, 92578, 92577, 92575] by Demod 13781 with 2 at 2
+Id : 13971, {_}: inverse (multiply ?92575 (inverse ?92575)) =?= inverse (multiply ?92579 (inverse ?92579)) [92579, 92575] by Demod 13970 with 2 at 1,1,3
+Id : 14410, {_}: multiply (inverse (inverse (multiply ?96419 (inverse ?96419)))) (multiply (inverse ?96420) (multiply ?96420 (inverse (multiply ?96421 (inverse ?96421))))) =?= multiply ?96422 (inverse ?96422) [96422, 96421, 96420, 96419] by Super 13510 with 13971 at 1,1,2
+Id : 14473, {_}: multiply ?96419 (inverse ?96419) =?= multiply ?96422 (inverse ?96422) [96422, 96419] by Demod 14410 with 13510 at 2
+Id : 14531, {_}: multiply (multiply (inverse ?96810) (multiply ?96811 (inverse ?96811))) (inverse (multiply ?96812 (inverse ?96812))) =>= inverse ?96810 [96812, 96811, 96810] by Super 7272 with 14473 at 2,1,2
+Id : 15237, {_}: multiply ?101459 (inverse (multiply (multiply (inverse ?101460) (multiply ?101460 (inverse (multiply ?101461 (inverse ?101461))))) (inverse (multiply ?101462 (inverse ?101462))))) =>= inverse (inverse ?101459) [101462, 101461, 101460, 101459] by Super 1878 with 14531 at 2,1,2,1,2,2
+Id : 15353, {_}: multiply ?101459 (inverse (inverse (multiply ?101461 (inverse ?101461)))) =>= inverse (inverse ?101459) [101461, 101459] by Demod 15237 with 7272 at 1,2,2
+Id : 16356, {_}: multiply (inverse (inverse ?111717)) (multiply (inverse (multiply (inverse ?111718) (inverse (inverse ?111718)))) (inverse (inverse (multiply ?111719 (inverse ?111719))))) =>= ?111717 [111719, 111718, 111717] by Super 9553 with 15353 at 2,1,1,2,2
+Id : 18221, {_}: multiply (inverse (inverse ?121427)) (inverse (inverse (inverse (multiply (inverse ?121428) (inverse (inverse ?121428)))))) =>= ?121427 [121428, 121427] by Demod 16356 with 15353 at 2,2
+Id : 16345, {_}: multiply ?111675 (inverse ?111675) =?= inverse (inverse (inverse (multiply ?111676 (inverse ?111676)))) [111676, 111675] by Super 14473 with 15353 at 3
+Id : 18293, {_}: multiply (inverse (inverse ?121732)) (multiply ?121733 (inverse ?121733)) =>= ?121732 [121733, 121732] by Super 18221 with 16345 at 2,2
+Id : 18567, {_}: multiply ?122956 (inverse (multiply ?122957 (inverse ?122957))) =>= inverse (inverse ?122956) [122957, 122956] by Super 7272 with 18293 at 1,2
+Id : 18716, {_}: multiply (inverse ?89741) (multiply ?89741 (inverse (inverse ?89742))) =>= ?89742 [89742, 89741] by Demod 13145 with 18567 at 2,2,2
+Id : 18916, {_}: multiply (inverse (inverse ?124642)) (inverse (inverse (multiply ?124643 (inverse ?124643)))) =>= ?124642 [124643, 124642] by Super 18293 with 18567 at 2,2
+Id : 18985, {_}: inverse (inverse (inverse (inverse ?124642))) =>= ?124642 [124642] by Demod 18916 with 15353 at 2
+Id : 19175, {_}: multiply (inverse ?124947) (multiply ?124947 ?124948) =>= inverse (inverse ?124948) [124948, 124947] by Super 18716 with 18985 at 2,2,2
+Id : 19474, {_}: inverse (multiply (multiply (inverse (inverse (inverse (multiply (inverse ?18342) (multiply ?18342 ?18343))))) ?18344) (inverse (multiply (inverse (inverse ?18345)) ?18344))) =>= multiply ?18345 ?18343 [18345, 18344, 18343, 18342] by Demod 2876 with 19175 at 1,1,1,1,2
+Id : 19475, {_}: inverse (multiply (multiply (inverse (inverse (inverse (inverse (inverse ?18343))))) ?18344) (inverse (multiply (inverse (inverse ?18345)) ?18344))) =>= multiply ?18345 ?18343 [18345, 18344, 18343] by Demod 19474 with 19175 at 1,1,1,1,1,1,2
+Id : 19512, {_}: inverse (multiply (multiply (inverse ?18343) ?18344) (inverse (multiply (inverse (inverse ?18345)) ?18344))) =>= multiply ?18345 ?18343 [18345, 18344, 18343] by Demod 19475 with 18985 at 1,1,1,2
+Id : 19345, {_}: multiply ?126114 (multiply ?126115 (inverse ?126115)) =>= inverse (inverse ?126114) [126115, 126114] by Super 18293 with 18985 at 1,2
+Id : 19935, {_}: inverse (multiply (multiply (inverse ?128594) (multiply ?128595 (inverse ?128595))) (inverse (inverse (inverse (inverse (inverse ?128596)))))) =>= multiply ?128596 ?128594 [128596, 128595, 128594] by Super 19512 with 19345 at 1,2,1,2
+Id : 19990, {_}: inverse (multiply (inverse (inverse (inverse ?128594))) (inverse (inverse (inverse (inverse (inverse ?128596)))))) =>= multiply ?128596 ?128594 [128596, 128594] by Demod 19935 with 19345 at 1,1,2
+Id : 20507, {_}: inverse (multiply (inverse (inverse (inverse ?130153))) (inverse ?130154)) =>= multiply ?130154 ?130153 [130154, 130153] by Demod 19990 with 18985 at 2,1,2
+Id : 20571, {_}: inverse (multiply ?130433 (inverse ?130434)) =>= multiply ?130434 (inverse ?130433) [130434, 130433] by Super 20507 with 18985 at 1,1,2
+Id : 21794, {_}: multiply (multiply (inverse (inverse ?18345)) ?18344) (inverse (multiply (inverse ?18343) ?18344)) =>= multiply ?18345 ?18343 [18343, 18344, 18345] by Demod 19512 with 20571 at 2
+Id : 21760, {_}: multiply ?19 (multiply (multiply ?20 ?22) (inverse (multiply (inverse (multiply (inverse ?20) ?21)) ?22))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24) (inverse (multiply ?23 ?24))) [24, 23, 21, 22, 20, 19] by Demod 5 with 20571 at 2,2
+Id : 21761, {_}: multiply ?19 (multiply (multiply ?20 ?22) (inverse (multiply (inverse (multiply (inverse ?20) ?21)) ?22))) =?= multiply (multiply ?23 ?24) (inverse (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24)) [24, 23, 21, 22, 20, 19] by Demod 21760 with 20571 at 3
+Id : 19480, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?1912) ?1913)) ?1914) (inverse (multiply ?1912 ?1914))))) =>= ?1913 [1914, 1913, 1912] by Demod 472 with 19175 at 2
+Id : 21790, {_}: inverse (inverse (multiply (multiply ?1912 ?1914) (inverse (multiply (inverse (multiply (inverse ?1912) ?1913)) ?1914)))) =>= ?1913 [1913, 1914, 1912] by Demod 19480 with 20571 at 1,1,2
+Id : 21791, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1912) ?1913)) ?1914) (inverse (multiply ?1912 ?1914))) =>= ?1913 [1914, 1913, 1912] by Demod 21790 with 20571 at 1,2
+Id : 21792, {_}: multiply (multiply ?1912 ?1914) (inverse (multiply (inverse (multiply (inverse ?1912) ?1913)) ?1914)) =>= ?1913 [1913, 1914, 1912] by Demod 21791 with 20571 at 2
+Id : 21810, {_}: multiply ?19 ?21 =<= multiply (multiply ?23 ?24) (inverse (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24)) [24, 23, 21, 19] by Demod 21761 with 21792 at 2,2
+Id : 21811, {_}: multiply ?19 ?21 =<= multiply (inverse (inverse ?19)) ?21 [21, 19] by Demod 21810 with 21792 at 3
+Id : 21822, {_}: multiply (multiply ?18345 ?18344) (inverse (multiply (inverse ?18343) ?18344)) =>= multiply ?18345 ?18343 [18343, 18344, 18345] by Demod 21794 with 21811 at 1,2
+Id : 21949, {_}: multiply (multiply ?139581 (inverse ?139582)) (multiply ?139582 (inverse (inverse ?139583))) =>= multiply ?139581 ?139583 [139583, 139582, 139581] by Super 21822 with 20571 at 2,2
+Id : 19491, {_}: multiply ?12021 (inverse (multiply (inverse (inverse ?12023)) (inverse (multiply ?12024 (multiply (multiply (inverse ?12024) (multiply (inverse ?12021) ?12025)) ?12023))))) =>= ?12025 [12025, 12024, 12023, 12021] by Demod 1878 with 19175 at 1,1,2,2
+Id : 21735, {_}: multiply ?12021 (multiply (multiply ?12024 (multiply (multiply (inverse ?12024) (multiply (inverse ?12021) ?12025)) ?12023)) (inverse (inverse (inverse ?12023)))) =>= ?12025 [12023, 12025, 12024, 12021] by Demod 19491 with 20571 at 2,2
+Id : 3075, {_}: multiply (inverse ?19377) (multiply ?19377 (multiply ?19378 (inverse (multiply (multiply (inverse (multiply (inverse ?19379) ?19380)) ?19381) (inverse (multiply ?19379 ?19381)))))) =>= multiply (inverse (inverse ?19378)) ?19380 [19381, 19380, 19379, 19378, 19377] by Super 930 with 5 at 2,2,2
+Id : 1191, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?5982) (multiply (inverse ?5985) (multiply ?5985 ?5987)))) ?5988) (inverse (multiply ?5982 ?5988))) =>= ?5987 [5988, 5987, 5985, 5982] by Demod 1106 with 473 at 1,1,2,1,1,1,1,2
+Id : 3153, {_}: multiply (inverse ?20008) (multiply ?20008 (multiply ?20009 ?20010)) =?= multiply (inverse (inverse ?20009)) (multiply (inverse ?20011) (multiply ?20011 ?20010)) [20011, 20010, 20009, 20008] by Super 3075 with 1191 at 2,2,2,2
+Id : 19484, {_}: inverse (inverse (multiply ?20009 ?20010)) =<= multiply (inverse (inverse ?20009)) (multiply (inverse ?20011) (multiply ?20011 ?20010)) [20011, 20010, 20009] by Demod 3153 with 19175 at 2
+Id : 19485, {_}: inverse (inverse (multiply ?20009 ?20010)) =<= multiply (inverse (inverse ?20009)) (inverse (inverse ?20010)) [20010, 20009] by Demod 19484 with 19175 at 2,3
+Id : 21818, {_}: inverse (inverse (multiply ?20009 ?20010)) =<= multiply ?20009 (inverse (inverse ?20010)) [20010, 20009] by Demod 19485 with 21811 at 3
+Id : 21880, {_}: multiply ?12021 (inverse (inverse (multiply (multiply ?12024 (multiply (multiply (inverse ?12024) (multiply (inverse ?12021) ?12025)) ?12023)) (inverse ?12023)))) =>= ?12025 [12023, 12025, 12024, 12021] by Demod 21735 with 21818 at 2,2
+Id : 21881, {_}: inverse (inverse (multiply ?12021 (multiply (multiply ?12024 (multiply (multiply (inverse ?12024) (multiply (inverse ?12021) ?12025)) ?12023)) (inverse ?12023)))) =>= ?12025 [12023, 12025, 12024, 12021] by Demod 21880 with 21818 at 2
+Id : 1840, {_}: multiply (inverse ?11749) (multiply ?11749 (inverse (multiply (multiply (inverse ?11750) (multiply ?11750 ?11751)) (inverse (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)))))) =>= ?11753 [11753, 11752, 11751, 11750, 11749] by Super 472 with 1735 at 1,1,2,2,2
+Id : 19489, {_}: inverse (inverse (inverse (multiply (multiply (inverse ?11750) (multiply ?11750 ?11751)) (inverse (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)))))) =>= ?11753 [11753, 11752, 11751, 11750] by Demod 1840 with 19175 at 2
+Id : 19490, {_}: inverse (inverse (inverse (multiply (inverse (inverse ?11751)) (inverse (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)))))) =>= ?11753 [11753, 11752, 11751] by Demod 19489 with 19175 at 1,1,1,1,2
+Id : 21784, {_}: inverse (inverse (multiply (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)) (inverse (inverse (inverse ?11751))))) =>= ?11753 [11751, 11753, 11752] by Demod 19490 with 20571 at 1,1,2
+Id : 21785, {_}: inverse (multiply (inverse (inverse ?11751)) (inverse (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)))) =>= ?11753 [11753, 11752, 11751] by Demod 21784 with 20571 at 1,2
+Id : 21786, {_}: multiply (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)) (inverse (inverse (inverse ?11751))) =>= ?11753 [11751, 11753, 11752] by Demod 21785 with 20571 at 2
+Id : 21834, {_}: inverse (inverse (multiply (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)) (inverse ?11751))) =>= ?11753 [11751, 11753, 11752] by Demod 21786 with 21818 at 2
+Id : 21842, {_}: inverse (multiply ?11751 (inverse (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)))) =>= ?11753 [11753, 11752, 11751] by Demod 21834 with 20571 at 1,2
+Id : 21843, {_}: multiply (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)) (inverse ?11751) =>= ?11753 [11751, 11753, 11752] by Demod 21842 with 20571 at 2
+Id : 21882, {_}: inverse (inverse (multiply ?12021 (multiply (inverse ?12021) ?12025))) =>= ?12025 [12025, 12021] by Demod 21881 with 21843 at 2,1,1,2
+Id : 1876, {_}: multiply ?12011 (inverse (multiply (multiply (inverse (multiply (inverse ?12012) (multiply ?12012 ?12013))) ?12014) (inverse (multiply (inverse ?12011) ?12014)))) =>= ?12013 [12014, 12013, 12012, 12011] by Super 2 with 1735 at 1,1,1,1,2,2
+Id : 19478, {_}: multiply ?12011 (inverse (multiply (multiply (inverse (inverse (inverse ?12013))) ?12014) (inverse (multiply (inverse ?12011) ?12014)))) =>= ?12013 [12014, 12013, 12011] by Demod 1876 with 19175 at 1,1,1,1,2,2
+Id : 21793, {_}: multiply ?12011 (multiply (multiply (inverse ?12011) ?12014) (inverse (multiply (inverse (inverse (inverse ?12013))) ?12014))) =>= ?12013 [12013, 12014, 12011] by Demod 19478 with 20571 at 2,2
+Id : 19486, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?11738) (multiply ?11738 ?11739))) ?11740) (inverse (multiply ?11741 ?11740))))) =>= multiply ?11741 ?11739 [11741, 11740, 11739, 11738] by Demod 1838 with 19175 at 2
+Id : 19487, {_}: inverse (inverse (inverse (multiply (multiply (inverse (inverse (inverse ?11739))) ?11740) (inverse (multiply ?11741 ?11740))))) =>= multiply ?11741 ?11739 [11741, 11740, 11739] by Demod 19486 with 19175 at 1,1,1,1,1,1,2
+Id : 21787, {_}: inverse (inverse (multiply (multiply ?11741 ?11740) (inverse (multiply (inverse (inverse (inverse ?11739))) ?11740)))) =>= multiply ?11741 ?11739 [11739, 11740, 11741] by Demod 19487 with 20571 at 1,1,2
+Id : 21788, {_}: inverse (multiply (multiply (inverse (inverse (inverse ?11739))) ?11740) (inverse (multiply ?11741 ?11740))) =>= multiply ?11741 ?11739 [11741, 11740, 11739] by Demod 21787 with 20571 at 1,2
+Id : 21789, {_}: multiply (multiply ?11741 ?11740) (inverse (multiply (inverse (inverse (inverse ?11739))) ?11740)) =>= multiply ?11741 ?11739 [11739, 11740, 11741] by Demod 21788 with 20571 at 2
+Id : 21802, {_}: multiply ?12011 (multiply (inverse ?12011) ?12013) =>= ?12013 [12013, 12011] by Demod 21793 with 21789 at 2,2
+Id : 21883, {_}: inverse (inverse ?12025) =>= ?12025 [12025] by Demod 21882 with 21802 at 1,1,2
+Id : 22088, {_}: multiply (multiply ?140028 (inverse ?140029)) (multiply ?140029 ?140030) =>= multiply ?140028 ?140030 [140030, 140029, 140028] by Demod 21949 with 21883 at 2,2,2
+Id : 21892, {_}: multiply (inverse ?124947) (multiply ?124947 ?124948) =>= ?124948 [124948, 124947] by Demod 19175 with 21883 at 3
+Id : 22102, {_}: multiply (multiply ?140094 (inverse (inverse ?140095))) ?140096 =>= multiply ?140094 (multiply ?140095 ?140096) [140096, 140095, 140094] by Super 22088 with 21892 at 2,2
+Id : 22180, {_}: multiply (multiply ?140094 ?140095) ?140096 =>= multiply ?140094 (multiply ?140095 ?140096) [140096, 140095, 140094] by Demod 22102 with 21883 at 2,1,2
+Id : 22441, {_}: multiply a3 (multiply b3 c3) =?= multiply a3 (multiply b3 c3) [] by Demod 1 with 22180 at 2
+Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
+% SZS output end CNFRefutation for GRP429-1.p
+11197: solved GRP429-1.p in 30.365897 using kbo
+11197: status Unsatisfiable for GRP429-1.p
+NO CLASH, using fixed ground order
+11215: Facts:
+11215: Id : 2, {_}:
+ inverse
+ (multiply ?2
+ (multiply ?3
+ (multiply (multiply ?4 (inverse ?4))
+ (inverse (multiply ?5 (multiply ?2 ?3))))))
+ =>=
+ ?5
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11215: Goal:
+11215: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+11215: Order:
+11215: nrkbo
+11215: Leaf order:
+11215: inverse 3 1 0
+11215: c3 2 0 2 2,2
+11215: multiply 10 2 4 0,2
+11215: b3 2 0 2 2,1,2
+11215: a3 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+11216: Facts:
+11216: Id : 2, {_}:
+ inverse
+ (multiply ?2
+ (multiply ?3
+ (multiply (multiply ?4 (inverse ?4))
+ (inverse (multiply ?5 (multiply ?2 ?3))))))
+ =>=
+ ?5
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11216: Goal:
+11216: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+11216: Order:
+11216: kbo
+11216: Leaf order:
+11216: inverse 3 1 0
+11216: c3 2 0 2 2,2
+11216: multiply 10 2 4 0,2
+11216: b3 2 0 2 2,1,2
+11216: a3 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+11217: Facts:
+11217: Id : 2, {_}:
+ inverse
+ (multiply ?2
+ (multiply ?3
+ (multiply (multiply ?4 (inverse ?4))
+ (inverse (multiply ?5 (multiply ?2 ?3))))))
+ =>=
+ ?5
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11217: Goal:
+11217: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+11217: Order:
+11217: lpo
+11217: Leaf order:
+11217: inverse 3 1 0
+11217: c3 2 0 2 2,2
+11217: multiply 10 2 4 0,2
+11217: b3 2 0 2 2,1,2
+11217: a3 2 0 2 1,1,2
+% SZS status Timeout for GRP444-1.p
+NO CLASH, using fixed ground order
+11235: Facts:
+NO CLASH, using fixed ground order
+11236: Facts:
+11236: Id : 2, {_}:
+ divide
+ (divide (divide ?2 ?2)
+ (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
+ ?4
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+11236: Id : 3, {_}:
+ multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
+ [8, 7, 6] by multiply ?6 ?7 ?8
+11236: Id : 4, {_}:
+ inverse ?10 =<= divide (divide ?11 ?11) ?10
+ [11, 10] by inverse ?10 ?11
+11236: Goal:
+11236: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+11236: Order:
+11236: kbo
+11236: Leaf order:
+11236: divide 13 2 0
+11236: a2 2 0 2 2,2
+11236: multiply 3 2 2 0,2
+11236: inverse 2 1 1 0,1,1,2
+11236: b2 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+11237: Facts:
+11237: Id : 2, {_}:
+ divide
+ (divide (divide ?2 ?2)
+ (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
+ ?4
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+11237: Id : 3, {_}:
+ multiply ?6 ?7 =?= divide ?6 (divide (divide ?8 ?8) ?7)
+ [8, 7, 6] by multiply ?6 ?7 ?8
+11237: Id : 4, {_}:
+ inverse ?10 =?= divide (divide ?11 ?11) ?10
+ [11, 10] by inverse ?10 ?11
+11237: Goal:
+11237: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+11237: Order:
+11237: lpo
+11237: Leaf order:
+11237: divide 13 2 0
+11237: a2 2 0 2 2,2
+11237: multiply 3 2 2 0,2
+11237: inverse 2 1 1 0,1,1,2
+11237: b2 2 0 2 1,1,1,2
+11235: Id : 2, {_}:
+ divide
+ (divide (divide ?2 ?2)
+ (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
+ ?4
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+11235: Id : 3, {_}:
+ multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
+ [8, 7, 6] by multiply ?6 ?7 ?8
+11235: Id : 4, {_}:
+ inverse ?10 =<= divide (divide ?11 ?11) ?10
+ [11, 10] by inverse ?10 ?11
+11235: Goal:
+11235: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+11235: Order:
+11235: nrkbo
+11235: Leaf order:
+11235: divide 13 2 0
+11235: a2 2 0 2 2,2
+11235: multiply 3 2 2 0,2
+11235: inverse 2 1 1 0,1,1,2
+11235: b2 2 0 2 1,1,1,2
+Statistics :
+Max weight : 38
+Found proof, 1.775197s
+% SZS status Unsatisfiable for GRP452-1.p
+% SZS output start CNFRefutation for GRP452-1.p
+Id : 5, {_}: divide (divide (divide ?13 ?13) (divide ?13 (divide ?14 (divide (divide (divide ?13 ?13) ?13) ?15)))) ?15 =>= ?14 [15, 14, 13] by single_axiom ?13 ?14 ?15
+Id : 35, {_}: inverse ?90 =<= divide (divide ?91 ?91) ?90 [91, 90] by inverse ?90 ?91
+Id : 2, {_}: divide (divide (divide ?2 ?2) (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
+Id : 4, {_}: inverse ?10 =<= divide (divide ?11 ?11) ?10 [11, 10] by inverse ?10 ?11
+Id : 3, {_}: multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) [8, 7, 6] by multiply ?6 ?7 ?8
+Id : 29, {_}: multiply ?6 ?7 =<= divide ?6 (inverse ?7) [7, 6] by Demod 3 with 4 at 2,3
+Id : 122, {_}: multiply (divide ?250 ?250) ?251 =>= inverse (inverse ?251) [251, 250] by Super 29 with 4 at 3
+Id : 128, {_}: multiply (multiply (inverse ?268) ?268) ?269 =>= inverse (inverse ?269) [269, 268] by Super 122 with 29 at 1,2
+Id : 13, {_}: divide (multiply (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50))) ?50 =>= ?49 [50, 49, 48] by Super 2 with 3 at 1,2
+Id : 32, {_}: multiply (divide ?79 ?79) ?80 =>= inverse (inverse ?80) [80, 79] by Super 29 with 4 at 3
+Id : 481, {_}: divide (inverse (inverse (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 13 with 32 at 1,2
+Id : 482, {_}: divide (inverse (inverse (divide ?49 (divide (inverse (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 481 with 4 at 1,2,1,1,1,2
+Id : 36, {_}: inverse ?93 =<= divide (inverse (divide ?94 ?94)) ?93 [94, 93] by Super 35 with 4 at 1,3
+Id : 483, {_}: divide (inverse (inverse (divide ?49 (inverse ?50)))) ?50 =>= ?49 [50, 49] by Demod 482 with 36 at 2,1,1,1,2
+Id : 484, {_}: divide (inverse (inverse (multiply ?49 ?50))) ?50 =>= ?49 [50, 49] by Demod 483 with 29 at 1,1,1,2
+Id : 6, {_}: divide (divide (divide ?17 ?17) (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Super 5 with 2 at 2,2,1,2
+Id : 142, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 6 with 4 at 1,2
+Id : 143, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 142 with 4 at 3
+Id : 144, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 143 with 4 at 1,2,2,1,3
+Id : 145, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (inverse ?17) ?19)))) [20, 19, 18, 17] by Demod 144 with 4 at 1,2,2,2,1,3
+Id : 226, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (divide (divide ?529 ?529) (divide ?527 (inverse (divide (inverse ?526) ?528)))) [529, 528, 527, 526] by Super 145 with 36 at 2,2,1,3
+Id : 249, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (inverse (divide ?527 (inverse (divide (inverse ?526) ?528)))) [528, 527, 526] by Demod 226 with 4 at 1,3
+Id : 250, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (inverse (multiply ?527 (divide (inverse ?526) ?528))) [528, 527, 526] by Demod 249 with 29 at 1,1,3
+Id : 896, {_}: divide (inverse (divide ?1873 ?1874)) ?1875 =<= inverse (inverse (multiply ?1874 (divide (inverse ?1873) ?1875))) [1875, 1874, 1873] by Demod 249 with 29 at 1,1,3
+Id : 911, {_}: divide (inverse (divide (divide ?1940 ?1940) ?1941)) ?1942 =>= inverse (inverse (multiply ?1941 (inverse ?1942))) [1942, 1941, 1940] by Super 896 with 36 at 2,1,1,3
+Id : 944, {_}: divide (inverse (inverse ?1941)) ?1942 =<= inverse (inverse (multiply ?1941 (inverse ?1942))) [1942, 1941] by Demod 911 with 4 at 1,1,2
+Id : 978, {_}: divide (inverse (inverse ?2088)) ?2089 =<= inverse (inverse (multiply ?2088 (inverse ?2089))) [2089, 2088] by Demod 911 with 4 at 1,1,2
+Id : 989, {_}: divide (inverse (inverse (divide ?2127 ?2127))) ?2128 =?= inverse (inverse (inverse (inverse (inverse ?2128)))) [2128, 2127] by Super 978 with 32 at 1,1,3
+Id : 223, {_}: inverse ?515 =<= divide (inverse (inverse (divide ?516 ?516))) ?515 [516, 515] by Super 4 with 36 at 1,3
+Id : 1018, {_}: inverse ?2128 =<= inverse (inverse (inverse (inverse (inverse ?2128)))) [2128] by Demod 989 with 223 at 2
+Id : 1036, {_}: multiply ?2199 (inverse (inverse (inverse (inverse ?2200)))) =>= divide ?2199 (inverse ?2200) [2200, 2199] by Super 29 with 1018 at 2,3
+Id : 1074, {_}: multiply ?2199 (inverse (inverse (inverse (inverse ?2200)))) =>= multiply ?2199 ?2200 [2200, 2199] by Demod 1036 with 29 at 3
+Id : 1107, {_}: divide (inverse (inverse ?2287)) (inverse (inverse (inverse ?2288))) =>= inverse (inverse (multiply ?2287 ?2288)) [2288, 2287] by Super 944 with 1074 at 1,1,3
+Id : 1180, {_}: multiply (inverse (inverse ?2287)) (inverse (inverse ?2288)) =>= inverse (inverse (multiply ?2287 ?2288)) [2288, 2287] by Demod 1107 with 29 at 2
+Id : 1223, {_}: divide (inverse (inverse (inverse (inverse ?2471)))) (inverse ?2472) =>= inverse (inverse (inverse (inverse (multiply ?2471 ?2472)))) [2472, 2471] by Super 944 with 1180 at 1,1,3
+Id : 1540, {_}: multiply (inverse (inverse (inverse (inverse ?3274)))) ?3275 =<= inverse (inverse (inverse (inverse (multiply ?3274 ?3275)))) [3275, 3274] by Demod 1223 with 29 at 2
+Id : 10, {_}: divide (divide (divide ?34 ?34) (divide ?34 (divide ?35 (multiply (divide (divide ?34 ?34) ?34) ?36)))) (divide (divide ?37 ?37) ?36) =>= ?35 [37, 36, 35, 34] by Super 2 with 3 at 2,2,2,1,2
+Id : 24, {_}: multiply (divide (divide ?34 ?34) (divide ?34 (divide ?35 (multiply (divide (divide ?34 ?34) ?34) ?36)))) ?36 =>= ?35 [36, 35, 34] by Demod 10 with 3 at 2
+Id : 793, {_}: multiply (inverse (divide ?34 (divide ?35 (multiply (divide (divide ?34 ?34) ?34) ?36)))) ?36 =>= ?35 [36, 35, 34] by Demod 24 with 4 at 1,2
+Id : 794, {_}: multiply (inverse (divide ?34 (divide ?35 (multiply (inverse ?34) ?36)))) ?36 =>= ?35 [36, 35, 34] by Demod 793 with 4 at 1,2,2,1,1,2
+Id : 1550, {_}: multiply (inverse (inverse (inverse (inverse (inverse (divide ?3307 (divide ?3308 (multiply (inverse ?3307) ?3309)))))))) ?3309 =>= inverse (inverse (inverse (inverse ?3308))) [3309, 3308, 3307] by Super 1540 with 794 at 1,1,1,1,3
+Id : 1600, {_}: multiply (inverse (divide ?3307 (divide ?3308 (multiply (inverse ?3307) ?3309)))) ?3309 =>= inverse (inverse (inverse (inverse ?3308))) [3309, 3308, 3307] by Demod 1550 with 1018 at 1,2
+Id : 1601, {_}: ?3308 =<= inverse (inverse (inverse (inverse ?3308))) [3308] by Demod 1600 with 794 at 2
+Id : 1634, {_}: multiply ?3404 (inverse (inverse (inverse ?3405))) =>= divide ?3404 ?3405 [3405, 3404] by Super 29 with 1601 at 2,3
+Id : 1707, {_}: divide (inverse (inverse ?3544)) (inverse (inverse ?3545)) =>= inverse (inverse (divide ?3544 ?3545)) [3545, 3544] by Super 944 with 1634 at 1,1,3
+Id : 1741, {_}: multiply (inverse (inverse ?3544)) (inverse ?3545) =>= inverse (inverse (divide ?3544 ?3545)) [3545, 3544] by Demod 1707 with 29 at 2
+Id : 1807, {_}: divide (inverse (inverse (inverse (inverse (divide ?3666 ?3667))))) (inverse ?3667) =>= inverse (inverse ?3666) [3667, 3666] by Super 484 with 1741 at 1,1,1,2
+Id : 1849, {_}: multiply (inverse (inverse (inverse (inverse (divide ?3666 ?3667))))) ?3667 =>= inverse (inverse ?3666) [3667, 3666] by Demod 1807 with 29 at 2
+Id : 1850, {_}: multiply (divide ?3666 ?3667) ?3667 =>= inverse (inverse ?3666) [3667, 3666] by Demod 1849 with 1601 at 1,2
+Id : 1880, {_}: inverse (inverse ?3792) =<= divide (divide ?3792 (inverse (inverse (inverse ?3793)))) ?3793 [3793, 3792] by Super 1634 with 1850 at 2
+Id : 2688, {_}: inverse (inverse ?5905) =<= divide (multiply ?5905 (inverse (inverse ?5906))) ?5906 [5906, 5905] by Demod 1880 with 29 at 1,3
+Id : 224, {_}: multiply (inverse (inverse (divide ?518 ?518))) ?519 =>= inverse (inverse ?519) [519, 518] by Super 32 with 36 at 1,2
+Id : 2714, {_}: inverse (inverse (inverse (inverse (divide ?5996 ?5996)))) =?= divide (inverse (inverse (inverse (inverse ?5997)))) ?5997 [5997, 5996] by Super 2688 with 224 at 1,3
+Id : 2767, {_}: divide ?5996 ?5996 =?= divide (inverse (inverse (inverse (inverse ?5997)))) ?5997 [5997, 5996] by Demod 2714 with 1601 at 2
+Id : 2768, {_}: divide ?5996 ?5996 =?= divide ?5997 ?5997 [5997, 5996] by Demod 2767 with 1601 at 1,3
+Id : 2830, {_}: divide (inverse (divide ?6176 (divide (inverse ?6177) (divide (inverse ?6176) ?6178)))) ?6178 =?= inverse (divide ?6177 (divide ?6179 ?6179)) [6179, 6178, 6177, 6176] by Super 145 with 2768 at 2,1,3
+Id : 30, {_}: divide (inverse (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 2 with 4 at 1,2
+Id : 31, {_}: divide (inverse (divide ?2 (divide ?3 (divide (inverse ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 30 with 4 at 1,2,2,1,1,2
+Id : 2905, {_}: inverse ?6177 =<= inverse (divide ?6177 (divide ?6179 ?6179)) [6179, 6177] by Demod 2830 with 31 at 2
+Id : 2962, {_}: divide ?6532 (divide ?6533 ?6533) =?= inverse (inverse (inverse (inverse ?6532))) [6533, 6532] by Super 1601 with 2905 at 1,1,1,3
+Id : 3014, {_}: divide ?6532 (divide ?6533 ?6533) =>= ?6532 [6533, 6532] by Demod 2962 with 1601 at 3
+Id : 3088, {_}: divide (inverse (divide ?6789 ?6790)) (divide ?6791 ?6791) =>= inverse (inverse (multiply ?6790 (inverse ?6789))) [6791, 6790, 6789] by Super 250 with 3014 at 2,1,1,3
+Id : 3148, {_}: inverse (divide ?6789 ?6790) =<= inverse (inverse (multiply ?6790 (inverse ?6789))) [6790, 6789] by Demod 3088 with 3014 at 2
+Id : 3149, {_}: inverse (divide ?6789 ?6790) =<= divide (inverse (inverse ?6790)) ?6789 [6790, 6789] by Demod 3148 with 944 at 3
+Id : 3377, {_}: inverse (divide ?50 (multiply ?49 ?50)) =>= ?49 [49, 50] by Demod 484 with 3149 at 2
+Id : 3423, {_}: inverse (divide ?7500 ?7501) =<= divide (inverse (inverse ?7501)) ?7500 [7501, 7500] by Demod 3148 with 944 at 3
+Id : 3441, {_}: inverse (divide ?7566 (inverse (inverse ?7567))) =>= divide ?7567 ?7566 [7567, 7566] by Super 3423 with 1601 at 1,3
+Id : 3536, {_}: inverse (multiply ?7566 (inverse ?7567)) =>= divide ?7567 ?7566 [7567, 7566] by Demod 3441 with 29 at 1,2
+Id : 229, {_}: inverse ?541 =<= divide (inverse (divide ?542 ?542)) ?541 [542, 541] by Super 35 with 4 at 1,3
+Id : 236, {_}: inverse ?562 =<= divide (inverse (inverse (inverse (divide ?563 ?563)))) ?562 [563, 562] by Super 229 with 36 at 1,1,3
+Id : 3378, {_}: inverse ?562 =<= inverse (divide ?562 (inverse (divide ?563 ?563))) [563, 562] by Demod 236 with 3149 at 3
+Id : 3383, {_}: inverse ?562 =<= inverse (multiply ?562 (divide ?563 ?563)) [563, 562] by Demod 3378 with 29 at 1,3
+Id : 3089, {_}: multiply ?6793 (divide ?6794 ?6794) =>= inverse (inverse ?6793) [6794, 6793] by Super 1850 with 3014 at 1,2
+Id : 3760, {_}: inverse ?562 =<= inverse (inverse (inverse ?562)) [562] by Demod 3383 with 3089 at 1,3
+Id : 3763, {_}: multiply ?3404 (inverse ?3405) =>= divide ?3404 ?3405 [3405, 3404] by Demod 1634 with 3760 at 2,2
+Id : 3764, {_}: inverse (divide ?7566 ?7567) =>= divide ?7567 ?7566 [7567, 7566] by Demod 3536 with 3763 at 1,2
+Id : 3776, {_}: divide (multiply ?49 ?50) ?50 =>= ?49 [50, 49] by Demod 3377 with 3764 at 2
+Id : 1886, {_}: multiply (divide ?3813 ?3814) ?3814 =>= inverse (inverse ?3813) [3814, 3813] by Demod 1849 with 1601 at 1,2
+Id : 1895, {_}: multiply (multiply ?3842 ?3843) (inverse ?3843) =>= inverse (inverse ?3842) [3843, 3842] by Super 1886 with 29 at 1,2
+Id : 3766, {_}: divide (multiply ?3842 ?3843) ?3843 =>= inverse (inverse ?3842) [3843, 3842] by Demod 1895 with 3763 at 2
+Id : 3800, {_}: inverse (inverse ?49) =>= ?49 [49] by Demod 3776 with 3766 at 2
+Id : 3806, {_}: multiply (multiply (inverse ?268) ?268) ?269 =>= ?269 [269, 268] by Demod 128 with 3800 at 3
+Id : 3889, {_}: a2 =?= a2 [] by Demod 1 with 3806 at 2
+Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
+% SZS output end CNFRefutation for GRP452-1.p
+11236: solved GRP452-1.p in 0.984061 using kbo
+11236: status Unsatisfiable for GRP452-1.p
+NO CLASH, using fixed ground order
+11242: Facts:
+11242: Id : 2, {_}:
+ divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
+ (divide (divide ?5 ?4) ?2)
+ =>=
+ ?3
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11242: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11242: Goal:
+11242: Id : 1, {_}:
+ multiply (inverse a1) a1 =>= multiply (inverse b1) b1
+ [] by prove_these_axioms_1
+11242: Order:
+11242: nrkbo
+11242: Leaf order:
+11242: divide 7 2 0
+11242: b1 2 0 2 1,1,3
+11242: multiply 3 2 2 0,2
+11242: inverse 4 1 2 0,1,2
+11242: a1 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+11243: Facts:
+11243: Id : 2, {_}:
+ divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
+ (divide (divide ?5 ?4) ?2)
+ =>=
+ ?3
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11243: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11243: Goal:
+11243: Id : 1, {_}:
+ multiply (inverse a1) a1 =>= multiply (inverse b1) b1
+ [] by prove_these_axioms_1
+11243: Order:
+11243: kbo
+11243: Leaf order:
+11243: divide 7 2 0
+11243: b1 2 0 2 1,1,3
+11243: multiply 3 2 2 0,2
+11243: inverse 4 1 2 0,1,2
+11243: a1 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+11244: Facts:
+11244: Id : 2, {_}:
+ divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
+ (divide (divide ?5 ?4) ?2)
+ =>=
+ ?3
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11244: Id : 3, {_}:
+ multiply ?7 ?8 =?= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11244: Goal:
+11244: Id : 1, {_}:
+ multiply (inverse a1) a1 =>= multiply (inverse b1) b1
+ [] by prove_these_axioms_1
+11244: Order:
+11244: lpo
+11244: Leaf order:
+11244: divide 7 2 0
+11244: b1 2 0 2 1,1,3
+11244: multiply 3 2 2 0,2
+11244: inverse 4 1 2 0,1,2
+11244: a1 2 0 2 1,1,2
+% SZS status Timeout for GRP469-1.p
+NO CLASH, using fixed ground order
+11271: Facts:
+11271: Id : 2, {_}:
+ divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
+ (divide (divide ?5 ?4) ?2)
+ =>=
+ ?3
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11271: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11271: Goal:
+11271: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+11271: Order:
+11271: nrkbo
+11271: Leaf order:
+11271: divide 7 2 0
+11271: a2 2 0 2 2,2
+11271: multiply 3 2 2 0,2
+11271: inverse 3 1 1 0,1,1,2
+11271: b2 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+11272: Facts:
+11272: Id : 2, {_}:
+ divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
+ (divide (divide ?5 ?4) ?2)
+ =>=
+ ?3
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11272: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11272: Goal:
+11272: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+11272: Order:
+11272: kbo
+11272: Leaf order:
+11272: divide 7 2 0
+11272: a2 2 0 2 2,2
+11272: multiply 3 2 2 0,2
+11272: inverse 3 1 1 0,1,1,2
+11272: b2 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+11273: Facts:
+11273: Id : 2, {_}:
+ divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
+ (divide (divide ?5 ?4) ?2)
+ =>=
+ ?3
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11273: Id : 3, {_}:
+ multiply ?7 ?8 =?= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11273: Goal:
+11273: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+11273: Order:
+11273: lpo
+11273: Leaf order:
+11273: divide 7 2 0
+11273: a2 2 0 2 2,2
+11273: multiply 3 2 2 0,2
+11273: inverse 3 1 1 0,1,1,2
+11273: b2 2 0 2 1,1,1,2
+Statistics :
+Max weight : 55
+Found proof, 64.719986s
+% SZS status Unsatisfiable for GRP470-1.p
+% SZS output start CNFRefutation for GRP470-1.p
+Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
+Id : 2, {_}: divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) (divide (divide ?5 ?4) ?2) =>= ?3 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+Id : 4, {_}: divide (inverse (divide ?10 (divide ?11 (divide ?12 ?13)))) (divide (divide ?13 ?12) ?10) =>= ?11 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
+Id : 8, {_}: divide (inverse ?35) (divide (divide ?36 ?37) (inverse (divide (divide ?37 ?36) (divide ?35 (divide ?38 ?39))))) =>= divide ?39 ?38 [39, 38, 37, 36, 35] by Super 4 with 2 at 1,1,2
+Id : 377, {_}: divide (inverse ?1785) (multiply (divide ?1786 ?1787) (divide (divide ?1787 ?1786) (divide ?1785 (divide ?1788 ?1789)))) =>= divide ?1789 ?1788 [1789, 1788, 1787, 1786, 1785] by Demod 8 with 3 at 2,2
+Id : 362, {_}: divide (inverse ?35) (multiply (divide ?36 ?37) (divide (divide ?37 ?36) (divide ?35 (divide ?38 ?39)))) =>= divide ?39 ?38 [39, 38, 37, 36, 35] by Demod 8 with 3 at 2,2
+Id : 385, {_}: divide (inverse ?1855) (multiply (divide ?1856 ?1857) (divide (divide ?1857 ?1856) (divide ?1855 (divide ?1858 ?1859)))) =?= divide (multiply (divide ?1860 ?1861) (divide (divide ?1861 ?1860) (divide ?1862 (divide ?1859 ?1858)))) (inverse ?1862) [1862, 1861, 1860, 1859, 1858, 1857, 1856, 1855] by Super 377 with 362 at 2,2,2,2,2
+Id : 436, {_}: divide ?1859 ?1858 =<= divide (multiply (divide ?1860 ?1861) (divide (divide ?1861 ?1860) (divide ?1862 (divide ?1859 ?1858)))) (inverse ?1862) [1862, 1861, 1860, 1858, 1859] by Demod 385 with 362 at 2
+Id : 6830, {_}: divide ?34177 ?34178 =<= multiply (multiply (divide ?34179 ?34180) (divide (divide ?34180 ?34179) (divide ?34181 (divide ?34177 ?34178)))) ?34181 [34181, 34180, 34179, 34178, 34177] by Demod 436 with 3 at 3
+Id : 6831, {_}: divide (inverse (divide ?34183 (divide ?34184 (divide ?34185 ?34186)))) (divide (divide ?34186 ?34185) ?34183) =?= multiply (multiply (divide ?34187 ?34188) (divide (divide ?34188 ?34187) (divide ?34189 ?34184))) ?34189 [34189, 34188, 34187, 34186, 34185, 34184, 34183] by Super 6830 with 2 at 2,2,2,1,3
+Id : 7101, {_}: ?35399 =<= multiply (multiply (divide ?35400 ?35401) (divide (divide ?35401 ?35400) (divide ?35402 ?35399))) ?35402 [35402, 35401, 35400, 35399] by Demod 6831 with 2 at 2
+Id : 7613, {_}: ?38021 =<= multiply (multiply (divide (inverse ?38022) ?38023) (divide (multiply ?38023 ?38022) (divide ?38024 ?38021))) ?38024 [38024, 38023, 38022, 38021] by Super 7101 with 3 at 1,2,1,3
+Id : 7678, {_}: ?38552 =<= multiply (multiply (multiply (inverse ?38553) ?38554) (divide (multiply (inverse ?38554) ?38553) (divide ?38555 ?38552))) ?38555 [38555, 38554, 38553, 38552] by Super 7613 with 3 at 1,1,3
+Id : 5, {_}: divide (inverse (divide ?15 (divide ?16 (divide (divide (divide ?17 ?18) ?19) (inverse (divide ?19 (divide ?20 (divide ?18 ?17)))))))) (divide ?20 ?15) =>= ?16 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 1,2,2
+Id : 15, {_}: divide (inverse (divide ?15 (divide ?16 (multiply (divide (divide ?17 ?18) ?19) (divide ?19 (divide ?20 (divide ?18 ?17))))))) (divide ?20 ?15) =>= ?16 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 2,2,1,1,2
+Id : 18, {_}: divide (inverse (divide ?82 ?83)) (divide (divide ?84 ?85) ?82) =?= inverse (divide ?84 (divide ?83 (multiply (divide (divide ?86 ?87) ?88) (divide ?88 (divide ?85 (divide ?87 ?86)))))) [88, 87, 86, 85, 84, 83, 82] by Super 2 with 15 at 2,1,1,2
+Id : 1723, {_}: divide (divide (inverse (divide ?8026 ?8027)) (divide (divide ?8028 ?8029) ?8026)) (divide ?8029 ?8028) =>= ?8027 [8029, 8028, 8027, 8026] by Super 15 with 18 at 1,2
+Id : 1779, {_}: divide (divide (inverse (multiply ?8457 ?8458)) (divide (divide ?8459 ?8460) ?8457)) (divide ?8460 ?8459) =>= inverse ?8458 [8460, 8459, 8458, 8457] by Super 1723 with 3 at 1,1,1,2
+Id : 6854, {_}: divide (divide (inverse (multiply ?34395 ?34396)) (divide (divide ?34397 ?34398) ?34395)) (divide ?34398 ?34397) =?= multiply (multiply (divide ?34399 ?34400) (divide (divide ?34400 ?34399) (divide ?34401 (inverse ?34396)))) ?34401 [34401, 34400, 34399, 34398, 34397, 34396, 34395] by Super 6830 with 1779 at 2,2,2,1,3
+Id : 7005, {_}: inverse ?34396 =<= multiply (multiply (divide ?34399 ?34400) (divide (divide ?34400 ?34399) (divide ?34401 (inverse ?34396)))) ?34401 [34401, 34400, 34399, 34396] by Demod 6854 with 1779 at 2
+Id : 7303, {_}: inverse ?36376 =<= multiply (multiply (divide ?36377 ?36378) (divide (divide ?36378 ?36377) (multiply ?36379 ?36376))) ?36379 [36379, 36378, 36377, 36376] by Demod 7005 with 3 at 2,2,1,3
+Id : 7337, {_}: inverse ?36648 =<= multiply (multiply (divide (inverse ?36649) ?36650) (divide (multiply ?36650 ?36649) (multiply ?36651 ?36648))) ?36651 [36651, 36650, 36649, 36648] by Super 7303 with 3 at 1,2,1,3
+Id : 2771, {_}: divide (divide (inverse (multiply ?13734 ?13735)) (divide (divide ?13736 ?13737) ?13734)) (divide ?13737 ?13736) =>= inverse ?13735 [13737, 13736, 13735, 13734] by Super 1723 with 3 at 1,1,1,2
+Id : 2814, {_}: divide (divide (inverse (multiply (inverse ?14067) ?14068)) (multiply (divide ?14069 ?14070) ?14067)) (divide ?14070 ?14069) =>= inverse ?14068 [14070, 14069, 14068, 14067] by Super 2771 with 3 at 2,1,2
+Id : 7163, {_}: ?35873 =<= multiply (multiply (divide (multiply (divide ?35873 ?35874) ?35875) (inverse (multiply (inverse ?35875) ?35876))) (inverse ?35876)) ?35874 [35876, 35875, 35874, 35873] by Super 7101 with 2814 at 2,1,3
+Id : 7239, {_}: ?35873 =<= multiply (multiply (multiply (multiply (divide ?35873 ?35874) ?35875) (multiply (inverse ?35875) ?35876)) (inverse ?35876)) ?35874 [35876, 35875, 35874, 35873] by Demod 7163 with 3 at 1,1,3
+Id : 1759, {_}: divide (divide (inverse (divide ?8306 ?8307)) (divide (multiply ?8308 ?8309) ?8306)) (divide (inverse ?8309) ?8308) =>= ?8307 [8309, 8308, 8307, 8306] by Super 1723 with 3 at 1,2,1,2
+Id : 7159, {_}: ?35853 =<= multiply (multiply (divide (divide (multiply ?35853 ?35854) ?35855) (inverse (divide ?35855 ?35856))) ?35856) (inverse ?35854) [35856, 35855, 35854, 35853] by Super 7101 with 1759 at 2,1,3
+Id : 7892, {_}: ?39681 =<= multiply (multiply (multiply (divide (multiply ?39681 ?39682) ?39683) (divide ?39683 ?39684)) ?39684) (inverse ?39682) [39684, 39683, 39682, 39681] by Demod 7159 with 3 at 1,1,3
+Id : 9472, {_}: ?48735 =<= multiply (multiply (multiply (multiply (multiply ?48735 ?48736) ?48737) (divide (inverse ?48737) ?48738)) ?48738) (inverse ?48736) [48738, 48737, 48736, 48735] by Super 7892 with 3 at 1,1,1,3
+Id : 1266, {_}: divide (divide (inverse (divide ?5775 ?5776)) (divide (divide ?5777 ?5778) ?5775)) (divide ?5778 ?5777) =>= ?5776 [5778, 5777, 5776, 5775] by Super 15 with 18 at 1,2
+Id : 7158, {_}: ?35848 =<= multiply (multiply (divide (divide (divide ?35848 ?35849) ?35850) (inverse (divide ?35850 ?35851))) ?35851) ?35849 [35851, 35850, 35849, 35848] by Super 7101 with 1266 at 2,1,3
+Id : 7234, {_}: ?35848 =<= multiply (multiply (multiply (divide (divide ?35848 ?35849) ?35850) (divide ?35850 ?35851)) ?35851) ?35849 [35851, 35850, 35849, 35848] by Demod 7158 with 3 at 1,1,3
+Id : 9552, {_}: divide (divide ?49359 (divide (inverse ?49360) ?49361)) ?49362 =<= multiply (multiply ?49359 ?49361) (inverse (divide ?49362 ?49360)) [49362, 49361, 49360, 49359] by Super 9472 with 7234 at 1,1,3
+Id : 9555, {_}: multiply (divide ?49374 (divide (inverse (inverse ?49375)) ?49376)) ?49377 =<= multiply (multiply ?49374 ?49376) (inverse (multiply (inverse ?49377) ?49375)) [49377, 49376, 49375, 49374] by Super 9472 with 7239 at 1,1,3
+Id : 10048, {_}: divide (divide (multiply ?52036 ?52037) (divide (inverse ?52038) (inverse (multiply (inverse ?52039) ?52040)))) ?52041 =<= multiply (multiply (divide ?52036 (divide (inverse (inverse ?52040)) ?52037)) ?52039) (inverse (divide ?52041 ?52038)) [52041, 52040, 52039, 52038, 52037, 52036] by Super 9552 with 9555 at 1,3
+Id : 10181, {_}: divide (divide (multiply ?52036 ?52037) (multiply (inverse ?52038) (multiply (inverse ?52039) ?52040))) ?52041 =<= multiply (multiply (divide ?52036 (divide (inverse (inverse ?52040)) ?52037)) ?52039) (inverse (divide ?52041 ?52038)) [52041, 52040, 52039, 52038, 52037, 52036] by Demod 10048 with 3 at 2,1,2
+Id : 10182, {_}: divide (divide (multiply ?52036 ?52037) (multiply (inverse ?52038) (multiply (inverse ?52039) ?52040))) ?52041 =<= divide (divide (divide ?52036 (divide (inverse (inverse ?52040)) ?52037)) (divide (inverse ?52038) ?52039)) ?52041 [52041, 52040, 52039, 52038, 52037, 52036] by Demod 10181 with 9552 at 3
+Id : 7161, {_}: ?35863 =<= multiply (multiply (divide (divide (divide ?35863 ?35864) ?35865) (inverse (multiply ?35865 ?35866))) (inverse ?35866)) ?35864 [35866, 35865, 35864, 35863] by Super 7101 with 1779 at 2,1,3
+Id : 7237, {_}: ?35863 =<= multiply (multiply (multiply (divide (divide ?35863 ?35864) ?35865) (multiply ?35865 ?35866)) (inverse ?35866)) ?35864 [35866, 35865, 35864, 35863] by Demod 7161 with 3 at 1,1,3
+Id : 9554, {_}: divide (divide ?49369 (divide (inverse (inverse ?49370)) ?49371)) ?49372 =>= multiply (multiply ?49369 ?49371) (inverse (multiply ?49372 ?49370)) [49372, 49371, 49370, 49369] by Super 9472 with 7237 at 1,1,3
+Id : 10183, {_}: divide (divide (multiply ?52036 ?52037) (multiply (inverse ?52038) (multiply (inverse ?52039) ?52040))) ?52041 =<= divide (multiply (multiply ?52036 ?52037) (inverse (multiply (divide (inverse ?52038) ?52039) ?52040))) ?52041 [52041, 52040, 52039, 52038, 52037, 52036] by Demod 10182 with 9554 at 1,3
+Id : 12174, {_}: multiply (multiply ?64029 ?64030) (inverse (multiply (divide (inverse ?64031) ?64032) ?64033)) =<= multiply (multiply (multiply (multiply (divide (divide (multiply ?64029 ?64030) (multiply (inverse ?64031) (multiply (inverse ?64032) ?64033))) ?64034) ?64035) (multiply (inverse ?64035) ?64036)) (inverse ?64036)) ?64034 [64036, 64035, 64034, 64033, 64032, 64031, 64030, 64029] by Super 7239 with 10183 at 1,1,1,1,3
+Id : 12258, {_}: multiply (multiply ?64029 ?64030) (inverse (multiply (divide (inverse ?64031) ?64032) ?64033)) =>= divide (multiply ?64029 ?64030) (multiply (inverse ?64031) (multiply (inverse ?64032) ?64033)) [64033, 64032, 64031, 64030, 64029] by Demod 12174 with 7239 at 3
+Id : 12491, {_}: inverse (inverse (multiply (divide (inverse ?65291) ?65292) ?65293)) =<= multiply (multiply (divide (inverse ?65294) ?65295) (divide (multiply ?65295 ?65294) (divide (multiply ?65296 ?65297) (multiply (inverse ?65291) (multiply (inverse ?65292) ?65293))))) (multiply ?65296 ?65297) [65297, 65296, 65295, 65294, 65293, 65292, 65291] by Super 7337 with 12258 at 2,2,1,3
+Id : 7157, {_}: ?35843 =<= multiply (multiply (divide (inverse ?35844) ?35845) (divide (multiply ?35845 ?35844) (divide ?35846 ?35843))) ?35846 [35846, 35845, 35844, 35843] by Super 7101 with 3 at 1,2,1,3
+Id : 12726, {_}: inverse (inverse (multiply (divide (inverse ?66353) ?66354) ?66355)) =>= multiply (inverse ?66353) (multiply (inverse ?66354) ?66355) [66355, 66354, 66353] by Demod 12491 with 7157 at 3
+Id : 7, {_}: divide (inverse (divide ?29 ?30)) (divide (divide ?31 (divide ?32 ?33)) ?29) =>= inverse (divide ?31 (divide ?30 (divide ?33 ?32))) [33, 32, 31, 30, 29] by Super 4 with 2 at 2,1,1,2
+Id : 53, {_}: inverse (divide ?279 (divide (divide ?280 (divide (divide ?281 ?282) ?279)) (divide ?282 ?281))) =>= ?280 [282, 281, 280, 279] by Super 2 with 7 at 2
+Id : 12727, {_}: inverse (inverse (multiply (divide ?66357 ?66358) ?66359)) =<= multiply (inverse (divide ?66360 (divide (divide ?66357 (divide (divide ?66361 ?66362) ?66360)) (divide ?66362 ?66361)))) (multiply (inverse ?66358) ?66359) [66362, 66361, 66360, 66359, 66358, 66357] by Super 12726 with 53 at 1,1,1,1,2
+Id : 12770, {_}: inverse (inverse (multiply (divide ?66357 ?66358) ?66359)) =>= multiply ?66357 (multiply (inverse ?66358) ?66359) [66359, 66358, 66357] by Demod 12727 with 53 at 1,3
+Id : 12807, {_}: multiply ?66813 (inverse (multiply (divide ?66814 ?66815) ?66816)) =>= divide ?66813 (multiply ?66814 (multiply (inverse ?66815) ?66816)) [66816, 66815, 66814, 66813] by Super 3 with 12770 at 2,3
+Id : 12991, {_}: inverse (inverse (divide (divide ?67798 ?67799) (multiply ?67800 (multiply (inverse ?67801) ?67802)))) =>= multiply ?67798 (multiply (inverse ?67799) (inverse (multiply (divide ?67800 ?67801) ?67802))) [67802, 67801, 67800, 67799, 67798] by Super 12770 with 12807 at 1,1,2
+Id : 15565, {_}: inverse (inverse (divide (divide ?82879 ?82880) (multiply ?82881 (multiply (inverse ?82882) ?82883)))) =>= multiply ?82879 (divide (inverse ?82880) (multiply ?82881 (multiply (inverse ?82882) ?82883))) [82883, 82882, 82881, 82880, 82879] by Demod 12991 with 12807 at 2,3
+Id : 6973, {_}: ?34184 =<= multiply (multiply (divide ?34187 ?34188) (divide (divide ?34188 ?34187) (divide ?34189 ?34184))) ?34189 [34189, 34188, 34187, 34184] by Demod 6831 with 2 at 2
+Id : 15584, {_}: inverse (inverse (divide (divide ?83055 ?83056) ?83057)) =<= multiply ?83055 (divide (inverse ?83056) (multiply (multiply (divide ?83058 ?83059) (divide (divide ?83059 ?83058) (divide (multiply (inverse ?83060) ?83061) ?83057))) (multiply (inverse ?83060) ?83061))) [83061, 83060, 83059, 83058, 83057, 83056, 83055] by Super 15565 with 6973 at 2,1,1,2
+Id : 15659, {_}: inverse (inverse (divide (divide ?83055 ?83056) ?83057)) =>= multiply ?83055 (divide (inverse ?83056) ?83057) [83057, 83056, 83055] by Demod 15584 with 6973 at 2,2,3
+Id : 12825, {_}: inverse (inverse (multiply (divide ?66943 ?66944) ?66945)) =>= multiply ?66943 (multiply (inverse ?66944) ?66945) [66945, 66944, 66943] by Demod 12727 with 53 at 1,3
+Id : 12858, {_}: inverse (inverse (multiply (multiply ?67174 ?67175) ?67176)) =>= multiply ?67174 (multiply (inverse (inverse ?67175)) ?67176) [67176, 67175, 67174] by Super 12825 with 3 at 1,1,1,2
+Id : 13083, {_}: inverse (inverse (divide (multiply ?68472 ?68473) (multiply ?68474 (multiply (inverse ?68475) ?68476)))) =>= multiply ?68472 (multiply (inverse (inverse ?68473)) (inverse (multiply (divide ?68474 ?68475) ?68476))) [68476, 68475, 68474, 68473, 68472] by Super 12858 with 12807 at 1,1,2
+Id : 14137, {_}: inverse (inverse (divide (multiply ?73757 ?73758) (multiply ?73759 (multiply (inverse ?73760) ?73761)))) =>= multiply ?73757 (divide (inverse (inverse ?73758)) (multiply ?73759 (multiply (inverse ?73760) ?73761))) [73761, 73760, 73759, 73758, 73757] by Demod 13083 with 12807 at 2,3
+Id : 14155, {_}: inverse (inverse (divide (multiply ?73925 ?73926) ?73927)) =<= multiply ?73925 (divide (inverse (inverse ?73926)) (multiply (multiply (divide ?73928 ?73929) (divide (divide ?73929 ?73928) (divide (multiply (inverse ?73930) ?73931) ?73927))) (multiply (inverse ?73930) ?73931))) [73931, 73930, 73929, 73928, 73927, 73926, 73925] by Super 14137 with 6973 at 2,1,1,2
+Id : 14212, {_}: inverse (inverse (divide (multiply ?73925 ?73926) ?73927)) =>= multiply ?73925 (divide (inverse (inverse ?73926)) ?73927) [73927, 73926, 73925] by Demod 14155 with 6973 at 2,2,3
+Id : 15715, {_}: multiply ?83687 (inverse (divide (divide ?83688 ?83689) ?83690)) =>= divide ?83687 (multiply ?83688 (divide (inverse ?83689) ?83690)) [83690, 83689, 83688, 83687] by Super 3 with 15659 at 2,3
+Id : 15912, {_}: divide (divide ?84886 (divide (inverse ?84887) ?84888)) (divide ?84889 ?84890) =<= divide (multiply ?84886 ?84888) (multiply ?84889 (divide (inverse ?84890) ?84887)) [84890, 84889, 84888, 84887, 84886] by Super 9552 with 15715 at 3
+Id : 16736, {_}: inverse (inverse (divide (divide ?88411 (divide (inverse ?88412) ?88413)) (divide ?88414 ?88415))) =>= multiply ?88411 (divide (inverse (inverse ?88413)) (multiply ?88414 (divide (inverse ?88415) ?88412))) [88415, 88414, 88413, 88412, 88411] by Super 14212 with 15912 at 1,1,2
+Id : 16823, {_}: multiply ?88411 (divide (inverse (divide (inverse ?88412) ?88413)) (divide ?88414 ?88415)) =<= multiply ?88411 (divide (inverse (inverse ?88413)) (multiply ?88414 (divide (inverse ?88415) ?88412))) [88415, 88414, 88413, 88412, 88411] by Demod 16736 with 15659 at 2
+Id : 19503, {_}: inverse (divide (inverse (inverse ?101466)) (multiply ?101467 (divide (inverse ?101468) ?101469))) =<= multiply (multiply (divide (inverse ?101470) ?101471) (divide (multiply ?101471 ?101470) (multiply ?101472 (divide (inverse (divide (inverse ?101469) ?101466)) (divide ?101467 ?101468))))) ?101472 [101472, 101471, 101470, 101469, 101468, 101467, 101466] by Super 7337 with 16823 at 2,2,1,3
+Id : 20509, {_}: inverse (divide (inverse (inverse ?107024)) (multiply ?107025 (divide (inverse ?107026) ?107027))) =>= inverse (divide (inverse (divide (inverse ?107027) ?107024)) (divide ?107025 ?107026)) [107027, 107026, 107025, 107024] by Demod 19503 with 7337 at 3
+Id : 15122, {_}: multiply ?80264 (inverse (divide (multiply ?80265 ?80266) ?80267)) =<= divide ?80264 (multiply ?80265 (divide (inverse (inverse ?80266)) ?80267)) [80267, 80266, 80265, 80264] by Super 3 with 14212 at 2,3
+Id : 20594, {_}: inverse (multiply (inverse (inverse ?107698)) (inverse (divide (multiply ?107699 ?107700) ?107701))) =>= inverse (divide (inverse (divide (inverse ?107701) ?107698)) (divide ?107699 (inverse ?107700))) [107701, 107700, 107699, 107698] by Super 20509 with 15122 at 1,2
+Id : 20893, {_}: inverse (multiply (inverse (inverse ?108369)) (inverse (divide (multiply ?108370 ?108371) ?108372))) =>= inverse (divide (inverse (divide (inverse ?108372) ?108369)) (multiply ?108370 ?108371)) [108372, 108371, 108370, 108369] by Demod 20594 with 3 at 2,1,3
+Id : 20903, {_}: inverse (multiply (inverse (inverse ?108447)) (inverse (divide ?108448 ?108449))) =<= inverse (divide (inverse (divide (inverse ?108449) ?108447)) (multiply (multiply (divide ?108450 ?108451) (divide (divide ?108451 ?108450) (divide ?108452 ?108448))) ?108452)) [108452, 108451, 108450, 108449, 108448, 108447] by Super 20893 with 6973 at 1,1,2,1,2
+Id : 21279, {_}: inverse (multiply (inverse (inverse ?109423)) (inverse (divide ?109424 ?109425))) =>= inverse (divide (inverse (divide (inverse ?109425) ?109423)) ?109424) [109425, 109424, 109423] by Demod 20903 with 6973 at 2,1,3
+Id : 21354, {_}: inverse (multiply (multiply ?109942 (divide (inverse ?109943) ?109944)) (inverse (divide ?109945 ?109946))) =>= inverse (divide (inverse (divide (inverse ?109946) (divide (divide ?109942 ?109943) ?109944))) ?109945) [109946, 109945, 109944, 109943, 109942] by Super 21279 with 15659 at 1,1,2
+Id : 25671, {_}: inverse (divide (divide ?128948 (divide (inverse ?128949) (divide (inverse ?128950) ?128951))) ?128952) =<= inverse (divide (inverse (divide (inverse ?128949) (divide (divide ?128948 ?128950) ?128951))) ?128952) [128952, 128951, 128950, 128949, 128948] by Demod 21354 with 9552 at 1,2
+Id : 25729, {_}: inverse (divide (divide ?129446 (divide (inverse (divide ?129447 (divide (divide ?129448 (divide (divide ?129449 ?129450) ?129447)) (divide ?129450 ?129449)))) (divide (inverse ?129451) ?129452))) ?129453) =>= inverse (divide (inverse (divide ?129448 (divide (divide ?129446 ?129451) ?129452))) ?129453) [129453, 129452, 129451, 129450, 129449, 129448, 129447, 129446] by Super 25671 with 53 at 1,1,1,1,3
+Id : 26075, {_}: inverse (divide (divide ?131096 (divide ?131097 (divide (inverse ?131098) ?131099))) ?131100) =<= inverse (divide (inverse (divide ?131097 (divide (divide ?131096 ?131098) ?131099))) ?131100) [131100, 131099, 131098, 131097, 131096] by Demod 25729 with 53 at 1,2,1,1,2
+Id : 26111, {_}: inverse (divide (divide ?131425 (divide ?131426 (divide (inverse (inverse ?131427)) ?131428))) ?131429) =>= inverse (divide (inverse (divide ?131426 (divide (multiply ?131425 ?131427) ?131428))) ?131429) [131429, 131428, 131427, 131426, 131425] by Super 26075 with 3 at 1,2,1,1,1,3
+Id : 30666, {_}: inverse (inverse (divide (inverse (divide ?153822 (divide (multiply ?153823 ?153824) ?153825))) ?153826)) =>= multiply ?153823 (divide (inverse (divide ?153822 (divide (inverse (inverse ?153824)) ?153825))) ?153826) [153826, 153825, 153824, 153823, 153822] by Super 15659 with 26111 at 1,2
+Id : 30731, {_}: inverse (inverse (multiply ?154370 ?154371)) =<= multiply ?154370 (divide (inverse (divide ?154372 (divide (inverse (inverse ?154371)) (divide ?154373 ?154374)))) (divide (divide ?154374 ?154373) ?154372)) [154374, 154373, 154372, 154371, 154370] by Super 30666 with 2 at 1,1,2
+Id : 31025, {_}: inverse (inverse (multiply ?155310 ?155311)) =>= multiply ?155310 (inverse (inverse ?155311)) [155311, 155310] by Demod 30731 with 2 at 2,3
+Id : 7367, {_}: inverse ?36880 =<= multiply (multiply (multiply ?36881 ?36882) (divide (divide (inverse ?36882) ?36881) (multiply ?36883 ?36880))) ?36883 [36883, 36882, 36881, 36880] by Super 7303 with 3 at 1,1,3
+Id : 15740, {_}: inverse (inverse (divide (divide ?83867 ?83868) ?83869)) =>= multiply ?83867 (divide (inverse ?83868) ?83869) [83869, 83868, 83867] by Demod 15584 with 6973 at 2,2,3
+Id : 15787, {_}: inverse (inverse (multiply (multiply ?84179 ?84180) (inverse (multiply ?84181 ?84182)))) =>= multiply ?84179 (divide (inverse (divide (inverse (inverse ?84182)) ?84180)) ?84181) [84182, 84181, 84180, 84179] by Super 15740 with 9554 at 1,1,2
+Id : 15809, {_}: multiply ?84179 (multiply (inverse (inverse ?84180)) (inverse (multiply ?84181 ?84182))) =>= multiply ?84179 (divide (inverse (divide (inverse (inverse ?84182)) ?84180)) ?84181) [84182, 84181, 84180, 84179] by Demod 15787 with 12858 at 2
+Id : 16238, {_}: inverse (multiply (inverse (inverse ?86040)) (inverse (multiply ?86041 ?86042))) =<= multiply (multiply (multiply ?86043 ?86044) (divide (divide (inverse ?86044) ?86043) (multiply ?86045 (divide (inverse (divide (inverse (inverse ?86042)) ?86040)) ?86041)))) ?86045 [86045, 86044, 86043, 86042, 86041, 86040] by Super 7367 with 15809 at 2,2,1,3
+Id : 16326, {_}: inverse (multiply (inverse (inverse ?86040)) (inverse (multiply ?86041 ?86042))) =>= inverse (divide (inverse (divide (inverse (inverse ?86042)) ?86040)) ?86041) [86042, 86041, 86040] by Demod 16238 with 7367 at 3
+Id : 31064, {_}: inverse (inverse (divide (inverse (divide (inverse (inverse ?155519)) ?155520)) ?155521)) =>= multiply (inverse (inverse ?155520)) (inverse (inverse (inverse (multiply ?155521 ?155519)))) [155521, 155520, 155519] by Super 31025 with 16326 at 1,2
+Id : 30884, {_}: inverse (inverse (multiply ?154370 ?154371)) =>= multiply ?154370 (inverse (inverse ?154371)) [154371, 154370] by Demod 30731 with 2 at 2,3
+Id : 32647, {_}: inverse (inverse (divide (inverse (divide (inverse (inverse ?161221)) ?161222)) ?161223)) =>= multiply (inverse (inverse ?161222)) (inverse (multiply ?161223 (inverse (inverse ?161221)))) [161223, 161222, 161221] by Demod 31064 with 30884 at 1,2,3
+Id : 32648, {_}: inverse (inverse (divide (inverse (divide (inverse ?161225) ?161226)) ?161227)) =<= multiply (inverse (inverse ?161226)) (inverse (multiply ?161227 (inverse (inverse (divide ?161228 (divide (divide ?161225 (divide (divide ?161229 ?161230) ?161228)) (divide ?161230 ?161229))))))) [161230, 161229, 161228, 161227, 161226, 161225] by Super 32647 with 53 at 1,1,1,1,1,1,2
+Id : 33188, {_}: inverse (inverse (divide (inverse (divide (inverse ?162681) ?162682)) ?162683)) =>= multiply (inverse (inverse ?162682)) (inverse (multiply ?162683 (inverse ?162681))) [162683, 162682, 162681] by Demod 32648 with 53 at 1,2,1,2,3
+Id : 33189, {_}: inverse (inverse (divide (inverse (divide ?162685 ?162686)) ?162687)) =<= multiply (inverse (inverse ?162686)) (inverse (multiply ?162687 (inverse (divide ?162688 (divide (divide ?162685 (divide (divide ?162689 ?162690) ?162688)) (divide ?162690 ?162689)))))) [162690, 162689, 162688, 162687, 162686, 162685] by Super 33188 with 53 at 1,1,1,1,1,2
+Id : 33732, {_}: inverse (inverse (divide (inverse (divide ?164373 ?164374)) ?164375)) =>= multiply (inverse (inverse ?164374)) (inverse (multiply ?164375 ?164373)) [164375, 164374, 164373] by Demod 33189 with 53 at 2,1,2,3
+Id : 33815, {_}: inverse (inverse (multiply (inverse (divide ?164946 ?164947)) ?164948)) =<= multiply (inverse (inverse ?164947)) (inverse (multiply (inverse ?164948) ?164946)) [164948, 164947, 164946] by Super 33732 with 3 at 1,1,2
+Id : 34748, {_}: multiply (inverse (divide ?166758 ?166759)) (inverse (inverse ?166760)) =<= multiply (inverse (inverse ?166759)) (inverse (multiply (inverse ?166760) ?166758)) [166760, 166759, 166758] by Demod 33815 with 30884 at 2
+Id : 34749, {_}: multiply (inverse (divide ?166762 ?166763)) (inverse (inverse (divide ?166764 (divide (divide ?166765 (divide (divide ?166766 ?166767) ?166764)) (divide ?166767 ?166766))))) =>= multiply (inverse (inverse ?166763)) (inverse (multiply ?166765 ?166762)) [166767, 166766, 166765, 166764, 166763, 166762] by Super 34748 with 53 at 1,1,2,3
+Id : 35052, {_}: multiply (inverse (divide ?166762 ?166763)) (inverse ?166765) =<= multiply (inverse (inverse ?166763)) (inverse (multiply ?166765 ?166762)) [166765, 166763, 166762] by Demod 34749 with 53 at 1,2,2
+Id : 35278, {_}: multiply (inverse (divide ?167869 ?167870)) (inverse (divide ?167871 ?167872)) =<= divide (inverse (inverse ?167870)) (multiply ?167871 (multiply (inverse ?167872) ?167869)) [167872, 167871, 167870, 167869] by Super 12807 with 35052 at 2
+Id : 33419, {_}: inverse (inverse (divide (inverse (divide ?162685 ?162686)) ?162687)) =>= multiply (inverse (inverse ?162686)) (inverse (multiply ?162687 ?162685)) [162687, 162686, 162685] by Demod 33189 with 53 at 2,1,2,3
+Id : 35198, {_}: inverse (inverse (divide (inverse (divide ?162685 ?162686)) ?162687)) =>= multiply (inverse (divide ?162685 ?162686)) (inverse ?162687) [162687, 162686, 162685] by Demod 33419 with 35052 at 3
+Id : 16, {_}: divide (inverse (divide ?64 (divide ?65 (divide (divide ?66 ?67) (inverse (divide ?67 (divide ?68 (multiply (divide (divide ?69 ?70) ?71) (divide ?71 (divide ?66 (divide ?70 ?69))))))))))) (divide ?68 ?64) =>= ?65 [71, 70, 69, 68, 67, 66, 65, 64] by Super 2 with 15 at 1,2,2
+Id : 38, {_}: divide (inverse (divide ?64 (divide ?65 (multiply (divide ?66 ?67) (divide ?67 (divide ?68 (multiply (divide (divide ?69 ?70) ?71) (divide ?71 (divide ?66 (divide ?70 ?69)))))))))) (divide ?68 ?64) =>= ?65 [71, 70, 69, 68, 67, 66, 65, 64] by Demod 16 with 3 at 2,2,1,1,2
+Id : 38131, {_}: inverse (inverse (divide (inverse ?178374) ?178375)) =<= multiply (inverse (divide (inverse (divide ?178376 (divide ?178374 (multiply (divide ?178377 ?178378) (divide ?178378 (divide ?178379 (multiply (divide (divide ?178380 ?178381) ?178382) (divide ?178382 (divide ?178377 (divide ?178381 ?178380)))))))))) (divide ?178379 ?178376))) (inverse ?178375) [178382, 178381, 178380, 178379, 178378, 178377, 178376, 178375, 178374] by Super 35198 with 38 at 1,1,1,1,2
+Id : 38834, {_}: inverse (inverse (divide (inverse ?178374) ?178375)) =>= multiply (inverse ?178374) (inverse ?178375) [178375, 178374] by Demod 38131 with 38 at 1,1,3
+Id : 39627, {_}: multiply ?187316 (inverse (divide (inverse ?187317) ?187318)) =>= divide ?187316 (multiply (inverse ?187317) (inverse ?187318)) [187318, 187317, 187316] by Super 3 with 38834 at 2,3
+Id : 39628, {_}: multiply ?187320 (inverse (divide ?187321 ?187322)) =<= divide ?187320 (multiply (inverse (divide ?187323 (divide (divide ?187321 (divide (divide ?187324 ?187325) ?187323)) (divide ?187325 ?187324)))) (inverse ?187322)) [187325, 187324, 187323, 187322, 187321, 187320] by Super 39627 with 53 at 1,1,2,2
+Id : 39950, {_}: multiply ?187320 (inverse (divide ?187321 ?187322)) =>= divide ?187320 (multiply ?187321 (inverse ?187322)) [187322, 187321, 187320] by Demod 39628 with 53 at 1,2,3
+Id : 45468, {_}: divide (inverse (divide ?167869 ?167870)) (multiply ?167871 (inverse ?167872)) =<= divide (inverse (inverse ?167870)) (multiply ?167871 (multiply (inverse ?167872) ?167869)) [167872, 167871, 167870, 167869] by Demod 35278 with 39950 at 2
+Id : 45552, {_}: divide (inverse ?204144) (multiply (divide ?204145 ?204146) (divide (divide ?204146 ?204145) (divide ?204144 (divide (inverse (divide ?204147 ?204148)) (multiply ?204149 (inverse ?204150)))))) =>= divide (multiply ?204149 (multiply (inverse ?204150) ?204147)) (inverse (inverse ?204148)) [204150, 204149, 204148, 204147, 204146, 204145, 204144] by Super 362 with 45468 at 2,2,2,2,2
+Id : 45856, {_}: divide (multiply ?204149 (inverse ?204150)) (inverse (divide ?204147 ?204148)) =<= divide (multiply ?204149 (multiply (inverse ?204150) ?204147)) (inverse (inverse ?204148)) [204148, 204147, 204150, 204149] by Demod 45552 with 362 at 2
+Id : 45857, {_}: divide (multiply ?204149 (inverse ?204150)) (inverse (divide ?204147 ?204148)) =<= multiply (multiply ?204149 (multiply (inverse ?204150) ?204147)) (inverse ?204148) [204148, 204147, 204150, 204149] by Demod 45856 with 3 at 3
+Id : 46240, {_}: multiply (multiply ?206273 (inverse ?206274)) (divide ?206275 ?206276) =<= multiply (multiply ?206273 (multiply (inverse ?206274) ?206275)) (inverse ?206276) [206276, 206275, 206274, 206273] by Demod 45857 with 3 at 2
+Id : 30915, {_}: multiply (multiply ?67174 ?67175) (inverse (inverse ?67176)) =?= multiply ?67174 (multiply (inverse (inverse ?67175)) ?67176) [67176, 67175, 67174] by Demod 12858 with 30884 at 2
+Id : 46333, {_}: multiply (multiply ?207013 (inverse (inverse ?207014))) (divide ?207015 ?207016) =<= multiply (multiply (multiply ?207013 ?207014) (inverse (inverse ?207015))) (inverse ?207016) [207016, 207015, 207014, 207013] by Super 46240 with 30915 at 1,3
+Id : 1890, {_}: divide (inverse (divide (divide ?8674 ?8675) ?8676)) ?8677 =<= inverse (divide (inverse (divide ?8678 ?8677)) (divide ?8676 (divide ?8678 (divide ?8675 ?8674)))) [8678, 8677, 8676, 8675, 8674] by Super 7 with 1266 at 2,2
+Id : 1908, {_}: divide (inverse (divide (divide (inverse ?8832) ?8833) ?8834)) ?8835 =<= inverse (divide (inverse (divide ?8836 ?8835)) (divide ?8834 (divide ?8836 (multiply ?8833 ?8832)))) [8836, 8835, 8834, 8833, 8832] by Super 1890 with 3 at 2,2,2,1,3
+Id : 61, {_}: divide (inverse (divide ?349 ?350)) (divide (divide ?351 (divide ?352 ?353)) ?349) =>= inverse (divide ?351 (divide ?350 (divide ?353 ?352))) [353, 352, 351, 350, 349] by Super 4 with 2 at 2,1,1,2
+Id : 65, {_}: divide (inverse (divide ?382 ?383)) (divide (divide ?384 (multiply ?385 ?386)) ?382) =>= inverse (divide ?384 (divide ?383 (divide (inverse ?386) ?385))) [386, 385, 384, 383, 382] by Super 61 with 3 at 2,1,2,2
+Id : 16676, {_}: divide (inverse ?87869) (multiply (divide ?87870 ?87871) (divide (divide ?87871 ?87870) (divide ?87869 (divide (divide ?87872 (divide (inverse ?87873) ?87874)) (divide ?87875 ?87876))))) =>= divide (multiply ?87875 (divide (inverse ?87876) ?87873)) (multiply ?87872 ?87874) [87876, 87875, 87874, 87873, 87872, 87871, 87870, 87869] by Super 362 with 15912 at 2,2,2,2,2
+Id : 16850, {_}: divide (divide ?87875 ?87876) (divide ?87872 (divide (inverse ?87873) ?87874)) =<= divide (multiply ?87875 (divide (inverse ?87876) ?87873)) (multiply ?87872 ?87874) [87874, 87873, 87872, 87876, 87875] by Demod 16676 with 362 at 2
+Id : 17219, {_}: inverse (inverse (divide (divide ?91192 ?91193) (divide ?91194 (divide (inverse ?91195) ?91196)))) =>= multiply ?91192 (divide (inverse (inverse (divide (inverse ?91193) ?91195))) (multiply ?91194 ?91196)) [91196, 91195, 91194, 91193, 91192] by Super 14212 with 16850 at 1,1,2
+Id : 17309, {_}: multiply ?91192 (divide (inverse ?91193) (divide ?91194 (divide (inverse ?91195) ?91196))) =<= multiply ?91192 (divide (inverse (inverse (divide (inverse ?91193) ?91195))) (multiply ?91194 ?91196)) [91196, 91195, 91194, 91193, 91192] by Demod 17219 with 15659 at 2
+Id : 22082, {_}: inverse (divide (inverse (inverse (divide (inverse ?112093) ?112094))) (multiply ?112095 ?112096)) =<= multiply (multiply (divide (inverse ?112097) ?112098) (divide (multiply ?112098 ?112097) (multiply ?112099 (divide (inverse ?112093) (divide ?112095 (divide (inverse ?112094) ?112096)))))) ?112099 [112099, 112098, 112097, 112096, 112095, 112094, 112093] by Super 7337 with 17309 at 2,2,1,3
+Id : 22476, {_}: inverse (divide (inverse (inverse (divide (inverse ?113967) ?113968))) (multiply ?113969 ?113970)) =>= inverse (divide (inverse ?113967) (divide ?113969 (divide (inverse ?113968) ?113970))) [113970, 113969, 113968, 113967] by Demod 22082 with 7337 at 3
+Id : 22508, {_}: inverse (divide (inverse (inverse (divide ?114204 ?114205))) (multiply ?114206 ?114207)) =<= inverse (divide (inverse (divide ?114208 (divide (divide ?114204 (divide (divide ?114209 ?114210) ?114208)) (divide ?114210 ?114209)))) (divide ?114206 (divide (inverse ?114205) ?114207))) [114210, 114209, 114208, 114207, 114206, 114205, 114204] by Super 22476 with 53 at 1,1,1,1,1,2
+Id : 22780, {_}: inverse (divide (inverse (inverse (divide ?114204 ?114205))) (multiply ?114206 ?114207)) =>= inverse (divide ?114204 (divide ?114206 (divide (inverse ?114205) ?114207))) [114207, 114206, 114205, 114204] by Demod 22508 with 53 at 1,1,3
+Id : 40158, {_}: inverse (inverse (divide ?188657 ?188658)) =<= multiply (multiply (multiply ?188659 ?188660) (divide (divide (inverse ?188660) ?188659) (divide ?188661 (multiply ?188657 (inverse ?188658))))) ?188661 [188661, 188660, 188659, 188658, 188657] by Super 7367 with 39950 at 2,2,1,3
+Id : 7191, {_}: ?36095 =<= multiply (multiply (multiply ?36096 ?36097) (divide (divide (inverse ?36097) ?36096) (divide ?36098 ?36095))) ?36098 [36098, 36097, 36096, 36095] by Super 7101 with 3 at 1,1,3
+Id : 40350, {_}: inverse (inverse (divide ?188657 ?188658)) =>= multiply ?188657 (inverse ?188658) [188658, 188657] by Demod 40158 with 7191 at 3
+Id : 40577, {_}: inverse (divide (multiply ?114204 (inverse ?114205)) (multiply ?114206 ?114207)) =?= inverse (divide ?114204 (divide ?114206 (divide (inverse ?114205) ?114207))) [114207, 114206, 114205, 114204] by Demod 22780 with 40350 at 1,1,2
+Id : 40645, {_}: divide (divide ?189801 (divide (multiply ?189802 (inverse ?189803)) ?189804)) ?189805 =<= multiply (multiply ?189801 ?189804) (inverse (multiply ?189805 (divide ?189802 ?189803))) [189805, 189804, 189803, 189802, 189801] by Super 9554 with 40350 at 1,2,1,2
+Id : 30968, {_}: multiply ?154958 (inverse (multiply ?154959 ?154960)) =<= divide ?154958 (multiply ?154959 (inverse (inverse ?154960))) [154960, 154959, 154958] by Super 3 with 30884 at 2,3
+Id : 40629, {_}: multiply ?189704 (inverse (multiply ?189705 (divide ?189706 ?189707))) =>= divide ?189704 (multiply ?189705 (multiply ?189706 (inverse ?189707))) [189707, 189706, 189705, 189704] by Super 30968 with 40350 at 2,2,3
+Id : 62131, {_}: divide (divide ?257834 (divide (multiply ?257835 (inverse ?257836)) ?257837)) ?257838 =<= divide (multiply ?257834 ?257837) (multiply ?257838 (multiply ?257835 (inverse ?257836))) [257838, 257837, 257836, 257835, 257834] by Demod 40645 with 40629 at 3
+Id : 62178, {_}: divide (divide ?258249 (divide (multiply (multiply (divide ?258250 ?258251) (divide (divide ?258251 ?258250) (divide (inverse ?258252) ?258253))) (inverse ?258252)) ?258254)) ?258255 =>= divide (multiply ?258249 ?258254) (multiply ?258255 ?258253) [258255, 258254, 258253, 258252, 258251, 258250, 258249] by Super 62131 with 6973 at 2,2,3
+Id : 62493, {_}: divide (divide ?258249 (divide ?258253 ?258254)) ?258255 =<= divide (multiply ?258249 ?258254) (multiply ?258255 ?258253) [258255, 258254, 258253, 258249] by Demod 62178 with 6973 at 1,2,1,2
+Id : 62632, {_}: inverse (divide (divide ?114204 (divide ?114207 (inverse ?114205))) ?114206) =?= inverse (divide ?114204 (divide ?114206 (divide (inverse ?114205) ?114207))) [114206, 114205, 114207, 114204] by Demod 40577 with 62493 at 1,2
+Id : 62637, {_}: inverse (divide (divide ?114204 (multiply ?114207 ?114205)) ?114206) =<= inverse (divide ?114204 (divide ?114206 (divide (inverse ?114205) ?114207))) [114206, 114205, 114207, 114204] by Demod 62632 with 3 at 2,1,1,2
+Id : 62641, {_}: divide (inverse (divide ?382 ?383)) (divide (divide ?384 (multiply ?385 ?386)) ?382) =>= inverse (divide (divide ?384 (multiply ?385 ?386)) ?383) [386, 385, 384, 383, 382] by Demod 65 with 62637 at 3
+Id : 19, {_}: divide (inverse ?90) (divide (divide ?91 ?92) (inverse (divide (divide ?92 ?91) (divide ?90 (multiply (divide (divide ?93 ?94) ?95) (divide ?95 (divide ?96 (divide ?94 ?93)))))))) =>= ?96 [96, 95, 94, 93, 92, 91, 90] by Super 2 with 15 at 1,1,2
+Id : 40, {_}: divide (inverse ?90) (multiply (divide ?91 ?92) (divide (divide ?92 ?91) (divide ?90 (multiply (divide (divide ?93 ?94) ?95) (divide ?95 (divide ?96 (divide ?94 ?93))))))) =>= ?96 [96, 95, 94, 93, 92, 91, 90] by Demod 19 with 3 at 2,2
+Id : 89822, {_}: divide (inverse (divide ?333797 ?333798)) (divide ?333799 ?333797) =?= inverse (divide (divide (inverse ?333800) (multiply (divide ?333801 ?333802) (divide (divide ?333802 ?333801) (divide ?333800 (multiply (divide (divide ?333803 ?333804) ?333805) (divide ?333805 (divide ?333799 (divide ?333804 ?333803)))))))) ?333798) [333805, 333804, 333803, 333802, 333801, 333800, 333799, 333798, 333797] by Super 62641 with 40 at 1,2,2
+Id : 90396, {_}: divide (inverse (divide ?333797 ?333798)) (divide ?333799 ?333797) =>= inverse (divide ?333799 ?333798) [333799, 333798, 333797] by Demod 89822 with 40 at 1,1,3
+Id : 101099, {_}: inverse (divide (divide ?31 (divide ?32 ?33)) ?30) =?= inverse (divide ?31 (divide ?30 (divide ?33 ?32))) [30, 33, 32, 31] by Demod 7 with 90396 at 2
+Id : 101112, {_}: divide (inverse (divide (divide (inverse ?8832) ?8833) ?8834)) ?8835 =<= inverse (divide (divide (inverse (divide ?8836 ?8835)) (divide (multiply ?8833 ?8832) ?8836)) ?8834) [8836, 8835, 8834, 8833, 8832] by Demod 1908 with 101099 at 3
+Id : 101118, {_}: divide (inverse (divide (divide (inverse ?8832) ?8833) ?8834)) ?8835 =<= inverse (divide (inverse (divide (multiply ?8833 ?8832) ?8835)) ?8834) [8835, 8834, 8833, 8832] by Demod 101112 with 90396 at 1,1,3
+Id : 101316, {_}: divide (inverse (divide (divide (inverse ?356253) ?356254) (divide ?356255 (multiply ?356254 ?356253)))) ?356256 =>= inverse (inverse (divide ?356255 ?356256)) [356256, 356255, 356254, 356253] by Super 101118 with 90396 at 1,3
+Id : 12, {_}: divide (inverse (divide ?53 (divide ?54 (multiply ?55 ?56)))) (divide (divide (inverse ?56) ?55) ?53) =>= ?54 [56, 55, 54, 53] by Super 2 with 3 at 2,2,1,1,2
+Id : 101095, {_}: inverse (divide (divide (inverse ?56) ?55) (divide ?54 (multiply ?55 ?56))) =>= ?54 [54, 55, 56] by Demod 12 with 90396 at 2
+Id : 101519, {_}: divide ?356255 ?356256 =<= inverse (inverse (divide ?356255 ?356256)) [356256, 356255] by Demod 101316 with 101095 at 1,2
+Id : 101520, {_}: divide ?356255 ?356256 =<= multiply ?356255 (inverse ?356256) [356256, 356255] by Demod 101519 with 40350 at 3
+Id : 102152, {_}: multiply (divide ?207013 (inverse ?207014)) (divide ?207015 ?207016) =<= multiply (multiply (multiply ?207013 ?207014) (inverse (inverse ?207015))) (inverse ?207016) [207016, 207015, 207014, 207013] by Demod 46333 with 101520 at 1,2
+Id : 102153, {_}: multiply (divide ?207013 (inverse ?207014)) (divide ?207015 ?207016) =<= divide (multiply (multiply ?207013 ?207014) (inverse (inverse ?207015))) ?207016 [207016, 207015, 207014, 207013] by Demod 102152 with 101520 at 3
+Id : 102154, {_}: multiply (divide ?207013 (inverse ?207014)) (divide ?207015 ?207016) =>= divide (divide (multiply ?207013 ?207014) (inverse ?207015)) ?207016 [207016, 207015, 207014, 207013] by Demod 102153 with 101520 at 1,3
+Id : 102308, {_}: multiply (multiply ?207013 ?207014) (divide ?207015 ?207016) =<= divide (divide (multiply ?207013 ?207014) (inverse ?207015)) ?207016 [207016, 207015, 207014, 207013] by Demod 102154 with 3 at 1,2
+Id : 102309, {_}: multiply (multiply ?207013 ?207014) (divide ?207015 ?207016) =>= divide (multiply (multiply ?207013 ?207014) ?207015) ?207016 [207016, 207015, 207014, 207013] by Demod 102308 with 3 at 1,3
+Id : 102310, {_}: ?38552 =<= multiply (divide (multiply (multiply (inverse ?38553) ?38554) (multiply (inverse ?38554) ?38553)) (divide ?38555 ?38552)) ?38555 [38555, 38554, 38553, 38552] by Demod 7678 with 102309 at 1,3
+Id : 52549, {_}: multiply (multiply ?225200 (inverse (inverse ?225201))) (divide ?225202 ?225203) =<= multiply (multiply (multiply ?225200 ?225201) (inverse (inverse ?225202))) (inverse ?225203) [225203, 225202, 225201, 225200] by Super 46240 with 30915 at 1,3
+Id : 52684, {_}: multiply (multiply ?226211 (inverse (inverse ?226212))) (divide ?226213 (inverse ?226214)) =<= multiply (multiply ?226211 ?226212) (multiply (inverse (inverse (inverse (inverse ?226213)))) ?226214) [226214, 226213, 226212, 226211] by Super 52549 with 30915 at 3
+Id : 53235, {_}: multiply (multiply ?226211 (inverse (inverse ?226212))) (multiply ?226213 ?226214) =<= multiply (multiply ?226211 ?226212) (multiply (inverse (inverse (inverse (inverse ?226213)))) ?226214) [226214, 226213, 226212, 226211] by Demod 52684 with 3 at 2,2
+Id : 102165, {_}: multiply (divide ?226211 (inverse ?226212)) (multiply ?226213 ?226214) =<= multiply (multiply ?226211 ?226212) (multiply (inverse (inverse (inverse (inverse ?226213)))) ?226214) [226214, 226213, 226212, 226211] by Demod 53235 with 101520 at 1,2
+Id : 102295, {_}: multiply (multiply ?226211 ?226212) (multiply ?226213 ?226214) =<= multiply (multiply ?226211 ?226212) (multiply (inverse (inverse (inverse (inverse ?226213)))) ?226214) [226214, 226213, 226212, 226211] by Demod 102165 with 3 at 1,2
+Id : 30916, {_}: multiply (divide ?66357 ?66358) (inverse (inverse ?66359)) =>= multiply ?66357 (multiply (inverse ?66358) ?66359) [66359, 66358, 66357] by Demod 12770 with 30884 at 2
+Id : 9965, {_}: divide (divide ?51846 (divide (inverse (inverse ?51847)) ?51848)) ?51849 =>= multiply (multiply ?51846 ?51848) (inverse (multiply ?51849 ?51847)) [51849, 51848, 51847, 51846] by Super 9472 with 7237 at 1,1,3
+Id : 9976, {_}: divide (divide ?51938 (multiply (inverse (inverse ?51939)) ?51940)) ?51941 =<= multiply (multiply ?51938 (inverse ?51940)) (inverse (multiply ?51941 ?51939)) [51941, 51940, 51939, 51938] by Super 9965 with 3 at 2,1,2
+Id : 40724, {_}: inverse (inverse (divide ?190294 ?190295)) =>= multiply ?190294 (inverse ?190295) [190295, 190294] by Demod 40158 with 7191 at 3
+Id : 40043, {_}: divide (divide ?49359 (divide (inverse ?49360) ?49361)) ?49362 =<= divide (multiply ?49359 ?49361) (multiply ?49362 (inverse ?49360)) [49362, 49361, 49360, 49359] by Demod 9552 with 39950 at 3
+Id : 40771, {_}: inverse (inverse (divide (divide ?190577 (divide (inverse ?190578) ?190579)) ?190580)) =>= multiply (multiply ?190577 ?190579) (inverse (multiply ?190580 (inverse ?190578))) [190580, 190579, 190578, 190577] by Super 40724 with 40043 at 1,1,2
+Id : 42949, {_}: multiply (divide ?196696 (divide (inverse ?196697) ?196698)) (inverse ?196699) =<= multiply (multiply ?196696 ?196698) (inverse (multiply ?196699 (inverse ?196697))) [196699, 196698, 196697, 196696] by Demod 40771 with 40350 at 2
+Id : 42950, {_}: multiply (divide ?196701 (divide (inverse (divide ?196702 (divide (divide ?196703 (divide (divide ?196704 ?196705) ?196702)) (divide ?196705 ?196704)))) ?196706)) (inverse ?196707) =>= multiply (multiply ?196701 ?196706) (inverse (multiply ?196707 ?196703)) [196707, 196706, 196705, 196704, 196703, 196702, 196701] by Super 42949 with 53 at 2,1,2,3
+Id : 43226, {_}: multiply (divide ?196701 (divide ?196703 ?196706)) (inverse ?196707) =<= multiply (multiply ?196701 ?196706) (inverse (multiply ?196707 ?196703)) [196707, 196706, 196703, 196701] by Demod 42950 with 53 at 1,2,1,2
+Id : 43404, {_}: divide (divide ?51938 (multiply (inverse (inverse ?51939)) ?51940)) ?51941 =<= multiply (divide ?51938 (divide ?51939 (inverse ?51940))) (inverse ?51941) [51941, 51940, 51939, 51938] by Demod 9976 with 43226 at 3
+Id : 43406, {_}: divide (divide ?51938 (multiply (inverse (inverse ?51939)) ?51940)) ?51941 =>= multiply (divide ?51938 (multiply ?51939 ?51940)) (inverse ?51941) [51941, 51940, 51939, 51938] by Demod 43404 with 3 at 2,1,3
+Id : 62671, {_}: divide (divide (divide ?259262 (divide ?259263 ?259264)) (inverse (inverse ?259265))) ?259266 =>= multiply (divide (multiply ?259262 ?259264) (multiply ?259265 ?259263)) (inverse ?259266) [259266, 259265, 259264, 259263, 259262] by Super 43406 with 62493 at 1,2
+Id : 63074, {_}: divide (multiply (divide ?259262 (divide ?259263 ?259264)) (inverse ?259265)) ?259266 =<= multiply (divide (multiply ?259262 ?259264) (multiply ?259265 ?259263)) (inverse ?259266) [259266, 259265, 259264, 259263, 259262] by Demod 62671 with 3 at 1,2
+Id : 84448, {_}: divide (multiply (divide ?320603 (divide ?320604 ?320605)) (inverse ?320606)) ?320607 =<= multiply (divide (divide ?320603 (divide ?320604 ?320605)) ?320606) (inverse ?320607) [320607, 320606, 320605, 320604, 320603] by Demod 63074 with 62493 at 1,3
+Id : 84555, {_}: divide (multiply (divide (inverse (divide ?321565 (divide ?321566 (multiply (divide (divide ?321567 ?321568) ?321569) (divide ?321569 (divide ?321570 (divide ?321568 ?321567))))))) (divide ?321570 ?321565)) (inverse ?321571)) ?321572 =>= multiply (divide ?321566 ?321571) (inverse ?321572) [321572, 321571, 321570, 321569, 321568, 321567, 321566, 321565] by Super 84448 with 15 at 1,1,3
+Id : 85061, {_}: divide (multiply ?321566 (inverse ?321571)) ?321572 =<= multiply (divide ?321566 ?321571) (inverse ?321572) [321572, 321571, 321566] by Demod 84555 with 15 at 1,1,2
+Id : 85186, {_}: divide (multiply ?66357 (inverse ?66358)) (inverse ?66359) =>= multiply ?66357 (multiply (inverse ?66358) ?66359) [66359, 66358, 66357] by Demod 30916 with 85061 at 2
+Id : 85229, {_}: multiply (multiply ?66357 (inverse ?66358)) ?66359 =?= multiply ?66357 (multiply (inverse ?66358) ?66359) [66359, 66358, 66357] by Demod 85186 with 3 at 2
+Id : 102180, {_}: multiply (divide ?66357 ?66358) ?66359 =<= multiply ?66357 (multiply (inverse ?66358) ?66359) [66359, 66358, 66357] by Demod 85229 with 101520 at 1,2
+Id : 102296, {_}: multiply (multiply ?226211 ?226212) (multiply ?226213 ?226214) =<= multiply (divide (multiply ?226211 ?226212) (inverse (inverse (inverse ?226213)))) ?226214 [226214, 226213, 226212, 226211] by Demod 102295 with 102180 at 3
+Id : 102297, {_}: multiply (multiply ?226211 ?226212) (multiply ?226213 ?226214) =<= multiply (multiply (multiply ?226211 ?226212) (inverse (inverse ?226213))) ?226214 [226214, 226213, 226212, 226211] by Demod 102296 with 3 at 1,3
+Id : 102298, {_}: multiply (multiply ?226211 ?226212) (multiply ?226213 ?226214) =<= multiply (divide (multiply ?226211 ?226212) (inverse ?226213)) ?226214 [226214, 226213, 226212, 226211] by Demod 102297 with 101520 at 1,3
+Id : 102299, {_}: multiply (multiply ?226211 ?226212) (multiply ?226213 ?226214) =?= multiply (multiply (multiply ?226211 ?226212) ?226213) ?226214 [226214, 226213, 226212, 226211] by Demod 102298 with 3 at 1,3
+Id : 102317, {_}: ?38552 =<= multiply (divide (multiply (multiply (multiply (inverse ?38553) ?38554) (inverse ?38554)) ?38553) (divide ?38555 ?38552)) ?38555 [38555, 38554, 38553, 38552] by Demod 102310 with 102299 at 1,1,3
+Id : 102318, {_}: ?38552 =<= multiply (divide (multiply (divide (multiply (inverse ?38553) ?38554) ?38554) ?38553) (divide ?38555 ?38552)) ?38555 [38555, 38554, 38553, 38552] by Demod 102317 with 101520 at 1,1,1,3
+Id : 2791, {_}: divide (divide (inverse (multiply ?13892 ?13893)) (divide (divide (inverse ?13894) ?13895) ?13892)) (multiply ?13895 ?13894) =>= inverse ?13893 [13895, 13894, 13893, 13892] by Super 2771 with 3 at 2,2
+Id : 89847, {_}: divide (inverse ?334058) (multiply (divide ?334059 ?334060) (divide (divide ?334060 ?334059) (divide ?334058 (multiply (divide (divide ?334061 ?334062) ?334063) (divide ?334063 (divide ?334064 (divide ?334062 ?334061))))))) =>= ?334064 [334064, 334063, 334062, 334061, 334060, 334059, 334058] by Demod 19 with 3 at 2,2
+Id : 43403, {_}: divide (divide ?49369 (divide (inverse (inverse ?49370)) ?49371)) ?49372 =>= multiply (divide ?49369 (divide ?49370 ?49371)) (inverse ?49372) [49372, 49371, 49370, 49369] by Demod 9554 with 43226 at 3
+Id : 85181, {_}: divide (divide ?49369 (divide (inverse (inverse ?49370)) ?49371)) ?49372 =>= divide (multiply ?49369 (inverse (divide ?49370 ?49371))) ?49372 [49372, 49371, 49370, 49369] by Demod 43403 with 85061 at 3
+Id : 85235, {_}: divide (divide ?49369 (divide (inverse (inverse ?49370)) ?49371)) ?49372 =>= divide (divide ?49369 (multiply ?49370 (inverse ?49371))) ?49372 [49372, 49371, 49370, 49369] by Demod 85181 with 39950 at 1,3
+Id : 89956, {_}: divide (inverse ?335244) (multiply (divide ?335245 ?335246) (divide (divide ?335246 ?335245) (divide ?335244 (multiply (divide (divide ?335247 ?335248) ?335249) (divide ?335249 (divide (divide ?335250 (multiply ?335251 (inverse ?335252))) (divide ?335248 ?335247))))))) =>= divide ?335250 (divide (inverse (inverse ?335251)) ?335252) [335252, 335251, 335250, 335249, 335248, 335247, 335246, 335245, 335244] by Super 89847 with 85235 at 2,2,2,2,2,2,2
+Id : 90764, {_}: divide ?335250 (multiply ?335251 (inverse ?335252)) =<= divide ?335250 (divide (inverse (inverse ?335251)) ?335252) [335252, 335251, 335250] by Demod 89956 with 40 at 2
+Id : 92959, {_}: divide (inverse (inverse ?344076)) ?344077 =<= multiply (multiply (multiply (inverse ?344078) ?344079) (divide (multiply (inverse ?344079) ?344078) (divide ?344080 (multiply ?344076 (inverse ?344077))))) ?344080 [344080, 344079, 344078, 344077, 344076] by Super 7678 with 90764 at 2,2,1,3
+Id : 93432, {_}: divide (inverse (inverse ?344076)) ?344077 =>= multiply ?344076 (inverse ?344077) [344077, 344076] by Demod 92959 with 7678 at 3
+Id : 94198, {_}: multiply (inverse (inverse ?346092)) (inverse (multiply ?346093 ?346094)) =?= multiply ?346092 (inverse (multiply ?346093 (inverse (inverse ?346094)))) [346094, 346093, 346092] by Super 30968 with 93432 at 3
+Id : 95063, {_}: multiply (inverse (divide ?346094 ?346092)) (inverse ?346093) =<= multiply ?346092 (inverse (multiply ?346093 (inverse (inverse ?346094)))) [346093, 346092, 346094] by Demod 94198 with 35052 at 2
+Id : 102213, {_}: divide (inverse (divide ?346094 ?346092)) ?346093 =<= multiply ?346092 (inverse (multiply ?346093 (inverse (inverse ?346094)))) [346093, 346092, 346094] by Demod 95063 with 101520 at 2
+Id : 102214, {_}: divide (inverse (divide ?346094 ?346092)) ?346093 =<= divide ?346092 (multiply ?346093 (inverse (inverse ?346094))) [346093, 346092, 346094] by Demod 102213 with 101520 at 3
+Id : 102215, {_}: divide (inverse (divide ?346094 ?346092)) ?346093 =?= divide ?346092 (divide ?346093 (inverse ?346094)) [346093, 346092, 346094] by Demod 102214 with 101520 at 2,3
+Id : 102222, {_}: divide (inverse (divide ?346094 ?346092)) ?346093 =>= divide ?346092 (multiply ?346093 ?346094) [346093, 346092, 346094] by Demod 102215 with 3 at 2,3
+Id : 102235, {_}: divide ?8834 (multiply ?8835 (divide (inverse ?8832) ?8833)) =<= inverse (divide (inverse (divide (multiply ?8833 ?8832) ?8835)) ?8834) [8833, 8832, 8835, 8834] by Demod 101118 with 102222 at 2
+Id : 102236, {_}: divide ?8834 (multiply ?8835 (divide (inverse ?8832) ?8833)) =<= inverse (divide ?8835 (multiply ?8834 (multiply ?8833 ?8832))) [8833, 8832, 8835, 8834] by Demod 102235 with 102222 at 1,3
+Id : 35199, {_}: inverse (multiply (inverse (divide ?86042 ?86040)) (inverse ?86041)) =<= inverse (divide (inverse (divide (inverse (inverse ?86042)) ?86040)) ?86041) [86041, 86040, 86042] by Demod 16326 with 35052 at 1,2
+Id : 40695, {_}: inverse (multiply (inverse (divide (divide ?190115 ?190116) ?190117)) (inverse ?190118)) =>= inverse (divide (inverse (divide (multiply ?190115 (inverse ?190116)) ?190117)) ?190118) [190118, 190117, 190116, 190115] by Super 35199 with 40350 at 1,1,1,1,3
+Id : 46674, {_}: inverse (inverse (divide (inverse (divide (multiply ?207380 (inverse ?207381)) ?207382)) ?207383)) =>= multiply (inverse (divide (divide ?207380 ?207381) ?207382)) (inverse (inverse (inverse ?207383))) [207383, 207382, 207381, 207380] by Super 30884 with 40695 at 1,2
+Id : 47015, {_}: multiply (inverse (divide (multiply ?207380 (inverse ?207381)) ?207382)) (inverse ?207383) =<= multiply (inverse (divide (divide ?207380 ?207381) ?207382)) (inverse (inverse (inverse ?207383))) [207383, 207382, 207381, 207380] by Demod 46674 with 40350 at 2
+Id : 31439, {_}: multiply ?157170 (inverse (multiply ?157171 ?157172)) =<= divide ?157170 (multiply ?157171 (inverse (inverse ?157172))) [157172, 157171, 157170] by Super 3 with 30884 at 2,3
+Id : 31475, {_}: multiply ?157430 (inverse (multiply ?157431 (multiply ?157432 ?157433))) =<= divide ?157430 (multiply ?157431 (multiply ?157432 (inverse (inverse ?157433)))) [157433, 157432, 157431, 157430] by Super 31439 with 30884 at 2,2,3
+Id : 45490, {_}: multiply (inverse (inverse ?203652)) (inverse (multiply ?203653 (multiply (inverse ?203654) ?203655))) =>= divide (inverse (divide (inverse (inverse ?203655)) ?203652)) (multiply ?203653 (inverse ?203654)) [203655, 203654, 203653, 203652] by Super 31475 with 45468 at 3
+Id : 71413, {_}: multiply (inverse (divide (multiply (inverse ?287029) ?287030) ?287031)) (inverse ?287032) =<= divide (inverse (divide (inverse (inverse ?287030)) ?287031)) (multiply ?287032 (inverse ?287029)) [287032, 287031, 287030, 287029] by Demod 45490 with 35052 at 2
+Id : 71414, {_}: multiply (inverse (divide (multiply (inverse (divide ?287034 (divide (divide ?287035 (divide (divide ?287036 ?287037) ?287034)) (divide ?287037 ?287036)))) ?287038) ?287039)) (inverse ?287040) =>= divide (inverse (divide (inverse (inverse ?287038)) ?287039)) (multiply ?287040 ?287035) [287040, 287039, 287038, 287037, 287036, 287035, 287034] by Super 71413 with 53 at 2,2,3
+Id : 72001, {_}: multiply (inverse (divide (multiply ?287035 ?287038) ?287039)) (inverse ?287040) =<= divide (inverse (divide (inverse (inverse ?287038)) ?287039)) (multiply ?287040 ?287035) [287040, 287039, 287038, 287035] by Demod 71414 with 53 at 1,1,1,1,2
+Id : 94096, {_}: multiply (inverse (divide (multiply ?287035 ?287038) ?287039)) (inverse ?287040) =>= divide (inverse (multiply ?287038 (inverse ?287039))) (multiply ?287040 ?287035) [287040, 287039, 287038, 287035] by Demod 72001 with 93432 at 1,1,3
+Id : 94118, {_}: divide (inverse (multiply (inverse ?207381) (inverse ?207382))) (multiply ?207383 ?207380) =<= multiply (inverse (divide (divide ?207380 ?207381) ?207382)) (inverse (inverse (inverse ?207383))) [207380, 207383, 207382, 207381] by Demod 47015 with 94096 at 2
+Id : 102205, {_}: divide (inverse (divide (inverse ?207381) ?207382)) (multiply ?207383 ?207380) =<= multiply (inverse (divide (divide ?207380 ?207381) ?207382)) (inverse (inverse (inverse ?207383))) [207380, 207383, 207382, 207381] by Demod 94118 with 101520 at 1,1,2
+Id : 102206, {_}: divide (inverse (divide (inverse ?207381) ?207382)) (multiply ?207383 ?207380) =<= divide (inverse (divide (divide ?207380 ?207381) ?207382)) (inverse (inverse ?207383)) [207380, 207383, 207382, 207381] by Demod 102205 with 101520 at 3
+Id : 102244, {_}: divide ?207382 (multiply (multiply ?207383 ?207380) (inverse ?207381)) =<= divide (inverse (divide (divide ?207380 ?207381) ?207382)) (inverse (inverse ?207383)) [207381, 207380, 207383, 207382] by Demod 102206 with 102222 at 2
+Id : 102245, {_}: divide ?207382 (multiply (multiply ?207383 ?207380) (inverse ?207381)) =<= divide ?207382 (multiply (inverse (inverse ?207383)) (divide ?207380 ?207381)) [207381, 207380, 207383, 207382] by Demod 102244 with 102222 at 3
+Id : 102246, {_}: divide ?207382 (divide (multiply ?207383 ?207380) ?207381) =<= divide ?207382 (multiply (inverse (inverse ?207383)) (divide ?207380 ?207381)) [207381, 207380, 207383, 207382] by Demod 102245 with 101520 at 2,2
+Id : 85182, {_}: divide (divide ?51938 (multiply (inverse (inverse ?51939)) ?51940)) ?51941 =>= divide (multiply ?51938 (inverse (multiply ?51939 ?51940))) ?51941 [51941, 51940, 51939, 51938] by Demod 43406 with 85061 at 3
+Id : 89950, {_}: divide (inverse ?335180) (multiply (divide ?335181 ?335182) (divide (divide ?335182 ?335181) (divide ?335180 (multiply (divide (divide ?335183 ?335184) ?335185) (divide ?335185 (divide (multiply ?335186 (inverse (multiply ?335187 ?335188))) (divide ?335184 ?335183))))))) =>= divide ?335186 (multiply (inverse (inverse ?335187)) ?335188) [335188, 335187, 335186, 335185, 335184, 335183, 335182, 335181, 335180] by Super 89847 with 85182 at 2,2,2,2,2,2,2
+Id : 90760, {_}: multiply ?335186 (inverse (multiply ?335187 ?335188)) =<= divide ?335186 (multiply (inverse (inverse ?335187)) ?335188) [335188, 335187, 335186] by Demod 89950 with 40 at 2
+Id : 94126, {_}: multiply (inverse (inverse ?345644)) (inverse (multiply ?345645 ?345646)) =?= multiply ?345644 (inverse (multiply (inverse (inverse ?345645)) ?345646)) [345646, 345645, 345644] by Super 90760 with 93432 at 3
+Id : 95228, {_}: multiply (inverse (divide ?345646 ?345644)) (inverse ?345645) =<= multiply ?345644 (inverse (multiply (inverse (inverse ?345645)) ?345646)) [345645, 345644, 345646] by Demod 94126 with 35052 at 2
+Id : 102219, {_}: divide (inverse (divide ?345646 ?345644)) ?345645 =<= multiply ?345644 (inverse (multiply (inverse (inverse ?345645)) ?345646)) [345645, 345644, 345646] by Demod 95228 with 101520 at 2
+Id : 102220, {_}: divide (inverse (divide ?345646 ?345644)) ?345645 =<= divide ?345644 (multiply (inverse (inverse ?345645)) ?345646) [345645, 345644, 345646] by Demod 102219 with 101520 at 3
+Id : 102238, {_}: divide ?345644 (multiply ?345645 ?345646) =<= divide ?345644 (multiply (inverse (inverse ?345645)) ?345646) [345646, 345645, 345644] by Demod 102220 with 102222 at 2
+Id : 102247, {_}: divide ?207382 (divide (multiply ?207383 ?207380) ?207381) =<= divide ?207382 (multiply ?207383 (divide ?207380 ?207381)) [207381, 207380, 207383, 207382] by Demod 102246 with 102238 at 3
+Id : 102262, {_}: divide ?8834 (divide (multiply ?8835 (inverse ?8832)) ?8833) =<= inverse (divide ?8835 (multiply ?8834 (multiply ?8833 ?8832))) [8833, 8832, 8835, 8834] by Demod 102236 with 102247 at 2
+Id : 102264, {_}: divide ?8834 (divide (divide ?8835 ?8832) ?8833) =<= inverse (divide ?8835 (multiply ?8834 (multiply ?8833 ?8832))) [8833, 8832, 8835, 8834] by Demod 102262 with 101520 at 1,2,2
+Id : 101098, {_}: inverse (divide (divide ?5 ?4) (divide ?3 (divide ?4 ?5))) =>= ?3 [3, 4, 5] by Demod 2 with 90396 at 2
+Id : 102493, {_}: divide (divide (inverse (divide (inverse ?357684) ?357685)) (multiply (divide ?357686 ?357687) ?357684)) (divide ?357687 ?357686) =>= inverse (inverse ?357685) [357687, 357686, 357685, 357684] by Super 2814 with 101520 at 1,1,1,2
+Id : 102761, {_}: divide (divide ?357685 (multiply (multiply (divide ?357686 ?357687) ?357684) (inverse ?357684))) (divide ?357687 ?357686) =>= inverse (inverse ?357685) [357684, 357687, 357686, 357685] by Demod 102493 with 102222 at 1,2
+Id : 102131, {_}: divide ?157430 (multiply ?157431 (multiply ?157432 ?157433)) =<= divide ?157430 (multiply ?157431 (multiply ?157432 (inverse (inverse ?157433)))) [157433, 157432, 157431, 157430] by Demod 31475 with 101520 at 2
+Id : 102132, {_}: divide ?157430 (multiply ?157431 (multiply ?157432 ?157433)) =<= divide ?157430 (multiply ?157431 (divide ?157432 (inverse ?157433))) [157433, 157432, 157431, 157430] by Demod 102131 with 101520 at 2,2,3
+Id : 102348, {_}: divide ?157430 (multiply ?157431 (multiply ?157432 ?157433)) =<= divide ?157430 (divide (multiply ?157431 ?157432) (inverse ?157433)) [157433, 157432, 157431, 157430] by Demod 102132 with 102247 at 3
+Id : 102349, {_}: divide ?157430 (multiply ?157431 (multiply ?157432 ?157433)) =?= divide ?157430 (multiply (multiply ?157431 ?157432) ?157433) [157433, 157432, 157431, 157430] by Demod 102348 with 3 at 2,3
+Id : 102762, {_}: divide (divide ?357685 (multiply (divide ?357686 ?357687) (multiply ?357684 (inverse ?357684)))) (divide ?357687 ?357686) =>= inverse (inverse ?357685) [357684, 357687, 357686, 357685] by Demod 102761 with 102349 at 1,2
+Id : 102763, {_}: divide (divide ?357685 (multiply (divide ?357686 ?357687) (divide ?357684 ?357684))) (divide ?357687 ?357686) =>= inverse (inverse ?357685) [357684, 357687, 357686, 357685] by Demod 102762 with 101520 at 2,2,1,2
+Id : 41245, {_}: multiply ?191831 (inverse (multiply ?191832 (divide ?191833 ?191834))) =>= divide ?191831 (multiply ?191832 (multiply ?191833 (inverse ?191834))) [191834, 191833, 191832, 191831] by Super 30968 with 40350 at 2,2,3
+Id : 40574, {_}: multiply (divide ?83055 ?83056) (inverse ?83057) =?= multiply ?83055 (divide (inverse ?83056) ?83057) [83057, 83056, 83055] by Demod 15659 with 40350 at 2
+Id : 41328, {_}: multiply ?192465 (divide (inverse ?192466) (multiply ?192467 (divide ?192468 ?192469))) =>= divide (divide ?192465 ?192466) (multiply ?192467 (multiply ?192468 (inverse ?192469))) [192469, 192468, 192467, 192466, 192465] by Super 41245 with 40574 at 2
+Id : 85188, {_}: divide (multiply ?83055 (inverse ?83056)) ?83057 =<= multiply ?83055 (divide (inverse ?83056) ?83057) [83057, 83056, 83055] by Demod 40574 with 85061 at 2
+Id : 85202, {_}: divide (multiply ?192465 (inverse ?192466)) (multiply ?192467 (divide ?192468 ?192469)) =>= divide (divide ?192465 ?192466) (multiply ?192467 (multiply ?192468 (inverse ?192469))) [192469, 192468, 192467, 192466, 192465] by Demod 41328 with 85188 at 2
+Id : 85220, {_}: divide (divide ?192465 (divide (divide ?192468 ?192469) (inverse ?192466))) ?192467 =?= divide (divide ?192465 ?192466) (multiply ?192467 (multiply ?192468 (inverse ?192469))) [192467, 192466, 192469, 192468, 192465] by Demod 85202 with 62493 at 2
+Id : 85221, {_}: divide (divide ?192465 (multiply (divide ?192468 ?192469) ?192466)) ?192467 =<= divide (divide ?192465 ?192466) (multiply ?192467 (multiply ?192468 (inverse ?192469))) [192467, 192466, 192469, 192468, 192465] by Demod 85220 with 3 at 2,1,2
+Id : 102178, {_}: divide (divide ?192465 (multiply (divide ?192468 ?192469) ?192466)) ?192467 =?= divide (divide ?192465 ?192466) (multiply ?192467 (divide ?192468 ?192469)) [192467, 192466, 192469, 192468, 192465] by Demod 85221 with 101520 at 2,2,3
+Id : 102288, {_}: divide (divide ?192465 (multiply (divide ?192468 ?192469) ?192466)) ?192467 =?= divide (divide ?192465 ?192466) (divide (multiply ?192467 ?192468) ?192469) [192467, 192466, 192469, 192468, 192465] by Demod 102178 with 102247 at 3
+Id : 102764, {_}: divide (divide ?357685 (divide ?357684 ?357684)) (divide (multiply (divide ?357687 ?357686) ?357686) ?357687) =>= inverse (inverse ?357685) [357686, 357687, 357684, 357685] by Demod 102763 with 102288 at 2
+Id : 101094, {_}: divide (inverse (divide (divide ?5777 ?5778) ?5776)) (divide ?5778 ?5777) =>= ?5776 [5776, 5778, 5777] by Demod 1266 with 90396 at 1,2
+Id : 102237, {_}: divide ?5776 (multiply (divide ?5778 ?5777) (divide ?5777 ?5778)) =>= ?5776 [5777, 5778, 5776] by Demod 101094 with 102222 at 2
+Id : 102251, {_}: divide ?5776 (divide (multiply (divide ?5778 ?5777) ?5777) ?5778) =>= ?5776 [5777, 5778, 5776] by Demod 102237 with 102247 at 2
+Id : 102765, {_}: divide ?357685 (divide ?357684 ?357684) =>= inverse (inverse ?357685) [357684, 357685] by Demod 102764 with 102251 at 2
+Id : 102313, {_}: inverse ?36880 =<= multiply (divide (multiply (multiply ?36881 ?36882) (divide (inverse ?36882) ?36881)) (multiply ?36883 ?36880)) ?36883 [36883, 36882, 36881, 36880] by Demod 7367 with 102309 at 1,3
+Id : 102314, {_}: inverse ?36880 =<= multiply (divide (divide (multiply (multiply ?36881 ?36882) (inverse ?36882)) ?36881) (multiply ?36883 ?36880)) ?36883 [36883, 36882, 36881, 36880] by Demod 102313 with 102309 at 1,1,3
+Id : 102315, {_}: inverse ?36880 =<= multiply (divide (divide (divide (multiply ?36881 ?36882) ?36882) ?36881) (multiply ?36883 ?36880)) ?36883 [36883, 36882, 36881, 36880] by Demod 102314 with 101520 at 1,1,1,3
+Id : 102533, {_}: inverse (inverse ?357905) =<= multiply (divide (divide (divide (multiply ?357906 ?357907) ?357907) ?357906) (divide ?357908 ?357905)) ?357908 [357908, 357907, 357906, 357905] by Super 102315 with 101520 at 2,1,3
+Id : 102311, {_}: ?36095 =<= multiply (divide (multiply (multiply ?36096 ?36097) (divide (inverse ?36097) ?36096)) (divide ?36098 ?36095)) ?36098 [36098, 36097, 36096, 36095] by Demod 7191 with 102309 at 1,3
+Id : 102312, {_}: ?36095 =<= multiply (divide (divide (multiply (multiply ?36096 ?36097) (inverse ?36097)) ?36096) (divide ?36098 ?36095)) ?36098 [36098, 36097, 36096, 36095] by Demod 102311 with 102309 at 1,1,3
+Id : 102316, {_}: ?36095 =<= multiply (divide (divide (divide (multiply ?36096 ?36097) ?36097) ?36096) (divide ?36098 ?36095)) ?36098 [36098, 36097, 36096, 36095] by Demod 102312 with 101520 at 1,1,1,3
+Id : 102664, {_}: inverse (inverse ?357905) =>= ?357905 [357905] by Demod 102533 with 102316 at 3
+Id : 103069, {_}: divide ?357685 (divide ?357684 ?357684) =>= ?357685 [357684, 357685] by Demod 102765 with 102664 at 3
+Id : 103199, {_}: inverse (divide ?359423 ?359424) =>= divide ?359424 ?359423 [359424, 359423] by Super 101098 with 103069 at 1,2
+Id : 103718, {_}: divide ?8834 (divide (divide ?8835 ?8832) ?8833) =?= divide (multiply ?8834 (multiply ?8833 ?8832)) ?8835 [8833, 8832, 8835, 8834] by Demod 102264 with 103199 at 3
+Id : 103734, {_}: divide (divide (multiply (inverse (multiply ?13892 ?13893)) (multiply ?13892 ?13895)) (inverse ?13894)) (multiply ?13895 ?13894) =>= inverse ?13893 [13894, 13895, 13893, 13892] by Demod 2791 with 103718 at 1,2
+Id : 40697, {_}: multiply (inverse (divide ?190125 (divide ?190126 ?190127))) (inverse ?190128) =>= multiply (multiply ?190126 (inverse ?190127)) (inverse (multiply ?190128 ?190125)) [190128, 190127, 190126, 190125] by Super 35052 with 40350 at 1,3
+Id : 40823, {_}: multiply (inverse (divide ?190125 (divide ?190126 ?190127))) (inverse ?190128) =>= divide (divide ?190126 (multiply (inverse (inverse ?190125)) ?190127)) ?190128 [190128, 190127, 190126, 190125] by Demod 40697 with 9976 at 3
+Id : 43409, {_}: multiply (inverse (divide ?190125 (divide ?190126 ?190127))) (inverse ?190128) =>= multiply (divide ?190126 (multiply ?190125 ?190127)) (inverse ?190128) [190128, 190127, 190126, 190125] by Demod 40823 with 43406 at 3
+Id : 85192, {_}: multiply (inverse (divide ?190125 (divide ?190126 ?190127))) (inverse ?190128) =>= divide (multiply ?190126 (inverse (multiply ?190125 ?190127))) ?190128 [190128, 190127, 190126, 190125] by Demod 43409 with 85061 at 3
+Id : 102170, {_}: divide (inverse (divide ?190125 (divide ?190126 ?190127))) ?190128 =>= divide (multiply ?190126 (inverse (multiply ?190125 ?190127))) ?190128 [190128, 190127, 190126, 190125] by Demod 85192 with 101520 at 2
+Id : 102171, {_}: divide (inverse (divide ?190125 (divide ?190126 ?190127))) ?190128 =>= divide (divide ?190126 (multiply ?190125 ?190127)) ?190128 [190128, 190127, 190126, 190125] by Demod 102170 with 101520 at 1,3
+Id : 102293, {_}: divide (divide ?190126 ?190127) (multiply ?190128 ?190125) =?= divide (divide ?190126 (multiply ?190125 ?190127)) ?190128 [190125, 190128, 190127, 190126] by Demod 102171 with 102222 at 2
+Id : 103736, {_}: divide (divide (multiply (inverse (multiply ?13892 ?13893)) (multiply ?13892 ?13895)) (multiply ?13894 (inverse ?13894))) ?13895 =>= inverse ?13893 [13894, 13895, 13893, 13892] by Demod 103734 with 102293 at 2
+Id : 103737, {_}: divide (divide (divide (inverse (multiply ?13892 ?13893)) (divide (inverse ?13894) (multiply ?13892 ?13895))) ?13894) ?13895 =>= inverse ?13893 [13895, 13894, 13893, 13892] by Demod 103736 with 62493 at 1,2
+Id : 40061, {_}: divide (divide ?188028 (divide (inverse (divide ?188029 ?188030)) ?188031)) ?188032 =<= divide (multiply ?188028 ?188031) (divide ?188032 (multiply ?188029 (inverse ?188030))) [188032, 188031, 188030, 188029, 188028] by Super 40043 with 39950 at 2,3
+Id : 102158, {_}: divide (divide ?188028 (divide (inverse (divide ?188029 ?188030)) ?188031)) ?188032 =>= divide (multiply ?188028 ?188031) (divide ?188032 (divide ?188029 ?188030)) [188032, 188031, 188030, 188029, 188028] by Demod 40061 with 101520 at 2,2,3
+Id : 102302, {_}: divide (divide ?188028 (divide ?188030 (multiply ?188031 ?188029))) ?188032 =<= divide (multiply ?188028 ?188031) (divide ?188032 (divide ?188029 ?188030)) [188032, 188029, 188031, 188030, 188028] by Demod 102158 with 102222 at 2,1,2
+Id : 103711, {_}: divide ?30 (divide ?31 (divide ?32 ?33)) =<= inverse (divide ?31 (divide ?30 (divide ?33 ?32))) [33, 32, 31, 30] by Demod 101099 with 103199 at 2
+Id : 103712, {_}: divide ?30 (divide ?31 (divide ?32 ?33)) =?= divide (divide ?30 (divide ?33 ?32)) ?31 [33, 32, 31, 30] by Demod 103711 with 103199 at 3
+Id : 103741, {_}: divide (divide ?188028 (divide ?188030 (multiply ?188031 ?188029))) ?188032 =?= divide (divide (multiply ?188028 ?188031) (divide ?188030 ?188029)) ?188032 [188032, 188029, 188031, 188030, 188028] by Demod 102302 with 103712 at 3
+Id : 103744, {_}: divide (divide (divide (multiply (inverse (multiply ?13892 ?13893)) ?13892) (divide (inverse ?13894) ?13895)) ?13894) ?13895 =>= inverse ?13893 [13895, 13894, 13893, 13892] by Demod 103737 with 103741 at 1,2
+Id : 103708, {_}: divide ?114206 (divide ?114204 (multiply ?114207 ?114205)) =<= inverse (divide ?114204 (divide ?114206 (divide (inverse ?114205) ?114207))) [114205, 114207, 114204, 114206] by Demod 62637 with 103199 at 2
+Id : 103709, {_}: divide ?114206 (divide ?114204 (multiply ?114207 ?114205)) =<= divide (divide ?114206 (divide (inverse ?114205) ?114207)) ?114204 [114205, 114207, 114204, 114206] by Demod 103708 with 103199 at 3
+Id : 103749, {_}: divide (divide (multiply (inverse (multiply ?13892 ?13893)) ?13892) (divide ?13894 (multiply ?13895 ?13894))) ?13895 =>= inverse ?13893 [13895, 13894, 13893, 13892] by Demod 103744 with 103709 at 1,2
+Id : 103750, {_}: divide (divide (multiply (multiply (inverse (multiply ?13892 ?13893)) ?13892) ?13895) (divide ?13894 ?13894)) ?13895 =>= inverse ?13893 [13894, 13895, 13893, 13892] by Demod 103749 with 103741 at 2
+Id : 103751, {_}: divide (multiply (multiply (inverse (multiply ?13892 ?13893)) ?13892) ?13895) ?13895 =>= inverse ?13893 [13895, 13893, 13892] by Demod 103750 with 103069 at 1,2
+Id : 2811, {_}: divide (divide (inverse (multiply ?14050 ?14051)) (divide (multiply ?14052 ?14053) ?14050)) (divide (inverse ?14053) ?14052) =>= inverse ?14051 [14053, 14052, 14051, 14050] by Super 2771 with 3 at 1,2,1,2
+Id : 103699, {_}: divide (divide ?346092 ?346094) ?346093 =?= divide ?346092 (multiply ?346093 ?346094) [346093, 346094, 346092] by Demod 102222 with 103199 at 1,2
+Id : 103754, {_}: divide (divide ?258249 (divide ?258253 ?258254)) ?258255 =?= divide (divide (multiply ?258249 ?258254) ?258253) ?258255 [258255, 258254, 258253, 258249] by Demod 62493 with 103699 at 3
+Id : 103756, {_}: divide (divide (multiply (inverse (multiply ?14050 ?14051)) ?14050) (multiply ?14052 ?14053)) (divide (inverse ?14053) ?14052) =>= inverse ?14051 [14053, 14052, 14051, 14050] by Demod 2811 with 103754 at 2
+Id : 103714, {_}: divide (divide ?54 (multiply ?55 ?56)) (divide (inverse ?56) ?55) =>= ?54 [56, 55, 54] by Demod 101095 with 103199 at 2
+Id : 103765, {_}: multiply (inverse (multiply ?14050 ?14051)) ?14050 =>= inverse ?14051 [14051, 14050] by Demod 103756 with 103714 at 2
+Id : 103766, {_}: divide (multiply (inverse ?13893) ?13895) ?13895 =>= inverse ?13893 [13895, 13893] by Demod 103751 with 103765 at 1,1,2
+Id : 103767, {_}: ?38552 =<= multiply (divide (multiply (inverse ?38553) ?38553) (divide ?38555 ?38552)) ?38555 [38555, 38553, 38552] by Demod 102318 with 103766 at 1,1,1,3
+Id : 103801, {_}: multiply ?360754 (divide ?360755 ?360756) =>= divide ?360754 (divide ?360756 ?360755) [360756, 360755, 360754] by Super 3 with 103199 at 2,3
+Id : 102172, {_}: divide (divide ?83055 ?83056) ?83057 =<= multiply ?83055 (divide (inverse ?83056) ?83057) [83057, 83056, 83055] by Demod 85188 with 101520 at 1,2
+Id : 102958, {_}: divide (divide ?358448 (inverse ?358449)) ?358450 =>= multiply ?358448 (divide ?358449 ?358450) [358450, 358449, 358448] by Super 102172 with 102664 at 1,2,3
+Id : 103012, {_}: divide (multiply ?358448 ?358449) ?358450 =<= multiply ?358448 (divide ?358449 ?358450) [358450, 358449, 358448] by Demod 102958 with 3 at 1,2
+Id : 104738, {_}: divide (multiply ?360754 ?360755) ?360756 =?= divide ?360754 (divide ?360756 ?360755) [360756, 360755, 360754] by Demod 103801 with 103012 at 2
+Id : 104742, {_}: ?38552 =<= multiply (divide (multiply (multiply (inverse ?38553) ?38553) ?38552) ?38555) ?38555 [38555, 38553, 38552] by Demod 103767 with 104738 at 1,3
+Id : 102256, {_}: divide (inverse ?35) (divide (multiply (divide ?36 ?37) (divide ?37 ?36)) (divide ?35 (divide ?38 ?39))) =>= divide ?39 ?38 [39, 38, 37, 36, 35] by Demod 362 with 102247 at 2
+Id : 102304, {_}: divide (inverse ?35) (divide (divide (divide ?36 ?37) (divide ?39 (multiply (divide ?37 ?36) ?38))) ?35) =>= divide ?39 ?38 [38, 39, 37, 36, 35] by Demod 102256 with 102302 at 2,2
+Id : 103730, {_}: divide (multiply (inverse ?35) (multiply ?35 (divide ?39 (multiply (divide ?37 ?36) ?38)))) (divide ?36 ?37) =>= divide ?39 ?38 [38, 36, 37, 39, 35] by Demod 102304 with 103718 at 2
+Id : 104003, {_}: divide (multiply (inverse ?35) (divide (multiply ?35 ?39) (multiply (divide ?37 ?36) ?38))) (divide ?36 ?37) =>= divide ?39 ?38 [38, 36, 37, 39, 35] by Demod 103730 with 103012 at 2,1,2
+Id : 104004, {_}: divide (divide (multiply (inverse ?35) (multiply ?35 ?39)) (multiply (divide ?37 ?36) ?38)) (divide ?36 ?37) =>= divide ?39 ?38 [38, 36, 37, 39, 35] by Demod 104003 with 103012 at 1,2
+Id : 104036, {_}: divide (divide (divide (multiply (inverse ?35) (multiply ?35 ?39)) ?38) (divide ?37 ?36)) (divide ?36 ?37) =>= divide ?39 ?38 [36, 37, 38, 39, 35] by Demod 104004 with 103699 at 1,2
+Id : 103700, {_}: divide (divide ?3 (divide ?4 ?5)) (divide ?5 ?4) =>= ?3 [5, 4, 3] by Demod 101098 with 103199 at 2
+Id : 104037, {_}: divide (multiply (inverse ?35) (multiply ?35 ?39)) ?38 =>= divide ?39 ?38 [38, 39, 35] by Demod 104036 with 103700 at 2
+Id : 21134, {_}: inverse (multiply (inverse (inverse ?108447)) (inverse (divide ?108448 ?108449))) =>= inverse (divide (inverse (divide (inverse ?108449) ?108447)) ?108448) [108449, 108448, 108447] by Demod 20903 with 6973 at 2,1,3
+Id : 40046, {_}: inverse (divide (inverse (inverse ?108447)) (multiply ?108448 (inverse ?108449))) =>= inverse (divide (inverse (divide (inverse ?108449) ?108447)) ?108448) [108449, 108448, 108447] by Demod 21134 with 39950 at 1,2
+Id : 40707, {_}: inverse (divide (multiply ?190184 (inverse ?190185)) (multiply ?190186 (inverse ?190187))) =<= inverse (divide (inverse (divide (inverse ?190187) (divide ?190184 ?190185))) ?190186) [190187, 190186, 190185, 190184] by Super 40046 with 40350 at 1,1,2
+Id : 40813, {_}: inverse (divide (divide ?190184 (divide (inverse ?190187) (inverse ?190185))) ?190186) =<= inverse (divide (inverse (divide (inverse ?190187) (divide ?190184 ?190185))) ?190186) [190186, 190185, 190187, 190184] by Demod 40707 with 40043 at 1,2
+Id : 47405, {_}: inverse (divide (divide ?210380 (multiply (inverse ?210381) ?210382)) ?210383) =<= inverse (divide (inverse (divide (inverse ?210381) (divide ?210380 ?210382))) ?210383) [210383, 210382, 210381, 210380] by Demod 40813 with 3 at 2,1,1,2
+Id : 47459, {_}: inverse (divide (divide ?210809 (multiply (inverse (divide ?210810 (divide (divide ?210811 (divide (divide ?210812 ?210813) ?210810)) (divide ?210813 ?210812)))) ?210814)) ?210815) =>= inverse (divide (inverse (divide ?210811 (divide ?210809 ?210814))) ?210815) [210815, 210814, 210813, 210812, 210811, 210810, 210809] by Super 47405 with 53 at 1,1,1,1,3
+Id : 48148, {_}: inverse (divide (divide ?212886 (multiply ?212887 ?212888)) ?212889) =<= inverse (divide (inverse (divide ?212887 (divide ?212886 ?212888))) ?212889) [212889, 212888, 212887, 212886] by Demod 47459 with 53 at 1,2,1,1,2
+Id : 48271, {_}: inverse (divide (divide ?213823 (multiply ?213824 ?213825)) (inverse ?213826)) =<= inverse (multiply (inverse (divide ?213824 (divide ?213823 ?213825))) ?213826) [213826, 213825, 213824, 213823] by Super 48148 with 3 at 1,3
+Id : 48613, {_}: inverse (multiply (divide ?213823 (multiply ?213824 ?213825)) ?213826) =<= inverse (multiply (inverse (divide ?213824 (divide ?213823 ?213825))) ?213826) [213826, 213825, 213824, 213823] by Demod 48271 with 3 at 1,2
+Id : 103705, {_}: inverse (multiply (divide ?213823 (multiply ?213824 ?213825)) ?213826) =?= inverse (multiply (divide (divide ?213823 ?213825) ?213824) ?213826) [213826, 213825, 213824, 213823] by Demod 48613 with 103199 at 1,1,3
+Id : 106200, {_}: divide (multiply ?367270 ?367271) ?367271 =>= ?367270 [367271, 367270] by Super 103069 with 104738 at 2
+Id : 106204, {_}: divide (inverse ?367290) ?367291 =<= inverse (multiply ?367291 ?367290) [367291, 367290] by Super 106200 with 103765 at 1,2
+Id : 106549, {_}: divide (inverse ?213826) (divide ?213823 (multiply ?213824 ?213825)) =<= inverse (multiply (divide (divide ?213823 ?213825) ?213824) ?213826) [213825, 213824, 213823, 213826] by Demod 103705 with 106204 at 2
+Id : 106550, {_}: divide (inverse ?213826) (divide ?213823 (multiply ?213824 ?213825)) =?= divide (inverse ?213826) (divide (divide ?213823 ?213825) ?213824) [213825, 213824, 213823, 213826] by Demod 106549 with 106204 at 3
+Id : 47859, {_}: inverse (divide (divide ?210809 (multiply ?210811 ?210814)) ?210815) =<= inverse (divide (inverse (divide ?210811 (divide ?210809 ?210814))) ?210815) [210815, 210814, 210811, 210809] by Demod 47459 with 53 at 1,2,1,1,2
+Id : 102230, {_}: inverse (divide (divide ?210809 (multiply ?210811 ?210814)) ?210815) =?= inverse (divide (divide ?210809 ?210814) (multiply ?210815 ?210811)) [210815, 210814, 210811, 210809] by Demod 47859 with 102222 at 1,3
+Id : 103696, {_}: divide ?210815 (divide ?210809 (multiply ?210811 ?210814)) =<= inverse (divide (divide ?210809 ?210814) (multiply ?210815 ?210811)) [210814, 210811, 210809, 210815] by Demod 102230 with 103199 at 2
+Id : 103697, {_}: divide ?210815 (divide ?210809 (multiply ?210811 ?210814)) =?= divide (multiply ?210815 ?210811) (divide ?210809 ?210814) [210814, 210811, 210809, 210815] by Demod 103696 with 103199 at 3
+Id : 106566, {_}: divide (multiply (inverse ?213826) ?213824) (divide ?213823 ?213825) =<= divide (inverse ?213826) (divide (divide ?213823 ?213825) ?213824) [213825, 213823, 213824, 213826] by Demod 106550 with 103697 at 2
+Id : 106567, {_}: divide (multiply (inverse ?213826) ?213824) (divide ?213823 ?213825) =?= divide (multiply (inverse ?213826) (multiply ?213824 ?213825)) ?213823 [213825, 213823, 213824, 213826] by Demod 106566 with 103718 at 3
+Id : 106568, {_}: divide (multiply (multiply (inverse ?213826) ?213824) ?213825) ?213823 =<= divide (multiply (inverse ?213826) (multiply ?213824 ?213825)) ?213823 [213823, 213825, 213824, 213826] by Demod 106567 with 104738 at 2
+Id : 106569, {_}: divide (multiply (multiply (inverse ?35) ?35) ?39) ?38 =>= divide ?39 ?38 [38, 39, 35] by Demod 104037 with 106568 at 2
+Id : 106570, {_}: ?38552 =<= multiply (divide ?38552 ?38555) ?38555 [38555, 38552] by Demod 104742 with 106569 at 1,3
+Id : 104876, {_}: divide (multiply ?363468 ?363469) ?363469 =>= ?363468 [363469, 363468] by Super 103069 with 104738 at 2
+Id : 106173, {_}: inverse ?367130 =<= divide ?367131 (multiply ?367130 ?367131) [367131, 367130] by Super 103199 with 104876 at 1,2
+Id : 106805, {_}: ?367778 =<= multiply (inverse ?367779) (multiply ?367779 ?367778) [367779, 367778] by Super 106570 with 106173 at 1,3
+Id : 106633, {_}: multiply ?367594 (multiply ?367595 ?367596) =<= divide ?367594 (divide (inverse ?367596) ?367595) [367596, 367595, 367594] by Super 3 with 106204 at 2,3
+Id : 104940, {_}: multiply (multiply ?363900 ?363901) ?363902 =<= divide ?363900 (divide (inverse ?363902) ?363901) [363902, 363901, 363900] by Super 3 with 104738 at 3
+Id : 108764, {_}: multiply ?367594 (multiply ?367595 ?367596) =?= multiply (multiply ?367594 ?367595) ?367596 [367596, 367595, 367594] by Demod 106633 with 104940 at 3
+Id : 109130, {_}: ?367778 =<= multiply (multiply (inverse ?367779) ?367779) ?367778 [367779, 367778] by Demod 106805 with 108764 at 3
+Id : 109444, {_}: a2 === a2 [] by Demod 1 with 109130 at 2
+Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
+% SZS output end CNFRefutation for GRP470-1.p
+11271: solved GRP470-1.p in 32.33802 using nrkbo
+11271: status Unsatisfiable for GRP470-1.p
+NO CLASH, using fixed ground order
+11326: Facts:
+11326: Id : 2, {_}:
+ divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
+ (divide (divide ?5 ?4) ?2)
+ =>=
+ ?3
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11326: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11326: Goal:
+11326: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+11326: Order:
+11326: nrkbo
+11326: Leaf order:
+11326: inverse 2 1 0
+11326: divide 7 2 0
+11326: c3 2 0 2 2,2
+11326: multiply 5 2 4 0,2
+11326: b3 2 0 2 2,1,2
+11326: a3 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+11327: Facts:
+11327: Id : 2, {_}:
+ divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
+ (divide (divide ?5 ?4) ?2)
+ =>=
+ ?3
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11327: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11327: Goal:
+11327: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+11327: Order:
+11327: kbo
+11327: Leaf order:
+11327: inverse 2 1 0
+11327: divide 7 2 0
+11327: c3 2 0 2 2,2
+11327: multiply 5 2 4 0,2
+11327: b3 2 0 2 2,1,2
+11327: a3 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+11328: Facts:
+11328: Id : 2, {_}:
+ divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
+ (divide (divide ?5 ?4) ?2)
+ =>=
+ ?3
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11328: Id : 3, {_}:
+ multiply ?7 ?8 =>= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11328: Goal:
+11328: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+11328: Order:
+11328: lpo
+11328: Leaf order:
+11328: inverse 2 1 0
+11328: divide 7 2 0
+11328: c3 2 0 2 2,2
+11328: multiply 5 2 4 0,2
+11328: b3 2 0 2 2,1,2
+11328: a3 2 0 2 1,1,2
+Statistics :
+Max weight : 52
+Found proof, 38.615883s
+% SZS status Unsatisfiable for GRP471-1.p
+% SZS output start CNFRefutation for GRP471-1.p
+Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
+Id : 2, {_}: divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) (divide (divide ?5 ?4) ?2) =>= ?3 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+Id : 4, {_}: divide (inverse (divide ?10 (divide ?11 (divide ?12 ?13)))) (divide (divide ?13 ?12) ?10) =>= ?11 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
+Id : 8, {_}: divide (inverse ?35) (divide (divide ?36 ?37) (inverse (divide (divide ?37 ?36) (divide ?35 (divide ?38 ?39))))) =>= divide ?39 ?38 [39, 38, 37, 36, 35] by Super 4 with 2 at 1,1,2
+Id : 377, {_}: divide (inverse ?1785) (multiply (divide ?1786 ?1787) (divide (divide ?1787 ?1786) (divide ?1785 (divide ?1788 ?1789)))) =>= divide ?1789 ?1788 [1789, 1788, 1787, 1786, 1785] by Demod 8 with 3 at 2,2
+Id : 362, {_}: divide (inverse ?35) (multiply (divide ?36 ?37) (divide (divide ?37 ?36) (divide ?35 (divide ?38 ?39)))) =>= divide ?39 ?38 [39, 38, 37, 36, 35] by Demod 8 with 3 at 2,2
+Id : 385, {_}: divide (inverse ?1855) (multiply (divide ?1856 ?1857) (divide (divide ?1857 ?1856) (divide ?1855 (divide ?1858 ?1859)))) =?= divide (multiply (divide ?1860 ?1861) (divide (divide ?1861 ?1860) (divide ?1862 (divide ?1859 ?1858)))) (inverse ?1862) [1862, 1861, 1860, 1859, 1858, 1857, 1856, 1855] by Super 377 with 362 at 2,2,2,2,2
+Id : 436, {_}: divide ?1859 ?1858 =<= divide (multiply (divide ?1860 ?1861) (divide (divide ?1861 ?1860) (divide ?1862 (divide ?1859 ?1858)))) (inverse ?1862) [1862, 1861, 1860, 1858, 1859] by Demod 385 with 362 at 2
+Id : 6830, {_}: divide ?34177 ?34178 =<= multiply (multiply (divide ?34179 ?34180) (divide (divide ?34180 ?34179) (divide ?34181 (divide ?34177 ?34178)))) ?34181 [34181, 34180, 34179, 34178, 34177] by Demod 436 with 3 at 3
+Id : 5, {_}: divide (inverse (divide ?15 (divide ?16 (divide (divide (divide ?17 ?18) ?19) (inverse (divide ?19 (divide ?20 (divide ?18 ?17)))))))) (divide ?20 ?15) =>= ?16 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 1,2,2
+Id : 15, {_}: divide (inverse (divide ?15 (divide ?16 (multiply (divide (divide ?17 ?18) ?19) (divide ?19 (divide ?20 (divide ?18 ?17))))))) (divide ?20 ?15) =>= ?16 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 2,2,1,1,2
+Id : 18, {_}: divide (inverse (divide ?82 ?83)) (divide (divide ?84 ?85) ?82) =?= inverse (divide ?84 (divide ?83 (multiply (divide (divide ?86 ?87) ?88) (divide ?88 (divide ?85 (divide ?87 ?86)))))) [88, 87, 86, 85, 84, 83, 82] by Super 2 with 15 at 2,1,1,2
+Id : 1723, {_}: divide (divide (inverse (divide ?8026 ?8027)) (divide (divide ?8028 ?8029) ?8026)) (divide ?8029 ?8028) =>= ?8027 [8029, 8028, 8027, 8026] by Super 15 with 18 at 1,2
+Id : 1779, {_}: divide (divide (inverse (multiply ?8457 ?8458)) (divide (divide ?8459 ?8460) ?8457)) (divide ?8460 ?8459) =>= inverse ?8458 [8460, 8459, 8458, 8457] by Super 1723 with 3 at 1,1,1,2
+Id : 6854, {_}: divide (divide (inverse (multiply ?34395 ?34396)) (divide (divide ?34397 ?34398) ?34395)) (divide ?34398 ?34397) =?= multiply (multiply (divide ?34399 ?34400) (divide (divide ?34400 ?34399) (divide ?34401 (inverse ?34396)))) ?34401 [34401, 34400, 34399, 34398, 34397, 34396, 34395] by Super 6830 with 1779 at 2,2,2,1,3
+Id : 7005, {_}: inverse ?34396 =<= multiply (multiply (divide ?34399 ?34400) (divide (divide ?34400 ?34399) (divide ?34401 (inverse ?34396)))) ?34401 [34401, 34400, 34399, 34396] by Demod 6854 with 1779 at 2
+Id : 7303, {_}: inverse ?36376 =<= multiply (multiply (divide ?36377 ?36378) (divide (divide ?36378 ?36377) (multiply ?36379 ?36376))) ?36379 [36379, 36378, 36377, 36376] by Demod 7005 with 3 at 2,2,1,3
+Id : 7337, {_}: inverse ?36648 =<= multiply (multiply (divide (inverse ?36649) ?36650) (divide (multiply ?36650 ?36649) (multiply ?36651 ?36648))) ?36651 [36651, 36650, 36649, 36648] by Super 7303 with 3 at 1,2,1,3
+Id : 6831, {_}: divide (inverse (divide ?34183 (divide ?34184 (divide ?34185 ?34186)))) (divide (divide ?34186 ?34185) ?34183) =?= multiply (multiply (divide ?34187 ?34188) (divide (divide ?34188 ?34187) (divide ?34189 ?34184))) ?34189 [34189, 34188, 34187, 34186, 34185, 34184, 34183] by Super 6830 with 2 at 2,2,2,1,3
+Id : 7101, {_}: ?35399 =<= multiply (multiply (divide ?35400 ?35401) (divide (divide ?35401 ?35400) (divide ?35402 ?35399))) ?35402 [35402, 35401, 35400, 35399] by Demod 6831 with 2 at 2
+Id : 2771, {_}: divide (divide (inverse (multiply ?13734 ?13735)) (divide (divide ?13736 ?13737) ?13734)) (divide ?13737 ?13736) =>= inverse ?13735 [13737, 13736, 13735, 13734] by Super 1723 with 3 at 1,1,1,2
+Id : 2814, {_}: divide (divide (inverse (multiply (inverse ?14067) ?14068)) (multiply (divide ?14069 ?14070) ?14067)) (divide ?14070 ?14069) =>= inverse ?14068 [14070, 14069, 14068, 14067] by Super 2771 with 3 at 2,1,2
+Id : 7163, {_}: ?35873 =<= multiply (multiply (divide (multiply (divide ?35873 ?35874) ?35875) (inverse (multiply (inverse ?35875) ?35876))) (inverse ?35876)) ?35874 [35876, 35875, 35874, 35873] by Super 7101 with 2814 at 2,1,3
+Id : 7239, {_}: ?35873 =<= multiply (multiply (multiply (multiply (divide ?35873 ?35874) ?35875) (multiply (inverse ?35875) ?35876)) (inverse ?35876)) ?35874 [35876, 35875, 35874, 35873] by Demod 7163 with 3 at 1,1,3
+Id : 1759, {_}: divide (divide (inverse (divide ?8306 ?8307)) (divide (multiply ?8308 ?8309) ?8306)) (divide (inverse ?8309) ?8308) =>= ?8307 [8309, 8308, 8307, 8306] by Super 1723 with 3 at 1,2,1,2
+Id : 7159, {_}: ?35853 =<= multiply (multiply (divide (divide (multiply ?35853 ?35854) ?35855) (inverse (divide ?35855 ?35856))) ?35856) (inverse ?35854) [35856, 35855, 35854, 35853] by Super 7101 with 1759 at 2,1,3
+Id : 7892, {_}: ?39681 =<= multiply (multiply (multiply (divide (multiply ?39681 ?39682) ?39683) (divide ?39683 ?39684)) ?39684) (inverse ?39682) [39684, 39683, 39682, 39681] by Demod 7159 with 3 at 1,1,3
+Id : 9472, {_}: ?48735 =<= multiply (multiply (multiply (multiply (multiply ?48735 ?48736) ?48737) (divide (inverse ?48737) ?48738)) ?48738) (inverse ?48736) [48738, 48737, 48736, 48735] by Super 7892 with 3 at 1,1,1,3
+Id : 1266, {_}: divide (divide (inverse (divide ?5775 ?5776)) (divide (divide ?5777 ?5778) ?5775)) (divide ?5778 ?5777) =>= ?5776 [5778, 5777, 5776, 5775] by Super 15 with 18 at 1,2
+Id : 7158, {_}: ?35848 =<= multiply (multiply (divide (divide (divide ?35848 ?35849) ?35850) (inverse (divide ?35850 ?35851))) ?35851) ?35849 [35851, 35850, 35849, 35848] by Super 7101 with 1266 at 2,1,3
+Id : 7234, {_}: ?35848 =<= multiply (multiply (multiply (divide (divide ?35848 ?35849) ?35850) (divide ?35850 ?35851)) ?35851) ?35849 [35851, 35850, 35849, 35848] by Demod 7158 with 3 at 1,1,3
+Id : 9552, {_}: divide (divide ?49359 (divide (inverse ?49360) ?49361)) ?49362 =<= multiply (multiply ?49359 ?49361) (inverse (divide ?49362 ?49360)) [49362, 49361, 49360, 49359] by Super 9472 with 7234 at 1,1,3
+Id : 9555, {_}: multiply (divide ?49374 (divide (inverse (inverse ?49375)) ?49376)) ?49377 =<= multiply (multiply ?49374 ?49376) (inverse (multiply (inverse ?49377) ?49375)) [49377, 49376, 49375, 49374] by Super 9472 with 7239 at 1,1,3
+Id : 10048, {_}: divide (divide (multiply ?52036 ?52037) (divide (inverse ?52038) (inverse (multiply (inverse ?52039) ?52040)))) ?52041 =<= multiply (multiply (divide ?52036 (divide (inverse (inverse ?52040)) ?52037)) ?52039) (inverse (divide ?52041 ?52038)) [52041, 52040, 52039, 52038, 52037, 52036] by Super 9552 with 9555 at 1,3
+Id : 10181, {_}: divide (divide (multiply ?52036 ?52037) (multiply (inverse ?52038) (multiply (inverse ?52039) ?52040))) ?52041 =<= multiply (multiply (divide ?52036 (divide (inverse (inverse ?52040)) ?52037)) ?52039) (inverse (divide ?52041 ?52038)) [52041, 52040, 52039, 52038, 52037, 52036] by Demod 10048 with 3 at 2,1,2
+Id : 10182, {_}: divide (divide (multiply ?52036 ?52037) (multiply (inverse ?52038) (multiply (inverse ?52039) ?52040))) ?52041 =<= divide (divide (divide ?52036 (divide (inverse (inverse ?52040)) ?52037)) (divide (inverse ?52038) ?52039)) ?52041 [52041, 52040, 52039, 52038, 52037, 52036] by Demod 10181 with 9552 at 3
+Id : 7161, {_}: ?35863 =<= multiply (multiply (divide (divide (divide ?35863 ?35864) ?35865) (inverse (multiply ?35865 ?35866))) (inverse ?35866)) ?35864 [35866, 35865, 35864, 35863] by Super 7101 with 1779 at 2,1,3
+Id : 7237, {_}: ?35863 =<= multiply (multiply (multiply (divide (divide ?35863 ?35864) ?35865) (multiply ?35865 ?35866)) (inverse ?35866)) ?35864 [35866, 35865, 35864, 35863] by Demod 7161 with 3 at 1,1,3
+Id : 9554, {_}: divide (divide ?49369 (divide (inverse (inverse ?49370)) ?49371)) ?49372 =>= multiply (multiply ?49369 ?49371) (inverse (multiply ?49372 ?49370)) [49372, 49371, 49370, 49369] by Super 9472 with 7237 at 1,1,3
+Id : 10183, {_}: divide (divide (multiply ?52036 ?52037) (multiply (inverse ?52038) (multiply (inverse ?52039) ?52040))) ?52041 =<= divide (multiply (multiply ?52036 ?52037) (inverse (multiply (divide (inverse ?52038) ?52039) ?52040))) ?52041 [52041, 52040, 52039, 52038, 52037, 52036] by Demod 10182 with 9554 at 1,3
+Id : 12174, {_}: multiply (multiply ?64029 ?64030) (inverse (multiply (divide (inverse ?64031) ?64032) ?64033)) =<= multiply (multiply (multiply (multiply (divide (divide (multiply ?64029 ?64030) (multiply (inverse ?64031) (multiply (inverse ?64032) ?64033))) ?64034) ?64035) (multiply (inverse ?64035) ?64036)) (inverse ?64036)) ?64034 [64036, 64035, 64034, 64033, 64032, 64031, 64030, 64029] by Super 7239 with 10183 at 1,1,1,1,3
+Id : 12258, {_}: multiply (multiply ?64029 ?64030) (inverse (multiply (divide (inverse ?64031) ?64032) ?64033)) =>= divide (multiply ?64029 ?64030) (multiply (inverse ?64031) (multiply (inverse ?64032) ?64033)) [64033, 64032, 64031, 64030, 64029] by Demod 12174 with 7239 at 3
+Id : 12491, {_}: inverse (inverse (multiply (divide (inverse ?65291) ?65292) ?65293)) =<= multiply (multiply (divide (inverse ?65294) ?65295) (divide (multiply ?65295 ?65294) (divide (multiply ?65296 ?65297) (multiply (inverse ?65291) (multiply (inverse ?65292) ?65293))))) (multiply ?65296 ?65297) [65297, 65296, 65295, 65294, 65293, 65292, 65291] by Super 7337 with 12258 at 2,2,1,3
+Id : 7157, {_}: ?35843 =<= multiply (multiply (divide (inverse ?35844) ?35845) (divide (multiply ?35845 ?35844) (divide ?35846 ?35843))) ?35846 [35846, 35845, 35844, 35843] by Super 7101 with 3 at 1,2,1,3
+Id : 12726, {_}: inverse (inverse (multiply (divide (inverse ?66353) ?66354) ?66355)) =>= multiply (inverse ?66353) (multiply (inverse ?66354) ?66355) [66355, 66354, 66353] by Demod 12491 with 7157 at 3
+Id : 7, {_}: divide (inverse (divide ?29 ?30)) (divide (divide ?31 (divide ?32 ?33)) ?29) =>= inverse (divide ?31 (divide ?30 (divide ?33 ?32))) [33, 32, 31, 30, 29] by Super 4 with 2 at 2,1,1,2
+Id : 53, {_}: inverse (divide ?279 (divide (divide ?280 (divide (divide ?281 ?282) ?279)) (divide ?282 ?281))) =>= ?280 [282, 281, 280, 279] by Super 2 with 7 at 2
+Id : 12727, {_}: inverse (inverse (multiply (divide ?66357 ?66358) ?66359)) =<= multiply (inverse (divide ?66360 (divide (divide ?66357 (divide (divide ?66361 ?66362) ?66360)) (divide ?66362 ?66361)))) (multiply (inverse ?66358) ?66359) [66362, 66361, 66360, 66359, 66358, 66357] by Super 12726 with 53 at 1,1,1,1,2
+Id : 12825, {_}: inverse (inverse (multiply (divide ?66943 ?66944) ?66945)) =>= multiply ?66943 (multiply (inverse ?66944) ?66945) [66945, 66944, 66943] by Demod 12727 with 53 at 1,3
+Id : 12858, {_}: inverse (inverse (multiply (multiply ?67174 ?67175) ?67176)) =<= multiply ?67174 (multiply (inverse (inverse ?67175)) ?67176) [67176, 67175, 67174] by Super 12825 with 3 at 1,1,1,2
+Id : 12, {_}: divide (inverse (divide ?53 (divide ?54 (multiply ?55 ?56)))) (divide (divide (inverse ?56) ?55) ?53) =>= ?54 [56, 55, 54, 53] by Super 2 with 3 at 2,2,1,1,2
+Id : 17, {_}: divide (inverse (divide ?73 (divide ?74 ?75))) (divide (divide (divide ?76 ?77) (inverse (divide ?77 (divide ?75 (multiply (divide (divide ?78 ?79) ?80) (divide ?80 (divide ?76 (divide ?79 ?78)))))))) ?73) =>= ?74 [80, 79, 78, 77, 76, 75, 74, 73] by Super 2 with 15 at 2,2,1,1,2
+Id : 66361, {_}: divide (inverse (divide ?259836 (divide ?259837 ?259838))) (divide (multiply (divide ?259839 ?259840) (divide ?259840 (divide ?259838 (multiply (divide (divide ?259841 ?259842) ?259843) (divide ?259843 (divide ?259839 (divide ?259842 ?259841))))))) ?259836) =>= ?259837 [259843, 259842, 259841, 259840, 259839, 259838, 259837, 259836] by Demod 17 with 3 at 1,2,2
+Id : 12770, {_}: inverse (inverse (multiply (divide ?66357 ?66358) ?66359)) =>= multiply ?66357 (multiply (inverse ?66358) ?66359) [66359, 66358, 66357] by Demod 12727 with 53 at 1,3
+Id : 12807, {_}: multiply ?66813 (inverse (multiply (divide ?66814 ?66815) ?66816)) =>= divide ?66813 (multiply ?66814 (multiply (inverse ?66815) ?66816)) [66816, 66815, 66814, 66813] by Super 3 with 12770 at 2,3
+Id : 13153, {_}: inverse (inverse (multiply (multiply ?68629 ?68630) (inverse (multiply (divide ?68631 ?68632) ?68633)))) =<= multiply ?68629 (divide (inverse (inverse ?68630)) (multiply ?68631 (multiply (inverse ?68632) ?68633))) [68633, 68632, 68631, 68630, 68629] by Super 12858 with 12807 at 2,3
+Id : 15503, {_}: inverse (inverse (divide (multiply ?81665 ?81666) (multiply ?81667 (multiply (inverse ?81668) ?81669)))) =<= multiply ?81665 (divide (inverse (inverse ?81666)) (multiply ?81667 (multiply (inverse ?81668) ?81669))) [81669, 81668, 81667, 81666, 81665] by Demod 13153 with 12807 at 1,1,2
+Id : 6973, {_}: ?34184 =<= multiply (multiply (divide ?34187 ?34188) (divide (divide ?34188 ?34187) (divide ?34189 ?34184))) ?34189 [34189, 34188, 34187, 34184] by Demod 6831 with 2 at 2
+Id : 15524, {_}: inverse (inverse (divide (multiply ?81857 ?81858) (multiply (multiply (divide ?81859 ?81860) (divide (divide ?81860 ?81859) (divide (multiply (inverse ?81861) ?81862) ?81863))) (multiply (inverse ?81861) ?81862)))) =>= multiply ?81857 (divide (inverse (inverse ?81858)) ?81863) [81863, 81862, 81861, 81860, 81859, 81858, 81857] by Super 15503 with 6973 at 2,2,3
+Id : 15656, {_}: inverse (inverse (divide (multiply ?81857 ?81858) ?81863)) =<= multiply ?81857 (divide (inverse (inverse ?81858)) ?81863) [81863, 81858, 81857] by Demod 15524 with 6973 at 2,1,1,2
+Id : 23797, {_}: divide (divide ?119374 (divide (inverse ?119375) (divide (inverse (inverse ?119376)) ?119377))) ?119378 =<= multiply (inverse (inverse (divide (multiply ?119374 ?119376) ?119377))) (inverse (divide ?119378 ?119375)) [119378, 119377, 119376, 119375, 119374] by Super 9552 with 15656 at 1,3
+Id : 23859, {_}: divide (divide (multiply (divide (inverse ?119930) ?119931) (divide (multiply ?119931 ?119930) (divide ?119932 ?119933))) (divide (inverse ?119934) (divide (inverse (inverse ?119932)) ?119935))) ?119936 =>= multiply (inverse (inverse (divide ?119933 ?119935))) (inverse (divide ?119936 ?119934)) [119936, 119935, 119934, 119933, 119932, 119931, 119930] by Super 23797 with 7157 at 1,1,1,1,3
+Id : 13062, {_}: inverse (inverse (divide (divide ?67961 ?67962) (multiply ?67963 (multiply (inverse ?67964) ?67965)))) =>= multiply ?67961 (multiply (inverse ?67962) (inverse (multiply (divide ?67963 ?67964) ?67965))) [67965, 67964, 67963, 67962, 67961] by Super 12770 with 12807 at 1,1,2
+Id : 16664, {_}: inverse (inverse (divide (divide ?87645 ?87646) (multiply ?87647 (multiply (inverse ?87648) ?87649)))) =>= multiply ?87645 (divide (inverse ?87646) (multiply ?87647 (multiply (inverse ?87648) ?87649))) [87649, 87648, 87647, 87646, 87645] by Demod 13062 with 12807 at 2,3
+Id : 16690, {_}: inverse (inverse (divide (divide ?87882 ?87883) ?87884)) =<= multiply ?87882 (divide (inverse ?87883) (multiply (multiply (divide ?87885 ?87886) (divide (divide ?87886 ?87885) (divide (multiply (inverse ?87887) ?87888) ?87884))) (multiply (inverse ?87887) ?87888))) [87888, 87887, 87886, 87885, 87884, 87883, 87882] by Super 16664 with 6973 at 2,1,1,2
+Id : 16778, {_}: inverse (inverse (divide (divide ?87882 ?87883) ?87884)) =>= multiply ?87882 (divide (inverse ?87883) ?87884) [87884, 87883, 87882] by Demod 16690 with 6973 at 2,2,3
+Id : 16836, {_}: multiply ?88530 (inverse (divide (divide ?88531 ?88532) ?88533)) =>= divide ?88530 (multiply ?88531 (divide (inverse ?88532) ?88533)) [88533, 88532, 88531, 88530] by Super 3 with 16778 at 2,3
+Id : 16941, {_}: divide (divide ?89130 (divide (inverse ?89131) ?89132)) (divide ?89133 ?89134) =<= divide (multiply ?89130 ?89132) (multiply ?89133 (divide (inverse ?89134) ?89131)) [89134, 89133, 89132, 89131, 89130] by Super 9552 with 16836 at 3
+Id : 17721, {_}: divide (inverse ?92223) (multiply (divide ?92224 ?92225) (divide (divide ?92225 ?92224) (divide ?92223 (divide (divide ?92226 (divide (inverse ?92227) ?92228)) (divide ?92229 ?92230))))) =>= divide (multiply ?92229 (divide (inverse ?92230) ?92227)) (multiply ?92226 ?92228) [92230, 92229, 92228, 92227, 92226, 92225, 92224, 92223] by Super 362 with 16941 at 2,2,2,2,2
+Id : 18088, {_}: divide (divide ?94725 ?94726) (divide ?94727 (divide (inverse ?94728) ?94729)) =<= divide (multiply ?94725 (divide (inverse ?94726) ?94728)) (multiply ?94727 ?94729) [94729, 94728, 94727, 94726, 94725] by Demod 17721 with 362 at 2
+Id : 18882, {_}: divide (divide ?99448 ?99449) (divide ?99450 (divide (inverse (inverse ?99451)) ?99452)) =>= divide (multiply ?99448 (multiply (inverse ?99449) ?99451)) (multiply ?99450 ?99452) [99452, 99451, 99450, 99449, 99448] by Super 18088 with 3 at 2,1,3
+Id : 18956, {_}: divide (multiply ?100120 ?100121) (divide ?100122 (divide (inverse (inverse ?100123)) ?100124)) =?= divide (multiply ?100120 (multiply (inverse (inverse ?100121)) ?100123)) (multiply ?100122 ?100124) [100124, 100123, 100122, 100121, 100120] by Super 18882 with 3 at 1,2
+Id : 19253, {_}: divide (multiply ?100120 ?100121) (divide ?100122 (divide (inverse (inverse ?100123)) ?100124)) =>= divide (inverse (inverse (multiply (multiply ?100120 ?100121) ?100123))) (multiply ?100122 ?100124) [100124, 100123, 100122, 100121, 100120] by Demod 18956 with 12858 at 1,3
+Id : 24073, {_}: divide (divide (inverse (inverse (multiply (multiply (divide (inverse ?119930) ?119931) (divide (multiply ?119931 ?119930) (divide ?119932 ?119933))) ?119932))) (multiply (inverse ?119934) ?119935)) ?119936 =>= multiply (inverse (inverse (divide ?119933 ?119935))) (inverse (divide ?119936 ?119934)) [119936, 119935, 119934, 119933, 119932, 119931, 119930] by Demod 23859 with 19253 at 1,2
+Id : 24074, {_}: divide (divide (inverse (inverse ?119933)) (multiply (inverse ?119934) ?119935)) ?119936 =<= multiply (inverse (inverse (divide ?119933 ?119935))) (inverse (divide ?119936 ?119934)) [119936, 119935, 119934, 119933] by Demod 24073 with 7157 at 1,1,1,1,2
+Id : 18174, {_}: divide (divide ?95484 (inverse ?95485)) (divide ?95486 (divide (inverse ?95487) ?95488)) =>= divide (inverse (inverse (divide (multiply ?95484 ?95485) ?95487))) (multiply ?95486 ?95488) [95488, 95487, 95486, 95485, 95484] by Super 18088 with 15656 at 1,3
+Id : 20071, {_}: divide (multiply ?105383 ?105384) (divide ?105385 (divide (inverse ?105386) ?105387)) =<= divide (inverse (inverse (divide (multiply ?105383 ?105384) ?105386))) (multiply ?105385 ?105387) [105387, 105386, 105385, 105384, 105383] by Demod 18174 with 3 at 1,2
+Id : 20108, {_}: divide (multiply (multiply (divide ?105694 ?105695) (divide (divide ?105695 ?105694) (divide ?105696 ?105697))) ?105696) (divide ?105698 (divide (inverse ?105699) ?105700)) =>= divide (inverse (inverse (divide ?105697 ?105699))) (multiply ?105698 ?105700) [105700, 105699, 105698, 105697, 105696, 105695, 105694] by Super 20071 with 6973 at 1,1,1,1,3
+Id : 20428, {_}: divide ?105697 (divide ?105698 (divide (inverse ?105699) ?105700)) =<= divide (inverse (inverse (divide ?105697 ?105699))) (multiply ?105698 ?105700) [105700, 105699, 105698, 105697] by Demod 20108 with 6973 at 1,2
+Id : 20476, {_}: inverse (inverse (divide (divide ?106039 (divide ?106040 (divide (inverse ?106041) ?106042))) ?106043)) =<= multiply (inverse (inverse (divide ?106039 ?106041))) (divide (inverse (multiply ?106040 ?106042)) ?106043) [106043, 106042, 106041, 106040, 106039] by Super 16778 with 20428 at 1,1,1,2
+Id : 20938, {_}: multiply ?106039 (divide (inverse (divide ?106040 (divide (inverse ?106041) ?106042))) ?106043) =<= multiply (inverse (inverse (divide ?106039 ?106041))) (divide (inverse (multiply ?106040 ?106042)) ?106043) [106043, 106042, 106041, 106040, 106039] by Demod 20476 with 16778 at 2
+Id : 24149, {_}: inverse (inverse (multiply (multiply ?120312 (divide ?120313 ?120314)) (inverse (divide ?120315 ?120316)))) =<= multiply ?120312 (divide (divide (inverse (inverse ?120313)) (multiply (inverse ?120316) ?120314)) ?120315) [120316, 120315, 120314, 120313, 120312] by Super 12858 with 24074 at 2,3
+Id : 24438, {_}: inverse (inverse (divide (divide ?120312 (divide (inverse ?120316) (divide ?120313 ?120314))) ?120315)) =<= multiply ?120312 (divide (divide (inverse (inverse ?120313)) (multiply (inverse ?120316) ?120314)) ?120315) [120315, 120314, 120313, 120316, 120312] by Demod 24149 with 9552 at 1,1,2
+Id : 24439, {_}: multiply ?120312 (divide (inverse (divide (inverse ?120316) (divide ?120313 ?120314))) ?120315) =<= multiply ?120312 (divide (divide (inverse (inverse ?120313)) (multiply (inverse ?120316) ?120314)) ?120315) [120315, 120314, 120313, 120316, 120312] by Demod 24438 with 16778 at 2
+Id : 33216, {_}: inverse (divide (divide (inverse (inverse ?156723)) (multiply (inverse ?156724) ?156725)) ?156726) =<= multiply (multiply (divide (inverse ?156727) ?156728) (divide (multiply ?156728 ?156727) (multiply ?156729 (divide (inverse (divide (inverse ?156724) (divide ?156723 ?156725))) ?156726)))) ?156729 [156729, 156728, 156727, 156726, 156725, 156724, 156723] by Super 7337 with 24439 at 2,2,1,3
+Id : 33721, {_}: inverse (divide (divide (inverse (inverse ?158945)) (multiply (inverse ?158946) ?158947)) ?158948) =>= inverse (divide (inverse (divide (inverse ?158946) (divide ?158945 ?158947))) ?158948) [158948, 158947, 158946, 158945] by Demod 33216 with 7337 at 3
+Id : 33722, {_}: inverse (divide (divide (inverse (inverse ?158950)) (multiply ?158951 ?158952)) ?158953) =<= inverse (divide (inverse (divide (inverse (divide ?158954 (divide (divide ?158951 (divide (divide ?158955 ?158956) ?158954)) (divide ?158956 ?158955)))) (divide ?158950 ?158952))) ?158953) [158956, 158955, 158954, 158953, 158952, 158951, 158950] by Super 33721 with 53 at 1,2,1,1,2
+Id : 34010, {_}: inverse (divide (divide (inverse (inverse ?158950)) (multiply ?158951 ?158952)) ?158953) =>= inverse (divide (inverse (divide ?158951 (divide ?158950 ?158952))) ?158953) [158953, 158952, 158951, 158950] by Demod 33722 with 53 at 1,1,1,1,3
+Id : 34077, {_}: inverse (inverse (divide (inverse (divide ?159790 (divide ?159791 ?159792))) ?159793)) =<= multiply (inverse (inverse ?159791)) (divide (inverse (multiply ?159790 ?159792)) ?159793) [159793, 159792, 159791, 159790] by Super 16778 with 34010 at 1,2
+Id : 34441, {_}: multiply ?106039 (divide (inverse (divide ?106040 (divide (inverse ?106041) ?106042))) ?106043) =<= inverse (inverse (divide (inverse (divide ?106040 (divide (divide ?106039 ?106041) ?106042))) ?106043)) [106043, 106042, 106041, 106040, 106039] by Demod 20938 with 34077 at 3
+Id : 16, {_}: divide (inverse (divide ?64 (divide ?65 (divide (divide ?66 ?67) (inverse (divide ?67 (divide ?68 (multiply (divide (divide ?69 ?70) ?71) (divide ?71 (divide ?66 (divide ?70 ?69))))))))))) (divide ?68 ?64) =>= ?65 [71, 70, 69, 68, 67, 66, 65, 64] by Super 2 with 15 at 1,2,2
+Id : 38, {_}: divide (inverse (divide ?64 (divide ?65 (multiply (divide ?66 ?67) (divide ?67 (divide ?68 (multiply (divide (divide ?69 ?70) ?71) (divide ?71 (divide ?66 (divide ?70 ?69)))))))))) (divide ?68 ?64) =>= ?65 [71, 70, 69, 68, 67, 66, 65, 64] by Demod 16 with 3 at 2,2,1,1,2
+Id : 43649, {_}: multiply ?191130 (divide (inverse (divide ?191131 (divide (inverse ?191132) (multiply (divide ?191133 ?191134) (divide ?191134 (divide ?191135 (multiply (divide (divide ?191136 ?191137) ?191138) (divide ?191138 (divide ?191133 (divide ?191137 ?191136)))))))))) (divide ?191135 ?191131)) =>= inverse (inverse (divide ?191130 ?191132)) [191138, 191137, 191136, 191135, 191134, 191133, 191132, 191131, 191130] by Super 34441 with 38 at 1,1,3
+Id : 44429, {_}: multiply ?191130 (inverse ?191132) =<= inverse (inverse (divide ?191130 ?191132)) [191132, 191130] by Demod 43649 with 38 at 2,2
+Id : 44886, {_}: divide (divide (inverse (inverse ?119933)) (multiply (inverse ?119934) ?119935)) ?119936 =>= multiply (multiply ?119933 (inverse ?119935)) (inverse (divide ?119936 ?119934)) [119936, 119935, 119934, 119933] by Demod 24074 with 44429 at 1,3
+Id : 44891, {_}: divide (divide (inverse (inverse ?119933)) (multiply (inverse ?119934) ?119935)) ?119936 =>= divide (divide ?119933 (divide (inverse ?119934) (inverse ?119935))) ?119936 [119936, 119935, 119934, 119933] by Demod 44886 with 9552 at 3
+Id : 44892, {_}: divide (divide (inverse (inverse ?119933)) (multiply (inverse ?119934) ?119935)) ?119936 =>= divide (divide ?119933 (multiply (inverse ?119934) ?119935)) ?119936 [119936, 119935, 119934, 119933] by Demod 44891 with 3 at 2,1,3
+Id : 66804, {_}: divide (inverse (divide ?265003 (divide (divide ?265004 (multiply (inverse ?265005) ?265006)) ?265007))) (divide (multiply (divide ?265008 ?265009) (divide ?265009 (divide ?265007 (multiply (divide (divide ?265010 ?265011) ?265012) (divide ?265012 (divide ?265008 (divide ?265011 ?265010))))))) ?265003) =>= divide (inverse (inverse ?265004)) (multiply (inverse ?265005) ?265006) [265012, 265011, 265010, 265009, 265008, 265007, 265006, 265005, 265004, 265003] by Super 66361 with 44892 at 2,1,1,2
+Id : 39, {_}: divide (inverse (divide ?73 (divide ?74 ?75))) (divide (multiply (divide ?76 ?77) (divide ?77 (divide ?75 (multiply (divide (divide ?78 ?79) ?80) (divide ?80 (divide ?76 (divide ?79 ?78))))))) ?73) =>= ?74 [80, 79, 78, 77, 76, 75, 74, 73] by Demod 17 with 3 at 1,2,2
+Id : 67572, {_}: divide ?265004 (multiply (inverse ?265005) ?265006) =<= divide (inverse (inverse ?265004)) (multiply (inverse ?265005) ?265006) [265006, 265005, 265004] by Demod 66804 with 39 at 2
+Id : 67796, {_}: divide (inverse (divide ?266802 (divide ?266803 (multiply (inverse ?266804) ?266805)))) (divide (divide (inverse ?266805) (inverse ?266804)) ?266802) =>= inverse (inverse ?266803) [266805, 266804, 266803, 266802] by Super 12 with 67572 at 2,1,1,2
+Id : 68093, {_}: ?266803 =<= inverse (inverse ?266803) [266803] by Demod 67796 with 12 at 2
+Id : 68404, {_}: multiply (multiply ?67174 ?67175) ?67176 =<= multiply ?67174 (multiply (inverse (inverse ?67175)) ?67176) [67176, 67175, 67174] by Demod 12858 with 68093 at 2
+Id : 68405, {_}: multiply (multiply ?67174 ?67175) ?67176 =?= multiply ?67174 (multiply ?67175 ?67176) [67176, 67175, 67174] by Demod 68404 with 68093 at 1,2,3
+Id : 68861, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 1 with 68405 at 2
+Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
+% SZS output end CNFRefutation for GRP471-1.p
+11326: solved GRP471-1.p in 19.353208 using nrkbo
+11326: status Unsatisfiable for GRP471-1.p
+NO CLASH, using fixed ground order
+11333: Facts:
+11333: Id : 2, {_}:
+ divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
+ (divide ?3 ?2)
+ =>=
+ ?5
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11333: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11333: Goal:
+11333: Id : 1, {_}:
+ multiply (inverse a1) a1 =>= multiply (inverse b1) b1
+ [] by prove_these_axioms_1
+11333: Order:
+11333: nrkbo
+11333: Leaf order:
+11333: divide 7 2 0
+11333: b1 2 0 2 1,1,3
+11333: multiply 3 2 2 0,2
+11333: inverse 4 1 2 0,1,2
+11333: a1 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+11334: Facts:
+11334: Id : 2, {_}:
+ divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
+ (divide ?3 ?2)
+ =>=
+ ?5
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11334: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11334: Goal:
+11334: Id : 1, {_}:
+ multiply (inverse a1) a1 =>= multiply (inverse b1) b1
+ [] by prove_these_axioms_1
+11334: Order:
+11334: kbo
+11334: Leaf order:
+11334: divide 7 2 0
+11334: b1 2 0 2 1,1,3
+11334: multiply 3 2 2 0,2
+11334: inverse 4 1 2 0,1,2
+11334: a1 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+11335: Facts:
+11335: Id : 2, {_}:
+ divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
+ (divide ?3 ?2)
+ =>=
+ ?5
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11335: Id : 3, {_}:
+ multiply ?7 ?8 =?= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11335: Goal:
+11335: Id : 1, {_}:
+ multiply (inverse a1) a1 =>= multiply (inverse b1) b1
+ [] by prove_these_axioms_1
+11335: Order:
+11335: lpo
+11335: Leaf order:
+11335: divide 7 2 0
+11335: b1 2 0 2 1,1,3
+11335: multiply 3 2 2 0,2
+11335: inverse 4 1 2 0,1,2
+11335: a1 2 0 2 1,1,2
+% SZS status Timeout for GRP475-1.p
+NO CLASH, using fixed ground order
+11373: Facts:
+11373: Id : 2, {_}:
+ divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
+ (divide ?3 ?2)
+ =>=
+ ?5
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11373: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11373: Goal:
+11373: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+11373: Order:
+11373: nrkbo
+11373: Leaf order:
+11373: divide 7 2 0
+11373: a2 2 0 2 2,2
+11373: multiply 3 2 2 0,2
+11373: inverse 3 1 1 0,1,1,2
+11373: b2 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+11374: Facts:
+11374: Id : 2, {_}:
+ divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
+ (divide ?3 ?2)
+ =>=
+ ?5
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11374: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11374: Goal:
+11374: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+11374: Order:
+11374: kbo
+11374: Leaf order:
+11374: divide 7 2 0
+11374: a2 2 0 2 2,2
+11374: multiply 3 2 2 0,2
+11374: inverse 3 1 1 0,1,1,2
+11374: b2 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+11375: Facts:
+11375: Id : 2, {_}:
+ divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
+ (divide ?3 ?2)
+ =>=
+ ?5
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11375: Id : 3, {_}:
+ multiply ?7 ?8 =?= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11375: Goal:
+11375: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+11375: Order:
+11375: lpo
+11375: Leaf order:
+11375: divide 7 2 0
+11375: a2 2 0 2 2,2
+11375: multiply 3 2 2 0,2
+11375: inverse 3 1 1 0,1,1,2
+11375: b2 2 0 2 1,1,1,2
+Statistics :
+Max weight : 49
+Found proof, 60.308770s
+% SZS status Unsatisfiable for GRP476-1.p
+% SZS output start CNFRefutation for GRP476-1.p
+Id : 2, {_}: divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) (divide ?3 ?2) =>= ?5 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+Id : 4, {_}: divide (inverse (divide (divide (divide ?10 ?11) ?12) (divide ?13 ?12))) (divide ?11 ?10) =>= ?13 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
+Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
+Id : 5, {_}: divide (inverse (divide (divide (divide (divide ?15 ?16) (inverse (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17)))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 2,2
+Id : 17, {_}: divide (inverse (divide (divide (multiply (divide ?15 ?16) (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 1,1,1,1,2
+Id : 20, {_}: divide (inverse (divide (divide (divide ?80 ?81) ?82) ?83)) (divide ?81 ?80) =?= inverse (divide (divide (multiply (divide ?84 ?85) (divide (divide (divide ?85 ?84) ?86) (divide ?82 ?86))) ?87) (divide ?83 ?87)) [87, 86, 85, 84, 83, 82, 81, 80] by Super 2 with 17 at 2,1,1,2
+Id : 2201, {_}: divide (divide (inverse (divide (divide (divide ?9850 ?9851) ?9852) ?9853)) (divide ?9851 ?9850)) ?9852 =>= ?9853 [9853, 9852, 9851, 9850] by Super 17 with 20 at 1,2
+Id : 2522, {_}: divide (divide (inverse (multiply (divide (divide ?11173 ?11174) ?11175) ?11176)) (divide ?11174 ?11173)) ?11175 =>= inverse ?11176 [11176, 11175, 11174, 11173] by Super 2201 with 3 at 1,1,1,2
+Id : 3974, {_}: divide (divide (inverse (multiply (divide (divide (inverse ?18265) ?18266) ?18267) ?18268)) (multiply ?18266 ?18265)) ?18267 =>= inverse ?18268 [18268, 18267, 18266, 18265] by Super 2522 with 3 at 2,1,2
+Id : 4011, {_}: divide (divide (inverse (multiply (divide (multiply (inverse ?18535) ?18536) ?18537) ?18538)) (multiply (inverse ?18536) ?18535)) ?18537 =>= inverse ?18538 [18538, 18537, 18536, 18535] by Super 3974 with 3 at 1,1,1,1,1,2
+Id : 3335, {_}: divide (divide (inverse (divide (divide (divide (inverse ?15160) ?15161) ?15162) ?15163)) (multiply ?15161 ?15160)) ?15162 =>= ?15163 [15163, 15162, 15161, 15160] by Super 2201 with 3 at 2,1,2
+Id : 3370, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?15416) ?15417) ?15418) ?15419)) (multiply (inverse ?15417) ?15416)) ?15418 =>= ?15419 [15419, 15418, 15417, 15416] by Super 3335 with 3 at 1,1,1,1,1,2
+Id : 7, {_}: divide (inverse (divide (divide ?29 ?30) (divide ?31 ?30))) (divide (divide ?32 ?33) (inverse (divide (divide (divide ?33 ?32) ?34) (divide ?29 ?34)))) =>= ?31 [34, 33, 32, 31, 30, 29] by Super 4 with 2 at 1,1,1,1,2
+Id : 602, {_}: divide (inverse (divide (divide ?2300 ?2301) (divide ?2302 ?2301))) (multiply (divide ?2303 ?2304) (divide (divide (divide ?2304 ?2303) ?2305) (divide ?2300 ?2305))) =>= ?2302 [2305, 2304, 2303, 2302, 2301, 2300] by Demod 7 with 3 at 2,2
+Id : 6, {_}: divide (inverse (divide (divide (divide ?22 ?23) (divide ?24 ?25)) ?26)) (divide ?23 ?22) =?= inverse (divide (divide (divide ?25 ?24) ?27) (divide ?26 ?27)) [27, 26, 25, 24, 23, 22] by Super 4 with 2 at 2,1,1,2
+Id : 300, {_}: inverse (divide (divide (divide ?1003 ?1004) ?1005) (divide (divide ?1006 (divide ?1004 ?1003)) ?1005)) =>= ?1006 [1006, 1005, 1004, 1003] by Super 2 with 6 at 2
+Id : 673, {_}: divide ?2877 (multiply (divide ?2878 ?2879) (divide (divide (divide ?2879 ?2878) ?2880) (divide (divide ?2881 ?2882) ?2880))) =>= divide ?2877 (divide ?2882 ?2881) [2882, 2881, 2880, 2879, 2878, 2877] by Super 602 with 300 at 1,2
+Id : 18343, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?89645) ?89646) ?89647) (divide ?89648 ?89649))) (multiply (inverse ?89646) ?89645)) ?89647 =?= multiply (divide ?89650 ?89651) (divide (divide (divide ?89651 ?89650) ?89652) (divide (divide ?89649 ?89648) ?89652)) [89652, 89651, 89650, 89649, 89648, 89647, 89646, 89645] by Super 3370 with 673 at 1,1,1,2
+Id : 19039, {_}: divide ?92370 ?92371 =<= multiply (divide ?92372 ?92373) (divide (divide (divide ?92373 ?92372) ?92374) (divide (divide ?92371 ?92370) ?92374)) [92374, 92373, 92372, 92371, 92370] by Demod 18343 with 3370 at 2
+Id : 19158, {_}: divide ?93334 ?93335 =<= multiply (multiply ?93336 ?93337) (divide (divide (divide (inverse ?93337) ?93336) ?93338) (divide (divide ?93335 ?93334) ?93338)) [93338, 93337, 93336, 93335, 93334] by Super 19039 with 3 at 1,3
+Id : 2243, {_}: divide (divide (inverse (multiply (divide (divide ?10125 ?10126) ?10127) ?10128)) (divide ?10126 ?10125)) ?10127 =>= inverse ?10128 [10128, 10127, 10126, 10125] by Super 2201 with 3 at 1,1,1,2
+Id : 18627, {_}: divide ?89648 ?89649 =<= multiply (divide ?89650 ?89651) (divide (divide (divide ?89651 ?89650) ?89652) (divide (divide ?89649 ?89648) ?89652)) [89652, 89651, 89650, 89649, 89648] by Demod 18343 with 3370 at 2
+Id : 18986, {_}: divide (divide (inverse (divide ?91944 ?91945)) (divide ?91946 ?91947)) ?91948 =<= inverse (divide (divide (divide ?91948 (divide ?91947 ?91946)) ?91949) (divide (divide ?91945 ?91944) ?91949)) [91949, 91948, 91947, 91946, 91945, 91944] by Super 2243 with 18627 at 1,1,1,2
+Id : 19370, {_}: divide (divide (divide (inverse (divide ?93677 ?93678)) (divide ?93679 ?93680)) ?93681) (divide (divide ?93680 ?93679) ?93681) =>= divide ?93678 ?93677 [93681, 93680, 93679, 93678, 93677] by Super 2 with 18986 at 1,2
+Id : 33018, {_}: divide ?156119 ?156120 =<= multiply (multiply (divide ?156119 ?156120) (divide ?156121 ?156122)) (divide ?156122 ?156121) [156122, 156121, 156120, 156119] by Super 19158 with 19370 at 2,3
+Id : 33087, {_}: divide (inverse (divide (divide (divide ?156646 ?156647) ?156648) (divide ?156649 ?156648))) (divide ?156647 ?156646) =?= multiply (multiply ?156649 (divide ?156650 ?156651)) (divide ?156651 ?156650) [156651, 156650, 156649, 156648, 156647, 156646] by Super 33018 with 2 at 1,1,3
+Id : 33278, {_}: ?156649 =<= multiply (multiply ?156649 (divide ?156650 ?156651)) (divide ?156651 ?156650) [156651, 156650, 156649] by Demod 33087 with 2 at 2
+Id : 412, {_}: inverse (divide (divide (divide ?1605 ?1606) ?1607) (divide (divide ?1608 (divide ?1606 ?1605)) ?1607)) =>= ?1608 [1608, 1607, 1606, 1605] by Super 2 with 6 at 2
+Id : 433, {_}: inverse (divide (divide (divide ?1731 ?1732) (inverse ?1733)) (multiply (divide ?1734 (divide ?1732 ?1731)) ?1733)) =>= ?1734 [1734, 1733, 1732, 1731] by Super 412 with 3 at 2,1,2
+Id : 477, {_}: inverse (divide (multiply (divide ?1731 ?1732) ?1733) (multiply (divide ?1734 (divide ?1732 ?1731)) ?1733)) =>= ?1734 [1734, 1733, 1732, 1731] by Demod 433 with 3 at 1,1,2
+Id : 503, {_}: inverse (divide (multiply (divide ?1881 ?1882) ?1883) (multiply (divide ?1884 (divide ?1882 ?1881)) ?1883)) =>= ?1884 [1884, 1883, 1882, 1881] by Demod 433 with 3 at 1,1,2
+Id : 511, {_}: inverse (divide (multiply (divide (inverse ?1933) ?1934) ?1935) (multiply (divide ?1936 (multiply ?1934 ?1933)) ?1935)) =>= ?1936 [1936, 1935, 1934, 1933] by Super 503 with 3 at 2,1,2,1,2
+Id : 32469, {_}: divide (divide (inverse (divide ?153394 ?153395)) (divide ?153395 ?153394)) (inverse (divide ?153396 ?153397)) =>= inverse (divide ?153397 ?153396) [153397, 153396, 153395, 153394] by Super 18986 with 19370 at 1,3
+Id : 32700, {_}: multiply (divide (inverse (divide ?153394 ?153395)) (divide ?153395 ?153394)) (divide ?153396 ?153397) =>= inverse (divide ?153397 ?153396) [153397, 153396, 153395, 153394] by Demod 32469 with 3 at 2
+Id : 35765, {_}: inverse (divide (inverse (divide ?167563 ?167564)) (multiply (divide ?167565 (multiply (divide ?167566 ?167567) (divide ?167567 ?167566))) (divide ?167564 ?167563))) =>= ?167565 [167567, 167566, 167565, 167564, 167563] by Super 511 with 32700 at 1,1,2
+Id : 9, {_}: divide (inverse (divide (divide (divide (inverse ?38) ?39) ?40) (divide ?41 ?40))) (multiply ?39 ?38) =>= ?41 [41, 40, 39, 38] by Super 2 with 3 at 2,2
+Id : 32402, {_}: divide (inverse (divide ?152772 ?152773)) (multiply (divide ?152774 ?152775) (divide ?152773 ?152772)) =>= divide ?152775 ?152774 [152775, 152774, 152773, 152772] by Super 9 with 19370 at 1,1,2
+Id : 36094, {_}: inverse (divide (multiply (divide ?167566 ?167567) (divide ?167567 ?167566)) ?167565) =>= ?167565 [167565, 167567, 167566] by Demod 35765 with 32402 at 1,2
+Id : 36327, {_}: multiply (divide ?169738 (divide ?169739 ?169740)) (divide ?169739 ?169740) =>= ?169738 [169740, 169739, 169738] by Super 477 with 36094 at 2
+Id : 36681, {_}: divide ?171580 (divide ?171581 ?171582) =<= multiply ?171580 (divide ?171582 ?171581) [171582, 171581, 171580] by Super 33278 with 36327 at 1,3
+Id : 37087, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?173237) ?173238) ?173239) (divide ?173240 ?173241))) (multiply (inverse ?173238) ?173237)) ?173239 =>= inverse (divide ?173241 ?173240) [173241, 173240, 173239, 173238, 173237] by Super 4011 with 36681 at 1,1,1,2
+Id : 37291, {_}: divide ?173240 ?173241 =<= inverse (divide ?173241 ?173240) [173241, 173240] by Demod 37087 with 3370 at 2
+Id : 36954, {_}: inverse (divide (divide (divide ?167566 ?167567) (divide ?167566 ?167567)) ?167565) =>= ?167565 [167565, 167567, 167566] by Demod 36094 with 36681 at 1,1,2
+Id : 37568, {_}: divide ?167565 (divide (divide ?167566 ?167567) (divide ?167566 ?167567)) =>= ?167565 [167567, 167566, 167565] by Demod 36954 with 37291 at 2
+Id : 33466, {_}: ?158075 =<= multiply (multiply ?158075 (divide ?158076 ?158077)) (divide ?158077 ?158076) [158077, 158076, 158075] by Demod 33087 with 2 at 2
+Id : 33531, {_}: ?158517 =<= multiply (multiply ?158517 (multiply ?158518 ?158519)) (divide (inverse ?158519) ?158518) [158519, 158518, 158517] by Super 33466 with 3 at 2,1,3
+Id : 36952, {_}: ?158517 =<= divide (multiply ?158517 (multiply ?158518 ?158519)) (divide ?158518 (inverse ?158519)) [158519, 158518, 158517] by Demod 33531 with 36681 at 3
+Id : 36955, {_}: ?158517 =<= divide (multiply ?158517 (multiply ?158518 ?158519)) (multiply ?158518 ?158519) [158519, 158518, 158517] by Demod 36952 with 3 at 2,3
+Id : 36684, {_}: multiply (divide ?171593 (divide ?171594 ?171595)) (divide ?171594 ?171595) =>= ?171593 [171595, 171594, 171593] by Super 477 with 36094 at 2
+Id : 36687, {_}: multiply (divide ?171605 (divide (inverse (divide (divide (divide ?171606 ?171607) ?171608) (divide ?171609 ?171608))) (divide ?171607 ?171606))) ?171609 =>= ?171605 [171609, 171608, 171607, 171606, 171605] by Super 36684 with 2 at 2,2
+Id : 36819, {_}: multiply (divide ?171605 ?171609) ?171609 =>= ?171605 [171609, 171605] by Demod 36687 with 2 at 2,1,2
+Id : 38144, {_}: ?175420 =<= divide (multiply ?175420 (multiply (divide ?175421 ?175422) ?175422)) ?175421 [175422, 175421, 175420] by Super 36955 with 36819 at 2,3
+Id : 38311, {_}: ?175420 =<= divide (multiply ?175420 ?175421) ?175421 [175421, 175420] by Demod 38144 with 36819 at 2,1,3
+Id : 38590, {_}: divide ?177333 (divide (divide (multiply ?177334 ?177335) ?177335) ?177334) =>= ?177333 [177335, 177334, 177333] by Super 37568 with 38311 at 2,2,2
+Id : 38627, {_}: divide ?177333 (divide ?177334 ?177334) =>= ?177333 [177334, 177333] by Demod 38590 with 38311 at 1,2,2
+Id : 41488, {_}: divide (divide ?193733 ?193733) ?193734 =>= inverse ?193734 [193734, 193733] by Super 37291 with 38627 at 1,3
+Id : 42000, {_}: multiply (divide ?195057 ?195057) ?195058 =>= inverse (inverse ?195058) [195058, 195057] by Super 3 with 41488 at 3
+Id : 38603, {_}: divide ?177417 (multiply ?177418 ?177417) =>= inverse ?177418 [177418, 177417] by Super 37291 with 38311 at 1,3
+Id : 40108, {_}: divide (multiply ?188666 ?188667) ?188667 =>= inverse (inverse ?188666) [188667, 188666] by Super 37291 with 38603 at 1,3
+Id : 40636, {_}: ?188666 =<= inverse (inverse ?188666) [188666] by Demod 40108 with 38311 at 2
+Id : 43036, {_}: multiply (divide ?197334 ?197334) ?197335 =>= ?197335 [197335, 197334] by Demod 42000 with 40636 at 3
+Id : 43063, {_}: multiply (multiply (inverse ?197470) ?197470) ?197471 =>= ?197471 [197471, 197470] by Super 43036 with 3 at 1,2
+Id : 47549, {_}: a2 =?= a2 [] by Demod 1 with 43063 at 2
+Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
+% SZS output end CNFRefutation for GRP476-1.p
+11374: solved GRP476-1.p in 30.053878 using kbo
+11374: status Unsatisfiable for GRP476-1.p
+NO CLASH, using fixed ground order
+11392: Facts:
+11392: Id : 2, {_}:
+ divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
+ (divide ?3 ?2)
+ =>=
+ ?5
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11392: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11392: Goal:
+11392: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+11392: Order:
+11392: nrkbo
+11392: Leaf order:
+11392: inverse 2 1 0
+11392: divide 7 2 0
+11392: c3 2 0 2 2,2
+11392: multiply 5 2 4 0,2
+11392: b3 2 0 2 2,1,2
+11392: a3 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+11393: Facts:
+11393: Id : 2, {_}:
+ divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
+ (divide ?3 ?2)
+ =>=
+ ?5
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11393: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11393: Goal:
+11393: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+11393: Order:
+11393: kbo
+11393: Leaf order:
+11393: inverse 2 1 0
+11393: divide 7 2 0
+11393: c3 2 0 2 2,2
+11393: multiply 5 2 4 0,2
+11393: b3 2 0 2 2,1,2
+11393: a3 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+11395: Facts:
+11395: Id : 2, {_}:
+ divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
+ (divide ?3 ?2)
+ =>=
+ ?5
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11395: Id : 3, {_}:
+ multiply ?7 ?8 =>= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11395: Goal:
+11395: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+11395: Order:
+11395: lpo
+11395: Leaf order:
+11395: inverse 2 1 0
+11395: divide 7 2 0
+11395: c3 2 0 2 2,2
+11395: multiply 5 2 4 0,2
+11395: b3 2 0 2 2,1,2
+11395: a3 2 0 2 1,1,2
+Statistics :
+Max weight : 49
+Found proof, 65.047626s
+% SZS status Unsatisfiable for GRP477-1.p
+% SZS output start CNFRefutation for GRP477-1.p
+Id : 2, {_}: divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) (divide ?3 ?2) =>= ?5 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+Id : 4, {_}: divide (inverse (divide (divide (divide ?10 ?11) ?12) (divide ?13 ?12))) (divide ?11 ?10) =>= ?13 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
+Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
+Id : 5, {_}: divide (inverse (divide (divide (divide (divide ?15 ?16) (inverse (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17)))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 2,2
+Id : 17, {_}: divide (inverse (divide (divide (multiply (divide ?15 ?16) (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 1,1,1,1,2
+Id : 20, {_}: divide (inverse (divide (divide (divide ?80 ?81) ?82) ?83)) (divide ?81 ?80) =?= inverse (divide (divide (multiply (divide ?84 ?85) (divide (divide (divide ?85 ?84) ?86) (divide ?82 ?86))) ?87) (divide ?83 ?87)) [87, 86, 85, 84, 83, 82, 81, 80] by Super 2 with 17 at 2,1,1,2
+Id : 2201, {_}: divide (divide (inverse (divide (divide (divide ?9850 ?9851) ?9852) ?9853)) (divide ?9851 ?9850)) ?9852 =>= ?9853 [9853, 9852, 9851, 9850] by Super 17 with 20 at 1,2
+Id : 2216, {_}: divide (divide (inverse (divide (divide (divide (inverse ?9957) ?9958) ?9959) ?9960)) (multiply ?9958 ?9957)) ?9959 =>= ?9960 [9960, 9959, 9958, 9957] by Super 2201 with 3 at 2,1,2
+Id : 2522, {_}: divide (divide (inverse (multiply (divide (divide ?11173 ?11174) ?11175) ?11176)) (divide ?11174 ?11173)) ?11175 =>= inverse ?11176 [11176, 11175, 11174, 11173] by Super 2201 with 3 at 1,1,1,2
+Id : 3974, {_}: divide (divide (inverse (multiply (divide (divide (inverse ?18265) ?18266) ?18267) ?18268)) (multiply ?18266 ?18265)) ?18267 =>= inverse ?18268 [18268, 18267, 18266, 18265] by Super 2522 with 3 at 2,1,2
+Id : 4011, {_}: divide (divide (inverse (multiply (divide (multiply (inverse ?18535) ?18536) ?18537) ?18538)) (multiply (inverse ?18536) ?18535)) ?18537 =>= inverse ?18538 [18538, 18537, 18536, 18535] by Super 3974 with 3 at 1,1,1,1,1,2
+Id : 3335, {_}: divide (divide (inverse (divide (divide (divide (inverse ?15160) ?15161) ?15162) ?15163)) (multiply ?15161 ?15160)) ?15162 =>= ?15163 [15163, 15162, 15161, 15160] by Super 2201 with 3 at 2,1,2
+Id : 3370, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?15416) ?15417) ?15418) ?15419)) (multiply (inverse ?15417) ?15416)) ?15418 =>= ?15419 [15419, 15418, 15417, 15416] by Super 3335 with 3 at 1,1,1,1,1,2
+Id : 7, {_}: divide (inverse (divide (divide ?29 ?30) (divide ?31 ?30))) (divide (divide ?32 ?33) (inverse (divide (divide (divide ?33 ?32) ?34) (divide ?29 ?34)))) =>= ?31 [34, 33, 32, 31, 30, 29] by Super 4 with 2 at 1,1,1,1,2
+Id : 602, {_}: divide (inverse (divide (divide ?2300 ?2301) (divide ?2302 ?2301))) (multiply (divide ?2303 ?2304) (divide (divide (divide ?2304 ?2303) ?2305) (divide ?2300 ?2305))) =>= ?2302 [2305, 2304, 2303, 2302, 2301, 2300] by Demod 7 with 3 at 2,2
+Id : 6, {_}: divide (inverse (divide (divide (divide ?22 ?23) (divide ?24 ?25)) ?26)) (divide ?23 ?22) =?= inverse (divide (divide (divide ?25 ?24) ?27) (divide ?26 ?27)) [27, 26, 25, 24, 23, 22] by Super 4 with 2 at 2,1,1,2
+Id : 300, {_}: inverse (divide (divide (divide ?1003 ?1004) ?1005) (divide (divide ?1006 (divide ?1004 ?1003)) ?1005)) =>= ?1006 [1006, 1005, 1004, 1003] by Super 2 with 6 at 2
+Id : 673, {_}: divide ?2877 (multiply (divide ?2878 ?2879) (divide (divide (divide ?2879 ?2878) ?2880) (divide (divide ?2881 ?2882) ?2880))) =>= divide ?2877 (divide ?2882 ?2881) [2882, 2881, 2880, 2879, 2878, 2877] by Super 602 with 300 at 1,2
+Id : 18343, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?89645) ?89646) ?89647) (divide ?89648 ?89649))) (multiply (inverse ?89646) ?89645)) ?89647 =?= multiply (divide ?89650 ?89651) (divide (divide (divide ?89651 ?89650) ?89652) (divide (divide ?89649 ?89648) ?89652)) [89652, 89651, 89650, 89649, 89648, 89647, 89646, 89645] by Super 3370 with 673 at 1,1,1,2
+Id : 19039, {_}: divide ?92370 ?92371 =<= multiply (divide ?92372 ?92373) (divide (divide (divide ?92373 ?92372) ?92374) (divide (divide ?92371 ?92370) ?92374)) [92374, 92373, 92372, 92371, 92370] by Demod 18343 with 3370 at 2
+Id : 19158, {_}: divide ?93334 ?93335 =<= multiply (multiply ?93336 ?93337) (divide (divide (divide (inverse ?93337) ?93336) ?93338) (divide (divide ?93335 ?93334) ?93338)) [93338, 93337, 93336, 93335, 93334] by Super 19039 with 3 at 1,3
+Id : 2243, {_}: divide (divide (inverse (multiply (divide (divide ?10125 ?10126) ?10127) ?10128)) (divide ?10126 ?10125)) ?10127 =>= inverse ?10128 [10128, 10127, 10126, 10125] by Super 2201 with 3 at 1,1,1,2
+Id : 18627, {_}: divide ?89648 ?89649 =<= multiply (divide ?89650 ?89651) (divide (divide (divide ?89651 ?89650) ?89652) (divide (divide ?89649 ?89648) ?89652)) [89652, 89651, 89650, 89649, 89648] by Demod 18343 with 3370 at 2
+Id : 18986, {_}: divide (divide (inverse (divide ?91944 ?91945)) (divide ?91946 ?91947)) ?91948 =<= inverse (divide (divide (divide ?91948 (divide ?91947 ?91946)) ?91949) (divide (divide ?91945 ?91944) ?91949)) [91949, 91948, 91947, 91946, 91945, 91944] by Super 2243 with 18627 at 1,1,1,2
+Id : 19370, {_}: divide (divide (divide (inverse (divide ?93677 ?93678)) (divide ?93679 ?93680)) ?93681) (divide (divide ?93680 ?93679) ?93681) =>= divide ?93678 ?93677 [93681, 93680, 93679, 93678, 93677] by Super 2 with 18986 at 1,2
+Id : 33018, {_}: divide ?156119 ?156120 =<= multiply (multiply (divide ?156119 ?156120) (divide ?156121 ?156122)) (divide ?156122 ?156121) [156122, 156121, 156120, 156119] by Super 19158 with 19370 at 2,3
+Id : 33087, {_}: divide (inverse (divide (divide (divide ?156646 ?156647) ?156648) (divide ?156649 ?156648))) (divide ?156647 ?156646) =?= multiply (multiply ?156649 (divide ?156650 ?156651)) (divide ?156651 ?156650) [156651, 156650, 156649, 156648, 156647, 156646] by Super 33018 with 2 at 1,1,3
+Id : 33278, {_}: ?156649 =<= multiply (multiply ?156649 (divide ?156650 ?156651)) (divide ?156651 ?156650) [156651, 156650, 156649] by Demod 33087 with 2 at 2
+Id : 412, {_}: inverse (divide (divide (divide ?1605 ?1606) ?1607) (divide (divide ?1608 (divide ?1606 ?1605)) ?1607)) =>= ?1608 [1608, 1607, 1606, 1605] by Super 2 with 6 at 2
+Id : 433, {_}: inverse (divide (divide (divide ?1731 ?1732) (inverse ?1733)) (multiply (divide ?1734 (divide ?1732 ?1731)) ?1733)) =>= ?1734 [1734, 1733, 1732, 1731] by Super 412 with 3 at 2,1,2
+Id : 477, {_}: inverse (divide (multiply (divide ?1731 ?1732) ?1733) (multiply (divide ?1734 (divide ?1732 ?1731)) ?1733)) =>= ?1734 [1734, 1733, 1732, 1731] by Demod 433 with 3 at 1,1,2
+Id : 503, {_}: inverse (divide (multiply (divide ?1881 ?1882) ?1883) (multiply (divide ?1884 (divide ?1882 ?1881)) ?1883)) =>= ?1884 [1884, 1883, 1882, 1881] by Demod 433 with 3 at 1,1,2
+Id : 511, {_}: inverse (divide (multiply (divide (inverse ?1933) ?1934) ?1935) (multiply (divide ?1936 (multiply ?1934 ?1933)) ?1935)) =>= ?1936 [1936, 1935, 1934, 1933] by Super 503 with 3 at 2,1,2,1,2
+Id : 32469, {_}: divide (divide (inverse (divide ?153394 ?153395)) (divide ?153395 ?153394)) (inverse (divide ?153396 ?153397)) =>= inverse (divide ?153397 ?153396) [153397, 153396, 153395, 153394] by Super 18986 with 19370 at 1,3
+Id : 32700, {_}: multiply (divide (inverse (divide ?153394 ?153395)) (divide ?153395 ?153394)) (divide ?153396 ?153397) =>= inverse (divide ?153397 ?153396) [153397, 153396, 153395, 153394] by Demod 32469 with 3 at 2
+Id : 35765, {_}: inverse (divide (inverse (divide ?167563 ?167564)) (multiply (divide ?167565 (multiply (divide ?167566 ?167567) (divide ?167567 ?167566))) (divide ?167564 ?167563))) =>= ?167565 [167567, 167566, 167565, 167564, 167563] by Super 511 with 32700 at 1,1,2
+Id : 9, {_}: divide (inverse (divide (divide (divide (inverse ?38) ?39) ?40) (divide ?41 ?40))) (multiply ?39 ?38) =>= ?41 [41, 40, 39, 38] by Super 2 with 3 at 2,2
+Id : 32402, {_}: divide (inverse (divide ?152772 ?152773)) (multiply (divide ?152774 ?152775) (divide ?152773 ?152772)) =>= divide ?152775 ?152774 [152775, 152774, 152773, 152772] by Super 9 with 19370 at 1,1,2
+Id : 36094, {_}: inverse (divide (multiply (divide ?167566 ?167567) (divide ?167567 ?167566)) ?167565) =>= ?167565 [167565, 167567, 167566] by Demod 35765 with 32402 at 1,2
+Id : 36327, {_}: multiply (divide ?169738 (divide ?169739 ?169740)) (divide ?169739 ?169740) =>= ?169738 [169740, 169739, 169738] by Super 477 with 36094 at 2
+Id : 36681, {_}: divide ?171580 (divide ?171581 ?171582) =<= multiply ?171580 (divide ?171582 ?171581) [171582, 171581, 171580] by Super 33278 with 36327 at 1,3
+Id : 37087, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?173237) ?173238) ?173239) (divide ?173240 ?173241))) (multiply (inverse ?173238) ?173237)) ?173239 =>= inverse (divide ?173241 ?173240) [173241, 173240, 173239, 173238, 173237] by Super 4011 with 36681 at 1,1,1,2
+Id : 37291, {_}: divide ?173240 ?173241 =<= inverse (divide ?173241 ?173240) [173241, 173240] by Demod 37087 with 3370 at 2
+Id : 37631, {_}: divide (divide (divide ?9960 (divide (divide (inverse ?9957) ?9958) ?9959)) (multiply ?9958 ?9957)) ?9959 =>= ?9960 [9959, 9958, 9957, 9960] by Demod 2216 with 37291 at 1,1,2
+Id : 37745, {_}: divide ?174363 ?174364 =<= inverse (divide ?174364 ?174363) [174364, 174363] by Demod 37087 with 3370 at 2
+Id : 37810, {_}: divide (inverse ?174753) ?174754 =>= inverse (multiply ?174754 ?174753) [174754, 174753] by Super 37745 with 3 at 1,3
+Id : 38028, {_}: divide (divide (divide ?9960 (divide (inverse (multiply ?9958 ?9957)) ?9959)) (multiply ?9958 ?9957)) ?9959 =>= ?9960 [9959, 9957, 9958, 9960] by Demod 37631 with 37810 at 1,2,1,1,2
+Id : 38029, {_}: divide (divide (divide ?9960 (inverse (multiply ?9959 (multiply ?9958 ?9957)))) (multiply ?9958 ?9957)) ?9959 =>= ?9960 [9957, 9958, 9959, 9960] by Demod 38028 with 37810 at 2,1,1,2
+Id : 38096, {_}: divide (divide (multiply ?9960 (multiply ?9959 (multiply ?9958 ?9957))) (multiply ?9958 ?9957)) ?9959 =>= ?9960 [9957, 9958, 9959, 9960] by Demod 38029 with 3 at 1,1,2
+Id : 36684, {_}: multiply (divide ?171593 (divide ?171594 ?171595)) (divide ?171594 ?171595) =>= ?171593 [171595, 171594, 171593] by Super 477 with 36094 at 2
+Id : 36687, {_}: multiply (divide ?171605 (divide (inverse (divide (divide (divide ?171606 ?171607) ?171608) (divide ?171609 ?171608))) (divide ?171607 ?171606))) ?171609 =>= ?171605 [171609, 171608, 171607, 171606, 171605] by Super 36684 with 2 at 2,2
+Id : 36819, {_}: multiply (divide ?171605 ?171609) ?171609 =>= ?171605 [171609, 171605] by Demod 36687 with 2 at 2,1,2
+Id : 51854, {_}: divide (divide ?212601 (multiply ?212602 ?212603)) ?212604 =>= divide ?212601 (multiply ?212604 (multiply ?212602 ?212603)) [212604, 212603, 212602, 212601] by Super 38096 with 36819 at 1,1,2
+Id : 18, {_}: multiply (inverse (divide (divide (multiply (divide ?64 ?65) (divide (divide (divide ?65 ?64) ?66) (divide (inverse ?67) ?66))) ?68) (divide ?69 ?68))) ?67 =>= ?69 [69, 68, 67, 66, 65, 64] by Super 3 with 17 at 3
+Id : 1822, {_}: multiply (divide (inverse (divide (divide (divide ?7521 ?7522) (inverse ?7523)) ?7524)) (divide ?7522 ?7521)) ?7523 =>= ?7524 [7524, 7523, 7522, 7521] by Super 18 with 20 at 1,2
+Id : 2348, {_}: multiply (divide (inverse (divide (multiply (divide ?10333 ?10334) ?10335) ?10336)) (divide ?10334 ?10333)) ?10335 =>= ?10336 [10336, 10335, 10334, 10333] by Demod 1822 with 3 at 1,1,1,1,2
+Id : 2690, {_}: multiply (divide (inverse (multiply (multiply (divide ?11645 ?11646) ?11647) ?11648)) (divide ?11646 ?11645)) ?11647 =>= inverse ?11648 [11648, 11647, 11646, 11645] by Super 2348 with 3 at 1,1,1,2
+Id : 2723, {_}: multiply (divide (inverse (multiply (multiply (multiply ?11878 ?11879) ?11880) ?11881)) (divide (inverse ?11879) ?11878)) ?11880 =>= inverse ?11881 [11881, 11880, 11879, 11878] by Super 2690 with 3 at 1,1,1,1,1,2
+Id : 38038, {_}: multiply (inverse (multiply (divide (inverse ?11879) ?11878) (multiply (multiply (multiply ?11878 ?11879) ?11880) ?11881))) ?11880 =>= inverse ?11881 [11881, 11880, 11878, 11879] by Demod 2723 with 37810 at 1,2
+Id : 38039, {_}: multiply (inverse (multiply (inverse (multiply ?11878 ?11879)) (multiply (multiply (multiply ?11878 ?11879) ?11880) ?11881))) ?11880 =>= inverse ?11881 [11881, 11880, 11879, 11878] by Demod 38038 with 37810 at 1,1,1,2
+Id : 38184, {_}: multiply (inverse ?175473) ?175474 =<= inverse (multiply (inverse ?175474) ?175473) [175474, 175473] by Super 3 with 37810 at 3
+Id : 38716, {_}: multiply (multiply (inverse (multiply (multiply (multiply ?11878 ?11879) ?11880) ?11881)) (multiply ?11878 ?11879)) ?11880 =>= inverse ?11881 [11881, 11880, 11879, 11878] by Demod 38039 with 38184 at 1,2
+Id : 51866, {_}: divide (divide ?212677 (inverse ?212678)) ?212679 =<= divide ?212677 (multiply ?212679 (multiply (multiply (inverse (multiply (multiply (multiply ?212680 ?212681) ?212682) ?212678)) (multiply ?212680 ?212681)) ?212682)) [212682, 212681, 212680, 212679, 212678, 212677] by Super 51854 with 38716 at 2,1,2
+Id : 52301, {_}: divide (multiply ?212677 ?212678) ?212679 =<= divide ?212677 (multiply ?212679 (multiply (multiply (inverse (multiply (multiply (multiply ?212680 ?212681) ?212682) ?212678)) (multiply ?212680 ?212681)) ?212682)) [212682, 212681, 212680, 212679, 212678, 212677] by Demod 51866 with 3 at 1,2
+Id : 52302, {_}: divide (multiply ?212677 ?212678) ?212679 =<= divide ?212677 (multiply ?212679 (inverse ?212678)) [212679, 212678, 212677] by Demod 52301 with 38716 at 2,2,3
+Id : 38247, {_}: divide ?175863 (inverse ?175864) =<= inverse (inverse (multiply ?175863 ?175864)) [175864, 175863] by Super 37291 with 37810 at 1,3
+Id : 38843, {_}: multiply ?176435 ?176436 =<= inverse (inverse (multiply ?176435 ?176436)) [176436, 176435] by Demod 38247 with 3 at 2
+Id : 3670, {_}: multiply (divide (inverse (divide (multiply (divide (inverse ?16718) ?16719) ?16720) ?16721)) (multiply ?16719 ?16718)) ?16720 =>= ?16721 [16721, 16720, 16719, 16718] by Super 2348 with 3 at 2,1,2
+Id : 3706, {_}: multiply (divide (inverse (divide (multiply (multiply (inverse ?16981) ?16982) ?16983) ?16984)) (multiply (inverse ?16982) ?16981)) ?16983 =>= ?16984 [16984, 16983, 16982, 16981] by Super 3670 with 3 at 1,1,1,1,1,2
+Id : 37609, {_}: multiply (divide (divide ?16984 (multiply (multiply (inverse ?16981) ?16982) ?16983)) (multiply (inverse ?16982) ?16981)) ?16983 =>= ?16984 [16983, 16982, 16981, 16984] by Demod 3706 with 37291 at 1,1,2
+Id : 38847, {_}: multiply (divide (divide ?176447 (multiply (multiply (inverse ?176448) ?176449) ?176450)) (multiply (inverse ?176449) ?176448)) ?176450 =>= inverse (inverse ?176447) [176450, 176449, 176448, 176447] by Super 38843 with 37609 at 1,1,3
+Id : 38880, {_}: ?176447 =<= inverse (inverse ?176447) [176447] by Demod 38847 with 37609 at 2
+Id : 40331, {_}: multiply ?187278 (inverse ?187279) =>= divide ?187278 ?187279 [187279, 187278] by Super 3 with 38880 at 2,3
+Id : 52303, {_}: divide (multiply ?212677 ?212678) ?212679 =>= divide ?212677 (divide ?212679 ?212678) [212679, 212678, 212677] by Demod 52302 with 40331 at 2,3
+Id : 53261, {_}: multiply (multiply ?214472 ?214473) ?214474 =<= divide ?214472 (divide (inverse ?214474) ?214473) [214474, 214473, 214472] by Super 3 with 52303 at 3
+Id : 53437, {_}: multiply (multiply ?214472 ?214473) ?214474 =<= divide ?214472 (inverse (multiply ?214473 ?214474)) [214474, 214473, 214472] by Demod 53261 with 37810 at 2,3
+Id : 53438, {_}: multiply (multiply ?214472 ?214473) ?214474 =>= multiply ?214472 (multiply ?214473 ?214474) [214474, 214473, 214472] by Demod 53437 with 3 at 3
+Id : 53834, {_}: multiply a3 (multiply b3 c3) =?= multiply a3 (multiply b3 c3) [] by Demod 1 with 53438 at 2
+Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
+% SZS output end CNFRefutation for GRP477-1.p
+11393: solved GRP477-1.p in 32.410025 using kbo
+11393: status Unsatisfiable for GRP477-1.p
+NO CLASH, using fixed ground order
+11411: Facts:
+11411: Id : 2, {_}:
+ divide
+ (inverse
+ (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
+ ?5
+ =>=
+ ?4
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11411: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11411: Goal:
+11411: Id : 1, {_}:
+ multiply (inverse a1) a1 =>= multiply (inverse b1) b1
+ [] by prove_these_axioms_1
+11411: Order:
+11411: nrkbo
+11411: Leaf order:
+11411: divide 7 2 0
+11411: b1 2 0 2 1,1,3
+11411: multiply 3 2 2 0,2
+11411: inverse 4 1 2 0,1,2
+11411: a1 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+11412: Facts:
+11412: Id : 2, {_}:
+ divide
+ (inverse
+ (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
+ ?5
+ =>=
+ ?4
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11412: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11412: Goal:
+11412: Id : 1, {_}:
+ multiply (inverse a1) a1 =>= multiply (inverse b1) b1
+ [] by prove_these_axioms_1
+11412: Order:
+11412: kbo
+11412: Leaf order:
+11412: divide 7 2 0
+11412: b1 2 0 2 1,1,3
+11412: multiply 3 2 2 0,2
+11412: inverse 4 1 2 0,1,2
+11412: a1 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+11413: Facts:
+11413: Id : 2, {_}:
+ divide
+ (inverse
+ (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
+ ?5
+ =>=
+ ?4
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11413: Id : 3, {_}:
+ multiply ?7 ?8 =?= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11413: Goal:
+11413: Id : 1, {_}:
+ multiply (inverse a1) a1 =>= multiply (inverse b1) b1
+ [] by prove_these_axioms_1
+11413: Order:
+11413: lpo
+11413: Leaf order:
+11413: divide 7 2 0
+11413: b1 2 0 2 1,1,3
+11413: multiply 3 2 2 0,2
+11413: inverse 4 1 2 0,1,2
+11413: a1 2 0 2 1,1,2
+% SZS status Timeout for GRP478-1.p
+NO CLASH, using fixed ground order
+11446: Facts:
+11446: Id : 2, {_}:
+ divide
+ (inverse
+ (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
+ ?5
+ =>=
+ ?4
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11446: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11446: Goal:
+11446: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+11446: Order:
+11446: nrkbo
+11446: Leaf order:
+11446: divide 7 2 0
+11446: a2 2 0 2 2,2
+11446: multiply 3 2 2 0,2
+11446: inverse 3 1 1 0,1,1,2
+11446: b2 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+11447: Facts:
+11447: Id : 2, {_}:
+ divide
+ (inverse
+ (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
+ ?5
+ =>=
+ ?4
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11447: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11447: Goal:
+11447: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+11447: Order:
+11447: kbo
+11447: Leaf order:
+11447: divide 7 2 0
+11447: a2 2 0 2 2,2
+11447: multiply 3 2 2 0,2
+11447: inverse 3 1 1 0,1,1,2
+11447: b2 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+11448: Facts:
+11448: Id : 2, {_}:
+ divide
+ (inverse
+ (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
+ ?5
+ =>=
+ ?4
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11448: Id : 3, {_}:
+ multiply ?7 ?8 =?= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11448: Goal:
+11448: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+11448: Order:
+11448: lpo
+11448: Leaf order:
+11448: divide 7 2 0
+11448: a2 2 0 2 2,2
+11448: multiply 3 2 2 0,2
+11448: inverse 3 1 1 0,1,1,2
+11448: b2 2 0 2 1,1,1,2
+% SZS status Timeout for GRP479-1.p
+NO CLASH, using fixed ground order
+11491: Facts:
+NO CLASH, using fixed ground order
+11492: Facts:
+11492: Id : 2, {_}:
+ divide
+ (inverse
+ (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
+ ?5
+ =>=
+ ?4
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11492: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11492: Goal:
+11492: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+11492: Order:
+11492: kbo
+11492: Leaf order:
+11492: inverse 2 1 0
+11492: divide 7 2 0
+11492: c3 2 0 2 2,2
+11492: multiply 5 2 4 0,2
+11492: b3 2 0 2 2,1,2
+11492: a3 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+11493: Facts:
+11493: Id : 2, {_}:
+ divide
+ (inverse
+ (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
+ ?5
+ =>=
+ ?4
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11493: Id : 3, {_}:
+ multiply ?7 ?8 =>= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11493: Goal:
+11493: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+11493: Order:
+11493: lpo
+11493: Leaf order:
+11493: inverse 2 1 0
+11493: divide 7 2 0
+11493: c3 2 0 2 2,2
+11493: multiply 5 2 4 0,2
+11493: b3 2 0 2 2,1,2
+11493: a3 2 0 2 1,1,2
+11491: Id : 2, {_}:
+ divide
+ (inverse
+ (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
+ ?5
+ =>=
+ ?4
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+11491: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+11491: Goal:
+11491: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+11491: Order:
+11491: nrkbo
+11491: Leaf order:
+11491: inverse 2 1 0
+11491: divide 7 2 0
+11491: c3 2 0 2 2,2
+11491: multiply 5 2 4 0,2
+11491: b3 2 0 2 2,1,2
+11491: a3 2 0 2 1,1,2
+Statistics :
+Max weight : 78
+Found proof, 69.885629s
+% SZS status Unsatisfiable for GRP480-1.p
+% SZS output start CNFRefutation for GRP480-1.p
+Id : 4, {_}: divide (inverse (divide (divide (divide ?10 ?10) ?11) (divide ?12 (divide ?11 ?13)))) ?13 =>= ?12 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
+Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
+Id : 2, {_}: divide (inverse (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) ?5 =>= ?4 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+Id : 8, {_}: divide (inverse (divide (divide (divide ?31 ?31) ?32) (divide ?33 (multiply ?32 ?34)))) (inverse ?34) =>= ?33 [34, 33, 32, 31] by Super 2 with 3 at 2,2,1,1,2
+Id : 44, {_}: multiply (inverse (divide (divide (divide ?198 ?198) ?199) (divide ?200 (multiply ?199 ?201)))) ?201 =>= ?200 [201, 200, 199, 198] by Demod 8 with 3 at 2
+Id : 46, {_}: multiply (inverse (divide (divide (divide ?210 ?210) ?211) ?212)) ?213 =?= inverse (divide (divide (divide ?214 ?214) ?215) (divide ?212 (divide ?215 (multiply ?211 ?213)))) [215, 214, 213, 212, 211, 210] by Super 44 with 2 at 2,1,1,2
+Id : 5, {_}: divide (inverse (divide (divide (divide ?15 ?15) (inverse (divide (divide (divide ?16 ?16) ?17) (divide ?18 (divide ?17 ?19))))) (divide ?20 ?18))) ?19 =>= ?20 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 2,2,1,1,2
+Id : 22, {_}: divide (inverse (divide (multiply (divide ?87 ?87) (divide (divide (divide ?88 ?88) ?89) (divide ?90 (divide ?89 ?91)))) (divide ?92 ?90))) ?91 =>= ?92 [92, 91, 90, 89, 88, 87] by Demod 5 with 3 at 1,1,1,2
+Id : 18, {_}: divide (inverse (divide (multiply (divide ?15 ?15) (divide (divide (divide ?16 ?16) ?17) (divide ?18 (divide ?17 ?19)))) (divide ?20 ?18))) ?19 =>= ?20 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 1,1,1,2
+Id : 30, {_}: divide (inverse (divide (multiply (divide ?157 ?157) (divide (divide (divide ?158 ?158) ?159) ?160)) (divide ?161 (inverse (divide (multiply (divide ?162 ?162) (divide (divide (divide ?163 ?163) ?164) (divide ?165 (divide ?164 (divide ?159 ?166))))) (divide ?160 ?165)))))) ?166 =>= ?161 [166, 165, 164, 163, 162, 161, 160, 159, 158, 157] by Super 22 with 18 at 2,2,1,1,1,2
+Id : 42, {_}: divide (inverse (divide (multiply (divide ?157 ?157) (divide (divide (divide ?158 ?158) ?159) ?160)) (multiply ?161 (divide (multiply (divide ?162 ?162) (divide (divide (divide ?163 ?163) ?164) (divide ?165 (divide ?164 (divide ?159 ?166))))) (divide ?160 ?165))))) ?166 =>= ?161 [166, 165, 164, 163, 162, 161, 160, 159, 158, 157] by Demod 30 with 3 at 2,1,1,2
+Id : 6, {_}: divide (inverse (divide (divide (divide ?22 ?22) ?23) ?24)) ?25 =?= inverse (divide (divide (divide ?26 ?26) ?27) (divide ?24 (divide ?27 (divide ?23 ?25)))) [27, 26, 25, 24, 23, 22] by Super 4 with 2 at 2,1,1,2
+Id : 202, {_}: divide (divide (inverse (divide (divide (divide ?974 ?974) ?975) ?976)) ?977) (divide ?975 ?977) =>= ?976 [977, 976, 975, 974] by Super 2 with 6 at 1,2
+Id : 208, {_}: divide (divide (inverse (divide (divide (divide ?1018 ?1018) ?1019) ?1020)) (inverse ?1021)) (multiply ?1019 ?1021) =>= ?1020 [1021, 1020, 1019, 1018] by Super 202 with 3 at 2,2
+Id : 372, {_}: divide (multiply (inverse (divide (divide (divide ?1664 ?1664) ?1665) ?1666)) ?1667) (multiply ?1665 ?1667) =>= ?1666 [1667, 1666, 1665, 1664] by Demod 208 with 3 at 1,2
+Id : 378, {_}: divide (multiply (inverse (divide (multiply (divide ?1702 ?1702) ?1703) ?1704)) ?1705) (multiply (inverse ?1703) ?1705) =>= ?1704 [1705, 1704, 1703, 1702] by Super 372 with 3 at 1,1,1,1,2
+Id : 15, {_}: multiply (inverse (divide (divide (divide ?31 ?31) ?32) (divide ?33 (multiply ?32 ?34)))) ?34 =>= ?33 [34, 33, 32, 31] by Demod 8 with 3 at 2
+Id : 86, {_}: divide (divide (inverse (divide (divide (divide ?404 ?404) ?405) ?406)) ?407) (divide ?405 ?407) =>= ?406 [407, 406, 405, 404] by Super 2 with 6 at 1,2
+Id : 193, {_}: multiply (inverse (divide ?902 (divide ?903 (multiply (divide ?904 (inverse (divide (divide (divide ?905 ?905) ?904) ?902))) ?906)))) ?906 =>= ?903 [906, 905, 904, 903, 902] by Super 15 with 86 at 1,1,1,2
+Id : 223, {_}: multiply (inverse (divide ?902 (divide ?903 (multiply (multiply ?904 (divide (divide (divide ?905 ?905) ?904) ?902)) ?906)))) ?906 =>= ?903 [906, 905, 904, 903, 902] by Demod 193 with 3 at 1,2,2,1,1,2
+Id : 88082, {_}: divide ?485240 (multiply (inverse ?485241) ?485242) =<= divide ?485240 (multiply (multiply ?485243 (divide (divide (divide ?485244 ?485244) ?485243) (multiply (divide ?485245 ?485245) ?485241))) ?485242) [485245, 485244, 485243, 485242, 485241, 485240] by Super 378 with 223 at 1,2
+Id : 89234, {_}: divide (inverse (divide (multiply (divide ?494319 ?494319) (divide (divide (divide ?494320 ?494320) ?494321) ?494322)) (multiply (inverse ?494323) (divide (multiply (divide ?494324 ?494324) (divide (divide (divide ?494325 ?494325) ?494326) (divide ?494327 (divide ?494326 (divide ?494321 ?494328))))) (divide ?494322 ?494327))))) ?494328 =?= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (multiply (divide ?494331 ?494331) ?494323)) [494331, 494330, 494329, 494328, 494327, 494326, 494325, 494324, 494323, 494322, 494321, 494320, 494319] by Super 42 with 88082 at 1,1,2
+Id : 89554, {_}: inverse ?494323 =<= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (multiply (divide ?494331 ?494331) ?494323)) [494331, 494330, 494329, 494323] by Demod 89234 with 42 at 2
+Id : 23, {_}: divide (inverse (divide (multiply (divide ?94 ?94) (divide (divide (divide ?95 ?95) ?96) (divide ?97 (divide ?96 ?98)))) ?99)) ?98 =?= inverse (divide (divide (divide ?100 ?100) ?101) (divide ?99 (divide ?101 ?97))) [101, 100, 99, 98, 97, 96, 95, 94] by Super 22 with 2 at 2,1,1,2
+Id : 1304, {_}: inverse (divide (divide (divide ?6515 ?6515) ?6516) (divide (divide ?6517 ?6518) (divide ?6516 ?6518))) =>= ?6517 [6518, 6517, 6516, 6515] by Super 18 with 23 at 2
+Id : 2998, {_}: inverse (divide (divide (multiply (inverse ?16319) ?16319) ?16320) (divide (divide ?16321 ?16322) (divide ?16320 ?16322))) =>= ?16321 [16322, 16321, 16320, 16319] by Super 1304 with 3 at 1,1,1,2
+Id : 3072, {_}: inverse (divide (multiply (multiply (inverse ?16865) ?16865) ?16866) (divide (divide ?16867 ?16868) (divide (inverse ?16866) ?16868))) =>= ?16867 [16868, 16867, 16866, 16865] by Super 2998 with 3 at 1,1,2
+Id : 1319, {_}: inverse (divide (divide (divide ?6630 ?6630) ?6631) (divide (divide ?6632 (inverse ?6633)) (multiply ?6631 ?6633))) =>= ?6632 [6633, 6632, 6631, 6630] by Super 1304 with 3 at 2,2,1,2
+Id : 1369, {_}: inverse (divide (divide (divide ?6630 ?6630) ?6631) (divide (multiply ?6632 ?6633) (multiply ?6631 ?6633))) =>= ?6632 [6633, 6632, 6631, 6630] by Demod 1319 with 3 at 1,2,1,2
+Id : 1389, {_}: multiply ?6881 (divide (divide (divide ?6882 ?6882) ?6883) (divide (multiply ?6884 ?6885) (multiply ?6883 ?6885))) =>= divide ?6881 ?6884 [6885, 6884, 6883, 6882, 6881] by Super 3 with 1369 at 2,3
+Id : 90512, {_}: multiply (inverse (divide ?497368 (divide ?497369 (inverse ?497370)))) (divide (divide (divide ?497371 ?497371) (multiply ?497372 (divide (divide (divide ?497373 ?497373) ?497372) ?497368))) (multiply (divide ?497374 ?497374) ?497370)) =>= ?497369 [497374, 497373, 497372, 497371, 497370, 497369, 497368] by Super 223 with 89554 at 2,2,1,1,2
+Id : 196, {_}: divide (inverse (divide (divide (divide ?925 ?925) ?926) (divide (inverse (divide (divide (divide ?927 ?927) ?928) ?929)) (divide ?926 ?930)))) ?930 =?= inverse (divide (divide (divide ?931 ?931) ?928) ?929) [931, 930, 929, 928, 927, 926, 925] by Super 6 with 86 at 2,1,3
+Id : 6409, {_}: inverse (divide (divide (divide ?34204 ?34204) ?34205) ?34206) =?= inverse (divide (divide (divide ?34207 ?34207) ?34205) ?34206) [34207, 34206, 34205, 34204] by Demod 196 with 2 at 2
+Id : 6420, {_}: inverse (divide (divide (divide ?34278 ?34278) (divide ?34279 (inverse (divide (divide (divide ?34280 ?34280) ?34279) ?34281)))) ?34282) =>= inverse (divide ?34281 ?34282) [34282, 34281, 34280, 34279, 34278] by Super 6409 with 86 at 1,1,3
+Id : 6497, {_}: inverse (divide (divide (divide ?34278 ?34278) (multiply ?34279 (divide (divide (divide ?34280 ?34280) ?34279) ?34281))) ?34282) =>= inverse (divide ?34281 ?34282) [34282, 34281, 34280, 34279, 34278] by Demod 6420 with 3 at 2,1,1,2
+Id : 28325, {_}: multiply ?153090 (divide (divide (divide ?153091 ?153091) (multiply ?153092 (divide (divide (divide ?153093 ?153093) ?153092) ?153094))) ?153095) =>= divide ?153090 (inverse (divide ?153094 ?153095)) [153095, 153094, 153093, 153092, 153091, 153090] by Super 3 with 6497 at 2,3
+Id : 28522, {_}: multiply ?153090 (divide (divide (divide ?153091 ?153091) (multiply ?153092 (divide (divide (divide ?153093 ?153093) ?153092) ?153094))) ?153095) =>= multiply ?153090 (divide ?153094 ?153095) [153095, 153094, 153093, 153092, 153091, 153090] by Demod 28325 with 3 at 3
+Id : 91190, {_}: multiply (inverse (divide ?497368 (divide ?497369 (inverse ?497370)))) (divide ?497368 (multiply (divide ?497374 ?497374) ?497370)) =>= ?497369 [497374, 497370, 497369, 497368] by Demod 90512 with 28522 at 2
+Id : 91665, {_}: multiply (inverse (divide ?503116 (multiply ?503117 ?503118))) (divide ?503116 (multiply (divide ?503119 ?503119) ?503118)) =>= ?503117 [503119, 503118, 503117, 503116] by Demod 91190 with 3 at 2,1,1,2
+Id : 231, {_}: divide (multiply (inverse (divide (divide (divide ?1018 ?1018) ?1019) ?1020)) ?1021) (multiply ?1019 ?1021) =>= ?1020 [1021, 1020, 1019, 1018] by Demod 208 with 3 at 1,2
+Id : 1057, {_}: inverse (divide (divide (divide ?5280 ?5280) ?5281) (divide (divide ?5282 ?5283) (divide ?5281 ?5283))) =>= ?5282 [5283, 5282, 5281, 5280] by Super 18 with 23 at 2
+Id : 1292, {_}: divide (divide ?6440 ?6441) (divide ?6442 ?6441) =?= divide (divide ?6440 ?6443) (divide ?6442 ?6443) [6443, 6442, 6441, 6440] by Super 86 with 1057 at 1,1,2
+Id : 2334, {_}: divide (multiply (inverse (divide (divide (divide ?12626 ?12626) ?12627) (divide ?12628 ?12627))) ?12629) (multiply ?12630 ?12629) =>= divide ?12628 ?12630 [12630, 12629, 12628, 12627, 12626] by Super 231 with 1292 at 1,1,1,2
+Id : 91784, {_}: multiply (inverse (divide (multiply (inverse (divide (divide (divide ?504066 ?504066) ?504067) (divide ?504068 ?504067))) ?504069) (multiply ?504070 ?504069))) (divide ?504068 (divide ?504071 ?504071)) =>= ?504070 [504071, 504070, 504069, 504068, 504067, 504066] by Super 91665 with 2334 at 2,2
+Id : 92186, {_}: multiply (inverse (divide ?504068 ?504070)) (divide ?504068 (divide ?504071 ?504071)) =>= ?504070 [504071, 504070, 504068] by Demod 91784 with 2334 at 1,1,2
+Id : 92346, {_}: ?505751 =<= divide (inverse (divide (divide (divide ?505752 ?505752) ?505753) ?505751)) ?505753 [505753, 505752, 505751] by Super 1389 with 92186 at 2
+Id : 93111, {_}: divide ?509269 (divide ?509270 ?509270) =>= ?509269 [509270, 509269] by Super 2 with 92346 at 2
+Id : 100321, {_}: inverse (multiply (multiply (inverse ?535124) ?535124) ?535125) =>= inverse ?535125 [535125, 535124] by Super 3072 with 93111 at 1,2
+Id : 100420, {_}: inverse (inverse ?535740) =<= inverse (divide (divide (divide ?535741 ?535741) (multiply (inverse ?535742) ?535742)) (multiply (divide ?535743 ?535743) ?535740)) [535743, 535742, 535741, 535740] by Super 100321 with 89554 at 1,2
+Id : 94282, {_}: divide ?515515 (divide ?515516 ?515516) =>= ?515515 [515516, 515515] by Super 2 with 92346 at 2
+Id : 94361, {_}: divide ?515973 (multiply (inverse ?515974) ?515974) =>= ?515973 [515974, 515973] by Super 94282 with 3 at 2,2
+Id : 100488, {_}: inverse (inverse ?535740) =<= inverse (divide (divide ?535741 ?535741) (multiply (divide ?535743 ?535743) ?535740)) [535743, 535741, 535740] by Demod 100420 with 94361 at 1,1,3
+Id : 93886, {_}: inverse (divide (divide ?513000 ?513000) ?513001) =>= ?513001 [513001, 513000] by Super 1369 with 93111 at 1,2
+Id : 100489, {_}: inverse (inverse ?535740) =<= multiply (divide ?535743 ?535743) ?535740 [535743, 535740] by Demod 100488 with 93886 at 3
+Id : 100491, {_}: inverse ?494323 =<= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (inverse (inverse ?494323))) [494330, 494329, 494323] by Demod 89554 with 100489 at 2,2,3
+Id : 100612, {_}: inverse ?494323 =<= multiply ?494329 (multiply (divide (divide ?494330 ?494330) ?494329) (inverse ?494323)) [494330, 494329, 494323] by Demod 100491 with 3 at 2,3
+Id : 1348, {_}: inverse (divide (multiply (divide ?6830 ?6830) ?6831) (divide (divide ?6832 ?6833) (divide (inverse ?6831) ?6833))) =>= ?6832 [6833, 6832, 6831, 6830] by Super 1304 with 3 at 1,1,2
+Id : 3107, {_}: multiply ?16917 (divide (multiply (divide ?16918 ?16918) ?16919) (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16918, 16917] by Super 3 with 1348 at 2,3
+Id : 100541, {_}: multiply ?16917 (divide (inverse (inverse ?16919)) (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16917] by Demod 3107 with 100489 at 1,2,2
+Id : 100747, {_}: inverse (inverse (divide (inverse (inverse ?536517)) (divide (divide ?536518 ?536519) (divide (inverse ?536517) ?536519)))) =?= divide (divide ?536520 ?536520) ?536518 [536520, 536519, 536518, 536517] by Super 100541 with 100489 at 2
+Id : 100526, {_}: inverse (divide (inverse (inverse ?6831)) (divide (divide ?6832 ?6833) (divide (inverse ?6831) ?6833))) =>= ?6832 [6833, 6832, 6831] by Demod 1348 with 100489 at 1,1,2
+Id : 100849, {_}: inverse ?536518 =<= divide (divide ?536520 ?536520) ?536518 [536520, 536518] by Demod 100747 with 100526 at 1,2
+Id : 101341, {_}: inverse ?494323 =<= multiply ?494329 (multiply (inverse ?494329) (inverse ?494323)) [494329, 494323] by Demod 100612 with 100849 at 1,2,3
+Id : 101328, {_}: inverse (inverse ?513001) =>= ?513001 [513001] by Demod 93886 with 100849 at 1,2
+Id : 101357, {_}: multiply ?16917 (divide ?16919 (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16917] by Demod 100541 with 101328 at 1,2,2
+Id : 210, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?1032) ?1032) ?1033) ?1034)) ?1035) (divide ?1033 ?1035) =>= ?1034 [1035, 1034, 1033, 1032] by Super 202 with 3 at 1,1,1,1,1,2
+Id : 2224, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?11772) ?11772) ?11773) (divide ?11774 ?11773))) ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774, 11773, 11772] by Super 210 with 1292 at 1,1,1,2
+Id : 778, {_}: divide (inverse (divide (divide (divide ?3892 ?3892) ?3893) (divide (inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896)) (divide ?3893 ?3897)))) ?3897 =?= inverse (divide (divide (divide ?3898 ?3898) ?3895) ?3896) [3898, 3897, 3896, 3895, 3894, 3893, 3892] by Super 6 with 210 at 2,1,3
+Id : 811, {_}: inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896) =?= inverse (divide (divide (divide ?3898 ?3898) ?3895) ?3896) [3898, 3896, 3895, 3894] by Demod 778 with 2 at 2
+Id : 101312, {_}: inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896) =>= inverse (divide (inverse ?3895) ?3896) [3896, 3895, 3894] by Demod 811 with 100849 at 1,1,3
+Id : 101430, {_}: divide (divide (inverse (divide (inverse ?11773) (divide ?11774 ?11773))) ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774, 11773] by Demod 2224 with 101312 at 1,1,2
+Id : 375, {_}: divide (multiply (inverse (divide (divide (multiply (inverse ?1685) ?1685) ?1686) ?1687)) ?1688) (multiply ?1686 ?1688) =>= ?1687 [1688, 1687, 1686, 1685] by Super 372 with 3 at 1,1,1,1,1,2
+Id : 2362, {_}: divide (multiply (inverse (divide (divide (multiply (inverse ?12860) ?12860) ?12861) (divide ?12862 ?12861))) ?12863) (multiply ?12864 ?12863) =>= divide ?12862 ?12864 [12864, 12863, 12862, 12861, 12860] by Super 375 with 1292 at 1,1,1,2
+Id : 101423, {_}: divide (multiply (inverse (divide (inverse ?12861) (divide ?12862 ?12861))) ?12863) (multiply ?12864 ?12863) =>= divide ?12862 ?12864 [12864, 12863, 12862, 12861] by Demod 2362 with 101312 at 1,1,2
+Id : 1298, {_}: divide (multiply ?6472 ?6473) (multiply ?6474 ?6473) =?= divide (divide ?6472 ?6475) (divide ?6474 ?6475) [6475, 6474, 6473, 6472] by Super 231 with 1057 at 1,1,2
+Id : 2653, {_}: divide (multiply (inverse (divide (multiply (divide ?14473 ?14473) ?14474) (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474, 14473] by Super 231 with 1298 at 1,1,1,2
+Id : 100505, {_}: divide (multiply (inverse (divide (inverse (inverse ?14474)) (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474] by Demod 2653 with 100489 at 1,1,1,1,2
+Id : 101382, {_}: divide (multiply (inverse (divide ?14474 (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474] by Demod 100505 with 101328 at 1,1,1,1,2
+Id : 101429, {_}: divide (multiply (inverse (divide (inverse ?1686) ?1687)) ?1688) (multiply ?1686 ?1688) =>= ?1687 [1688, 1687, 1686] by Demod 375 with 101312 at 1,1,2
+Id : 101386, {_}: ?535740 =<= multiply (divide ?535743 ?535743) ?535740 [535743, 535740] by Demod 100489 with 101328 at 2
+Id : 101594, {_}: ?537458 =<= multiply (inverse (divide ?537459 ?537459)) ?537458 [537459, 537458] by Super 101386 with 100849 at 1,3
+Id : 101980, {_}: divide ?538112 (multiply ?538113 ?538112) =>= inverse ?538113 [538113, 538112] by Super 101429 with 101594 at 1,2
+Id : 102412, {_}: divide (multiply (inverse (inverse ?14475)) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475] by Demod 101382 with 101980 at 1,1,1,2
+Id : 102413, {_}: divide (multiply ?14475 ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475] by Demod 102412 with 101328 at 1,1,2
+Id : 102434, {_}: divide (inverse (divide (inverse ?12861) (divide ?12862 ?12861))) ?12864 =>= divide ?12862 ?12864 [12864, 12862, 12861] by Demod 101423 with 102413 at 2
+Id : 102436, {_}: divide (divide ?11774 ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774] by Demod 101430 with 102434 at 1,2
+Id : 102441, {_}: multiply ?16917 (divide ?16919 (divide ?16920 (inverse ?16919))) =>= divide ?16917 ?16920 [16920, 16919, 16917] by Demod 101357 with 102436 at 2,2,2
+Id : 102474, {_}: multiply ?16917 (divide ?16919 (multiply ?16920 ?16919)) =>= divide ?16917 ?16920 [16920, 16919, 16917] by Demod 102441 with 3 at 2,2,2
+Id : 102475, {_}: multiply ?16917 (inverse ?16920) =>= divide ?16917 ?16920 [16920, 16917] by Demod 102474 with 101980 at 2,2
+Id : 102476, {_}: inverse ?494323 =<= multiply ?494329 (divide (inverse ?494329) ?494323) [494329, 494323] by Demod 101341 with 102475 at 2,3
+Id : 102520, {_}: inverse (multiply ?538987 (inverse ?538988)) =>= multiply ?538988 (inverse ?538987) [538988, 538987] by Super 102476 with 101980 at 2,3
+Id : 102785, {_}: inverse (divide ?538987 ?538988) =<= multiply ?538988 (inverse ?538987) [538988, 538987] by Demod 102520 with 102475 at 1,2
+Id : 102786, {_}: inverse (divide ?538987 ?538988) =>= divide ?538988 ?538987 [538988, 538987] by Demod 102785 with 102475 at 3
+Id : 104734, {_}: multiply (divide ?212 (divide (divide ?210 ?210) ?211)) ?213 =?= inverse (divide (divide (divide ?214 ?214) ?215) (divide ?212 (divide ?215 (multiply ?211 ?213)))) [215, 214, 213, 211, 210, 212] by Demod 46 with 102786 at 1,2
+Id : 104735, {_}: multiply (divide ?212 (divide (divide ?210 ?210) ?211)) ?213 =?= divide (divide ?212 (divide ?215 (multiply ?211 ?213))) (divide (divide ?214 ?214) ?215) [214, 215, 213, 211, 210, 212] by Demod 104734 with 102786 at 3
+Id : 104736, {_}: multiply (divide ?212 (inverse ?211)) ?213 =<= divide (divide ?212 (divide ?215 (multiply ?211 ?213))) (divide (divide ?214 ?214) ?215) [214, 215, 213, 211, 212] by Demod 104735 with 100849 at 2,1,2
+Id : 104737, {_}: multiply (divide ?212 (inverse ?211)) ?213 =<= divide (divide ?212 (divide ?215 (multiply ?211 ?213))) (inverse ?215) [215, 213, 211, 212] by Demod 104736 with 100849 at 2,3
+Id : 104738, {_}: multiply (multiply ?212 ?211) ?213 =<= divide (divide ?212 (divide ?215 (multiply ?211 ?213))) (inverse ?215) [215, 213, 211, 212] by Demod 104737 with 3 at 1,2
+Id : 104739, {_}: multiply (multiply ?212 ?211) ?213 =<= multiply (divide ?212 (divide ?215 (multiply ?211 ?213))) ?215 [215, 213, 211, 212] by Demod 104738 with 3 at 3
+Id : 104774, {_}: multiply (multiply ?542474 ?542475) ?542476 =<= multiply (divide ?542474 (divide ?542477 (multiply ?542475 ?542476))) ?542477 [542477, 542476, 542475, 542474] by Demod 104738 with 3 at 3
+Id : 104783, {_}: multiply (multiply ?542524 (divide ?542525 ?542525)) ?542526 =?= multiply (divide ?542524 (divide ?542527 ?542526)) ?542527 [542527, 542526, 542525, 542524] by Super 104774 with 101386 at 2,2,1,3
+Id : 102917, {_}: multiply ?539648 (divide ?539649 ?539650) =>= divide ?539648 (divide ?539650 ?539649) [539650, 539649, 539648] by Super 102475 with 102786 at 2,2
+Id : 104878, {_}: multiply (divide ?542524 (divide ?542525 ?542525)) ?542526 =?= multiply (divide ?542524 (divide ?542527 ?542526)) ?542527 [542527, 542526, 542525, 542524] by Demod 104783 with 102917 at 1,2
+Id : 104879, {_}: multiply ?542524 ?542526 =<= multiply (divide ?542524 (divide ?542527 ?542526)) ?542527 [542527, 542526, 542524] by Demod 104878 with 93111 at 1,2
+Id : 107171, {_}: multiply (multiply ?212 ?211) ?213 =?= multiply ?212 (multiply ?211 ?213) [213, 211, 212] by Demod 104739 with 104879 at 3
+Id : 107392, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 1 with 107171 at 2
+Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
+% SZS output end CNFRefutation for GRP480-1.p
+11491: solved GRP480-1.p in 34.906181 using nrkbo
+11491: status Unsatisfiable for GRP480-1.p
+NO CLASH, using fixed ground order
+11510: Facts:
+11510: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+11510: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+11510: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+11510: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+11510: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+11510: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+11510: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+11510: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+11510: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?26 ?27)
+ (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
+ [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
+11510: Goal:
+11510: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H58
+11510: Order:
+11510: nrkbo
+11510: Leaf order:
+11510: meet 17 2 4 0,2
+11510: join 19 2 4 0,2,2
+11510: c 2 0 2 2,2,2
+11510: b 4 0 4 1,2,2
+11510: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+11511: Facts:
+11511: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+11511: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+11511: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+11511: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+11511: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+11511: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+11511: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+11511: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+11511: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?26 ?27)
+ (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
+ [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
+11511: Goal:
+11511: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H58
+11511: Order:
+11511: kbo
+11511: Leaf order:
+11511: meet 17 2 4 0,2
+11511: join 19 2 4 0,2,2
+11511: c 2 0 2 2,2,2
+11511: b 4 0 4 1,2,2
+11511: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+11512: Facts:
+11512: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+11512: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+11512: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+11512: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+11512: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+11512: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+11512: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+11512: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+11512: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?26 ?27)
+ (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
+ [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
+11512: Goal:
+11512: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H58
+11512: Order:
+11512: lpo
+11512: Leaf order:
+11512: meet 17 2 4 0,2
+11512: join 19 2 4 0,2,2
+11512: c 2 0 2 2,2,2
+11512: b 4 0 4 1,2,2
+11512: a 4 0 4 1,2
+% SZS status Timeout for LAT168-1.p
+NO CLASH, using fixed ground order
+11539: Facts:
+11539: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+11539: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+11539: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+11539: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+11539: Goal:
+11539: Id : 1, {_}:
+ implies (implies (implies a b) (implies b a)) (implies b a) =>= truth
+ [] by prove_wajsberg_mv_4
+11539: Order:
+11539: nrkbo
+11539: Leaf order:
+11539: not 2 1 0
+11539: truth 4 0 1 3
+11539: implies 18 2 5 0,2
+11539: b 3 0 3 2,1,1,2
+11539: a 3 0 3 1,1,1,2
+NO CLASH, using fixed ground order
+11540: Facts:
+11540: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+11540: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+11540: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+11540: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+11540: Goal:
+11540: Id : 1, {_}:
+ implies (implies (implies a b) (implies b a)) (implies b a) =>= truth
+ [] by prove_wajsberg_mv_4
+11540: Order:
+11540: kbo
+11540: Leaf order:
+11540: not 2 1 0
+11540: truth 4 0 1 3
+11540: implies 18 2 5 0,2
+11540: b 3 0 3 2,1,1,2
+11540: a 3 0 3 1,1,1,2
+NO CLASH, using fixed ground order
+11541: Facts:
+11541: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+11541: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+11541: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+11541: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+11541: Goal:
+11541: Id : 1, {_}:
+ implies (implies (implies a b) (implies b a)) (implies b a) =>= truth
+ [] by prove_wajsberg_mv_4
+11541: Order:
+11541: lpo
+11541: Leaf order:
+11541: not 2 1 0
+11541: truth 4 0 1 3
+11541: implies 18 2 5 0,2
+11541: b 3 0 3 2,1,1,2
+11541: a 3 0 3 1,1,1,2
+% SZS status Timeout for LCL109-2.p
+NO CLASH, using fixed ground order
+11558: Facts:
+11558: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+11558: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+11558: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+11558: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+11558: Goal:
+11558: Id : 1, {_}:
+ implies x (implies y z) =>= implies y (implies x z)
+ [] by prove_wajsberg_lemma
+11558: Order:
+11558: nrkbo
+11558: Leaf order:
+11558: not 2 1 0
+11558: truth 3 0 0
+11558: implies 17 2 4 0,2
+11558: z 2 0 2 2,2,2
+11558: y 2 0 2 1,2,2
+11558: x 2 0 2 1,2
+NO CLASH, using fixed ground order
+11559: Facts:
+11559: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+11559: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+11559: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+11559: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+11559: Goal:
+11559: Id : 1, {_}:
+ implies x (implies y z) =>= implies y (implies x z)
+ [] by prove_wajsberg_lemma
+11559: Order:
+11559: kbo
+11559: Leaf order:
+11559: not 2 1 0
+11559: truth 3 0 0
+11559: implies 17 2 4 0,2
+11559: z 2 0 2 2,2,2
+11559: y 2 0 2 1,2,2
+11559: x 2 0 2 1,2
+NO CLASH, using fixed ground order
+11560: Facts:
+11560: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+11560: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+11560: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+11560: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+11560: Goal:
+11560: Id : 1, {_}:
+ implies x (implies y z) =>= implies y (implies x z)
+ [] by prove_wajsberg_lemma
+11560: Order:
+11560: lpo
+11560: Leaf order:
+11560: not 2 1 0
+11560: truth 3 0 0
+11560: implies 17 2 4 0,2
+11560: z 2 0 2 2,2,2
+11560: y 2 0 2 1,2,2
+11560: x 2 0 2 1,2
+% SZS status Timeout for LCL138-1.p
+NO CLASH, using fixed ground order
+11593: Facts:
+11593: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+11593: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+11593: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+11593: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+11593: Id : 6, {_}:
+ or ?14 ?15 =<= implies (not ?14) ?15
+ [15, 14] by or_definition ?14 ?15
+11593: Id : 7, {_}:
+ or (or ?17 ?18) ?19 =?= or ?17 (or ?18 ?19)
+ [19, 18, 17] by or_associativity ?17 ?18 ?19
+11593: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
+11593: Id : 9, {_}:
+ and ?24 ?25 =<= not (or (not ?24) (not ?25))
+ [25, 24] by and_definition ?24 ?25
+11593: Id : 10, {_}:
+ and (and ?27 ?28) ?29 =?= and ?27 (and ?28 ?29)
+ [29, 28, 27] by and_associativity ?27 ?28 ?29
+11593: Id : 11, {_}:
+ and ?31 ?32 =?= and ?32 ?31
+ [32, 31] by and_commutativity ?31 ?32
+11593: Id : 12, {_}:
+ xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
+ [35, 34] by xor_definition ?34 ?35
+11593: Id : 13, {_}:
+ xor ?37 ?38 =?= xor ?38 ?37
+ [38, 37] by xor_commutativity ?37 ?38
+11593: Id : 14, {_}:
+ and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
+ [41, 40] by and_star_definition ?40 ?41
+11593: Id : 15, {_}:
+ and_star (and_star ?43 ?44) ?45 =?= and_star ?43 (and_star ?44 ?45)
+ [45, 44, 43] by and_star_associativity ?43 ?44 ?45
+11593: Id : 16, {_}:
+ and_star ?47 ?48 =?= and_star ?48 ?47
+ [48, 47] by and_star_commutativity ?47 ?48
+11593: Id : 17, {_}: not truth =>= falsehood [] by false_definition
+11593: Goal:
+11593: Id : 1, {_}:
+ xor x (xor truth y) =<= xor (xor x truth) y
+ [] by prove_alternative_wajsberg_axiom
+11593: Order:
+11593: nrkbo
+11593: Leaf order:
+11593: falsehood 1 0 0
+11593: and_star 7 2 0
+11593: and 9 2 0
+11593: or 10 2 0
+11593: not 12 1 0
+11593: implies 14 2 0
+11593: xor 7 2 4 0,2
+11593: y 2 0 2 2,2,2
+11593: truth 6 0 2 1,2,2
+11593: x 2 0 2 1,2
+NO CLASH, using fixed ground order
+11594: Facts:
+11594: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+11594: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+11594: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+11594: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+11594: Id : 6, {_}:
+ or ?14 ?15 =<= implies (not ?14) ?15
+ [15, 14] by or_definition ?14 ?15
+11594: Id : 7, {_}:
+ or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
+ [19, 18, 17] by or_associativity ?17 ?18 ?19
+11594: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
+11594: Id : 9, {_}:
+ and ?24 ?25 =<= not (or (not ?24) (not ?25))
+ [25, 24] by and_definition ?24 ?25
+11594: Id : 10, {_}:
+ and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
+ [29, 28, 27] by and_associativity ?27 ?28 ?29
+11594: Id : 11, {_}:
+ and ?31 ?32 =?= and ?32 ?31
+ [32, 31] by and_commutativity ?31 ?32
+11594: Id : 12, {_}:
+ xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
+ [35, 34] by xor_definition ?34 ?35
+11594: Id : 13, {_}:
+ xor ?37 ?38 =?= xor ?38 ?37
+ [38, 37] by xor_commutativity ?37 ?38
+11594: Id : 14, {_}:
+ and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
+ [41, 40] by and_star_definition ?40 ?41
+11594: Id : 15, {_}:
+ and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45)
+ [45, 44, 43] by and_star_associativity ?43 ?44 ?45
+11594: Id : 16, {_}:
+ and_star ?47 ?48 =?= and_star ?48 ?47
+ [48, 47] by and_star_commutativity ?47 ?48
+11594: Id : 17, {_}: not truth =>= falsehood [] by false_definition
+11594: Goal:
+11594: Id : 1, {_}:
+ xor x (xor truth y) =<= xor (xor x truth) y
+ [] by prove_alternative_wajsberg_axiom
+11594: Order:
+11594: kbo
+11594: Leaf order:
+11594: falsehood 1 0 0
+11594: and_star 7 2 0
+11594: and 9 2 0
+11594: or 10 2 0
+11594: not 12 1 0
+11594: implies 14 2 0
+11594: xor 7 2 4 0,2
+11594: y 2 0 2 2,2,2
+11594: truth 6 0 2 1,2,2
+11594: x 2 0 2 1,2
+NO CLASH, using fixed ground order
+11595: Facts:
+11595: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+11595: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+11595: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+11595: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+11595: Id : 6, {_}:
+ or ?14 ?15 =<= implies (not ?14) ?15
+ [15, 14] by or_definition ?14 ?15
+11595: Id : 7, {_}:
+ or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
+ [19, 18, 17] by or_associativity ?17 ?18 ?19
+11595: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
+11595: Id : 9, {_}:
+ and ?24 ?25 =<= not (or (not ?24) (not ?25))
+ [25, 24] by and_definition ?24 ?25
+11595: Id : 10, {_}:
+ and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
+ [29, 28, 27] by and_associativity ?27 ?28 ?29
+11595: Id : 11, {_}:
+ and ?31 ?32 =?= and ?32 ?31
+ [32, 31] by and_commutativity ?31 ?32
+11595: Id : 12, {_}:
+ xor ?34 ?35 =>= or (and ?34 (not ?35)) (and (not ?34) ?35)
+ [35, 34] by xor_definition ?34 ?35
+11595: Id : 13, {_}:
+ xor ?37 ?38 =?= xor ?38 ?37
+ [38, 37] by xor_commutativity ?37 ?38
+11595: Id : 14, {_}:
+ and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
+ [41, 40] by and_star_definition ?40 ?41
+11595: Id : 15, {_}:
+ and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45)
+ [45, 44, 43] by and_star_associativity ?43 ?44 ?45
+11595: Id : 16, {_}:
+ and_star ?47 ?48 =?= and_star ?48 ?47
+ [48, 47] by and_star_commutativity ?47 ?48
+11595: Id : 17, {_}: not truth =>= falsehood [] by false_definition
+11595: Goal:
+11595: Id : 1, {_}:
+ xor x (xor truth y) =<= xor (xor x truth) y
+ [] by prove_alternative_wajsberg_axiom
+11595: Order:
+11595: lpo
+11595: Leaf order:
+11595: falsehood 1 0 0
+11595: and_star 7 2 0
+11595: and 9 2 0
+11595: or 10 2 0
+11595: not 12 1 0
+11595: implies 14 2 0
+11595: xor 7 2 4 0,2
+11595: y 2 0 2 2,2,2
+11595: truth 6 0 2 1,2,2
+11595: x 2 0 2 1,2
+Statistics :
+Max weight : 25
+Found proof, 7.279985s
+% SZS status Unsatisfiable for LCL159-1.p
+% SZS output start CNFRefutation for LCL159-1.p
+Id : 5, {_}: implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth [12, 11] by wajsberg_4 ?11 ?12
+Id : 7, {_}: or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19) [19, 18, 17] by or_associativity ?17 ?18 ?19
+Id : 39, {_}: implies (implies ?111 ?112) ?112 =?= implies (implies ?112 ?111) ?111 [112, 111] by wajsberg_3 ?111 ?112
+Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+Id : 3, {_}: implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) =>= truth [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+Id : 20, {_}: implies (implies ?55 ?56) (implies (implies ?56 ?57) (implies ?55 ?57)) =>= truth [57, 56, 55] by wajsberg_2 ?55 ?56 ?57
+Id : 17, {_}: not truth =>= falsehood [] by false_definition
+Id : 6, {_}: or ?14 ?15 =<= implies (not ?14) ?15 [15, 14] by or_definition ?14 ?15
+Id : 4, {_}: implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 [9, 8] by wajsberg_3 ?8 ?9
+Id : 11, {_}: and ?31 ?32 =?= and ?32 ?31 [32, 31] by and_commutativity ?31 ?32
+Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
+Id : 9, {_}: and ?24 ?25 =<= not (or (not ?24) (not ?25)) [25, 24] by and_definition ?24 ?25
+Id : 14, {_}: and_star ?40 ?41 =<= not (or (not ?40) (not ?41)) [41, 40] by and_star_definition ?40 ?41
+Id : 12, {_}: xor ?34 ?35 =>= or (and ?34 (not ?35)) (and (not ?34) ?35) [35, 34] by xor_definition ?34 ?35
+Id : 207, {_}: and_star ?40 ?41 =<= and ?40 ?41 [41, 40] by Demod 14 with 9 at 3
+Id : 212, {_}: xor ?34 ?35 =>= or (and_star ?34 (not ?35)) (and (not ?34) ?35) [35, 34] by Demod 12 with 207 at 1,3
+Id : 213, {_}: xor ?34 ?35 =>= or (and_star ?34 (not ?35)) (and_star (not ?34) ?35) [35, 34] by Demod 212 with 207 at 2,3
+Id : 219, {_}: and_star ?31 ?32 =<= and ?32 ?31 [32, 31] by Demod 11 with 207 at 2
+Id : 220, {_}: and_star ?31 ?32 =?= and_star ?32 ?31 [32, 31] by Demod 219 with 207 at 3
+Id : 240, {_}: or truth ?463 =<= implies falsehood ?463 [463] by Super 6 with 17 at 1,3
+Id : 286, {_}: implies (implies ?477 falsehood) falsehood =>= implies (or truth ?477) ?477 [477] by Super 4 with 240 at 1,3
+Id : 22, {_}: implies (implies (implies ?62 ?63) ?64) (implies (implies ?64 (implies (implies ?63 ?65) (implies ?62 ?65))) truth) =>= truth [65, 64, 63, 62] by Super 20 with 3 at 2,2,2
+Id : 784, {_}: implies (implies ?990 truth) (implies ?991 (implies ?990 ?991)) =>= truth [991, 990] by Super 20 with 2 at 1,2,2
+Id : 785, {_}: implies (implies truth truth) (implies ?993 ?993) =>= truth [993] by Super 784 with 2 at 2,2,2
+Id : 818, {_}: implies truth (implies ?993 ?993) =>= truth [993] by Demod 785 with 2 at 1,2
+Id : 819, {_}: implies ?993 ?993 =>= truth [993] by Demod 818 with 2 at 2
+Id : 870, {_}: implies (implies (implies ?1070 ?1070) ?1071) (implies (implies ?1071 truth) truth) =>= truth [1071, 1070] by Super 22 with 819 at 2,1,2,2
+Id : 898, {_}: implies (implies truth ?1071) (implies (implies ?1071 truth) truth) =>= truth [1071] by Demod 870 with 819 at 1,1,2
+Id : 40, {_}: implies (implies ?114 truth) truth =>= implies ?114 ?114 [114] by Super 39 with 2 at 1,3
+Id : 864, {_}: implies (implies ?114 truth) truth =>= truth [114] by Demod 40 with 819 at 3
+Id : 899, {_}: implies (implies truth ?1071) truth =>= truth [1071] by Demod 898 with 864 at 2,2
+Id : 900, {_}: implies ?1071 truth =>= truth [1071] by Demod 899 with 2 at 1,2
+Id : 980, {_}: or ?1117 truth =>= truth [1117] by Super 6 with 900 at 3
+Id : 1078, {_}: or truth ?1157 =>= truth [1157] by Super 8 with 980 at 3
+Id : 1116, {_}: implies (implies ?477 falsehood) falsehood =>= implies truth ?477 [477] by Demod 286 with 1078 at 1,3
+Id : 1117, {_}: implies (implies ?477 falsehood) falsehood =>= ?477 [477] by Demod 1116 with 2 at 3
+Id : 218, {_}: and_star ?24 ?25 =<= not (or (not ?24) (not ?25)) [25, 24] by Demod 9 with 207 at 2
+Id : 239, {_}: and_star truth ?461 =<= not (or falsehood (not ?461)) [461] by Super 218 with 17 at 1,1,3
+Id : 517, {_}: or (or falsehood (not ?805)) ?806 =<= implies (and_star truth ?805) ?806 [806, 805] by Super 6 with 239 at 1,3
+Id : 1565, {_}: or falsehood (or (not ?1468) ?1469) =<= implies (and_star truth ?1468) ?1469 [1469, 1468] by Demod 517 with 7 at 2
+Id : 1566, {_}: or falsehood (or (not ?1471) ?1472) =<= implies (and_star ?1471 truth) ?1472 [1472, 1471] by Super 1565 with 220 at 1,3
+Id : 525, {_}: or falsehood (or (not ?805) ?806) =<= implies (and_star truth ?805) ?806 [806, 805] by Demod 517 with 7 at 2
+Id : 520, {_}: and_star truth ?814 =<= not (or falsehood (not ?814)) [814] by Super 218 with 17 at 1,1,3
+Id : 521, {_}: and_star truth truth =<= not (or falsehood falsehood) [] by Super 520 with 17 at 2,1,3
+Id : 564, {_}: or (or falsehood falsehood) ?828 =<= implies (and_star truth truth) ?828 [828] by Super 6 with 521 at 1,3
+Id : 589, {_}: or falsehood (or falsehood ?828) =<= implies (and_star truth truth) ?828 [828] by Demod 564 with 7 at 2
+Id : 1273, {_}: implies (or falsehood (or falsehood falsehood)) falsehood =>= and_star truth truth [] by Super 1117 with 589 at 1,2
+Id : 69, {_}: implies (or ?11 (not ?12)) (implies ?12 ?11) =>= truth [12, 11] by Demod 5 with 6 at 1,2
+Id : 241, {_}: implies (or ?465 falsehood) (implies truth ?465) =>= truth [465] by Super 69 with 17 at 2,1,2
+Id : 260, {_}: implies (or ?465 falsehood) ?465 =>= truth [465] by Demod 241 with 2 at 2,2
+Id : 1322, {_}: implies truth falsehood =>= or falsehood falsehood [] by Super 1117 with 260 at 1,2
+Id : 1344, {_}: falsehood =<= or falsehood falsehood [] by Demod 1322 with 2 at 2
+Id : 1375, {_}: or falsehood ?1348 =<= or falsehood (or falsehood ?1348) [1348] by Super 7 with 1344 at 1,2
+Id : 2080, {_}: implies (or falsehood falsehood) falsehood =>= and_star truth truth [] by Demod 1273 with 1375 at 1,2
+Id : 2081, {_}: truth =<= and_star truth truth [] by Demod 2080 with 260 at 2
+Id : 2088, {_}: or falsehood (or (not truth) ?1976) =<= implies truth ?1976 [1976] by Super 525 with 2081 at 1,3
+Id : 2092, {_}: or falsehood (or falsehood ?1976) =<= implies truth ?1976 [1976] by Demod 2088 with 17 at 1,2,2
+Id : 2093, {_}: or falsehood (or falsehood ?1976) =>= ?1976 [1976] by Demod 2092 with 2 at 3
+Id : 2094, {_}: or falsehood ?1976 =>= ?1976 [1976] by Demod 2093 with 1375 at 2
+Id : 2619, {_}: or (not ?1471) ?1472 =<= implies (and_star ?1471 truth) ?1472 [1472, 1471] by Demod 1566 with 2094 at 2
+Id : 2636, {_}: implies (or (not ?2581) falsehood) falsehood =>= and_star ?2581 truth [2581] by Super 1117 with 2619 at 1,2
+Id : 2658, {_}: implies (or falsehood (not ?2581)) falsehood =>= and_star ?2581 truth [2581] by Demod 2636 with 8 at 1,2
+Id : 2659, {_}: implies (not ?2581) falsehood =>= and_star ?2581 truth [2581] by Demod 2658 with 2094 at 1,2
+Id : 2660, {_}: or ?2581 falsehood =>= and_star ?2581 truth [2581] by Demod 2659 with 6 at 2
+Id : 1407, {_}: or falsehood ?1358 =<= or falsehood (or falsehood ?1358) [1358] by Super 7 with 1344 at 1,2
+Id : 1408, {_}: or falsehood ?1360 =<= or falsehood (or ?1360 falsehood) [1360] by Super 1407 with 8 at 2,3
+Id : 2132, {_}: ?1360 =<= or falsehood (or ?1360 falsehood) [1360] by Demod 1408 with 2094 at 2
+Id : 2133, {_}: ?1360 =<= or ?1360 falsehood [1360] by Demod 2132 with 2094 at 3
+Id : 2661, {_}: ?2581 =<= and_star ?2581 truth [2581] by Demod 2660 with 2133 at 2
+Id : 2708, {_}: or (not ?1471) ?1472 =<= implies ?1471 ?1472 [1472, 1471] by Demod 2619 with 2661 at 1,3
+Id : 2725, {_}: or (not (implies ?477 falsehood)) falsehood =>= ?477 [477] by Demod 1117 with 2708 at 2
+Id : 2726, {_}: or (not (or (not ?477) falsehood)) falsehood =>= ?477 [477] by Demod 2725 with 2708 at 1,1,2
+Id : 2767, {_}: or falsehood (not (or (not ?477) falsehood)) =>= ?477 [477] by Demod 2726 with 8 at 2
+Id : 2768, {_}: not (or (not ?477) falsehood) =>= ?477 [477] by Demod 2767 with 2094 at 2
+Id : 2769, {_}: not (or falsehood (not ?477)) =>= ?477 [477] by Demod 2768 with 8 at 1,2
+Id : 2770, {_}: not (not ?477) =>= ?477 [477] by Demod 2769 with 2094 at 1,2
+Id : 2131, {_}: and_star truth ?461 =<= not (not ?461) [461] by Demod 239 with 2094 at 1,3
+Id : 2771, {_}: and_star truth ?477 =>= ?477 [477] by Demod 2770 with 2131 at 2
+Id : 563, {_}: and_star (or falsehood falsehood) ?826 =<= not (or (and_star truth truth) (not ?826)) [826] by Super 218 with 521 at 1,1,3
+Id : 3108, {_}: and_star falsehood ?826 =<= not (or (and_star truth truth) (not ?826)) [826] by Demod 563 with 2094 at 1,2
+Id : 3109, {_}: and_star falsehood ?826 =<= not (or truth (not ?826)) [826] by Demod 3108 with 2771 at 1,1,3
+Id : 3110, {_}: and_star falsehood ?826 =?= not truth [826] by Demod 3109 with 1078 at 1,3
+Id : 3111, {_}: and_star falsehood ?826 =>= falsehood [826] by Demod 3110 with 17 at 3
+Id : 2777, {_}: ?461 =<= not (not ?461) [461] by Demod 2131 with 2771 at 2
+Id : 3185, {_}: or (and_star y x) (and_star (not y) (not x)) === or (and_star y x) (and_star (not y) (not x)) [] by Demod 3184 with 220 at 1,2
+Id : 3184, {_}: or (and_star x y) (and_star (not y) (not x)) =>= or (and_star y x) (and_star (not y) (not x)) [] by Demod 3183 with 8 at 2
+Id : 3183, {_}: or (and_star (not y) (not x)) (and_star x y) =>= or (and_star y x) (and_star (not y) (not x)) [] by Demod 3182 with 2777 at 2,2,2
+Id : 3182, {_}: or (and_star (not y) (not x)) (and_star x (not (not y))) =>= or (and_star y x) (and_star (not y) (not x)) [] by Demod 3181 with 2094 at 1,1,2
+Id : 3181, {_}: or (and_star (or falsehood (not y)) (not x)) (and_star x (not (not y))) =>= or (and_star y x) (and_star (not y) (not x)) [] by Demod 3180 with 8 at 3
+Id : 3180, {_}: or (and_star (or falsehood (not y)) (not x)) (and_star x (not (not y))) =>= or (and_star (not y) (not x)) (and_star y x) [] by Demod 3179 with 2094 at 1,2,2,2
+Id : 3179, {_}: or (and_star (or falsehood (not y)) (not x)) (and_star x (not (or falsehood (not y)))) =>= or (and_star (not y) (not x)) (and_star y x) [] by Demod 3178 with 3111 at 1,1,1,2
+Id : 3178, {_}: or (and_star (or (and_star falsehood y) (not y)) (not x)) (and_star x (not (or falsehood (not y)))) =>= or (and_star (not y) (not x)) (and_star y x) [] by Demod 3177 with 2777 at 2,2,3
+Id : 3177, {_}: or (and_star (or (and_star falsehood y) (not y)) (not x)) (and_star x (not (or falsehood (not y)))) =<= or (and_star (not y) (not x)) (and_star y (not (not x))) [] by Demod 3176 with 3111 at 1,1,2,2,2
+Id : 3176, {_}: or (and_star (or (and_star falsehood y) (not y)) (not x)) (and_star x (not (or (and_star falsehood y) (not y)))) =<= or (and_star (not y) (not x)) (and_star y (not (not x))) [] by Demod 3175 with 220 at 1,1,1,2
+Id : 3175, {_}: or (and_star (or (and_star y falsehood) (not y)) (not x)) (and_star x (not (or (and_star falsehood y) (not y)))) =<= or (and_star (not y) (not x)) (and_star y (not (not x))) [] by Demod 3174 with 2094 at 1,2,2,3
+Id : 3174, {_}: or (and_star (or (and_star y falsehood) (not y)) (not x)) (and_star x (not (or (and_star falsehood y) (not y)))) =<= or (and_star (not y) (not x)) (and_star y (not (or falsehood (not x)))) [] by Demod 3173 with 2094 at 2,1,3
+Id : 3173, {_}: or (and_star (or (and_star y falsehood) (not y)) (not x)) (and_star x (not (or (and_star falsehood y) (not y)))) =<= or (and_star (not y) (or falsehood (not x))) (and_star y (not (or falsehood (not x)))) [] by Demod 3172 with 220 at 1,1,2,2,2
+Id : 3172, {_}: or (and_star (or (and_star y falsehood) (not y)) (not x)) (and_star x (not (or (and_star y falsehood) (not y)))) =<= or (and_star (not y) (or falsehood (not x))) (and_star y (not (or falsehood (not x)))) [] by Demod 3171 with 8 at 1,1,2
+Id : 3171, {_}: or (and_star (or (not y) (and_star y falsehood)) (not x)) (and_star x (not (or (and_star y falsehood) (not y)))) =<= or (and_star (not y) (or falsehood (not x))) (and_star y (not (or falsehood (not x)))) [] by Demod 3170 with 3111 at 1,1,2,2,3
+Id : 3170, {_}: or (and_star (or (not y) (and_star y falsehood)) (not x)) (and_star x (not (or (and_star y falsehood) (not y)))) =<= or (and_star (not y) (or falsehood (not x))) (and_star y (not (or (and_star falsehood x) (not x)))) [] by Demod 3169 with 3111 at 1,2,1,3
+Id : 3169, {_}: or (and_star (or (not y) (and_star y falsehood)) (not x)) (and_star x (not (or (and_star y falsehood) (not y)))) =<= or (and_star (not y) (or (and_star falsehood x) (not x))) (and_star y (not (or (and_star falsehood x) (not x)))) [] by Demod 3168 with 8 at 1,2,2,2
+Id : 3168, {_}: or (and_star (or (not y) (and_star y falsehood)) (not x)) (and_star x (not (or (not y) (and_star y falsehood)))) =<= or (and_star (not y) (or (and_star falsehood x) (not x))) (and_star y (not (or (and_star falsehood x) (not x)))) [] by Demod 3167 with 17 at 2,2,1,1,2
+Id : 3167, {_}: or (and_star (or (not y) (and_star y (not truth))) (not x)) (and_star x (not (or (not y) (and_star y falsehood)))) =<= or (and_star (not y) (or (and_star falsehood x) (not x))) (and_star y (not (or (and_star falsehood x) (not x)))) [] by Demod 3166 with 2771 at 2,1,2,2,3
+Id : 3166, {_}: or (and_star (or (not y) (and_star y (not truth))) (not x)) (and_star x (not (or (not y) (and_star y falsehood)))) =<= or (and_star (not y) (or (and_star falsehood x) (not x))) (and_star y (not (or (and_star falsehood x) (and_star truth (not x))))) [] by Demod 3165 with 220 at 1,1,2,2,3
+Id : 3165, {_}: or (and_star (or (not y) (and_star y (not truth))) (not x)) (and_star x (not (or (not y) (and_star y falsehood)))) =<= or (and_star (not y) (or (and_star falsehood x) (not x))) (and_star y (not (or (and_star x falsehood) (and_star truth (not x))))) [] by Demod 3164 with 2771 at 2,2,1,3
+Id : 3164, {_}: or (and_star (or (not y) (and_star y (not truth))) (not x)) (and_star x (not (or (not y) (and_star y falsehood)))) =<= or (and_star (not y) (or (and_star falsehood x) (and_star truth (not x)))) (and_star y (not (or (and_star x falsehood) (and_star truth (not x))))) [] by Demod 3163 with 220 at 1,2,1,3
+Id : 3163, {_}: or (and_star (or (not y) (and_star y (not truth))) (not x)) (and_star x (not (or (not y) (and_star y falsehood)))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star truth (not x)))) (and_star y (not (or (and_star x falsehood) (and_star truth (not x))))) [] by Demod 3162 with 17 at 2,2,1,2,2,2
+Id : 3162, {_}: or (and_star (or (not y) (and_star y (not truth))) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star truth (not x)))) (and_star y (not (or (and_star x falsehood) (and_star truth (not x))))) [] by Demod 3161 with 220 at 2,1,1,2
+Id : 3161, {_}: or (and_star (or (not y) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star truth (not x)))) (and_star y (not (or (and_star x falsehood) (and_star truth (not x))))) [] by Demod 3160 with 2771 at 1,1,1,2
+Id : 3160, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star truth (not x)))) (and_star y (not (or (and_star x falsehood) (and_star truth (not x))))) [] by Demod 3159 with 220 at 2,1,2,2,3
+Id : 3159, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star truth (not x)))) (and_star y (not (or (and_star x falsehood) (and_star (not x) truth)))) [] by Demod 3158 with 17 at 2,1,1,2,2,3
+Id : 3158, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star truth (not x)))) (and_star y (not (or (and_star x (not truth)) (and_star (not x) truth)))) [] by Demod 3157 with 220 at 2,2,1,3
+Id : 3157, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star (not x) truth))) (and_star y (not (or (and_star x (not truth)) (and_star (not x) truth)))) [] by Demod 3156 with 17 at 2,1,2,1,3
+Id : 3156, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x (not truth)) (and_star (not x) truth))) (and_star y (not (or (and_star x (not truth)) (and_star (not x) truth)))) [] by Demod 3155 with 220 at 2,1,2,2,2
+Id : 3155, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star (not truth) y)))) =<= or (and_star (not y) (or (and_star x (not truth)) (and_star (not x) truth))) (and_star y (not (or (and_star x (not truth)) (and_star (not x) truth)))) [] by Demod 3154 with 2771 at 1,1,2,2,2
+Id : 3154, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (and_star truth (not y)) (and_star (not truth) y)))) =<= or (and_star (not y) (or (and_star x (not truth)) (and_star (not x) truth))) (and_star y (not (or (and_star x (not truth)) (and_star (not x) truth)))) [] by Demod 3153 with 220 at 1,2
+Id : 3153, {_}: or (and_star (not x) (or (and_star truth (not y)) (and_star (not truth) y))) (and_star x (not (or (and_star truth (not y)) (and_star (not truth) y)))) =<= or (and_star (not y) (or (and_star x (not truth)) (and_star (not x) truth))) (and_star y (not (or (and_star x (not truth)) (and_star (not x) truth)))) [] by Demod 3152 with 213 at 1,2,2,3
+Id : 3152, {_}: or (and_star (not x) (or (and_star truth (not y)) (and_star (not truth) y))) (and_star x (not (or (and_star truth (not y)) (and_star (not truth) y)))) =<= or (and_star (not y) (or (and_star x (not truth)) (and_star (not x) truth))) (and_star y (not (xor x truth))) [] by Demod 3151 with 213 at 2,1,3
+Id : 3151, {_}: or (and_star (not x) (or (and_star truth (not y)) (and_star (not truth) y))) (and_star x (not (or (and_star truth (not y)) (and_star (not truth) y)))) =<= or (and_star (not y) (xor x truth)) (and_star y (not (xor x truth))) [] by Demod 3150 with 213 at 1,2,2,2
+Id : 3150, {_}: or (and_star (not x) (or (and_star truth (not y)) (and_star (not truth) y))) (and_star x (not (xor truth y))) =<= or (and_star (not y) (xor x truth)) (and_star y (not (xor x truth))) [] by Demod 3149 with 213 at 2,1,2
+Id : 3149, {_}: or (and_star (not x) (xor truth y)) (and_star x (not (xor truth y))) =<= or (and_star (not y) (xor x truth)) (and_star y (not (xor x truth))) [] by Demod 3148 with 220 at 2,3
+Id : 3148, {_}: or (and_star (not x) (xor truth y)) (and_star x (not (xor truth y))) =<= or (and_star (not y) (xor x truth)) (and_star (not (xor x truth)) y) [] by Demod 3147 with 220 at 1,3
+Id : 3147, {_}: or (and_star (not x) (xor truth y)) (and_star x (not (xor truth y))) =<= or (and_star (xor x truth) (not y)) (and_star (not (xor x truth)) y) [] by Demod 3146 with 8 at 2
+Id : 3146, {_}: or (and_star x (not (xor truth y))) (and_star (not x) (xor truth y)) =<= or (and_star (xor x truth) (not y)) (and_star (not (xor x truth)) y) [] by Demod 3145 with 213 at 3
+Id : 3145, {_}: or (and_star x (not (xor truth y))) (and_star (not x) (xor truth y)) =<= xor (xor x truth) y [] by Demod 1 with 213 at 2
+Id : 1, {_}: xor x (xor truth y) =<= xor (xor x truth) y [] by prove_alternative_wajsberg_axiom
+% SZS output end CNFRefutation for LCL159-1.p
+11595: solved LCL159-1.p in 3.608225 using lpo
+11595: status Unsatisfiable for LCL159-1.p
+NO CLASH, using fixed ground order
+11600: Facts:
+11600: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+11600: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+11600: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+11600: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+11600: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+11600: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+11600: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+11600: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+11600: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+11600: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+11600: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+11600: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+11600: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+11600: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+11600: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+11600: Goal:
+11600: Id : 1, {_}:
+ associator x y (add u v)
+ =<=
+ add (associator x y u) (associator x y v)
+ [] by prove_linearised_form1
+11600: Order:
+11600: nrkbo
+11600: Leaf order:
+11600: commutator 1 2 0
+11600: additive_inverse 6 1 0
+11600: multiply 22 2 0
+11600: additive_identity 8 0 0
+11600: associator 4 3 3 0,2
+11600: add 18 2 2 0,3,2
+11600: v 2 0 2 2,3,2
+11600: u 2 0 2 1,3,2
+11600: y 3 0 3 2,2
+11600: x 3 0 3 1,2
+NO CLASH, using fixed ground order
+11601: Facts:
+11601: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+11601: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+11601: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+11601: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+11601: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+11601: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+11601: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+11601: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+11601: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+11601: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+11601: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+11601: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+11601: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+11601: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+11601: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+11601: Goal:
+11601: Id : 1, {_}:
+ associator x y (add u v)
+ =<=
+ add (associator x y u) (associator x y v)
+ [] by prove_linearised_form1
+11601: Order:
+11601: kbo
+11601: Leaf order:
+11601: commutator 1 2 0
+11601: additive_inverse 6 1 0
+11601: multiply 22 2 0
+11601: additive_identity 8 0 0
+11601: associator 4 3 3 0,2
+11601: add 18 2 2 0,3,2
+11601: v 2 0 2 2,3,2
+11601: u 2 0 2 1,3,2
+11601: y 3 0 3 2,2
+11601: x 3 0 3 1,2
+NO CLASH, using fixed ground order
+11602: Facts:
+11602: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+11602: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+11602: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+11602: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+11602: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+11602: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+11602: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+11602: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+11602: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+11602: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+11602: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+11602: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+11602: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+11602: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+11602: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+11602: Goal:
+11602: Id : 1, {_}:
+ associator x y (add u v)
+ =<=
+ add (associator x y u) (associator x y v)
+ [] by prove_linearised_form1
+11602: Order:
+11602: lpo
+11602: Leaf order:
+11602: commutator 1 2 0
+11602: additive_inverse 6 1 0
+11602: multiply 22 2 0
+11602: additive_identity 8 0 0
+11602: associator 4 3 3 0,2
+11602: add 18 2 2 0,3,2
+11602: v 2 0 2 2,3,2
+11602: u 2 0 2 1,3,2
+11602: y 3 0 3 2,2
+11602: x 3 0 3 1,2
+% SZS status Timeout for RNG019-6.p
+NO CLASH, using fixed ground order
+11618: Facts:
+11618: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+11618: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+11618: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+11618: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+11618: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+11618: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+11618: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+11618: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+11618: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+11618: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+11618: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+11618: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+11618: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+11618: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+11618: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+11618: Goal:
+11618: Id : 1, {_}:
+ associator (add u v) x y
+ =<=
+ add (associator u x y) (associator v x y)
+ [] by prove_linearised_form3
+11618: Order:
+11618: nrkbo
+11618: Leaf order:
+11618: commutator 1 2 0
+11618: additive_inverse 6 1 0
+11618: multiply 22 2 0
+11618: additive_identity 8 0 0
+11618: associator 4 3 3 0,2
+11618: y 3 0 3 3,2
+11618: x 3 0 3 2,2
+11618: add 18 2 2 0,1,2
+11618: v 2 0 2 2,1,2
+11618: u 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+11619: Facts:
+11619: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+11619: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+11619: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+11619: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+11619: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+11619: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+11619: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+11619: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+11619: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+11619: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+11619: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+11619: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+11619: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+11619: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+11619: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+11619: Goal:
+11619: Id : 1, {_}:
+ associator (add u v) x y
+ =<=
+ add (associator u x y) (associator v x y)
+ [] by prove_linearised_form3
+11619: Order:
+11619: kbo
+11619: Leaf order:
+11619: commutator 1 2 0
+11619: additive_inverse 6 1 0
+11619: multiply 22 2 0
+11619: additive_identity 8 0 0
+11619: associator 4 3 3 0,2
+11619: y 3 0 3 3,2
+11619: x 3 0 3 2,2
+11619: add 18 2 2 0,1,2
+11619: v 2 0 2 2,1,2
+11619: u 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+11620: Facts:
+11620: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+11620: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+11620: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+11620: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+11620: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+11620: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+11620: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+11620: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+11620: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+11620: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+11620: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+11620: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+11620: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+11620: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+11620: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+11620: Goal:
+11620: Id : 1, {_}:
+ associator (add u v) x y
+ =<=
+ add (associator u x y) (associator v x y)
+ [] by prove_linearised_form3
+11620: Order:
+11620: lpo
+11620: Leaf order:
+11620: commutator 1 2 0
+11620: additive_inverse 6 1 0
+11620: multiply 22 2 0
+11620: additive_identity 8 0 0
+11620: associator 4 3 3 0,2
+11620: y 3 0 3 3,2
+11620: x 3 0 3 2,2
+11620: add 18 2 2 0,1,2
+11620: v 2 0 2 2,1,2
+11620: u 2 0 2 1,1,2
+% SZS status Timeout for RNG021-6.p
+NO CLASH, using fixed ground order
+11722: Facts:
+11722: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+11722: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+11722: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+11722: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+11722: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+11722: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+11722: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+11722: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+11722: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+11722: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+11722: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+11722: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+11722: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+11722: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+11722: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+11722: Goal:
+11722: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
+11722: Order:
+11722: nrkbo
+11722: Leaf order:
+11722: commutator 1 2 0
+11722: additive_inverse 6 1 0
+11722: multiply 22 2 0
+11722: add 16 2 0
+11722: additive_identity 9 0 1 3
+11722: associator 2 3 1 0,2
+11722: y 1 0 1 2,2
+11722: x 2 0 2 1,2
+NO CLASH, using fixed ground order
+11723: Facts:
+11723: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+11723: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+11723: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+11723: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+11723: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+11723: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+11723: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+11723: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+11723: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+11723: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+11723: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+11723: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+11723: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+11723: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+11723: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+11723: Goal:
+11723: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
+11723: Order:
+11723: kbo
+11723: Leaf order:
+11723: commutator 1 2 0
+11723: additive_inverse 6 1 0
+11723: multiply 22 2 0
+11723: add 16 2 0
+11723: additive_identity 9 0 1 3
+11723: associator 2 3 1 0,2
+11723: y 1 0 1 2,2
+11723: x 2 0 2 1,2
+NO CLASH, using fixed ground order
+11724: Facts:
+11724: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+11724: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+11724: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+11724: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+11724: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+11724: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+11724: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+11724: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+11724: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+11724: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+11724: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+11724: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+11724: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+11724: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+11724: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+11724: Goal:
+11724: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
+11724: Order:
+11724: lpo
+11724: Leaf order:
+11724: commutator 1 2 0
+11724: additive_inverse 6 1 0
+11724: multiply 22 2 0
+11724: add 16 2 0
+11724: additive_identity 9 0 1 3
+11724: associator 2 3 1 0,2
+11724: y 1 0 1 2,2
+11724: x 2 0 2 1,2
+% SZS status Timeout for RNG025-6.p
+NO CLASH, using fixed ground order
+11740: Facts:
+11740: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+11740: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+11740: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+11740: Id : 5, {_}: add c c =>= c [] by idempotence
+11740: Goal:
+11740: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+11740: Order:
+11740: nrkbo
+11740: Leaf order:
+11740: c 3 0 0
+11740: add 13 2 3 0,2
+11740: negate 9 1 5 0,1,2
+11740: b 3 0 3 1,2,1,1,2
+11740: a 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+11741: Facts:
+11741: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+11741: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+11741: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+11741: Id : 5, {_}: add c c =>= c [] by idempotence
+11741: Goal:
+11741: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+11741: Order:
+11741: kbo
+11741: Leaf order:
+11741: c 3 0 0
+11741: add 13 2 3 0,2
+11741: negate 9 1 5 0,1,2
+11741: b 3 0 3 1,2,1,1,2
+11741: a 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+11742: Facts:
+11742: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+11742: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+11742: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+11742: Id : 5, {_}: add c c =>= c [] by idempotence
+11742: Goal:
+11742: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+11742: Order:
+11742: lpo
+11742: Leaf order:
+11742: c 3 0 0
+11742: add 13 2 3 0,2
+11742: negate 9 1 5 0,1,2
+11742: b 3 0 3 1,2,1,1,2
+11742: a 2 0 2 1,1,1,2
+% SZS status Timeout for ROB005-1.p
+NO CLASH, using fixed ground order
+11769: Facts:
+11769: Id : 2, {_}:
+ multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
+ =>=
+ multiply ?2 ?3 (multiply ?4 ?5 ?6)
+ [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
+11769: Id : 3, {_}: multiply ?8 ?8 ?9 =>= ?8 [9, 8] by ternary_multiply_2 ?8 ?9
+11769: Id : 4, {_}:
+ multiply (inverse ?11) ?11 ?12 =>= ?12
+ [12, 11] by left_inverse ?11 ?12
+11769: Id : 5, {_}:
+ multiply ?14 ?15 (inverse ?15) =>= ?14
+ [15, 14] by right_inverse ?14 ?15
+11769: Goal:
+11769: Id : 1, {_}: multiply y x x =>= x [] by prove_ternary_multiply_1_independant
+11769: Order:
+11769: nrkbo
+11769: Leaf order:
+11769: inverse 2 1 0
+11769: multiply 9 3 1 0,2
+11769: x 3 0 3 2,2
+11769: y 1 0 1 1,2
+NO CLASH, using fixed ground order
+11770: Facts:
+11770: Id : 2, {_}:
+ multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
+ =>=
+ multiply ?2 ?3 (multiply ?4 ?5 ?6)
+ [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
+11770: Id : 3, {_}: multiply ?8 ?8 ?9 =>= ?8 [9, 8] by ternary_multiply_2 ?8 ?9
+11770: Id : 4, {_}:
+ multiply (inverse ?11) ?11 ?12 =>= ?12
+ [12, 11] by left_inverse ?11 ?12
+11770: Id : 5, {_}:
+ multiply ?14 ?15 (inverse ?15) =>= ?14
+ [15, 14] by right_inverse ?14 ?15
+11770: Goal:
+11770: Id : 1, {_}: multiply y x x =>= x [] by prove_ternary_multiply_1_independant
+11770: Order:
+11770: kbo
+11770: Leaf order:
+11770: inverse 2 1 0
+11770: multiply 9 3 1 0,2
+11770: x 3 0 3 2,2
+11770: y 1 0 1 1,2
+NO CLASH, using fixed ground order
+11771: Facts:
+11771: Id : 2, {_}:
+ multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
+ =>=
+ multiply ?2 ?3 (multiply ?4 ?5 ?6)
+ [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
+11771: Id : 3, {_}: multiply ?8 ?8 ?9 =>= ?8 [9, 8] by ternary_multiply_2 ?8 ?9
+11771: Id : 4, {_}:
+ multiply (inverse ?11) ?11 ?12 =>= ?12
+ [12, 11] by left_inverse ?11 ?12
+11771: Id : 5, {_}:
+ multiply ?14 ?15 (inverse ?15) =>= ?14
+ [15, 14] by right_inverse ?14 ?15
+11771: Goal:
+11771: Id : 1, {_}: multiply y x x =>= x [] by prove_ternary_multiply_1_independant
+11771: Order:
+11771: lpo
+11771: Leaf order:
+11771: inverse 2 1 0
+11771: multiply 9 3 1 0,2
+11771: x 3 0 3 2,2
+11771: y 1 0 1 1,2
+% SZS status Timeout for BOO019-1.p
+CLASH, statistics insufficient
+11791: Facts:
+11791: Id : 2, {_}:
+ add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
+ [4, 3, 2] by l1 ?2 ?3 ?4
+11791: Id : 3, {_}:
+ add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
+ [8, 7, 6] by l3 ?6 ?7 ?8
+11791: Id : 4, {_}:
+ multiply (add ?10 ?11) (add ?10 (inverse ?11)) =>= ?10
+ [11, 10] by b1 ?10 ?11
+11791: Id : 5, {_}:
+ multiply (add (multiply ?13 ?14) ?13) (add ?13 ?14) =>= ?13
+ [14, 13] by majority1 ?13 ?14
+11791: Id : 6, {_}:
+ multiply (add (multiply ?16 ?16) ?17) (add ?16 ?16) =>= ?16
+ [17, 16] by majority2 ?16 ?17
+11791: Id : 7, {_}:
+ multiply (add (multiply ?19 ?20) ?20) (add ?19 ?20) =>= ?20
+ [20, 19] by majority3 ?19 ?20
+11791: Goal:
+11791: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
+11791: Order:
+11791: nrkbo
+11791: Leaf order:
+11791: add 11 2 0
+11791: multiply 11 2 0
+11791: inverse 3 1 2 0,2
+11791: a 2 0 2 1,1,2
+CLASH, statistics insufficient
+11792: Facts:
+11792: Id : 2, {_}:
+ add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
+ [4, 3, 2] by l1 ?2 ?3 ?4
+11792: Id : 3, {_}:
+ add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
+ [8, 7, 6] by l3 ?6 ?7 ?8
+11792: Id : 4, {_}:
+ multiply (add ?10 ?11) (add ?10 (inverse ?11)) =>= ?10
+ [11, 10] by b1 ?10 ?11
+11792: Id : 5, {_}:
+ multiply (add (multiply ?13 ?14) ?13) (add ?13 ?14) =>= ?13
+ [14, 13] by majority1 ?13 ?14
+11792: Id : 6, {_}:
+ multiply (add (multiply ?16 ?16) ?17) (add ?16 ?16) =>= ?16
+ [17, 16] by majority2 ?16 ?17
+11792: Id : 7, {_}:
+ multiply (add (multiply ?19 ?20) ?20) (add ?19 ?20) =>= ?20
+ [20, 19] by majority3 ?19 ?20
+11792: Goal:
+11792: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
+11792: Order:
+11792: kbo
+11792: Leaf order:
+11792: add 11 2 0
+11792: multiply 11 2 0
+11792: inverse 3 1 2 0,2
+11792: a 2 0 2 1,1,2
+CLASH, statistics insufficient
+11793: Facts:
+11793: Id : 2, {_}:
+ add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
+ [4, 3, 2] by l1 ?2 ?3 ?4
+11793: Id : 3, {_}:
+ add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
+ [8, 7, 6] by l3 ?6 ?7 ?8
+11793: Id : 4, {_}:
+ multiply (add ?10 ?11) (add ?10 (inverse ?11)) =>= ?10
+ [11, 10] by b1 ?10 ?11
+11793: Id : 5, {_}:
+ multiply (add (multiply ?13 ?14) ?13) (add ?13 ?14) =>= ?13
+ [14, 13] by majority1 ?13 ?14
+11793: Id : 6, {_}:
+ multiply (add (multiply ?16 ?16) ?17) (add ?16 ?16) =>= ?16
+ [17, 16] by majority2 ?16 ?17
+11793: Id : 7, {_}:
+ multiply (add (multiply ?19 ?20) ?20) (add ?19 ?20) =>= ?20
+ [20, 19] by majority3 ?19 ?20
+11793: Goal:
+11793: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
+11793: Order:
+11793: lpo
+11793: Leaf order:
+11793: add 11 2 0
+11793: multiply 11 2 0
+11793: inverse 3 1 2 0,2
+11793: a 2 0 2 1,1,2
+% SZS status Timeout for BOO030-1.p
+CLASH, statistics insufficient
+11822: Facts:
+11822: Id : 2, {_}:
+ add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
+ [4, 3, 2] by l1 ?2 ?3 ?4
+11822: Id : 3, {_}:
+ add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
+ [8, 7, 6] by l3 ?6 ?7 ?8
+11822: Id : 4, {_}:
+ multiply (add ?10 (inverse ?10)) ?11 =>= ?11
+ [11, 10] by property3 ?10 ?11
+11822: Id : 5, {_}:
+ multiply ?13 (add ?14 (add ?13 ?15)) =>= ?13
+ [15, 14, 13] by l2 ?13 ?14 ?15
+11822: Id : 6, {_}:
+ multiply (multiply (add ?17 ?18) (add ?18 ?19)) ?18 =>= ?18
+ [19, 18, 17] by l4 ?17 ?18 ?19
+11822: Id : 7, {_}:
+ add (multiply ?21 (inverse ?21)) ?22 =>= ?22
+ [22, 21] by property3_dual ?21 ?22
+11822: Id : 8, {_}:
+ add (multiply (add ?24 ?25) ?24) (multiply ?24 ?25) =>= ?24
+ [25, 24] by majority1 ?24 ?25
+11822: Id : 9, {_}:
+ add (multiply (add ?27 ?27) ?28) (multiply ?27 ?27) =>= ?27
+ [28, 27] by majority2 ?27 ?28
+11822: Id : 10, {_}:
+ add (multiply (add ?30 ?31) ?31) (multiply ?30 ?31) =>= ?31
+ [31, 30] by majority3 ?30 ?31
+11822: Id : 11, {_}:
+ multiply (add (multiply ?33 ?34) ?33) (add ?33 ?34) =>= ?33
+ [34, 33] by majority1_dual ?33 ?34
+11822: Id : 12, {_}:
+ multiply (add (multiply ?36 ?36) ?37) (add ?36 ?36) =>= ?36
+ [37, 36] by majority2_dual ?36 ?37
+11822: Id : 13, {_}:
+ multiply (add (multiply ?39 ?40) ?40) (add ?39 ?40) =>= ?40
+ [40, 39] by majority3_dual ?39 ?40
+11822: Goal:
+11822: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
+11822: Order:
+11822: lpo
+11822: Leaf order:
+11822: add 21 2 0
+11822: multiply 21 2 0
+11822: inverse 4 1 2 0,2
+11822: a 2 0 2 1,1,2
+CLASH, statistics insufficient
+11821: Facts:
+11821: Id : 2, {_}:
+ add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
+ [4, 3, 2] by l1 ?2 ?3 ?4
+11821: Id : 3, {_}:
+ add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
+ [8, 7, 6] by l3 ?6 ?7 ?8
+11821: Id : 4, {_}:
+ multiply (add ?10 (inverse ?10)) ?11 =>= ?11
+ [11, 10] by property3 ?10 ?11
+11821: Id : 5, {_}:
+ multiply ?13 (add ?14 (add ?13 ?15)) =>= ?13
+ [15, 14, 13] by l2 ?13 ?14 ?15
+11821: Id : 6, {_}:
+ multiply (multiply (add ?17 ?18) (add ?18 ?19)) ?18 =>= ?18
+ [19, 18, 17] by l4 ?17 ?18 ?19
+11821: Id : 7, {_}:
+ add (multiply ?21 (inverse ?21)) ?22 =>= ?22
+ [22, 21] by property3_dual ?21 ?22
+11821: Id : 8, {_}:
+ add (multiply (add ?24 ?25) ?24) (multiply ?24 ?25) =>= ?24
+ [25, 24] by majority1 ?24 ?25
+11821: Id : 9, {_}:
+ add (multiply (add ?27 ?27) ?28) (multiply ?27 ?27) =>= ?27
+ [28, 27] by majority2 ?27 ?28
+11821: Id : 10, {_}:
+ add (multiply (add ?30 ?31) ?31) (multiply ?30 ?31) =>= ?31
+ [31, 30] by majority3 ?30 ?31
+11821: Id : 11, {_}:
+ multiply (add (multiply ?33 ?34) ?33) (add ?33 ?34) =>= ?33
+ [34, 33] by majority1_dual ?33 ?34
+11821: Id : 12, {_}:
+ multiply (add (multiply ?36 ?36) ?37) (add ?36 ?36) =>= ?36
+ [37, 36] by majority2_dual ?36 ?37
+11821: Id : 13, {_}:
+ multiply (add (multiply ?39 ?40) ?40) (add ?39 ?40) =>= ?40
+ [40, 39] by majority3_dual ?39 ?40
+11821: Goal:
+11821: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
+11821: Order:
+11821: kbo
+11821: Leaf order:
+11821: add 21 2 0
+11821: multiply 21 2 0
+11821: inverse 4 1 2 0,2
+11821: a 2 0 2 1,1,2
+CLASH, statistics insufficient
+11820: Facts:
+11820: Id : 2, {_}:
+ add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
+ [4, 3, 2] by l1 ?2 ?3 ?4
+11820: Id : 3, {_}:
+ add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
+ [8, 7, 6] by l3 ?6 ?7 ?8
+11820: Id : 4, {_}:
+ multiply (add ?10 (inverse ?10)) ?11 =>= ?11
+ [11, 10] by property3 ?10 ?11
+11820: Id : 5, {_}:
+ multiply ?13 (add ?14 (add ?13 ?15)) =>= ?13
+ [15, 14, 13] by l2 ?13 ?14 ?15
+11820: Id : 6, {_}:
+ multiply (multiply (add ?17 ?18) (add ?18 ?19)) ?18 =>= ?18
+ [19, 18, 17] by l4 ?17 ?18 ?19
+11820: Id : 7, {_}:
+ add (multiply ?21 (inverse ?21)) ?22 =>= ?22
+ [22, 21] by property3_dual ?21 ?22
+11820: Id : 8, {_}:
+ add (multiply (add ?24 ?25) ?24) (multiply ?24 ?25) =>= ?24
+ [25, 24] by majority1 ?24 ?25
+11820: Id : 9, {_}:
+ add (multiply (add ?27 ?27) ?28) (multiply ?27 ?27) =>= ?27
+ [28, 27] by majority2 ?27 ?28
+11820: Id : 10, {_}:
+ add (multiply (add ?30 ?31) ?31) (multiply ?30 ?31) =>= ?31
+ [31, 30] by majority3 ?30 ?31
+11820: Id : 11, {_}:
+ multiply (add (multiply ?33 ?34) ?33) (add ?33 ?34) =>= ?33
+ [34, 33] by majority1_dual ?33 ?34
+11820: Id : 12, {_}:
+ multiply (add (multiply ?36 ?36) ?37) (add ?36 ?36) =>= ?36
+ [37, 36] by majority2_dual ?36 ?37
+11820: Id : 13, {_}:
+ multiply (add (multiply ?39 ?40) ?40) (add ?39 ?40) =>= ?40
+ [40, 39] by majority3_dual ?39 ?40
+11820: Goal:
+11820: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
+11820: Order:
+11820: nrkbo
+11820: Leaf order:
+11820: add 21 2 0
+11820: multiply 21 2 0
+11820: inverse 4 1 2 0,2
+11820: a 2 0 2 1,1,2
+% SZS status Timeout for BOO032-1.p
+NO CLASH, using fixed ground order
+11838: Facts:
+11838: Id : 2, {_}:
+ add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
+ =<=
+ multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
+ [4, 3, 2] by distributivity ?2 ?3 ?4
+11838: Id : 3, {_}:
+ add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
+ [8, 7, 6] by l1 ?6 ?7 ?8
+11838: Id : 4, {_}:
+ add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
+ [12, 11, 10] by l3 ?10 ?11 ?12
+11838: Id : 5, {_}:
+ multiply (add ?14 (inverse ?14)) ?15 =>= ?15
+ [15, 14] by property3 ?14 ?15
+11838: Id : 6, {_}:
+ multiply (add (multiply ?17 ?18) ?17) (add ?17 ?18) =>= ?17
+ [18, 17] by majority1 ?17 ?18
+11838: Id : 7, {_}:
+ multiply (add (multiply ?20 ?20) ?21) (add ?20 ?20) =>= ?20
+ [21, 20] by majority2 ?20 ?21
+11838: Id : 8, {_}:
+ multiply (add (multiply ?23 ?24) ?24) (add ?23 ?24) =>= ?24
+ [24, 23] by majority3 ?23 ?24
+11838: Goal:
+11838: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
+11838: Order:
+11838: nrkbo
+11838: Leaf order:
+11838: add 15 2 0 multiply
+11838: multiply 16 2 0 add
+11838: inverse 3 1 2 0,2
+11838: a 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+11839: Facts:
+11839: Id : 2, {_}:
+ add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
+ =<=
+ multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
+ [4, 3, 2] by distributivity ?2 ?3 ?4
+11839: Id : 3, {_}:
+ add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
+ [8, 7, 6] by l1 ?6 ?7 ?8
+11839: Id : 4, {_}:
+ add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
+ [12, 11, 10] by l3 ?10 ?11 ?12
+11839: Id : 5, {_}:
+ multiply (add ?14 (inverse ?14)) ?15 =>= ?15
+ [15, 14] by property3 ?14 ?15
+11839: Id : 6, {_}:
+ multiply (add (multiply ?17 ?18) ?17) (add ?17 ?18) =>= ?17
+ [18, 17] by majority1 ?17 ?18
+11839: Id : 7, {_}:
+ multiply (add (multiply ?20 ?20) ?21) (add ?20 ?20) =>= ?20
+ [21, 20] by majority2 ?20 ?21
+11839: Id : 8, {_}:
+ multiply (add (multiply ?23 ?24) ?24) (add ?23 ?24) =>= ?24
+ [24, 23] by majority3 ?23 ?24
+11839: Goal:
+11839: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
+11839: Order:
+11839: kbo
+11839: Leaf order:
+11839: add 15 2 0 multiply
+11839: multiply 16 2 0 add
+11839: inverse 3 1 2 0,2
+11839: a 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+11840: Facts:
+11840: Id : 2, {_}:
+ add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
+ =<=
+ multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
+ [4, 3, 2] by distributivity ?2 ?3 ?4
+11840: Id : 3, {_}:
+ add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
+ [8, 7, 6] by l1 ?6 ?7 ?8
+11840: Id : 4, {_}:
+ add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
+ [12, 11, 10] by l3 ?10 ?11 ?12
+11840: Id : 5, {_}:
+ multiply (add ?14 (inverse ?14)) ?15 =>= ?15
+ [15, 14] by property3 ?14 ?15
+11840: Id : 6, {_}:
+ multiply (add (multiply ?17 ?18) ?17) (add ?17 ?18) =>= ?17
+ [18, 17] by majority1 ?17 ?18
+11840: Id : 7, {_}:
+ multiply (add (multiply ?20 ?20) ?21) (add ?20 ?20) =>= ?20
+ [21, 20] by majority2 ?20 ?21
+11840: Id : 8, {_}:
+ multiply (add (multiply ?23 ?24) ?24) (add ?23 ?24) =>= ?24
+ [24, 23] by majority3 ?23 ?24
+11840: Goal:
+11840: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
+11840: Order:
+11840: lpo
+11840: Leaf order:
+11840: add 15 2 0 multiply
+11840: multiply 16 2 0 add
+11840: inverse 3 1 2 0,2
+11840: a 2 0 2 1,1,2
+% SZS status Timeout for BOO033-1.p
+NO CLASH, using fixed ground order
+11868: Facts:
+11868: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+11868: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+11868: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply (apply b (apply w w))
+ (apply (apply b (apply b w)) (apply (apply b b) b))
+ [] by strong_fixed_point
+11868: Goal:
+11868: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+11868: Order:
+11868: nrkbo
+11868: Leaf order:
+11868: w 4 0 0
+11868: b 7 0 0
+11868: apply 20 2 3 0,2
+11868: fixed_pt 3 0 3 2,2
+11868: strong_fixed_point 3 0 2 1,2
+NO CLASH, using fixed ground order
+11869: Facts:
+11869: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+11869: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+11869: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply (apply b (apply w w))
+ (apply (apply b (apply b w)) (apply (apply b b) b))
+ [] by strong_fixed_point
+11869: Goal:
+11869: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+11869: Order:
+11869: kbo
+11869: Leaf order:
+11869: w 4 0 0
+11869: b 7 0 0
+11869: apply 20 2 3 0,2
+11869: fixed_pt 3 0 3 2,2
+11869: strong_fixed_point 3 0 2 1,2
+NO CLASH, using fixed ground order
+11870: Facts:
+11870: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+11870: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+11870: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply (apply b (apply w w))
+ (apply (apply b (apply b w)) (apply (apply b b) b))
+ [] by strong_fixed_point
+11870: Goal:
+11870: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+11870: Order:
+11870: lpo
+11870: Leaf order:
+11870: w 4 0 0
+11870: b 7 0 0
+11870: apply 20 2 3 0,2
+11870: fixed_pt 3 0 3 2,2
+11870: strong_fixed_point 3 0 2 1,2
+% SZS status Timeout for COL003-20.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+11889: Facts:
+11889: Id : 2, {_}:
+ apply (apply (apply s ?2) ?3) ?4
+ =?=
+ apply (apply ?2 ?4) (apply ?3 ?4)
+ [4, 3, 2] by s_definition ?2 ?3 ?4
+11889: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+11889: Goal:
+11889: Id : 1, {_}:
+ apply
+ (apply
+ (apply (apply s (apply k (apply s (apply (apply s k) k))))
+ (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))
+ x) y
+ =>=
+ apply y (apply (apply x x) y)
+ [] by prove_u_combinator
+11889: Order:
+11889: kbo
+11889: Leaf order:
+11889: y 3 0 3 2,2
+11889: x 3 0 3 2,1,2
+11889: apply 25 2 17 0,2
+11889: k 8 0 7 1,2,1,1,1,2
+11889: s 7 0 6 1,1,1,1,2
+11888: Facts:
+11888: Id : 2, {_}:
+ apply (apply (apply s ?2) ?3) ?4
+ =?=
+ apply (apply ?2 ?4) (apply ?3 ?4)
+ [4, 3, 2] by s_definition ?2 ?3 ?4
+11888: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+11888: Goal:
+11888: Id : 1, {_}:
+ apply
+ (apply
+ (apply (apply s (apply k (apply s (apply (apply s k) k))))
+ (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))
+ x) y
+ =>=
+ apply y (apply (apply x x) y)
+ [] by prove_u_combinator
+11888: Order:
+11888: nrkbo
+11888: Leaf order:
+11888: y 3 0 3 2,2
+11888: x 3 0 3 2,1,2
+11888: apply 25 2 17 0,2
+11888: k 8 0 7 1,2,1,1,1,2
+11888: s 7 0 6 1,1,1,1,2
+NO CLASH, using fixed ground order
+11890: Facts:
+11890: Id : 2, {_}:
+ apply (apply (apply s ?2) ?3) ?4
+ =?=
+ apply (apply ?2 ?4) (apply ?3 ?4)
+ [4, 3, 2] by s_definition ?2 ?3 ?4
+11890: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+11890: Goal:
+11890: Id : 1, {_}:
+ apply
+ (apply
+ (apply (apply s (apply k (apply s (apply (apply s k) k))))
+ (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))
+ x) y
+ =>=
+ apply y (apply (apply x x) y)
+ [] by prove_u_combinator
+11890: Order:
+11890: lpo
+11890: Leaf order:
+11890: y 3 0 3 2,2
+11890: x 3 0 3 2,1,2
+11890: apply 25 2 17 0,2
+11890: k 8 0 7 1,2,1,1,1,2
+11890: s 7 0 6 1,1,1,1,2
+Statistics :
+Max weight : 29
+Found proof, 0.014068s
+% SZS status Unsatisfiable for COL004-3.p
+% SZS output start CNFRefutation for COL004-3.p
+Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+Id : 2, {_}: apply (apply (apply s ?2) ?3) ?4 =?= apply (apply ?2 ?4) (apply ?3 ?4) [4, 3, 2] by s_definition ?2 ?3 ?4
+Id : 35, {_}: apply y (apply (apply x x) y) === apply y (apply (apply x x) y) [] by Demod 34 with 3 at 1,2
+Id : 34, {_}: apply (apply (apply k y) (apply k y)) (apply (apply x x) y) =>= apply y (apply (apply x x) y) [] by Demod 33 with 2 at 1,2
+Id : 33, {_}: apply (apply (apply (apply s k) k) y) (apply (apply x x) y) =>= apply y (apply (apply x x) y) [] by Demod 32 with 2 at 2
+Id : 32, {_}: apply (apply (apply s (apply (apply s k) k)) (apply x x)) y =>= apply y (apply (apply x x) y) [] by Demod 31 with 3 at 2,2,1,2
+Id : 31, {_}: apply (apply (apply s (apply (apply s k) k)) (apply x (apply (apply k x) (apply k x)))) y =>= apply y (apply (apply x x) y) [] by Demod 30 with 3 at 1,2,1,2
+Id : 30, {_}: apply (apply (apply s (apply (apply s k) k)) (apply (apply (apply k x) (apply k x)) (apply (apply k x) (apply k x)))) y =>= apply y (apply (apply x x) y) [] by Demod 20 with 3 at 1,1,2
+Id : 20, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply k x) (apply k x)) (apply (apply k x) (apply k x)))) y =>= apply y (apply (apply x x) y) [] by Demod 19 with 2 at 2,2,1,2
+Id : 19, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply k x) (apply k x)) (apply (apply (apply s k) k) x))) y =>= apply y (apply (apply x x) y) [] by Demod 18 with 2 at 1,2,1,2
+Id : 18, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply (apply s k) k) x) (apply (apply (apply s k) k) x))) y =>= apply y (apply (apply x x) y) [] by Demod 17 with 2 at 2,1,2
+Id : 17, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)) x)) y =>= apply y (apply (apply x x) y) [] by Demod 1 with 2 at 1,2
+Id : 1, {_}: apply (apply (apply (apply s (apply k (apply s (apply (apply s k) k)))) (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))) x) y =>= apply y (apply (apply x x) y) [] by prove_u_combinator
+% SZS output end CNFRefutation for COL004-3.p
+11890: solved COL004-3.p in 0.020001 using lpo
+11890: status Unsatisfiable for COL004-3.p
+CLASH, statistics insufficient
+11895: Facts:
+11895: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+11895: Id : 3, {_}:
+ apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
+ [8, 7] by w_definition ?7 ?8
+11895: Goal:
+11895: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_model ?1
+11895: Order:
+11895: nrkbo
+11895: Leaf order:
+11895: w 1 0 0
+11895: s 1 0 0
+11895: apply 11 2 1 0,3
+11895: combinator 1 0 1 1,3
+CLASH, statistics insufficient
+11896: Facts:
+11896: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+11896: Id : 3, {_}:
+ apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
+ [8, 7] by w_definition ?7 ?8
+11896: Goal:
+11896: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_model ?1
+11896: Order:
+11896: kbo
+11896: Leaf order:
+11896: w 1 0 0
+11896: s 1 0 0
+11896: apply 11 2 1 0,3
+11896: combinator 1 0 1 1,3
+CLASH, statistics insufficient
+11897: Facts:
+11897: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+11897: Id : 3, {_}:
+ apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
+ [8, 7] by w_definition ?7 ?8
+11897: Goal:
+11897: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_model ?1
+11897: Order:
+11897: lpo
+11897: Leaf order:
+11897: w 1 0 0
+11897: s 1 0 0
+11897: apply 11 2 1 0,3
+11897: combinator 1 0 1 1,3
+% SZS status Timeout for COL005-1.p
+CLASH, statistics insufficient
+11929: Facts:
+11929: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+11929: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
+11929: Id : 4, {_}:
+ apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10
+ [11, 10, 9] by v_definition ?9 ?10 ?11
+11929: Goal:
+11929: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+11929: Order:
+11929: nrkbo
+11929: Leaf order:
+11929: v 1 0 0
+11929: m 1 0 0
+11929: b 1 0 0
+11929: apply 15 2 3 0,2
+11929: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+11930: Facts:
+11930: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+11930: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
+11930: Id : 4, {_}:
+ apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10
+ [11, 10, 9] by v_definition ?9 ?10 ?11
+11930: Goal:
+11930: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+11930: Order:
+11930: kbo
+11930: Leaf order:
+11930: v 1 0 0
+11930: m 1 0 0
+11930: b 1 0 0
+11930: apply 15 2 3 0,2
+11930: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+11931: Facts:
+11931: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+11931: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
+11931: Id : 4, {_}:
+ apply (apply (apply v ?9) ?10) ?11 =?= apply (apply ?11 ?9) ?10
+ [11, 10, 9] by v_definition ?9 ?10 ?11
+11931: Goal:
+11931: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+11931: Order:
+11931: lpo
+11931: Leaf order:
+11931: v 1 0 0
+11931: m 1 0 0
+11931: b 1 0 0
+11931: apply 15 2 3 0,2
+11931: f 3 1 3 0,2,2
+Goal subsumed
+Statistics :
+Max weight : 78
+Found proof, 6.233757s
+% SZS status Unsatisfiable for COL038-1.p
+% SZS output start CNFRefutation for COL038-1.p
+Id : 4, {_}: apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10 [11, 10, 9] by v_definition ?9 ?10 ?11
+Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
+Id : 19, {_}: apply (apply (apply v ?47) ?48) ?49 =>= apply (apply ?49 ?47) ?48 [49, 48, 47] by v_definition ?47 ?48 ?49
+Id : 5, {_}: apply (apply (apply b ?13) ?14) ?15 =>= apply ?13 (apply ?14 ?15) [15, 14, 13] by b_definition ?13 ?14 ?15
+Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
+Id : 6, {_}: apply ?17 (apply ?18 ?19) =?= apply ?17 (apply ?18 ?19) [19, 18, 17] by Super 5 with 2 at 2
+Id : 1244, {_}: apply (apply m (apply v ?1596)) ?1597 =?= apply (apply ?1597 ?1596) (apply v ?1596) [1597, 1596] by Super 19 with 3 at 1,2
+Id : 18, {_}: apply m (apply (apply v ?44) ?45) =<= apply (apply (apply (apply v ?44) ?45) ?44) ?45 [45, 44] by Super 3 with 4 at 3
+Id : 224, {_}: apply m (apply (apply v ?485) ?486) =<= apply (apply (apply ?485 ?485) ?486) ?486 [486, 485] by Demod 18 with 4 at 1,3
+Id : 232, {_}: apply m (apply (apply v ?509) ?510) =<= apply (apply (apply m ?509) ?510) ?510 [510, 509] by Super 224 with 3 at 1,1,3
+Id : 7751, {_}: apply (apply m (apply v ?7787)) (apply (apply m ?7788) ?7787) =<= apply (apply m (apply (apply v ?7788) ?7787)) (apply v ?7787) [7788, 7787] by Super 1244 with 232 at 1,3
+Id : 9, {_}: apply (apply (apply m b) ?24) ?25 =>= apply b (apply ?24 ?25) [25, 24] by Super 2 with 3 at 1,1,2
+Id : 236, {_}: apply m (apply (apply v (apply v ?521)) ?522) =<= apply (apply (apply ?522 ?521) (apply v ?521)) ?522 [522, 521] by Super 224 with 4 at 1,3
+Id : 2866, {_}: apply m (apply (apply v (apply v b)) m) =>= apply b (apply (apply v b) m) [] by Super 9 with 236 at 2
+Id : 7790, {_}: apply (apply m (apply v m)) (apply (apply m (apply v b)) m) =>= apply (apply b (apply (apply v b) m)) (apply v m) [] by Super 7751 with 2866 at 1,3
+Id : 20, {_}: apply (apply m (apply v ?51)) ?52 =?= apply (apply ?52 ?51) (apply v ?51) [52, 51] by Super 19 with 3 at 1,2
+Id : 7860, {_}: apply (apply m (apply v m)) (apply (apply m b) (apply v b)) =>= apply (apply b (apply (apply v b) m)) (apply v m) [] by Demod 7790 with 20 at 2,2
+Id : 11, {_}: apply m (apply (apply b ?30) ?31) =<= apply ?30 (apply ?31 (apply (apply b ?30) ?31)) [31, 30] by Super 2 with 3 at 2
+Id : 9568, {_}: apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b)) (apply m (apply (apply b (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b))) m)) =?= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b)) (apply m (apply (apply b (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b))) m)) [] by Super 9567 with 11 at 2
+Id : 9567, {_}: apply m (apply (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) m) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply m (apply (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) m)) [8771] by Demod 9566 with 2 at 2,3
+Id : 9566, {_}: apply m (apply (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) m) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m) [8771] by Demod 9565 with 2 at 2
+Id : 9565, {_}: apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m) [8771] by Demod 9564 with 4 at 1,2,3
+Id : 9564, {_}: apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m) [8771] by Demod 9563 with 4 at 1,2
+Id : 9563, {_}: apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m) [8771] by Demod 9562 with 4 at 2,3
+Id : 9562, {_}: apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))))) [8771] by Demod 9561 with 4 at 2
+Id : 9561, {_}: apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))))) [8771] by Demod 9560 with 2 at 2,3
+Id : 9560, {_}: apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9559 with 2 at 2
+Id : 9559, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9558 with 7860 at 1,2,3
+Id : 9558, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9557 with 7860 at 2,1,1,1,3
+Id : 9557, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) =<= apply (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9556 with 7860 at 2,1,1,2,2,2
+Id : 9556, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771))) =<= apply (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9078 with 7860 at 1,2
+Id : 9078, {_}: apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771))) =<= apply (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Super 174 with 7860 at 2,1,1,2,2,2,3
+Id : 174, {_}: apply (apply ?379 ?380) (apply ?381 (f (apply (apply b (apply ?379 ?380)) ?381))) =<= apply (f (apply (apply b (apply ?379 ?380)) ?381)) (apply (apply ?379 ?380) (apply ?381 (f (apply (apply b (apply ?379 ?380)) ?381)))) [381, 380, 379] by Super 8 with 6 at 1,1,2,2,2,3
+Id : 8, {_}: apply ?21 (apply ?22 (f (apply (apply b ?21) ?22))) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Demod 7 with 2 at 2
+Id : 7, {_}: apply (apply (apply b ?21) ?22) (f (apply (apply b ?21) ?22)) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Super 1 with 2 at 2,3
+Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1
+% SZS output end CNFRefutation for COL038-1.p
+11930: solved COL038-1.p in 3.116194 using kbo
+11930: status Unsatisfiable for COL038-1.p
+CLASH, statistics insufficient
+11936: Facts:
+11936: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+11936: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+11936: Id : 4, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11
+11936: Goal:
+11936: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+11936: Order:
+11936: nrkbo
+11936: Leaf order:
+11936: m 1 0 0
+11936: b 1 0 0
+11936: s 1 0 0
+11936: apply 16 2 3 0,2
+11936: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+11937: Facts:
+11937: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+11937: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+11937: Id : 4, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11
+11937: Goal:
+11937: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+11937: Order:
+11937: kbo
+11937: Leaf order:
+11937: m 1 0 0
+11937: b 1 0 0
+11937: s 1 0 0
+11937: apply 16 2 3 0,2
+11937: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+11938: Facts:
+11938: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+11938: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+11938: Id : 4, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11
+11938: Goal:
+11938: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+11938: Order:
+11938: lpo
+11938: Leaf order:
+11938: m 1 0 0
+11938: b 1 0 0
+11938: s 1 0 0
+11938: apply 16 2 3 0,2
+11938: f 3 1 3 0,2,2
+% SZS status Timeout for COL046-1.p
+CLASH, statistics insufficient
+11954: Facts:
+11954: Id : 2, {_}:
+ apply (apply l ?3) ?4 =?= apply ?3 (apply ?4 ?4)
+ [4, 3] by l_definition ?3 ?4
+11954: Id : 3, {_}:
+ apply (apply (apply q ?6) ?7) ?8 =>= apply ?7 (apply ?6 ?8)
+ [8, 7, 6] by q_definition ?6 ?7 ?8
+11954: Goal:
+11954: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_model ?1
+11954: Order:
+11954: nrkbo
+11954: Leaf order:
+11954: q 1 0 0
+11954: l 1 0 0
+11954: apply 12 2 3 0,2
+11954: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+11955: Facts:
+11955: Id : 2, {_}:
+ apply (apply l ?3) ?4 =?= apply ?3 (apply ?4 ?4)
+ [4, 3] by l_definition ?3 ?4
+11955: Id : 3, {_}:
+ apply (apply (apply q ?6) ?7) ?8 =>= apply ?7 (apply ?6 ?8)
+ [8, 7, 6] by q_definition ?6 ?7 ?8
+11955: Goal:
+11955: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_model ?1
+11955: Order:
+11955: kbo
+11955: Leaf order:
+11955: q 1 0 0
+11955: l 1 0 0
+11955: apply 12 2 3 0,2
+11955: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+11956: Facts:
+11956: Id : 2, {_}:
+ apply (apply l ?3) ?4 =?= apply ?3 (apply ?4 ?4)
+ [4, 3] by l_definition ?3 ?4
+11956: Id : 3, {_}:
+ apply (apply (apply q ?6) ?7) ?8 =>= apply ?7 (apply ?6 ?8)
+ [8, 7, 6] by q_definition ?6 ?7 ?8
+11956: Goal:
+11956: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_model ?1
+11956: Order:
+11956: lpo
+11956: Leaf order:
+11956: q 1 0 0
+11956: l 1 0 0
+11956: apply 12 2 3 0,2
+11956: f 3 1 3 0,2,2
+% SZS status Timeout for COL047-1.p
+CLASH, statistics insufficient
+11983: Facts:
+11983: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+11983: Id : 3, {_}:
+ apply (apply t ?7) ?8 =>= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+11983: Goal:
+11983: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (g ?1) (apply (f ?1) (h ?1))
+ [1] by prove_q_combinator ?1
+11983: Order:
+11983: nrkbo
+11983: Leaf order:
+11983: t 1 0 0
+11983: b 1 0 0
+11983: h 2 1 2 0,2,2
+11983: g 2 1 2 0,2,1,2
+11983: apply 13 2 5 0,2
+11983: f 2 1 2 0,2,1,1,2
+CLASH, statistics insufficient
+11984: Facts:
+11984: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+11984: Id : 3, {_}:
+ apply (apply t ?7) ?8 =>= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+11984: Goal:
+11984: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (g ?1) (apply (f ?1) (h ?1))
+ [1] by prove_q_combinator ?1
+11984: Order:
+11984: kbo
+11984: Leaf order:
+11984: t 1 0 0
+11984: b 1 0 0
+11984: h 2 1 2 0,2,2
+11984: g 2 1 2 0,2,1,2
+11984: apply 13 2 5 0,2
+11984: f 2 1 2 0,2,1,1,2
+CLASH, statistics insufficient
+11985: Facts:
+11985: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+11985: Id : 3, {_}:
+ apply (apply t ?7) ?8 =?= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+11985: Goal:
+11985: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (g ?1) (apply (f ?1) (h ?1))
+ [1] by prove_q_combinator ?1
+11985: Order:
+11985: lpo
+11985: Leaf order:
+11985: t 1 0 0
+11985: b 1 0 0
+11985: h 2 1 2 0,2,2
+11985: g 2 1 2 0,2,1,2
+11985: apply 13 2 5 0,2
+11985: f 2 1 2 0,2,1,1,2
+Goal subsumed
+Statistics :
+Max weight : 76
+Found proof, 1.436300s
+% SZS status Unsatisfiable for COL060-1.p
+% SZS output start CNFRefutation for COL060-1.p
+Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
+Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
+Id : 447, {_}: apply (g (apply (apply b (apply t b)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t b)) (apply (apply b b) t))) (h (apply (apply b (apply t b)) (apply (apply b b) t)))) === apply (g (apply (apply b (apply t b)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t b)) (apply (apply b b) t))) (h (apply (apply b (apply t b)) (apply (apply b b) t)))) [] by Super 445 with 2 at 2
+Id : 445, {_}: apply (apply (apply ?1404 (g (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (f (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t))) =>= apply (g (apply (apply b (apply t ?1404)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t ?1404)) (apply (apply b b) t))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) [1404] by Super 277 with 3 at 1,2
+Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (apply (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) [901, 900] by Super 29 with 2 at 1,2
+Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (apply (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) [87, 86, 85] by Super 13 with 3 at 1,1,2
+Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (g (apply (apply b ?33) (apply (apply b ?34) ?35))) (apply (f (apply (apply b ?33) (apply (apply b ?34) ?35))) (h (apply (apply b ?33) (apply (apply b ?34) ?35)))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
+Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (g (apply (apply b ?18) ?19)) (apply (f (apply (apply b ?18) ?19)) (h (apply (apply b ?18) ?19))) [19, 18] by Super 1 with 2 at 1,1,2
+Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (g ?1) (apply (f ?1) (h ?1)) [1] by prove_q_combinator ?1
+% SZS output end CNFRefutation for COL060-1.p
+11983: solved COL060-1.p in 0.376023 using nrkbo
+11983: status Unsatisfiable for COL060-1.p
+CLASH, statistics insufficient
+11990: Facts:
+11990: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+11990: Id : 3, {_}:
+ apply (apply t ?7) ?8 =>= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+11990: Goal:
+11990: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (f ?1) (apply (h ?1) (g ?1))
+ [1] by prove_q1_combinator ?1
+11990: Order:
+11990: nrkbo
+11990: Leaf order:
+11990: t 1 0 0
+11990: b 1 0 0
+11990: h 2 1 2 0,2,2
+11990: g 2 1 2 0,2,1,2
+11990: apply 13 2 5 0,2
+11990: f 2 1 2 0,2,1,1,2
+CLASH, statistics insufficient
+11991: Facts:
+11991: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+11991: Id : 3, {_}:
+ apply (apply t ?7) ?8 =>= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+11991: Goal:
+11991: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (f ?1) (apply (h ?1) (g ?1))
+ [1] by prove_q1_combinator ?1
+11991: Order:
+11991: kbo
+11991: Leaf order:
+11991: t 1 0 0
+11991: b 1 0 0
+11991: h 2 1 2 0,2,2
+11991: g 2 1 2 0,2,1,2
+11991: apply 13 2 5 0,2
+11991: f 2 1 2 0,2,1,1,2
+CLASH, statistics insufficient
+11992: Facts:
+11992: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+11992: Id : 3, {_}:
+ apply (apply t ?7) ?8 =?= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+11992: Goal:
+11992: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (f ?1) (apply (h ?1) (g ?1))
+ [1] by prove_q1_combinator ?1
+11992: Order:
+11992: lpo
+11992: Leaf order:
+11992: t 1 0 0
+11992: b 1 0 0
+11992: h 2 1 2 0,2,2
+11992: g 2 1 2 0,2,1,2
+11992: apply 13 2 5 0,2
+11992: f 2 1 2 0,2,1,1,2
+Goal subsumed
+Statistics :
+Max weight : 76
+Found proof, 2.573692s
+% SZS status Unsatisfiable for COL061-1.p
+% SZS output start CNFRefutation for COL061-1.p
+Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
+Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
+Id : 447, {_}: apply (f (apply (apply b (apply t t)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) b))) (g (apply (apply b (apply t t)) (apply (apply b b) b)))) === apply (f (apply (apply b (apply t t)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) b))) (g (apply (apply b (apply t t)) (apply (apply b b) b)))) [] by Super 446 with 3 at 2,2
+Id : 446, {_}: apply (f (apply (apply b (apply t ?1406)) (apply (apply b b) b))) (apply (apply ?1406 (g (apply (apply b (apply t ?1406)) (apply (apply b b) b)))) (h (apply (apply b (apply t ?1406)) (apply (apply b b) b)))) =>= apply (f (apply (apply b (apply t ?1406)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t ?1406)) (apply (apply b b) b))) (g (apply (apply b (apply t ?1406)) (apply (apply b b) b)))) [1406] by Super 277 with 2 at 2
+Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (apply (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) [901, 900] by Super 29 with 2 at 1,2
+Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (apply (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) [87, 86, 85] by Super 13 with 3 at 1,1,2
+Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (f (apply (apply b ?33) (apply (apply b ?34) ?35))) (apply (h (apply (apply b ?33) (apply (apply b ?34) ?35))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
+Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (f (apply (apply b ?18) ?19)) (apply (h (apply (apply b ?18) ?19)) (g (apply (apply b ?18) ?19))) [19, 18] by Super 1 with 2 at 1,1,2
+Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (f ?1) (apply (h ?1) (g ?1)) [1] by prove_q1_combinator ?1
+% SZS output end CNFRefutation for COL061-1.p
+11990: solved COL061-1.p in 0.344021 using nrkbo
+11990: status Unsatisfiable for COL061-1.p
+CLASH, statistics insufficient
+11997: Facts:
+11997: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+11997: Id : 3, {_}:
+ apply (apply t ?7) ?8 =>= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+11997: Goal:
+11997: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (apply (f ?1) (h ?1)) (g ?1)
+ [1] by prove_c_combinator ?1
+11997: Order:
+11997: nrkbo
+11997: Leaf order:
+11997: t 1 0 0
+11997: b 1 0 0
+11997: h 2 1 2 0,2,2
+11997: g 2 1 2 0,2,1,2
+11997: apply 13 2 5 0,2
+11997: f 2 1 2 0,2,1,1,2
+CLASH, statistics insufficient
+11998: Facts:
+11998: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+11998: Id : 3, {_}:
+ apply (apply t ?7) ?8 =>= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+11998: Goal:
+11998: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (apply (f ?1) (h ?1)) (g ?1)
+ [1] by prove_c_combinator ?1
+11998: Order:
+11998: kbo
+11998: Leaf order:
+11998: t 1 0 0
+11998: b 1 0 0
+11998: h 2 1 2 0,2,2
+11998: g 2 1 2 0,2,1,2
+11998: apply 13 2 5 0,2
+11998: f 2 1 2 0,2,1,1,2
+CLASH, statistics insufficient
+11999: Facts:
+11999: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+11999: Id : 3, {_}:
+ apply (apply t ?7) ?8 =?= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+11999: Goal:
+11999: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (apply (f ?1) (h ?1)) (g ?1)
+ [1] by prove_c_combinator ?1
+11999: Order:
+11999: lpo
+11999: Leaf order:
+11999: t 1 0 0
+11999: b 1 0 0
+11999: h 2 1 2 0,2,2
+11999: g 2 1 2 0,2,1,2
+11999: apply 13 2 5 0,2
+11999: f 2 1 2 0,2,1,1,2
+Goal subsumed
+Statistics :
+Max weight : 100
+Found proof, 3.178698s
+% SZS status Unsatisfiable for COL062-1.p
+% SZS output start CNFRefutation for COL062-1.p
+Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
+Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
+Id : 1574, {_}: apply (apply (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) === apply (apply (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) [] by Super 1573 with 3 at 2
+Id : 1573, {_}: apply (apply ?5215 (g (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t)))) (apply (f (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t)))) =>= apply (apply (f (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t))) [5215] by Super 447 with 2 at 2
+Id : 447, {_}: apply (apply (apply ?1408 (apply ?1409 (g (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))))) (f (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t)))) (h (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))) =>= apply (apply (f (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))) [1409, 1408] by Super 445 with 2 at 1,1,2
+Id : 445, {_}: apply (apply (apply ?1404 (g (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (f (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t))) =>= apply (apply (f (apply (apply b (apply t ?1404)) (apply (apply b b) t))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (g (apply (apply b (apply t ?1404)) (apply (apply b b) t))) [1404] by Super 277 with 3 at 1,2
+Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (apply (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) [901, 900] by Super 29 with 2 at 1,2
+Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (apply (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) [87, 86, 85] by Super 13 with 3 at 1,1,2
+Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (apply (f (apply (apply b ?33) (apply (apply b ?34) ?35))) (h (apply (apply b ?33) (apply (apply b ?34) ?35)))) (g (apply (apply b ?33) (apply (apply b ?34) ?35))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
+Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (apply (f (apply (apply b ?18) ?19)) (h (apply (apply b ?18) ?19))) (g (apply (apply b ?18) ?19)) [19, 18] by Super 1 with 2 at 1,1,2
+Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (f ?1) (h ?1)) (g ?1) [1] by prove_c_combinator ?1
+% SZS output end CNFRefutation for COL062-1.p
+11997: solved COL062-1.p in 1.812113 using nrkbo
+11997: status Unsatisfiable for COL062-1.p
+CLASH, statistics insufficient
+12004: Facts:
+12004: Id : 2, {_}:
+ apply (apply (apply n ?3) ?4) ?5
+ =?=
+ apply (apply (apply ?3 ?5) ?4) ?5
+ [5, 4, 3] by n_definition ?3 ?4 ?5
+CLASH, statistics insufficient
+12006: Facts:
+12006: Id : 2, {_}:
+ apply (apply (apply n ?3) ?4) ?5
+ =?=
+ apply (apply (apply ?3 ?5) ?4) ?5
+ [5, 4, 3] by n_definition ?3 ?4 ?5
+12006: Id : 3, {_}:
+ apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
+ [9, 8, 7] by q_definition ?7 ?8 ?9
+12006: Goal:
+12006: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+12006: Order:
+12006: lpo
+12006: Leaf order:
+12006: q 1 0 0
+12006: n 1 0 0
+12006: apply 14 2 3 0,2
+12006: f 3 1 3 0,2,2
+12004: Id : 3, {_}:
+ apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
+ [9, 8, 7] by q_definition ?7 ?8 ?9
+12004: Goal:
+12004: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+12004: Order:
+12004: nrkbo
+12004: Leaf order:
+12004: q 1 0 0
+12004: n 1 0 0
+12004: apply 14 2 3 0,2
+12004: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+12005: Facts:
+12005: Id : 2, {_}:
+ apply (apply (apply n ?3) ?4) ?5
+ =?=
+ apply (apply (apply ?3 ?5) ?4) ?5
+ [5, 4, 3] by n_definition ?3 ?4 ?5
+12005: Id : 3, {_}:
+ apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
+ [9, 8, 7] by q_definition ?7 ?8 ?9
+12005: Goal:
+12005: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+12005: Order:
+12005: kbo
+12005: Leaf order:
+12005: q 1 0 0
+12005: n 1 0 0
+12005: apply 14 2 3 0,2
+12005: f 3 1 3 0,2,2
+% SZS status Timeout for COL071-1.p
+CLASH, statistics insufficient
+12093: Facts:
+12093: Id : 2, {_}:
+ apply (apply (apply n1 ?3) ?4) ?5
+ =?=
+ apply (apply (apply ?3 ?4) ?4) ?5
+ [5, 4, 3] by n1_definition ?3 ?4 ?5
+12093: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+12093: Goal:
+12093: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_strong_fixed_point ?1
+12093: Order:
+12093: nrkbo
+12093: Leaf order:
+12093: b 1 0 0
+12093: n1 1 0 0
+12093: apply 14 2 3 0,2
+12093: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+12094: Facts:
+12094: Id : 2, {_}:
+ apply (apply (apply n1 ?3) ?4) ?5
+ =?=
+ apply (apply (apply ?3 ?4) ?4) ?5
+ [5, 4, 3] by n1_definition ?3 ?4 ?5
+12094: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+12094: Goal:
+12094: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_strong_fixed_point ?1
+12094: Order:
+12094: kbo
+12094: Leaf order:
+12094: b 1 0 0
+12094: n1 1 0 0
+12094: apply 14 2 3 0,2
+12094: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+12095: Facts:
+12095: Id : 2, {_}:
+ apply (apply (apply n1 ?3) ?4) ?5
+ =?=
+ apply (apply (apply ?3 ?4) ?4) ?5
+ [5, 4, 3] by n1_definition ?3 ?4 ?5
+12095: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+12095: Goal:
+12095: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_strong_fixed_point ?1
+12095: Order:
+12095: lpo
+12095: Leaf order:
+12095: b 1 0 0
+12095: n1 1 0 0
+12095: apply 14 2 3 0,2
+12095: f 3 1 3 0,2,2
+% SZS status Timeout for COL073-1.p
+NO CLASH, using fixed ground order
+12117: Facts:
+12117: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12117: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12117: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12117: Id : 5, {_}:
+ commutator ?10 ?11
+ =<=
+ multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11))
+ [11, 10] by name ?10 ?11
+12117: Id : 6, {_}:
+ commutator (commutator ?13 ?14) ?15
+ =?=
+ commutator ?13 (commutator ?14 ?15)
+ [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15
+12117: Goal:
+12117: Id : 1, {_}:
+ multiply a (commutator b c) =<= multiply (commutator b c) a
+ [] by prove_center
+12117: Order:
+12117: nrkbo
+12117: Leaf order:
+12117: inverse 3 1 0
+12117: identity 2 0 0
+12117: multiply 11 2 2 0,2
+12117: commutator 7 2 2 0,2,2
+12117: c 2 0 2 2,2,2
+12117: b 2 0 2 1,2,2
+12117: a 2 0 2 1,2
+NO CLASH, using fixed ground order
+12118: Facts:
+12118: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12118: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12118: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12118: Id : 5, {_}:
+ commutator ?10 ?11
+ =<=
+ multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11))
+ [11, 10] by name ?10 ?11
+12118: Id : 6, {_}:
+ commutator (commutator ?13 ?14) ?15
+ =>=
+ commutator ?13 (commutator ?14 ?15)
+ [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15
+12118: Goal:
+12118: Id : 1, {_}:
+ multiply a (commutator b c) =<= multiply (commutator b c) a
+ [] by prove_center
+12118: Order:
+12118: kbo
+12118: Leaf order:
+12118: inverse 3 1 0
+12118: identity 2 0 0
+12118: multiply 11 2 2 0,2
+12118: commutator 7 2 2 0,2,2
+12118: c 2 0 2 2,2,2
+12118: b 2 0 2 1,2,2
+12118: a 2 0 2 1,2
+NO CLASH, using fixed ground order
+12119: Facts:
+12119: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12119: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12119: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12119: Id : 5, {_}:
+ commutator ?10 ?11
+ =>=
+ multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11))
+ [11, 10] by name ?10 ?11
+12119: Id : 6, {_}:
+ commutator (commutator ?13 ?14) ?15
+ =>=
+ commutator ?13 (commutator ?14 ?15)
+ [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15
+12119: Goal:
+12119: Id : 1, {_}:
+ multiply a (commutator b c) =<= multiply (commutator b c) a
+ [] by prove_center
+12119: Order:
+12119: lpo
+12119: Leaf order:
+12119: inverse 3 1 0
+12119: identity 2 0 0
+12119: multiply 11 2 2 0,2
+12119: commutator 7 2 2 0,2,2
+12119: c 2 0 2 2,2,2
+12119: b 2 0 2 1,2,2
+12119: a 2 0 2 1,2
+% SZS status Timeout for GRP024-5.p
+CLASH, statistics insufficient
+12145: Facts:
+12145: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12145: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12145: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12145: Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity
+12145: Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
+12145: Id : 7, {_}:
+ inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13)
+ [14, 13] by inverse_product_lemma ?13 ?14
+12145: Id : 8, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16
+12145: Id : 9, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18
+12145: Id : 10, {_}:
+ intersection ?20 ?21 =?= intersection ?21 ?20
+ [21, 20] by intersection_commutative ?20 ?21
+CLASH, statistics insufficient
+12146: Facts:
+12146: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12146: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12146: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12146: Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity
+12146: Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
+12146: Id : 7, {_}:
+ inverse (multiply ?13 ?14) =?= multiply (inverse ?14) (inverse ?13)
+ [14, 13] by inverse_product_lemma ?13 ?14
+12146: Id : 8, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16
+12146: Id : 9, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18
+12146: Id : 10, {_}:
+ intersection ?20 ?21 =?= intersection ?21 ?20
+ [21, 20] by intersection_commutative ?20 ?21
+12146: Id : 11, {_}:
+ union ?23 ?24 =?= union ?24 ?23
+ [24, 23] by union_commutative ?23 ?24
+12146: Id : 12, {_}:
+ intersection ?26 (intersection ?27 ?28)
+ =<=
+ intersection (intersection ?26 ?27) ?28
+ [28, 27, 26] by intersection_associative ?26 ?27 ?28
+12146: Id : 13, {_}:
+ union ?30 (union ?31 ?32) =<= union (union ?30 ?31) ?32
+ [32, 31, 30] by union_associative ?30 ?31 ?32
+12146: Id : 14, {_}:
+ union (intersection ?34 ?35) ?35 =>= ?35
+ [35, 34] by union_intersection_absorbtion ?34 ?35
+12146: Id : 15, {_}:
+ intersection (union ?37 ?38) ?38 =>= ?38
+ [38, 37] by intersection_union_absorbtion ?37 ?38
+12146: Id : 16, {_}:
+ multiply ?40 (union ?41 ?42)
+ =>=
+ union (multiply ?40 ?41) (multiply ?40 ?42)
+ [42, 41, 40] by multiply_union1 ?40 ?41 ?42
+12146: Id : 17, {_}:
+ multiply ?44 (intersection ?45 ?46)
+ =>=
+ intersection (multiply ?44 ?45) (multiply ?44 ?46)
+ [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
+12146: Id : 18, {_}:
+ multiply (union ?48 ?49) ?50
+ =>=
+ union (multiply ?48 ?50) (multiply ?49 ?50)
+ [50, 49, 48] by multiply_union2 ?48 ?49 ?50
+12146: Id : 19, {_}:
+ multiply (intersection ?52 ?53) ?54
+ =>=
+ intersection (multiply ?52 ?54) (multiply ?53 ?54)
+ [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54
+12146: Id : 20, {_}:
+ positive_part ?56 =>= union ?56 identity
+ [56] by positive_part ?56
+12146: Id : 21, {_}:
+ negative_part ?58 =>= intersection ?58 identity
+ [58] by negative_part ?58
+12146: Goal:
+12146: Id : 1, {_}:
+ multiply (positive_part a) (negative_part a) =>= a
+ [] by prove_product
+12146: Order:
+12146: lpo
+12146: Leaf order:
+12146: union 14 2 0
+12146: intersection 14 2 0
+12146: inverse 7 1 0
+12146: identity 6 0 0
+12146: multiply 21 2 1 0,2
+12146: negative_part 2 1 1 0,2,2
+12146: positive_part 2 1 1 0,1,2
+12146: a 3 0 3 1,1,2
+12145: Id : 11, {_}:
+ union ?23 ?24 =?= union ?24 ?23
+ [24, 23] by union_commutative ?23 ?24
+12145: Id : 12, {_}:
+ intersection ?26 (intersection ?27 ?28)
+ =<=
+ intersection (intersection ?26 ?27) ?28
+ [28, 27, 26] by intersection_associative ?26 ?27 ?28
+12145: Id : 13, {_}:
+ union ?30 (union ?31 ?32) =<= union (union ?30 ?31) ?32
+ [32, 31, 30] by union_associative ?30 ?31 ?32
+12145: Id : 14, {_}:
+ union (intersection ?34 ?35) ?35 =>= ?35
+ [35, 34] by union_intersection_absorbtion ?34 ?35
+12145: Id : 15, {_}:
+ intersection (union ?37 ?38) ?38 =>= ?38
+ [38, 37] by intersection_union_absorbtion ?37 ?38
+12145: Id : 16, {_}:
+ multiply ?40 (union ?41 ?42)
+ =<=
+ union (multiply ?40 ?41) (multiply ?40 ?42)
+ [42, 41, 40] by multiply_union1 ?40 ?41 ?42
+12145: Id : 17, {_}:
+ multiply ?44 (intersection ?45 ?46)
+ =<=
+ intersection (multiply ?44 ?45) (multiply ?44 ?46)
+ [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
+12145: Id : 18, {_}:
+ multiply (union ?48 ?49) ?50
+ =<=
+ union (multiply ?48 ?50) (multiply ?49 ?50)
+ [50, 49, 48] by multiply_union2 ?48 ?49 ?50
+12145: Id : 19, {_}:
+ multiply (intersection ?52 ?53) ?54
+ =<=
+ intersection (multiply ?52 ?54) (multiply ?53 ?54)
+ [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54
+12145: Id : 20, {_}:
+ positive_part ?56 =<= union ?56 identity
+ [56] by positive_part ?56
+12145: Id : 21, {_}:
+ negative_part ?58 =<= intersection ?58 identity
+ [58] by negative_part ?58
+12145: Goal:
+12145: Id : 1, {_}:
+ multiply (positive_part a) (negative_part a) =>= a
+ [] by prove_product
+12145: Order:
+12145: kbo
+12145: Leaf order:
+12145: union 14 2 0
+12145: intersection 14 2 0
+12145: inverse 7 1 0
+12145: identity 6 0 0
+12145: multiply 21 2 1 0,2
+12145: negative_part 2 1 1 0,2,2
+12145: positive_part 2 1 1 0,1,2
+12145: a 3 0 3 1,1,2
+CLASH, statistics insufficient
+12144: Facts:
+12144: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12144: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12144: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12144: Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity
+12144: Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
+12144: Id : 7, {_}:
+ inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13)
+ [14, 13] by inverse_product_lemma ?13 ?14
+12144: Id : 8, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16
+12144: Id : 9, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18
+12144: Id : 10, {_}:
+ intersection ?20 ?21 =?= intersection ?21 ?20
+ [21, 20] by intersection_commutative ?20 ?21
+12144: Id : 11, {_}:
+ union ?23 ?24 =?= union ?24 ?23
+ [24, 23] by union_commutative ?23 ?24
+12144: Id : 12, {_}:
+ intersection ?26 (intersection ?27 ?28)
+ =?=
+ intersection (intersection ?26 ?27) ?28
+ [28, 27, 26] by intersection_associative ?26 ?27 ?28
+12144: Id : 13, {_}:
+ union ?30 (union ?31 ?32) =?= union (union ?30 ?31) ?32
+ [32, 31, 30] by union_associative ?30 ?31 ?32
+12144: Id : 14, {_}:
+ union (intersection ?34 ?35) ?35 =>= ?35
+ [35, 34] by union_intersection_absorbtion ?34 ?35
+12144: Id : 15, {_}:
+ intersection (union ?37 ?38) ?38 =>= ?38
+ [38, 37] by intersection_union_absorbtion ?37 ?38
+12144: Id : 16, {_}:
+ multiply ?40 (union ?41 ?42)
+ =<=
+ union (multiply ?40 ?41) (multiply ?40 ?42)
+ [42, 41, 40] by multiply_union1 ?40 ?41 ?42
+12144: Id : 17, {_}:
+ multiply ?44 (intersection ?45 ?46)
+ =<=
+ intersection (multiply ?44 ?45) (multiply ?44 ?46)
+ [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
+12144: Id : 18, {_}:
+ multiply (union ?48 ?49) ?50
+ =<=
+ union (multiply ?48 ?50) (multiply ?49 ?50)
+ [50, 49, 48] by multiply_union2 ?48 ?49 ?50
+12144: Id : 19, {_}:
+ multiply (intersection ?52 ?53) ?54
+ =<=
+ intersection (multiply ?52 ?54) (multiply ?53 ?54)
+ [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54
+12144: Id : 20, {_}:
+ positive_part ?56 =<= union ?56 identity
+ [56] by positive_part ?56
+12144: Id : 21, {_}:
+ negative_part ?58 =<= intersection ?58 identity
+ [58] by negative_part ?58
+12144: Goal:
+12144: Id : 1, {_}:
+ multiply (positive_part a) (negative_part a) =>= a
+ [] by prove_product
+12144: Order:
+12144: nrkbo
+12144: Leaf order:
+12144: union 14 2 0
+12144: intersection 14 2 0
+12144: inverse 7 1 0
+12144: identity 6 0 0
+12144: multiply 21 2 1 0,2
+12144: negative_part 2 1 1 0,2,2
+12144: positive_part 2 1 1 0,1,2
+12144: a 3 0 3 1,1,2
+Statistics :
+Max weight : 15
+Found proof, 17.397670s
+% SZS status Unsatisfiable for GRP114-1.p
+% SZS output start CNFRefutation for GRP114-1.p
+Id : 12, {_}: intersection ?26 (intersection ?27 ?28) =<= intersection (intersection ?26 ?27) ?28 [28, 27, 26] by intersection_associative ?26 ?27 ?28
+Id : 14, {_}: union (intersection ?34 ?35) ?35 =>= ?35 [35, 34] by union_intersection_absorbtion ?34 ?35
+Id : 13, {_}: union ?30 (union ?31 ?32) =<= union (union ?30 ?31) ?32 [32, 31, 30] by union_associative ?30 ?31 ?32
+Id : 235, {_}: multiply (union ?499 ?500) ?501 =<= union (multiply ?499 ?501) (multiply ?500 ?501) [501, 500, 499] by multiply_union2 ?499 ?500 ?501
+Id : 15, {_}: intersection (union ?37 ?38) ?38 =>= ?38 [38, 37] by intersection_union_absorbtion ?37 ?38
+Id : 195, {_}: multiply ?427 (intersection ?428 ?429) =<= intersection (multiply ?427 ?428) (multiply ?427 ?429) [429, 428, 427] by multiply_intersection1 ?427 ?428 ?429
+Id : 10, {_}: intersection ?20 ?21 =?= intersection ?21 ?20 [21, 20] by intersection_commutative ?20 ?21
+Id : 21, {_}: negative_part ?58 =<= intersection ?58 identity [58] by negative_part ?58
+Id : 17, {_}: multiply ?44 (intersection ?45 ?46) =<= intersection (multiply ?44 ?45) (multiply ?44 ?46) [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
+Id : 7, {_}: inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13) [14, 13] by inverse_product_lemma ?13 ?14
+Id : 11, {_}: union ?23 ?24 =?= union ?24 ?23 [24, 23] by union_commutative ?23 ?24
+Id : 20, {_}: positive_part ?56 =<= union ?56 identity [56] by positive_part ?56
+Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity
+Id : 16, {_}: multiply ?40 (union ?41 ?42) =<= union (multiply ?40 ?41) (multiply ?40 ?42) [42, 41, 40] by multiply_union1 ?40 ?41 ?42
+Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
+Id : 48, {_}: inverse (multiply ?104 ?105) =<= multiply (inverse ?105) (inverse ?104) [105, 104] by inverse_product_lemma ?104 ?105
+Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+Id : 26, {_}: multiply (multiply ?67 ?68) ?69 =>= multiply ?67 (multiply ?68 ?69) [69, 68, 67] by associativity ?67 ?68 ?69
+Id : 28, {_}: multiply identity ?74 =<= multiply (inverse ?75) (multiply ?75 ?74) [75, 74] by Super 26 with 3 at 1,2
+Id : 32, {_}: ?74 =<= multiply (inverse ?75) (multiply ?75 ?74) [75, 74] by Demod 28 with 2 at 2
+Id : 50, {_}: inverse (multiply (inverse ?109) ?110) =>= multiply (inverse ?110) ?109 [110, 109] by Super 48 with 6 at 2,3
+Id : 49, {_}: inverse (multiply identity ?107) =<= multiply (inverse ?107) identity [107] by Super 48 with 5 at 2,3
+Id : 835, {_}: inverse ?1371 =<= multiply (inverse ?1371) identity [1371] by Demod 49 with 2 at 1,2
+Id : 841, {_}: inverse (inverse ?1382) =<= multiply ?1382 identity [1382] by Super 835 with 6 at 1,3
+Id : 864, {_}: ?1382 =<= multiply ?1382 identity [1382] by Demod 841 with 6 at 2
+Id : 881, {_}: multiply ?1419 (union ?1420 identity) =?= union (multiply ?1419 ?1420) ?1419 [1420, 1419] by Super 16 with 864 at 2,3
+Id : 900, {_}: multiply ?1419 (positive_part ?1420) =<= union (multiply ?1419 ?1420) ?1419 [1420, 1419] by Demod 881 with 20 at 2,2
+Id : 2897, {_}: multiply ?3964 (positive_part ?3965) =<= union ?3964 (multiply ?3964 ?3965) [3965, 3964] by Demod 900 with 11 at 3
+Id : 2901, {_}: multiply (inverse ?3975) (positive_part ?3975) =>= union (inverse ?3975) identity [3975] by Super 2897 with 3 at 2,3
+Id : 2938, {_}: multiply (inverse ?3975) (positive_part ?3975) =>= union identity (inverse ?3975) [3975] by Demod 2901 with 11 at 3
+Id : 296, {_}: union identity ?627 =>= positive_part ?627 [627] by Super 11 with 20 at 3
+Id : 2939, {_}: multiply (inverse ?3975) (positive_part ?3975) =>= positive_part (inverse ?3975) [3975] by Demod 2938 with 296 at 3
+Id : 2958, {_}: inverse (positive_part (inverse ?4028)) =<= multiply (inverse (positive_part ?4028)) ?4028 [4028] by Super 50 with 2939 at 1,2
+Id : 3609, {_}: ?4904 =<= multiply (inverse (inverse (positive_part ?4904))) (inverse (positive_part (inverse ?4904))) [4904] by Super 32 with 2958 at 2,3
+Id : 3661, {_}: ?4904 =<= inverse (multiply (positive_part (inverse ?4904)) (inverse (positive_part ?4904))) [4904] by Demod 3609 with 7 at 3
+Id : 52, {_}: inverse (multiply ?114 (inverse ?115)) =>= multiply ?115 (inverse ?114) [115, 114] by Super 48 with 6 at 1,3
+Id : 3662, {_}: ?4904 =<= multiply (positive_part ?4904) (inverse (positive_part (inverse ?4904))) [4904] by Demod 3661 with 52 at 3
+Id : 875, {_}: multiply ?1405 (intersection ?1406 identity) =?= intersection (multiply ?1405 ?1406) ?1405 [1406, 1405] by Super 17 with 864 at 2,3
+Id : 906, {_}: multiply ?1405 (negative_part ?1406) =<= intersection (multiply ?1405 ?1406) ?1405 [1406, 1405] by Demod 875 with 21 at 2,2
+Id : 3727, {_}: multiply ?5043 (negative_part ?5044) =<= intersection ?5043 (multiply ?5043 ?5044) [5044, 5043] by Demod 906 with 10 at 3
+Id : 40, {_}: multiply ?89 (inverse ?89) =>= identity [89] by Super 3 with 6 at 1,2
+Id : 3734, {_}: multiply ?5063 (negative_part (inverse ?5063)) =>= intersection ?5063 identity [5063] by Super 3727 with 40 at 2,3
+Id : 3782, {_}: multiply ?5063 (negative_part (inverse ?5063)) =>= negative_part ?5063 [5063] by Demod 3734 with 21 at 3
+Id : 201, {_}: multiply (inverse ?449) (intersection ?449 ?450) =>= intersection identity (multiply (inverse ?449) ?450) [450, 449] by Super 195 with 3 at 1,3
+Id : 311, {_}: intersection identity ?654 =>= negative_part ?654 [654] by Super 10 with 21 at 3
+Id : 8114, {_}: multiply (inverse ?449) (intersection ?449 ?450) =>= negative_part (multiply (inverse ?449) ?450) [450, 449] by Demod 201 with 311 at 3
+Id : 135, {_}: intersection ?38 (union ?37 ?38) =>= ?38 [37, 38] by Demod 15 with 10 at 2
+Id : 701, {_}: intersection ?1238 (positive_part ?1238) =>= ?1238 [1238] by Super 135 with 296 at 2,2
+Id : 241, {_}: multiply (union (inverse ?521) ?522) ?521 =>= union identity (multiply ?522 ?521) [522, 521] by Super 235 with 3 at 1,3
+Id : 8575, {_}: multiply (union (inverse ?10997) ?10998) ?10997 =>= positive_part (multiply ?10998 ?10997) [10998, 10997] by Demod 241 with 296 at 3
+Id : 699, {_}: union identity (union ?1233 ?1234) =>= union (positive_part ?1233) ?1234 [1234, 1233] by Super 13 with 296 at 1,3
+Id : 716, {_}: positive_part (union ?1233 ?1234) =>= union (positive_part ?1233) ?1234 [1234, 1233] by Demod 699 with 296 at 2
+Id : 299, {_}: union ?634 (union ?635 identity) =>= positive_part (union ?634 ?635) [635, 634] by Super 13 with 20 at 3
+Id : 307, {_}: union ?634 (positive_part ?635) =<= positive_part (union ?634 ?635) [635, 634] by Demod 299 with 20 at 2,2
+Id : 1223, {_}: union ?1233 (positive_part ?1234) =<= union (positive_part ?1233) ?1234 [1234, 1233] by Demod 716 with 307 at 2
+Id : 2971, {_}: multiply (inverse ?4064) (positive_part ?4064) =>= positive_part (inverse ?4064) [4064] by Demod 2938 with 296 at 3
+Id : 121, {_}: union ?35 (intersection ?34 ?35) =>= ?35 [34, 35] by Demod 14 with 11 at 2
+Id : 700, {_}: positive_part (intersection ?1236 identity) =>= identity [1236] by Super 121 with 296 at 2
+Id : 715, {_}: positive_part (negative_part ?1236) =>= identity [1236] by Demod 700 with 21 at 1,2
+Id : 2976, {_}: multiply (inverse (negative_part ?4073)) identity =>= positive_part (inverse (negative_part ?4073)) [4073] by Super 2971 with 715 at 2,2
+Id : 3014, {_}: inverse (negative_part ?4073) =<= positive_part (inverse (negative_part ?4073)) [4073] by Demod 2976 with 864 at 2
+Id : 3035, {_}: union (inverse (negative_part ?4112)) (positive_part ?4113) =>= union (inverse (negative_part ?4112)) ?4113 [4113, 4112] by Super 1223 with 3014 at 1,3
+Id : 8597, {_}: multiply (union (inverse (negative_part ?11063)) ?11064) (negative_part ?11063) =>= positive_part (multiply (positive_part ?11064) (negative_part ?11063)) [11064, 11063] by Super 8575 with 3035 at 1,2
+Id : 8560, {_}: multiply (union (inverse ?521) ?522) ?521 =>= positive_part (multiply ?522 ?521) [522, 521] by Demod 241 with 296 at 3
+Id : 8643, {_}: positive_part (multiply ?11064 (negative_part ?11063)) =<= positive_part (multiply (positive_part ?11064) (negative_part ?11063)) [11063, 11064] by Demod 8597 with 8560 at 2
+Id : 907, {_}: multiply ?1405 (negative_part ?1406) =<= intersection ?1405 (multiply ?1405 ?1406) [1406, 1405] by Demod 906 with 10 at 3
+Id : 8600, {_}: multiply (positive_part (inverse ?11072)) ?11072 =>= positive_part (multiply identity ?11072) [11072] by Super 8575 with 20 at 1,2
+Id : 8645, {_}: multiply (positive_part (inverse ?11072)) ?11072 =>= positive_part ?11072 [11072] by Demod 8600 with 2 at 1,3
+Id : 8660, {_}: multiply (positive_part (inverse ?11112)) (negative_part ?11112) =>= intersection (positive_part (inverse ?11112)) (positive_part ?11112) [11112] by Super 907 with 8645 at 2,3
+Id : 8719, {_}: multiply (positive_part (inverse ?11112)) (negative_part ?11112) =>= intersection (positive_part ?11112) (positive_part (inverse ?11112)) [11112] by Demod 8660 with 10 at 3
+Id : 9585, {_}: positive_part (multiply (inverse ?11973) (negative_part ?11973)) =<= positive_part (intersection (positive_part ?11973) (positive_part (inverse ?11973))) [11973] by Super 8643 with 8719 at 1,3
+Id : 3731, {_}: multiply (inverse ?5054) (negative_part ?5054) =>= intersection (inverse ?5054) identity [5054] by Super 3727 with 3 at 2,3
+Id : 3776, {_}: multiply (inverse ?5054) (negative_part ?5054) =>= intersection identity (inverse ?5054) [5054] by Demod 3731 with 10 at 3
+Id : 3777, {_}: multiply (inverse ?5054) (negative_part ?5054) =>= negative_part (inverse ?5054) [5054] by Demod 3776 with 311 at 3
+Id : 9660, {_}: positive_part (negative_part (inverse ?11973)) =<= positive_part (intersection (positive_part ?11973) (positive_part (inverse ?11973))) [11973] by Demod 9585 with 3777 at 1,2
+Id : 9661, {_}: identity =<= positive_part (intersection (positive_part ?11973) (positive_part (inverse ?11973))) [11973] by Demod 9660 with 715 at 2
+Id : 37105, {_}: intersection (intersection (positive_part ?38557) (positive_part (inverse ?38557))) identity =>= intersection (positive_part ?38557) (positive_part (inverse ?38557)) [38557] by Super 701 with 9661 at 2,2
+Id : 37338, {_}: intersection identity (intersection (positive_part ?38557) (positive_part (inverse ?38557))) =>= intersection (positive_part ?38557) (positive_part (inverse ?38557)) [38557] by Demod 37105 with 10 at 2
+Id : 37339, {_}: negative_part (intersection (positive_part ?38557) (positive_part (inverse ?38557))) =>= intersection (positive_part ?38557) (positive_part (inverse ?38557)) [38557] by Demod 37338 with 311 at 2
+Id : 314, {_}: intersection ?661 (intersection ?662 identity) =>= negative_part (intersection ?661 ?662) [662, 661] by Super 12 with 21 at 3
+Id : 321, {_}: intersection ?661 (negative_part ?662) =<= negative_part (intersection ?661 ?662) [662, 661] by Demod 314 with 21 at 2,2
+Id : 37340, {_}: intersection (positive_part ?38557) (negative_part (positive_part (inverse ?38557))) =>= intersection (positive_part ?38557) (positive_part (inverse ?38557)) [38557] by Demod 37339 with 321 at 2
+Id : 743, {_}: intersection identity (intersection ?1274 ?1275) =>= intersection (negative_part ?1274) ?1275 [1275, 1274] by Super 12 with 311 at 1,3
+Id : 757, {_}: negative_part (intersection ?1274 ?1275) =>= intersection (negative_part ?1274) ?1275 [1275, 1274] by Demod 743 with 311 at 2
+Id : 1432, {_}: intersection ?2159 (negative_part ?2160) =<= intersection (negative_part ?2159) ?2160 [2160, 2159] by Demod 757 with 321 at 2
+Id : 738, {_}: negative_part (union ?1265 identity) =>= identity [1265] by Super 135 with 311 at 2
+Id : 761, {_}: negative_part (positive_part ?1265) =>= identity [1265] by Demod 738 with 20 at 1,2
+Id : 1437, {_}: intersection (positive_part ?2173) (negative_part ?2174) =>= intersection identity ?2174 [2174, 2173] by Super 1432 with 761 at 1,3
+Id : 1472, {_}: intersection (positive_part ?2173) (negative_part ?2174) =>= negative_part ?2174 [2174, 2173] by Demod 1437 with 311 at 3
+Id : 37341, {_}: negative_part (positive_part (inverse ?38557)) =<= intersection (positive_part ?38557) (positive_part (inverse ?38557)) [38557] by Demod 37340 with 1472 at 2
+Id : 37342, {_}: identity =<= intersection (positive_part ?38557) (positive_part (inverse ?38557)) [38557] by Demod 37341 with 761 at 2
+Id : 37637, {_}: multiply (inverse (positive_part ?38828)) identity =<= negative_part (multiply (inverse (positive_part ?38828)) (positive_part (inverse ?38828))) [38828] by Super 8114 with 37342 at 2,2
+Id : 37769, {_}: inverse (positive_part ?38828) =<= negative_part (multiply (inverse (positive_part ?38828)) (positive_part (inverse ?38828))) [38828] by Demod 37637 with 864 at 2
+Id : 8675, {_}: multiply (positive_part (inverse ?11150)) ?11150 =>= positive_part ?11150 [11150] by Demod 8600 with 2 at 1,3
+Id : 8679, {_}: multiply (positive_part ?11157) (inverse ?11157) =>= positive_part (inverse ?11157) [11157] by Super 8675 with 6 at 1,1,2
+Id : 8754, {_}: inverse ?11202 =<= multiply (inverse (positive_part ?11202)) (positive_part (inverse ?11202)) [11202] by Super 32 with 8679 at 2,3
+Id : 37770, {_}: inverse (positive_part ?38828) =<= negative_part (inverse ?38828) [38828] by Demod 37769 with 8754 at 1,3
+Id : 37939, {_}: multiply ?5063 (inverse (positive_part ?5063)) =>= negative_part ?5063 [5063] by Demod 3782 with 37770 at 2,2
+Id : 8672, {_}: inverse (positive_part (inverse ?11144)) =<= multiply ?11144 (inverse (positive_part (inverse (inverse ?11144)))) [11144] by Super 52 with 8645 at 1,2
+Id : 8705, {_}: inverse (positive_part (inverse ?11144)) =<= multiply ?11144 (inverse (positive_part ?11144)) [11144] by Demod 8672 with 6 at 1,1,2,3
+Id : 37967, {_}: inverse (positive_part (inverse ?5063)) =>= negative_part ?5063 [5063] by Demod 37939 with 8705 at 2
+Id : 37970, {_}: ?4904 =<= multiply (positive_part ?4904) (negative_part ?4904) [4904] by Demod 3662 with 37967 at 2,3
+Id : 38259, {_}: a =?= a [] by Demod 1 with 37970 at 2
+Id : 1, {_}: multiply (positive_part a) (negative_part a) =>= a [] by prove_product
+% SZS output end CNFRefutation for GRP114-1.p
+12145: solved GRP114-1.p in 5.996374 using kbo
+12145: status Unsatisfiable for GRP114-1.p
+NO CLASH, using fixed ground order
+12157: Facts:
+12157: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12157: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12157: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12157: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12157: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12157: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12157: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12157: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12157: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12157: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12157: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12157: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12157: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12157: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12157: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12157: Id : 17, {_}: inverse identity =>= identity [] by p19_1
+12157: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p19_2 ?51
+12157: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p19_3 ?53 ?54
+12157: Goal:
+12157: Id : 1, {_}:
+ a
+ =<=
+ multiply (least_upper_bound a identity)
+ (greatest_lower_bound a identity)
+ [] by prove_p19
+12157: Order:
+12157: nrkbo
+12157: Leaf order:
+12157: inverse 7 1 0
+12157: multiply 21 2 1 0,3
+12157: greatest_lower_bound 14 2 1 0,2,3
+12157: least_upper_bound 14 2 1 0,1,3
+12157: identity 6 0 2 2,1,3
+12157: a 3 0 3 2
+NO CLASH, using fixed ground order
+12158: Facts:
+12158: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12158: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12158: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12158: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12158: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12158: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12158: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12158: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12158: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12158: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12158: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12158: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12158: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12158: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12158: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12158: Id : 17, {_}: inverse identity =>= identity [] by p19_1
+12158: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p19_2 ?51
+12158: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p19_3 ?53 ?54
+12158: Goal:
+12158: Id : 1, {_}:
+ a
+ =<=
+ multiply (least_upper_bound a identity)
+ (greatest_lower_bound a identity)
+ [] by prove_p19
+12158: Order:
+12158: kbo
+12158: Leaf order:
+12158: inverse 7 1 0
+12158: multiply 21 2 1 0,3
+12158: greatest_lower_bound 14 2 1 0,2,3
+12158: least_upper_bound 14 2 1 0,1,3
+12158: identity 6 0 2 2,1,3
+12158: a 3 0 3 2
+NO CLASH, using fixed ground order
+12159: Facts:
+12159: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12159: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12159: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12159: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12159: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12159: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12159: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12159: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12159: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12159: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12159: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12159: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12159: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12159: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12159: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12159: Id : 17, {_}: inverse identity =>= identity [] by p19_1
+12159: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p19_2 ?51
+12159: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p19_3 ?53 ?54
+12159: Goal:
+12159: Id : 1, {_}:
+ a
+ =<=
+ multiply (least_upper_bound a identity)
+ (greatest_lower_bound a identity)
+ [] by prove_p19
+12159: Order:
+12159: lpo
+12159: Leaf order:
+12159: inverse 7 1 0
+12159: multiply 21 2 1 0,3
+12159: greatest_lower_bound 14 2 1 0,2,3
+12159: least_upper_bound 14 2 1 0,1,3
+12159: identity 6 0 2 2,1,3
+12159: a 3 0 3 2
+% SZS status Timeout for GRP167-4.p
+NO CLASH, using fixed ground order
+12195: Facts:
+12195: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12195: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12195: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12195: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12195: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12195: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12195: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12195: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12195: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12195: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12195: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12195: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12195: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12195: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12195: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12195: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p08b_1
+12195: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p08b_2
+12195: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p08b_3
+12195: Goal:
+12195: Id : 1, {_}:
+ greatest_lower_bound (greatest_lower_bound a (multiply b c))
+ (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
+ =>=
+ greatest_lower_bound a (multiply b c)
+ [] by prove_p08b
+12195: Order:
+12195: nrkbo
+12195: Leaf order:
+12195: least_upper_bound 13 2 0
+12195: inverse 1 1 0
+12195: identity 8 0 0
+12195: greatest_lower_bound 21 2 5 0,2
+12195: multiply 21 2 3 0,2,1,2
+12195: c 4 0 3 2,2,1,2
+12195: b 4 0 3 1,2,1,2
+12195: a 5 0 4 1,1,2
+NO CLASH, using fixed ground order
+12196: Facts:
+12196: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12196: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12196: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12196: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12196: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12196: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12196: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12196: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12196: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12196: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12196: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12196: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12196: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12196: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12196: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12196: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p08b_1
+12196: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p08b_2
+12196: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p08b_3
+12196: Goal:
+12196: Id : 1, {_}:
+ greatest_lower_bound (greatest_lower_bound a (multiply b c))
+ (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
+ =>=
+ greatest_lower_bound a (multiply b c)
+ [] by prove_p08b
+12196: Order:
+12196: kbo
+12196: Leaf order:
+12196: least_upper_bound 13 2 0
+12196: inverse 1 1 0
+12196: identity 8 0 0
+12196: greatest_lower_bound 21 2 5 0,2
+12196: multiply 21 2 3 0,2,1,2
+12196: c 4 0 3 2,2,1,2
+12196: b 4 0 3 1,2,1,2
+12196: a 5 0 4 1,1,2
+NO CLASH, using fixed ground order
+12197: Facts:
+12197: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12197: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12197: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12197: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12197: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12197: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12197: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12197: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12197: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12197: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12197: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12197: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12197: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12197: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12197: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12197: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p08b_1
+12197: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p08b_2
+12197: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p08b_3
+12197: Goal:
+12197: Id : 1, {_}:
+ greatest_lower_bound (greatest_lower_bound a (multiply b c))
+ (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
+ =>=
+ greatest_lower_bound a (multiply b c)
+ [] by prove_p08b
+12197: Order:
+12197: lpo
+12197: Leaf order:
+12197: least_upper_bound 13 2 0
+12197: inverse 1 1 0
+12197: identity 8 0 0
+12197: greatest_lower_bound 21 2 5 0,2
+12197: multiply 21 2 3 0,2,1,2
+12197: c 4 0 3 2,2,1,2
+12197: b 4 0 3 1,2,1,2
+12197: a 5 0 4 1,1,2
+% SZS status Timeout for GRP177-2.p
+NO CLASH, using fixed ground order
+12224: Facts:
+12224: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12224: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12224: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12224: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12224: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12224: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12224: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12224: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12224: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12224: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12224: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12224: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12224: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12224: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12224: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12224: Id : 17, {_}: inverse identity =>= identity [] by p18_1
+12224: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p18_2 ?51
+12224: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p18_3 ?53 ?54
+12224: Goal:
+12224: Id : 1, {_}:
+ least_upper_bound (inverse a) identity
+ =<=
+ inverse (greatest_lower_bound a identity)
+ [] by prove_p18
+12224: Order:
+12224: nrkbo
+12224: Leaf order:
+12224: multiply 20 2 0
+12224: greatest_lower_bound 14 2 1 0,1,3
+12224: least_upper_bound 14 2 1 0,2
+12224: identity 6 0 2 2,2
+12224: inverse 9 1 2 0,1,2
+12224: a 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+12225: Facts:
+12225: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12225: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12225: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12225: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12225: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12225: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12225: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12225: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12225: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+NO CLASH, using fixed ground order
+12226: Facts:
+12226: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12226: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12226: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12226: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12226: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12226: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12226: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12226: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12226: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12226: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12226: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12226: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12226: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12226: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12226: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12226: Id : 17, {_}: inverse identity =>= identity [] by p18_1
+12226: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p18_2 ?51
+12226: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =>= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p18_3 ?53 ?54
+12226: Goal:
+12226: Id : 1, {_}:
+ least_upper_bound (inverse a) identity
+ =<=
+ inverse (greatest_lower_bound a identity)
+ [] by prove_p18
+12226: Order:
+12226: lpo
+12226: Leaf order:
+12226: multiply 20 2 0
+12226: greatest_lower_bound 14 2 1 0,1,3
+12226: least_upper_bound 14 2 1 0,2
+12226: identity 6 0 2 2,2
+12226: inverse 9 1 2 0,1,2
+12226: a 2 0 2 1,1,2
+12225: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12225: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12225: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12225: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12225: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12225: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12225: Id : 17, {_}: inverse identity =>= identity [] by p18_1
+12225: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p18_2 ?51
+12225: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p18_3 ?53 ?54
+12225: Goal:
+12225: Id : 1, {_}:
+ least_upper_bound (inverse a) identity
+ =<=
+ inverse (greatest_lower_bound a identity)
+ [] by prove_p18
+12225: Order:
+12225: kbo
+12225: Leaf order:
+12225: multiply 20 2 0
+12225: greatest_lower_bound 14 2 1 0,1,3
+12225: least_upper_bound 14 2 1 0,2
+12225: identity 6 0 2 2,2
+12225: inverse 9 1 2 0,1,2
+12225: a 2 0 2 1,1,2
+% SZS status Timeout for GRP179-3.p
+NO CLASH, using fixed ground order
+12243: Facts:
+12243: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12243: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12243: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12243: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12243: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12243: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12243: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12243: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12243: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12243: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12243: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12243: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12243: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12243: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12243: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12243: Id : 17, {_}: inverse identity =>= identity [] by p11_1
+12243: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p11_2 ?51
+12243: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p11_3 ?53 ?54
+12243: Goal:
+12243: Id : 1, {_}:
+ multiply a (multiply (inverse (greatest_lower_bound a b)) b)
+ =>=
+ least_upper_bound a b
+ [] by prove_p11
+12243: Order:
+12243: nrkbo
+12243: Leaf order:
+12243: identity 4 0 0
+12243: least_upper_bound 14 2 1 0,3
+12243: multiply 22 2 2 0,2
+12243: inverse 8 1 1 0,1,2,2
+12243: greatest_lower_bound 14 2 1 0,1,1,2,2
+12243: b 3 0 3 2,1,1,2,2
+12243: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+12244: Facts:
+12244: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12244: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12244: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12244: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12244: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12244: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12244: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12244: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12244: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12244: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12244: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12244: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12244: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12244: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12244: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12244: Id : 17, {_}: inverse identity =>= identity [] by p11_1
+12244: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p11_2 ?51
+12244: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p11_3 ?53 ?54
+12244: Goal:
+12244: Id : 1, {_}:
+ multiply a (multiply (inverse (greatest_lower_bound a b)) b)
+ =>=
+ least_upper_bound a b
+ [] by prove_p11
+12244: Order:
+12244: kbo
+12244: Leaf order:
+12244: identity 4 0 0
+12244: least_upper_bound 14 2 1 0,3
+12244: multiply 22 2 2 0,2
+12244: inverse 8 1 1 0,1,2,2
+12244: greatest_lower_bound 14 2 1 0,1,1,2,2
+12244: b 3 0 3 2,1,1,2,2
+12244: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+12245: Facts:
+12245: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12245: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12245: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12245: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12245: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12245: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12245: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12245: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12245: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12245: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12245: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12245: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12245: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12245: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12245: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12245: Id : 17, {_}: inverse identity =>= identity [] by p11_1
+12245: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p11_2 ?51
+12245: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =>= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p11_3 ?53 ?54
+12245: Goal:
+12245: Id : 1, {_}:
+ multiply a (multiply (inverse (greatest_lower_bound a b)) b)
+ =>=
+ least_upper_bound a b
+ [] by prove_p11
+12245: Order:
+12245: lpo
+12245: Leaf order:
+12245: identity 4 0 0
+12245: least_upper_bound 14 2 1 0,3
+12245: multiply 22 2 2 0,2
+12245: inverse 8 1 1 0,1,2,2
+12245: greatest_lower_bound 14 2 1 0,1,1,2,2
+12245: b 3 0 3 2,1,1,2,2
+12245: a 3 0 3 1,2
+% SZS status Timeout for GRP180-2.p
+CLASH, statistics insufficient
+12274: Facts:
+12274: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12274: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12274: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12274: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12274: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12274: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12274: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12274: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12274: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12274: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12274: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12274: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12274: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12274: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12274: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12274: Id : 17, {_}: inverse identity =>= identity [] by p12x_1
+12274: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
+12274: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p12x_3 ?53 ?54
+12274: Id : 20, {_}:
+ greatest_lower_bound a c =>= greatest_lower_bound b c
+ [] by p12x_4
+12274: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
+12274: Id : 22, {_}:
+ inverse (greatest_lower_bound ?58 ?59)
+ =<=
+ least_upper_bound (inverse ?58) (inverse ?59)
+ [59, 58] by p12x_6 ?58 ?59
+12274: Id : 23, {_}:
+ inverse (least_upper_bound ?61 ?62)
+ =<=
+ greatest_lower_bound (inverse ?61) (inverse ?62)
+ [62, 61] by p12x_7 ?61 ?62
+12274: Goal:
+12274: Id : 1, {_}: a =>= b [] by prove_p12x
+12274: Order:
+12274: nrkbo
+12274: Leaf order:
+12274: c 4 0 0
+12274: least_upper_bound 17 2 0
+12274: greatest_lower_bound 17 2 0
+12274: inverse 13 1 0
+12274: multiply 20 2 0
+12274: identity 4 0 0
+12274: b 3 0 1 3
+12274: a 3 0 1 2
+CLASH, statistics insufficient
+12275: Facts:
+12275: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12275: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12275: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12275: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12275: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12275: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12275: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12275: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12275: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12275: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12275: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12275: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12275: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12275: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12275: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12275: Id : 17, {_}: inverse identity =>= identity [] by p12x_1
+12275: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
+12275: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p12x_3 ?53 ?54
+12275: Id : 20, {_}:
+ greatest_lower_bound a c =>= greatest_lower_bound b c
+ [] by p12x_4
+12275: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
+12275: Id : 22, {_}:
+ inverse (greatest_lower_bound ?58 ?59)
+ =<=
+ least_upper_bound (inverse ?58) (inverse ?59)
+ [59, 58] by p12x_6 ?58 ?59
+12275: Id : 23, {_}:
+ inverse (least_upper_bound ?61 ?62)
+ =<=
+ greatest_lower_bound (inverse ?61) (inverse ?62)
+ [62, 61] by p12x_7 ?61 ?62
+12275: Goal:
+12275: Id : 1, {_}: a =>= b [] by prove_p12x
+12275: Order:
+12275: kbo
+12275: Leaf order:
+12275: c 4 0 0
+12275: least_upper_bound 17 2 0
+12275: greatest_lower_bound 17 2 0
+12275: inverse 13 1 0
+12275: multiply 20 2 0
+12275: identity 4 0 0
+12275: b 3 0 1 3
+12275: a 3 0 1 2
+CLASH, statistics insufficient
+12276: Facts:
+12276: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12276: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12276: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12276: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12276: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12276: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12276: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12276: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12276: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12276: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12276: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12276: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12276: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12276: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12276: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12276: Id : 17, {_}: inverse identity =>= identity [] by p12x_1
+12276: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
+12276: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p12x_3 ?53 ?54
+12276: Id : 20, {_}:
+ greatest_lower_bound a c =>= greatest_lower_bound b c
+ [] by p12x_4
+12276: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
+12276: Id : 22, {_}:
+ inverse (greatest_lower_bound ?58 ?59)
+ =>=
+ least_upper_bound (inverse ?58) (inverse ?59)
+ [59, 58] by p12x_6 ?58 ?59
+12276: Id : 23, {_}:
+ inverse (least_upper_bound ?61 ?62)
+ =>=
+ greatest_lower_bound (inverse ?61) (inverse ?62)
+ [62, 61] by p12x_7 ?61 ?62
+12276: Goal:
+12276: Id : 1, {_}: a =>= b [] by prove_p12x
+12276: Order:
+12276: lpo
+12276: Leaf order:
+12276: c 4 0 0
+12276: least_upper_bound 17 2 0
+12276: greatest_lower_bound 17 2 0
+12276: inverse 13 1 0
+12276: multiply 20 2 0
+12276: identity 4 0 0
+12276: b 3 0 1 3
+12276: a 3 0 1 2
+Statistics :
+Max weight : 16
+Found proof, 22.107626s
+% SZS status Unsatisfiable for GRP181-4.p
+% SZS output start CNFRefutation for GRP181-4.p
+Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
+Id : 20, {_}: greatest_lower_bound a c =>= greatest_lower_bound b c [] by p12x_4
+Id : 188, {_}: multiply ?586 (greatest_lower_bound ?587 ?588) =<= greatest_lower_bound (multiply ?586 ?587) (multiply ?586 ?588) [588, 587, 586] by monotony_glb1 ?586 ?587 ?588
+Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
+Id : 364, {_}: inverse (least_upper_bound ?929 ?930) =<= greatest_lower_bound (inverse ?929) (inverse ?930) [930, 929] by p12x_7 ?929 ?930
+Id : 342, {_}: inverse (greatest_lower_bound ?890 ?891) =<= least_upper_bound (inverse ?890) (inverse ?891) [891, 890] by p12x_6 ?890 ?891
+Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
+Id : 158, {_}: multiply ?515 (least_upper_bound ?516 ?517) =<= least_upper_bound (multiply ?515 ?516) (multiply ?515 ?517) [517, 516, 515] by monotony_lub1 ?515 ?516 ?517
+Id : 4, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
+Id : 19, {_}: inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) [54, 53] by p12x_3 ?53 ?54
+Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+Id : 17, {_}: inverse identity =>= identity [] by p12x_1
+Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+Id : 28, {_}: multiply (multiply ?71 ?72) ?73 =?= multiply ?71 (multiply ?72 ?73) [73, 72, 71] by associativity ?71 ?72 ?73
+Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
+Id : 302, {_}: inverse (multiply ?845 ?846) =<= multiply (inverse ?846) (inverse ?845) [846, 845] by p12x_3 ?845 ?846
+Id : 803, {_}: inverse (multiply ?1561 (inverse ?1562)) =>= multiply ?1562 (inverse ?1561) [1562, 1561] by Super 302 with 18 at 1,3
+Id : 30, {_}: multiply (multiply ?78 (inverse ?79)) ?79 =>= multiply ?78 identity [79, 78] by Super 28 with 3 at 2,3
+Id : 303, {_}: inverse (multiply identity ?848) =<= multiply (inverse ?848) identity [848] by Super 302 with 17 at 2,3
+Id : 394, {_}: inverse ?984 =<= multiply (inverse ?984) identity [984] by Demod 303 with 2 at 1,2
+Id : 396, {_}: inverse (inverse ?987) =<= multiply ?987 identity [987] by Super 394 with 18 at 1,3
+Id : 406, {_}: ?987 =<= multiply ?987 identity [987] by Demod 396 with 18 at 2
+Id : 638, {_}: multiply (multiply ?78 (inverse ?79)) ?79 =>= ?78 [79, 78] by Demod 30 with 406 at 3
+Id : 816, {_}: inverse ?1599 =<= multiply ?1600 (inverse (multiply ?1599 (inverse (inverse ?1600)))) [1600, 1599] by Super 803 with 638 at 1,2
+Id : 306, {_}: inverse (multiply ?855 (inverse ?856)) =>= multiply ?856 (inverse ?855) [856, 855] by Super 302 with 18 at 1,3
+Id : 837, {_}: inverse ?1599 =<= multiply ?1600 (multiply (inverse ?1600) (inverse ?1599)) [1600, 1599] by Demod 816 with 306 at 2,3
+Id : 838, {_}: inverse ?1599 =<= multiply ?1600 (inverse (multiply ?1599 ?1600)) [1600, 1599] by Demod 837 with 19 at 2,3
+Id : 285, {_}: multiply ?794 (inverse ?794) =>= identity [794] by Super 3 with 18 at 1,2
+Id : 607, {_}: multiply (multiply ?1261 ?1262) (inverse ?1262) =>= multiply ?1261 identity [1262, 1261] by Super 4 with 285 at 2,3
+Id : 19344, {_}: multiply (multiply ?27523 ?27524) (inverse ?27524) =>= ?27523 [27524, 27523] by Demod 607 with 406 at 3
+Id : 160, {_}: multiply (inverse ?522) (least_upper_bound ?523 ?522) =>= least_upper_bound (multiply (inverse ?522) ?523) identity [523, 522] by Super 158 with 3 at 2,3
+Id : 177, {_}: multiply (inverse ?522) (least_upper_bound ?523 ?522) =>= least_upper_bound identity (multiply (inverse ?522) ?523) [523, 522] by Demod 160 with 6 at 3
+Id : 345, {_}: inverse (greatest_lower_bound identity ?898) =>= least_upper_bound identity (inverse ?898) [898] by Super 342 with 17 at 1,3
+Id : 487, {_}: inverse (multiply (greatest_lower_bound identity ?1114) ?1115) =<= multiply (inverse ?1115) (least_upper_bound identity (inverse ?1114)) [1115, 1114] by Super 19 with 345 at 2,3
+Id : 11534, {_}: inverse (multiply (greatest_lower_bound identity ?15482) (inverse ?15482)) =>= least_upper_bound identity (multiply (inverse (inverse ?15482)) identity) [15482] by Super 177 with 487 at 2
+Id : 11607, {_}: multiply ?15482 (inverse (greatest_lower_bound identity ?15482)) =?= least_upper_bound identity (multiply (inverse (inverse ?15482)) identity) [15482] by Demod 11534 with 306 at 2
+Id : 11608, {_}: multiply ?15482 (inverse (greatest_lower_bound identity ?15482)) =>= least_upper_bound identity (inverse (inverse ?15482)) [15482] by Demod 11607 with 406 at 2,3
+Id : 11609, {_}: multiply ?15482 (least_upper_bound identity (inverse ?15482)) =>= least_upper_bound identity (inverse (inverse ?15482)) [15482] by Demod 11608 with 345 at 2,2
+Id : 11610, {_}: multiply ?15482 (least_upper_bound identity (inverse ?15482)) =>= least_upper_bound identity ?15482 [15482] by Demod 11609 with 18 at 2,3
+Id : 19409, {_}: multiply (least_upper_bound identity ?27743) (inverse (least_upper_bound identity (inverse ?27743))) =>= ?27743 [27743] by Super 19344 with 11610 at 1,2
+Id : 366, {_}: inverse (least_upper_bound ?934 (inverse ?935)) =>= greatest_lower_bound (inverse ?934) ?935 [935, 934] by Super 364 with 18 at 2,3
+Id : 19451, {_}: multiply (least_upper_bound identity ?27743) (greatest_lower_bound (inverse identity) ?27743) =>= ?27743 [27743] by Demod 19409 with 366 at 2,2
+Id : 44019, {_}: multiply (least_upper_bound identity ?52011) (greatest_lower_bound identity ?52011) =>= ?52011 [52011] by Demod 19451 with 17 at 1,2,2
+Id : 367, {_}: inverse (least_upper_bound identity ?937) =>= greatest_lower_bound identity (inverse ?937) [937] by Super 364 with 17 at 1,3
+Id : 8913, {_}: multiply (inverse ?11632) (least_upper_bound ?11632 ?11633) =>= least_upper_bound identity (multiply (inverse ?11632) ?11633) [11633, 11632] by Super 158 with 3 at 1,3
+Id : 326, {_}: least_upper_bound c a =<= least_upper_bound b c [] by Demod 21 with 6 at 2
+Id : 327, {_}: least_upper_bound c a =>= least_upper_bound c b [] by Demod 326 with 6 at 3
+Id : 8921, {_}: multiply (inverse c) (least_upper_bound c b) =>= least_upper_bound identity (multiply (inverse c) a) [] by Super 8913 with 327 at 2,2
+Id : 164, {_}: multiply (inverse ?538) (least_upper_bound ?538 ?539) =>= least_upper_bound identity (multiply (inverse ?538) ?539) [539, 538] by Super 158 with 3 at 1,3
+Id : 9001, {_}: least_upper_bound identity (multiply (inverse c) b) =<= least_upper_bound identity (multiply (inverse c) a) [] by Demod 8921 with 164 at 2
+Id : 9081, {_}: inverse (least_upper_bound identity (multiply (inverse c) b)) =>= greatest_lower_bound identity (inverse (multiply (inverse c) a)) [] by Super 367 with 9001 at 1,2
+Id : 9110, {_}: greatest_lower_bound identity (inverse (multiply (inverse c) b)) =<= greatest_lower_bound identity (inverse (multiply (inverse c) a)) [] by Demod 9081 with 367 at 2
+Id : 304, {_}: inverse (multiply (inverse ?850) ?851) =>= multiply (inverse ?851) ?850 [851, 850] by Super 302 with 18 at 2,3
+Id : 9111, {_}: greatest_lower_bound identity (inverse (multiply (inverse c) b)) =>= greatest_lower_bound identity (multiply (inverse a) c) [] by Demod 9110 with 304 at 2,3
+Id : 9112, {_}: greatest_lower_bound identity (multiply (inverse b) c) =<= greatest_lower_bound identity (multiply (inverse a) c) [] by Demod 9111 with 304 at 2,2
+Id : 44043, {_}: multiply (least_upper_bound identity (multiply (inverse a) c)) (greatest_lower_bound identity (multiply (inverse b) c)) =>= multiply (inverse a) c [] by Super 44019 with 9112 at 2,2
+Id : 10178, {_}: multiply (inverse ?13641) (greatest_lower_bound ?13641 ?13642) =>= greatest_lower_bound identity (multiply (inverse ?13641) ?13642) [13642, 13641] by Super 188 with 3 at 1,3
+Id : 315, {_}: greatest_lower_bound c a =<= greatest_lower_bound b c [] by Demod 20 with 5 at 2
+Id : 316, {_}: greatest_lower_bound c a =>= greatest_lower_bound c b [] by Demod 315 with 5 at 3
+Id : 10190, {_}: multiply (inverse c) (greatest_lower_bound c b) =>= greatest_lower_bound identity (multiply (inverse c) a) [] by Super 10178 with 316 at 2,2
+Id : 194, {_}: multiply (inverse ?609) (greatest_lower_bound ?609 ?610) =>= greatest_lower_bound identity (multiply (inverse ?609) ?610) [610, 609] by Super 188 with 3 at 1,3
+Id : 10270, {_}: greatest_lower_bound identity (multiply (inverse c) b) =<= greatest_lower_bound identity (multiply (inverse c) a) [] by Demod 10190 with 194 at 2
+Id : 10361, {_}: inverse (greatest_lower_bound identity (multiply (inverse c) b)) =>= least_upper_bound identity (inverse (multiply (inverse c) a)) [] by Super 345 with 10270 at 1,2
+Id : 10393, {_}: least_upper_bound identity (inverse (multiply (inverse c) b)) =<= least_upper_bound identity (inverse (multiply (inverse c) a)) [] by Demod 10361 with 345 at 2
+Id : 10394, {_}: least_upper_bound identity (inverse (multiply (inverse c) b)) =>= least_upper_bound identity (multiply (inverse a) c) [] by Demod 10393 with 304 at 2,3
+Id : 10395, {_}: least_upper_bound identity (multiply (inverse b) c) =<= least_upper_bound identity (multiply (inverse a) c) [] by Demod 10394 with 304 at 2,2
+Id : 44130, {_}: multiply (least_upper_bound identity (multiply (inverse b) c)) (greatest_lower_bound identity (multiply (inverse b) c)) =>= multiply (inverse a) c [] by Demod 44043 with 10395 at 1,2
+Id : 19452, {_}: multiply (least_upper_bound identity ?27743) (greatest_lower_bound identity ?27743) =>= ?27743 [27743] by Demod 19451 with 17 at 1,2,2
+Id : 44131, {_}: multiply (inverse b) c =<= multiply (inverse a) c [] by Demod 44130 with 19452 at 2
+Id : 44165, {_}: inverse (inverse a) =<= multiply c (inverse (multiply (inverse b) c)) [] by Super 838 with 44131 at 1,2,3
+Id : 44200, {_}: a =<= multiply c (inverse (multiply (inverse b) c)) [] by Demod 44165 with 18 at 2
+Id : 44201, {_}: a =<= inverse (inverse b) [] by Demod 44200 with 838 at 3
+Id : 44202, {_}: a =>= b [] by Demod 44201 with 18 at 3
+Id : 44399, {_}: b === b [] by Demod 1 with 44202 at 2
+Id : 1, {_}: a =>= b [] by prove_p12x
+% SZS output end CNFRefutation for GRP181-4.p
+12274: solved GRP181-4.p in 8.100505 using nrkbo
+12274: status Unsatisfiable for GRP181-4.p
+NO CLASH, using fixed ground order
+12282: Facts:
+12282: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12282: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12282: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12282: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12282: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12282: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12282: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12282: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12282: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12282: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12282: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12282: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12282: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12282: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12282: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12282: Goal:
+12282: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =>=
+ identity
+ [] by prove_p20
+12282: Order:
+12282: kbo
+12282: Leaf order:
+12282: multiply 18 2 0
+12282: inverse 2 1 1 0,2,2
+12282: greatest_lower_bound 15 2 2 0,2
+12282: least_upper_bound 14 2 1 0,1,2
+12282: identity 5 0 3 2,1,2
+12282: a 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+12283: Facts:
+12283: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12283: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12283: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12283: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12283: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12283: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12283: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12283: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12283: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12283: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12283: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12283: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12283: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12283: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12283: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12283: Goal:
+12283: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =>=
+ identity
+ [] by prove_p20
+12283: Order:
+12283: lpo
+12283: Leaf order:
+12283: multiply 18 2 0
+12283: inverse 2 1 1 0,2,2
+12283: greatest_lower_bound 15 2 2 0,2
+12283: least_upper_bound 14 2 1 0,1,2
+12283: identity 5 0 3 2,1,2
+12283: a 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+12281: Facts:
+12281: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12281: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12281: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12281: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12281: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12281: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12281: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12281: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12281: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12281: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12281: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12281: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12281: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12281: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12281: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12281: Goal:
+12281: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =>=
+ identity
+ [] by prove_p20
+12281: Order:
+12281: nrkbo
+12281: Leaf order:
+12281: multiply 18 2 0
+12281: inverse 2 1 1 0,2,2
+12281: greatest_lower_bound 15 2 2 0,2
+12281: least_upper_bound 14 2 1 0,1,2
+12281: identity 5 0 3 2,1,2
+12281: a 2 0 2 1,1,2
+% SZS status Timeout for GRP183-1.p
+NO CLASH, using fixed ground order
+12310: Facts:
+12310: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12310: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12310: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12310: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12310: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12310: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12310: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12310: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12310: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12310: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12310: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12310: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12310: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12310: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12310: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12310: Goal:
+12310: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound a identity)
+ (least_upper_bound (inverse a) identity)
+ =>=
+ identity
+ [] by prove_20x
+12310: Order:
+12310: nrkbo
+12310: Leaf order:
+12310: multiply 18 2 0
+12310: greatest_lower_bound 14 2 1 0,2
+12310: inverse 2 1 1 0,1,2,2
+12310: least_upper_bound 15 2 2 0,1,2
+12310: identity 5 0 3 2,1,2
+12310: a 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+12311: Facts:
+12311: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12311: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12311: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12311: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12311: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12311: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12311: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12311: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12311: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12311: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12311: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12311: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12311: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12311: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12311: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12311: Goal:
+12311: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound a identity)
+ (least_upper_bound (inverse a) identity)
+ =>=
+ identity
+ [] by prove_20x
+12311: Order:
+12311: kbo
+12311: Leaf order:
+12311: multiply 18 2 0
+12311: greatest_lower_bound 14 2 1 0,2
+12311: inverse 2 1 1 0,1,2,2
+12311: least_upper_bound 15 2 2 0,1,2
+12311: identity 5 0 3 2,1,2
+12311: a 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+12312: Facts:
+12312: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12312: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12312: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12312: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12312: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12312: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12312: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12312: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12312: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12312: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12312: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12312: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12312: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12312: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12312: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12312: Goal:
+12312: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound a identity)
+ (least_upper_bound (inverse a) identity)
+ =>=
+ identity
+ [] by prove_20x
+12312: Order:
+12312: lpo
+12312: Leaf order:
+12312: multiply 18 2 0
+12312: greatest_lower_bound 14 2 1 0,2
+12312: inverse 2 1 1 0,1,2,2
+12312: least_upper_bound 15 2 2 0,1,2
+12312: identity 5 0 3 2,1,2
+12312: a 2 0 2 1,1,2
+% SZS status Timeout for GRP183-3.p
+NO CLASH, using fixed ground order
+12349: Facts:
+12349: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12349: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12349: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12349: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12349: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12349: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12349: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12349: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12349: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12349: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12349: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12349: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12349: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12349: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12349: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12349: Id : 17, {_}: inverse identity =>= identity [] by p20x_1
+12349: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51
+12349: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p20x_3 ?53 ?54
+12349: Goal:
+12349: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound a identity)
+ (least_upper_bound (inverse a) identity)
+ =>=
+ identity
+ [] by prove_20x
+12349: Order:
+12349: nrkbo
+12349: Leaf order:
+12349: multiply 20 2 0
+12349: greatest_lower_bound 14 2 1 0,2
+12349: inverse 8 1 1 0,1,2,2
+12349: least_upper_bound 15 2 2 0,1,2
+12349: identity 7 0 3 2,1,2
+12349: a 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+12350: Facts:
+12350: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12350: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12350: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12350: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12350: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12350: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12350: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12350: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12350: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12350: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12350: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12350: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12350: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12350: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12350: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12350: Id : 17, {_}: inverse identity =>= identity [] by p20x_1
+12350: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51
+12350: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p20x_3 ?53 ?54
+12350: Goal:
+12350: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound a identity)
+ (least_upper_bound (inverse a) identity)
+ =>=
+ identity
+ [] by prove_20x
+12350: Order:
+12350: kbo
+12350: Leaf order:
+12350: multiply 20 2 0
+12350: greatest_lower_bound 14 2 1 0,2
+12350: inverse 8 1 1 0,1,2,2
+12350: least_upper_bound 15 2 2 0,1,2
+12350: identity 7 0 3 2,1,2
+12350: a 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+12351: Facts:
+12351: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12351: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12351: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12351: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12351: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12351: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12351: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12351: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12351: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12351: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12351: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12351: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12351: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12351: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12351: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12351: Id : 17, {_}: inverse identity =>= identity [] by p20x_1
+12351: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51
+12351: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =>= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p20x_3 ?53 ?54
+12351: Goal:
+12351: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound a identity)
+ (least_upper_bound (inverse a) identity)
+ =>=
+ identity
+ [] by prove_20x
+12351: Order:
+12351: lpo
+12351: Leaf order:
+12351: multiply 20 2 0
+12351: greatest_lower_bound 14 2 1 0,2
+12351: inverse 8 1 1 0,1,2,2
+12351: least_upper_bound 15 2 2 0,1,2
+12351: identity 7 0 3 2,1,2
+12351: a 2 0 2 1,1,2
+% SZS status Timeout for GRP183-4.p
+NO CLASH, using fixed ground order
+12378: Facts:
+12378: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12378: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12378: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12378: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12378: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12378: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12378: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12378: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12378: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12378: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12378: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12378: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12378: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12378: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12378: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12378: Goal:
+12378: Id : 1, {_}:
+ multiply (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =>=
+ multiply (inverse (greatest_lower_bound a identity))
+ (least_upper_bound a identity)
+ [] by prove_p21
+12378: Order:
+12378: nrkbo
+12378: Leaf order:
+12378: multiply 20 2 2 0,2
+12378: inverse 3 1 2 0,2,2
+12378: greatest_lower_bound 15 2 2 0,1,2,2
+12378: least_upper_bound 15 2 2 0,1,2
+12378: identity 6 0 4 2,1,2
+12378: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+12379: Facts:
+12379: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12379: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12379: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12379: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12379: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12379: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12379: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12379: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12379: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12379: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12379: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12379: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12379: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12379: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12379: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12379: Goal:
+12379: Id : 1, {_}:
+ multiply (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =<=
+ multiply (inverse (greatest_lower_bound a identity))
+ (least_upper_bound a identity)
+ [] by prove_p21
+12379: Order:
+12379: kbo
+12379: Leaf order:
+12379: multiply 20 2 2 0,2
+12379: inverse 3 1 2 0,2,2
+12379: greatest_lower_bound 15 2 2 0,1,2,2
+12379: least_upper_bound 15 2 2 0,1,2
+12379: identity 6 0 4 2,1,2
+12379: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+12380: Facts:
+12380: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12380: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12380: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12380: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12380: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12380: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12380: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12380: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12380: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12380: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12380: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12380: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12380: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12380: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12380: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12380: Goal:
+12380: Id : 1, {_}:
+ multiply (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =>=
+ multiply (inverse (greatest_lower_bound a identity))
+ (least_upper_bound a identity)
+ [] by prove_p21
+12380: Order:
+12380: lpo
+12380: Leaf order:
+12380: multiply 20 2 2 0,2
+12380: inverse 3 1 2 0,2,2
+12380: greatest_lower_bound 15 2 2 0,1,2,2
+12380: least_upper_bound 15 2 2 0,1,2
+12380: identity 6 0 4 2,1,2
+12380: a 4 0 4 1,1,2
+% SZS status Timeout for GRP184-1.p
+NO CLASH, using fixed ground order
+12396: Facts:
+12396: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12396: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12396: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12396: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12396: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12396: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12396: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12396: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12396: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12396: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12396: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12396: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12396: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12396: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12396: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12396: Goal:
+12396: Id : 1, {_}:
+ multiply (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =>=
+ multiply (inverse (greatest_lower_bound a identity))
+ (least_upper_bound a identity)
+ [] by prove_p21x
+12396: Order:
+12396: nrkbo
+12396: Leaf order:
+12396: multiply 20 2 2 0,2
+12396: inverse 3 1 2 0,2,2
+12396: greatest_lower_bound 15 2 2 0,1,2,2
+12396: least_upper_bound 15 2 2 0,1,2
+12396: identity 6 0 4 2,1,2
+12396: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+12397: Facts:
+12397: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12397: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12397: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12397: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12397: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12397: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12397: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12397: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12397: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12397: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12397: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12397: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12397: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12397: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12397: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12397: Goal:
+12397: Id : 1, {_}:
+ multiply (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =<=
+ multiply (inverse (greatest_lower_bound a identity))
+ (least_upper_bound a identity)
+ [] by prove_p21x
+12397: Order:
+12397: kbo
+12397: Leaf order:
+12397: multiply 20 2 2 0,2
+12397: inverse 3 1 2 0,2,2
+12397: greatest_lower_bound 15 2 2 0,1,2,2
+12397: least_upper_bound 15 2 2 0,1,2
+12397: identity 6 0 4 2,1,2
+12397: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+12398: Facts:
+12398: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12398: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12398: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12398: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12398: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12398: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12398: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12398: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12398: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12398: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12398: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12398: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12398: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12398: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12398: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12398: Goal:
+12398: Id : 1, {_}:
+ multiply (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =>=
+ multiply (inverse (greatest_lower_bound a identity))
+ (least_upper_bound a identity)
+ [] by prove_p21x
+12398: Order:
+12398: lpo
+12398: Leaf order:
+12398: multiply 20 2 2 0,2
+12398: inverse 3 1 2 0,2,2
+12398: greatest_lower_bound 15 2 2 0,1,2,2
+12398: least_upper_bound 15 2 2 0,1,2
+12398: identity 6 0 4 2,1,2
+12398: a 4 0 4 1,1,2
+% SZS status Timeout for GRP184-3.p
+NO CLASH, using fixed ground order
+12794: Facts:
+12794: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12794: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12794: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12794: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12794: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12794: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12794: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12794: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12794: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12794: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12794: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12794: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12794: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12794: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12794: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12794: Goal:
+12794: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound (multiply a b) identity)
+ (multiply (least_upper_bound a identity)
+ (least_upper_bound b identity))
+ =>=
+ least_upper_bound (multiply a b) identity
+ [] by prove_p22b
+12794: Order:
+12794: nrkbo
+12794: Leaf order:
+12794: inverse 1 1 0
+12794: greatest_lower_bound 14 2 1 0,2
+12794: least_upper_bound 17 2 4 0,1,2
+12794: identity 6 0 4 2,1,2
+12794: multiply 21 2 3 0,1,1,2
+12794: b 3 0 3 2,1,1,2
+12794: a 3 0 3 1,1,1,2
+NO CLASH, using fixed ground order
+12795: Facts:
+12795: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12795: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12795: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12795: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12795: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12795: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12795: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12795: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12795: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12795: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+NO CLASH, using fixed ground order
+12796: Facts:
+12796: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12796: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12796: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12796: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12796: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12796: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12796: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12796: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12796: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12796: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12796: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12795: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12795: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12795: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12795: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12795: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12795: Goal:
+12795: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound (multiply a b) identity)
+ (multiply (least_upper_bound a identity)
+ (least_upper_bound b identity))
+ =>=
+ least_upper_bound (multiply a b) identity
+ [] by prove_p22b
+12795: Order:
+12795: kbo
+12795: Leaf order:
+12795: inverse 1 1 0
+12795: greatest_lower_bound 14 2 1 0,2
+12795: least_upper_bound 17 2 4 0,1,2
+12795: identity 6 0 4 2,1,2
+12795: multiply 21 2 3 0,1,1,2
+12795: b 3 0 3 2,1,1,2
+12795: a 3 0 3 1,1,1,2
+12796: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12796: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12796: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12796: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12796: Goal:
+12796: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound (multiply a b) identity)
+ (multiply (least_upper_bound a identity)
+ (least_upper_bound b identity))
+ =>=
+ least_upper_bound (multiply a b) identity
+ [] by prove_p22b
+12796: Order:
+12796: lpo
+12796: Leaf order:
+12796: inverse 1 1 0
+12796: greatest_lower_bound 14 2 1 0,2
+12796: least_upper_bound 17 2 4 0,1,2
+12796: identity 6 0 4 2,1,2
+12796: multiply 21 2 3 0,1,1,2
+12796: b 3 0 3 2,1,1,2
+12796: a 3 0 3 1,1,1,2
+Statistics :
+Max weight : 21
+Found proof, 1.752071s
+% SZS status Unsatisfiable for GRP185-3.p
+% SZS output start CNFRefutation for GRP185-3.p
+Id : 120, {_}: greatest_lower_bound ?251 (least_upper_bound ?251 ?252) =>= ?251 [252, 251] by glb_absorbtion ?251 ?252
+Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+Id : 21, {_}: multiply (multiply ?57 ?58) ?59 =>= multiply ?57 (multiply ?58 ?59) [59, 58, 57] by associativity ?57 ?58 ?59
+Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
+Id : 23, {_}: multiply identity ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Super 21 with 3 at 1,2
+Id : 436, {_}: ?594 =<= multiply (inverse ?595) (multiply ?595 ?594) [595, 594] by Demod 23 with 2 at 2
+Id : 438, {_}: ?599 =<= multiply (inverse (inverse ?599)) identity [599] by Super 436 with 3 at 2,3
+Id : 27, {_}: ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Demod 23 with 2 at 2
+Id : 444, {_}: multiply ?621 ?622 =<= multiply (inverse (inverse ?621)) ?622 [622, 621] by Super 436 with 27 at 2,3
+Id : 599, {_}: ?599 =<= multiply ?599 identity [599] by Demod 438 with 444 at 3
+Id : 63, {_}: least_upper_bound ?143 (least_upper_bound ?144 ?145) =?= least_upper_bound ?144 (least_upper_bound ?145 ?143) [145, 144, 143] by Super 6 with 8 at 3
+Id : 894, {_}: greatest_lower_bound ?1092 (least_upper_bound ?1093 ?1092) =>= ?1092 [1093, 1092] by Super 120 with 6 at 2,2
+Id : 901, {_}: greatest_lower_bound ?1112 (least_upper_bound ?1113 (least_upper_bound ?1114 ?1112)) =>= ?1112 [1114, 1113, 1112] by Super 894 with 8 at 2,2
+Id : 2450, {_}: least_upper_bound identity (multiply a b) === least_upper_bound identity (multiply a b) [] by Demod 2449 with 901 at 2
+Id : 2449, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound b (least_upper_bound identity (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2448 with 2 at 1,2,2,2,2
+Id : 2448, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound b (least_upper_bound (multiply identity identity) (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2447 with 2 at 1,2,2,2
+Id : 2447, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound (multiply identity b) (least_upper_bound (multiply identity identity) (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2446 with 63 at 2,2,2
+Id : 2446, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a b) (multiply identity b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2445 with 599 at 1,2,2
+Id : 2445, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a b) (multiply identity b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2444 with 8 at 2,2
+Id : 2444, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a identity) (multiply identity identity)) (least_upper_bound (multiply a b) (multiply identity b))) =>= least_upper_bound identity (multiply a b) [] by Demod 2443 with 15 at 2,2,2
+Id : 2443, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a identity) (multiply identity identity)) (multiply (least_upper_bound a identity) b)) =>= least_upper_bound identity (multiply a b) [] by Demod 2442 with 15 at 1,2,2
+Id : 2442, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b)) =>= least_upper_bound identity (multiply a b) [] by Demod 2441 with 6 at 2,2
+Id : 2441, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound identity (multiply a b) [] by Demod 2440 with 6 at 3
+Id : 2440, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 2439 with 13 at 2,2
+Id : 2439, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 1 with 6 at 1,2
+Id : 1, {_}: greatest_lower_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by prove_p22b
+% SZS output end CNFRefutation for GRP185-3.p
+12796: solved GRP185-3.p in 0.64804 using lpo
+12796: status Unsatisfiable for GRP185-3.p
+NO CLASH, using fixed ground order
+12801: Facts:
+12801: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12801: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12801: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12801: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12801: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12801: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12801: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12801: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12801: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12801: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12801: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12801: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12801: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12801: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12801: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12801: Id : 17, {_}: inverse identity =>= identity [] by p22b_1
+12801: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51
+12801: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p22b_3 ?53 ?54
+12801: Goal:
+12801: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound (multiply a b) identity)
+ (multiply (least_upper_bound a identity)
+ (least_upper_bound b identity))
+ =>=
+ least_upper_bound (multiply a b) identity
+ [] by prove_p22b
+12801: Order:
+12801: nrkbo
+12801: Leaf order:
+12801: inverse 7 1 0
+12801: greatest_lower_bound 14 2 1 0,2
+12801: least_upper_bound 17 2 4 0,1,2
+12801: identity 8 0 4 2,1,2
+12801: multiply 23 2 3 0,1,1,2
+12801: b 3 0 3 2,1,1,2
+12801: a 3 0 3 1,1,1,2
+NO CLASH, using fixed ground order
+12802: Facts:
+12802: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12802: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12802: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12802: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12802: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12802: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12802: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12802: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12802: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12802: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12802: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12802: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12802: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12802: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12802: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12802: Id : 17, {_}: inverse identity =>= identity [] by p22b_1
+12802: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51
+12802: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p22b_3 ?53 ?54
+12802: Goal:
+12802: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound (multiply a b) identity)
+ (multiply (least_upper_bound a identity)
+ (least_upper_bound b identity))
+ =>=
+ least_upper_bound (multiply a b) identity
+ [] by prove_p22b
+12802: Order:
+12802: kbo
+12802: Leaf order:
+12802: inverse 7 1 0
+12802: greatest_lower_bound 14 2 1 0,2
+12802: least_upper_bound 17 2 4 0,1,2
+12802: identity 8 0 4 2,1,2
+12802: multiply 23 2 3 0,1,1,2
+12802: b 3 0 3 2,1,1,2
+12802: a 3 0 3 1,1,1,2
+NO CLASH, using fixed ground order
+12803: Facts:
+12803: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12803: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12803: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12803: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12803: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12803: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12803: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12803: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12803: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12803: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12803: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12803: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12803: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12803: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12803: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12803: Id : 17, {_}: inverse identity =>= identity [] by p22b_1
+12803: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51
+12803: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p22b_3 ?53 ?54
+12803: Goal:
+12803: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound (multiply a b) identity)
+ (multiply (least_upper_bound a identity)
+ (least_upper_bound b identity))
+ =>=
+ least_upper_bound (multiply a b) identity
+ [] by prove_p22b
+12803: Order:
+12803: lpo
+12803: Leaf order:
+12803: inverse 7 1 0
+12803: greatest_lower_bound 14 2 1 0,2
+12803: least_upper_bound 17 2 4 0,1,2
+12803: identity 8 0 4 2,1,2
+12803: multiply 23 2 3 0,1,1,2
+12803: b 3 0 3 2,1,1,2
+12803: a 3 0 3 1,1,1,2
+Statistics :
+Max weight : 21
+Found proof, 2.993705s
+% SZS status Unsatisfiable for GRP185-4.p
+% SZS output start CNFRefutation for GRP185-4.p
+Id : 123, {_}: greatest_lower_bound ?257 (least_upper_bound ?257 ?258) =>= ?257 [258, 257] by glb_absorbtion ?257 ?258
+Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51
+Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+Id : 17, {_}: inverse identity =>= identity [] by p22b_1
+Id : 382, {_}: inverse (multiply ?520 ?521) =?= multiply (inverse ?521) (inverse ?520) [521, 520] by p22b_3 ?520 ?521
+Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
+Id : 383, {_}: inverse (multiply identity ?523) =<= multiply (inverse ?523) identity [523] by Super 382 with 17 at 2,3
+Id : 422, {_}: inverse ?569 =<= multiply (inverse ?569) identity [569] by Demod 383 with 2 at 1,2
+Id : 424, {_}: inverse (inverse ?572) =<= multiply ?572 identity [572] by Super 422 with 18 at 1,3
+Id : 432, {_}: ?572 =<= multiply ?572 identity [572] by Demod 424 with 18 at 2
+Id : 66, {_}: least_upper_bound ?149 (least_upper_bound ?150 ?151) =?= least_upper_bound ?150 (least_upper_bound ?151 ?149) [151, 150, 149] by Super 6 with 8 at 3
+Id : 766, {_}: greatest_lower_bound ?881 (least_upper_bound ?882 ?881) =>= ?881 [882, 881] by Super 123 with 6 at 2,2
+Id : 773, {_}: greatest_lower_bound ?901 (least_upper_bound ?902 (least_upper_bound ?903 ?901)) =>= ?901 [903, 902, 901] by Super 766 with 8 at 2,2
+Id : 4003, {_}: least_upper_bound identity (multiply a b) === least_upper_bound identity (multiply a b) [] by Demod 4002 with 773 at 2
+Id : 4002, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound b (least_upper_bound identity (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 4001 with 2 at 1,2,2,2,2
+Id : 4001, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound b (least_upper_bound (multiply identity identity) (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 4000 with 2 at 1,2,2,2
+Id : 4000, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound (multiply identity b) (least_upper_bound (multiply identity identity) (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 3999 with 66 at 2,2,2
+Id : 3999, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a b) (multiply identity b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 3998 with 432 at 1,2,2
+Id : 3998, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a b) (multiply identity b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 3997 with 8 at 2,2
+Id : 3997, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a identity) (multiply identity identity)) (least_upper_bound (multiply a b) (multiply identity b))) =>= least_upper_bound identity (multiply a b) [] by Demod 3996 with 15 at 2,2,2
+Id : 3996, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a identity) (multiply identity identity)) (multiply (least_upper_bound a identity) b)) =>= least_upper_bound identity (multiply a b) [] by Demod 3995 with 15 at 1,2,2
+Id : 3995, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b)) =>= least_upper_bound identity (multiply a b) [] by Demod 3994 with 6 at 2,2
+Id : 3994, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound identity (multiply a b) [] by Demod 3993 with 6 at 3
+Id : 3993, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 3992 with 13 at 2,2
+Id : 3992, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 1 with 6 at 1,2
+Id : 1, {_}: greatest_lower_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by prove_p22b
+% SZS output end CNFRefutation for GRP185-4.p
+12803: solved GRP185-4.p in 0.988061 using lpo
+12803: status Unsatisfiable for GRP185-4.p
+NO CLASH, using fixed ground order
+12808: Facts:
+12808: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12808: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12808: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12808: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12808: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12808: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12808: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12808: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12808: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12808: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12808: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12808: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12808: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12808: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12808: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12808: Id : 17, {_}: inverse identity =>= identity [] by p23_1
+12808: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51
+12808: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p23_3 ?53 ?54
+12808: Goal:
+12808: Id : 1, {_}:
+ least_upper_bound (multiply a b) identity
+ =<=
+ multiply a (inverse (greatest_lower_bound a (inverse b)))
+ [] by prove_p23
+12808: Order:
+12808: nrkbo
+12808: Leaf order:
+12808: greatest_lower_bound 14 2 1 0,1,2,3
+12808: inverse 9 1 2 0,2,3
+12808: least_upper_bound 14 2 1 0,2
+12808: identity 5 0 1 2,2
+12808: multiply 22 2 2 0,1,2
+12808: b 2 0 2 2,1,2
+12808: a 3 0 3 1,1,2
+NO CLASH, using fixed ground order
+12809: Facts:
+12809: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12809: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12809: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12809: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12809: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12809: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12809: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12809: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12809: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12809: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12809: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12809: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12809: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12809: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12809: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12809: Id : 17, {_}: inverse identity =>= identity [] by p23_1
+12809: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51
+12809: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p23_3 ?53 ?54
+12809: Goal:
+12809: Id : 1, {_}:
+ least_upper_bound (multiply a b) identity
+ =<=
+ multiply a (inverse (greatest_lower_bound a (inverse b)))
+ [] by prove_p23
+12809: Order:
+12809: kbo
+12809: Leaf order:
+12809: greatest_lower_bound 14 2 1 0,1,2,3
+12809: inverse 9 1 2 0,2,3
+12809: least_upper_bound 14 2 1 0,2
+12809: identity 5 0 1 2,2
+12809: multiply 22 2 2 0,1,2
+12809: b 2 0 2 2,1,2
+12809: a 3 0 3 1,1,2
+NO CLASH, using fixed ground order
+12810: Facts:
+12810: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12810: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+12810: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+12810: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+12810: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+12810: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+12810: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+12810: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+12810: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+12810: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+12810: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+12810: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+12810: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+12810: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+12810: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+12810: Id : 17, {_}: inverse identity =>= identity [] by p23_1
+12810: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51
+12810: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p23_3 ?53 ?54
+12810: Goal:
+12810: Id : 1, {_}:
+ least_upper_bound (multiply a b) identity
+ =<=
+ multiply a (inverse (greatest_lower_bound a (inverse b)))
+ [] by prove_p23
+12810: Order:
+12810: lpo
+12810: Leaf order:
+12810: greatest_lower_bound 14 2 1 0,1,2,3
+12810: inverse 9 1 2 0,2,3
+12810: least_upper_bound 14 2 1 0,2
+12810: identity 5 0 1 2,2
+12810: multiply 22 2 2 0,1,2
+12810: b 2 0 2 2,1,2
+12810: a 3 0 3 1,1,2
+% SZS status Timeout for GRP186-2.p
+NO CLASH, using fixed ground order
+12831: Facts:
+12831: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12831: Id : 3, {_}:
+ multiply (left_inverse ?4) ?4 =>= identity
+ [4] by left_inverse ?4
+12831: Id : 4, {_}:
+ multiply (multiply ?6 (multiply ?7 ?8)) ?6
+ =?=
+ multiply (multiply ?6 ?7) (multiply ?8 ?6)
+ [8, 7, 6] by moufang1 ?6 ?7 ?8
+12831: Goal:
+12831: Id : 1, {_}:
+ multiply (multiply (multiply a b) c) b
+ =>=
+ multiply a (multiply b (multiply c b))
+ [] by prove_moufang2
+12831: Order:
+12831: nrkbo
+12831: Leaf order:
+12831: left_inverse 1 1 0
+12831: identity 2 0 0
+12831: c 2 0 2 2,1,2
+12831: multiply 14 2 6 0,2
+12831: b 4 0 4 2,1,1,2
+12831: a 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+12833: Facts:
+12833: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12833: Id : 3, {_}:
+ multiply (left_inverse ?4) ?4 =>= identity
+ [4] by left_inverse ?4
+12833: Id : 4, {_}:
+ multiply (multiply ?6 (multiply ?7 ?8)) ?6
+ =>=
+ multiply (multiply ?6 ?7) (multiply ?8 ?6)
+ [8, 7, 6] by moufang1 ?6 ?7 ?8
+12833: Goal:
+12833: Id : 1, {_}:
+ multiply (multiply (multiply a b) c) b
+ =>=
+ multiply a (multiply b (multiply c b))
+ [] by prove_moufang2
+12833: Order:
+12833: lpo
+12833: Leaf order:
+12833: left_inverse 1 1 0
+12833: identity 2 0 0
+12833: c 2 0 2 2,1,2
+12833: multiply 14 2 6 0,2
+12833: b 4 0 4 2,1,1,2
+12833: a 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+12832: Facts:
+12832: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12832: Id : 3, {_}:
+ multiply (left_inverse ?4) ?4 =>= identity
+ [4] by left_inverse ?4
+12832: Id : 4, {_}:
+ multiply (multiply ?6 (multiply ?7 ?8)) ?6
+ =>=
+ multiply (multiply ?6 ?7) (multiply ?8 ?6)
+ [8, 7, 6] by moufang1 ?6 ?7 ?8
+12832: Goal:
+12832: Id : 1, {_}:
+ multiply (multiply (multiply a b) c) b
+ =>=
+ multiply a (multiply b (multiply c b))
+ [] by prove_moufang2
+12832: Order:
+12832: kbo
+12832: Leaf order:
+12832: left_inverse 1 1 0
+12832: identity 2 0 0
+12832: c 2 0 2 2,1,2
+12832: multiply 14 2 6 0,2
+12832: b 4 0 4 2,1,1,2
+12832: a 2 0 2 1,1,1,2
+% SZS status Timeout for GRP204-1.p
+CLASH, statistics insufficient
+12860: Facts:
+12860: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12860: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+12860: Id : 4, {_}:
+ multiply ?6 (left_division ?6 ?7) =>= ?7
+ [7, 6] by multiply_left_division ?6 ?7
+12860: Id : 5, {_}:
+ left_division ?9 (multiply ?9 ?10) =>= ?10
+ [10, 9] by left_division_multiply ?9 ?10
+12860: Id : 6, {_}:
+ multiply (right_division ?12 ?13) ?13 =>= ?12
+ [13, 12] by multiply_right_division ?12 ?13
+12860: Id : 7, {_}:
+ right_division (multiply ?15 ?16) ?16 =>= ?15
+ [16, 15] by right_division_multiply ?15 ?16
+12860: Id : 8, {_}:
+ multiply ?18 (right_inverse ?18) =>= identity
+ [18] by right_inverse ?18
+12860: Id : 9, {_}:
+ multiply (left_inverse ?20) ?20 =>= identity
+ [20] by left_inverse ?20
+12860: Id : 10, {_}:
+ multiply (multiply (multiply ?22 ?23) ?22) ?24
+ =?=
+ multiply ?22 (multiply ?23 (multiply ?22 ?24))
+ [24, 23, 22] by moufang3 ?22 ?23 ?24
+12860: Goal:
+12860: Id : 1, {_}:
+ multiply x (multiply (multiply y z) x)
+ =<=
+ multiply (multiply x y) (multiply z x)
+ [] by prove_moufang4
+12860: Order:
+12860: nrkbo
+12860: Leaf order:
+12860: left_inverse 1 1 0
+12860: right_inverse 1 1 0
+12860: right_division 2 2 0
+12860: left_division 2 2 0
+12860: identity 4 0 0
+12860: multiply 20 2 6 0,2
+12860: z 2 0 2 2,1,2,2
+12860: y 2 0 2 1,1,2,2
+12860: x 4 0 4 1,2
+CLASH, statistics insufficient
+12861: Facts:
+12861: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12861: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+12861: Id : 4, {_}:
+ multiply ?6 (left_division ?6 ?7) =>= ?7
+ [7, 6] by multiply_left_division ?6 ?7
+12861: Id : 5, {_}:
+ left_division ?9 (multiply ?9 ?10) =>= ?10
+ [10, 9] by left_division_multiply ?9 ?10
+12861: Id : 6, {_}:
+ multiply (right_division ?12 ?13) ?13 =>= ?12
+ [13, 12] by multiply_right_division ?12 ?13
+12861: Id : 7, {_}:
+ right_division (multiply ?15 ?16) ?16 =>= ?15
+ [16, 15] by right_division_multiply ?15 ?16
+12861: Id : 8, {_}:
+ multiply ?18 (right_inverse ?18) =>= identity
+ [18] by right_inverse ?18
+12861: Id : 9, {_}:
+ multiply (left_inverse ?20) ?20 =>= identity
+ [20] by left_inverse ?20
+12861: Id : 10, {_}:
+ multiply (multiply (multiply ?22 ?23) ?22) ?24
+ =>=
+ multiply ?22 (multiply ?23 (multiply ?22 ?24))
+ [24, 23, 22] by moufang3 ?22 ?23 ?24
+12861: Goal:
+12861: Id : 1, {_}:
+ multiply x (multiply (multiply y z) x)
+ =<=
+ multiply (multiply x y) (multiply z x)
+ [] by prove_moufang4
+12861: Order:
+12861: kbo
+12861: Leaf order:
+12861: left_inverse 1 1 0
+12861: right_inverse 1 1 0
+12861: right_division 2 2 0
+12861: left_division 2 2 0
+12861: identity 4 0 0
+12861: multiply 20 2 6 0,2
+12861: z 2 0 2 2,1,2,2
+12861: y 2 0 2 1,1,2,2
+12861: x 4 0 4 1,2
+CLASH, statistics insufficient
+12862: Facts:
+12862: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+12862: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+12862: Id : 4, {_}:
+ multiply ?6 (left_division ?6 ?7) =>= ?7
+ [7, 6] by multiply_left_division ?6 ?7
+12862: Id : 5, {_}:
+ left_division ?9 (multiply ?9 ?10) =>= ?10
+ [10, 9] by left_division_multiply ?9 ?10
+12862: Id : 6, {_}:
+ multiply (right_division ?12 ?13) ?13 =>= ?12
+ [13, 12] by multiply_right_division ?12 ?13
+12862: Id : 7, {_}:
+ right_division (multiply ?15 ?16) ?16 =>= ?15
+ [16, 15] by right_division_multiply ?15 ?16
+12862: Id : 8, {_}:
+ multiply ?18 (right_inverse ?18) =>= identity
+ [18] by right_inverse ?18
+12862: Id : 9, {_}:
+ multiply (left_inverse ?20) ?20 =>= identity
+ [20] by left_inverse ?20
+12862: Id : 10, {_}:
+ multiply (multiply (multiply ?22 ?23) ?22) ?24
+ =>=
+ multiply ?22 (multiply ?23 (multiply ?22 ?24))
+ [24, 23, 22] by moufang3 ?22 ?23 ?24
+12862: Goal:
+12862: Id : 1, {_}:
+ multiply x (multiply (multiply y z) x)
+ =<=
+ multiply (multiply x y) (multiply z x)
+ [] by prove_moufang4
+12862: Order:
+12862: lpo
+12862: Leaf order:
+12862: left_inverse 1 1 0
+12862: right_inverse 1 1 0
+12862: right_division 2 2 0
+12862: left_division 2 2 0
+12862: identity 4 0 0
+12862: multiply 20 2 6 0,2
+12862: z 2 0 2 2,1,2,2
+12862: y 2 0 2 1,1,2,2
+12862: x 4 0 4 1,2
+Statistics :
+Max weight : 20
+Found proof, 29.150598s
+% SZS status Unsatisfiable for GRP205-1.p
+% SZS output start CNFRefutation for GRP205-1.p
+Id : 56, {_}: multiply (multiply (multiply ?126 ?127) ?126) ?128 =>= multiply ?126 (multiply ?127 (multiply ?126 ?128)) [128, 127, 126] by moufang3 ?126 ?127 ?128
+Id : 4, {_}: multiply ?6 (left_division ?6 ?7) =>= ?7 [7, 6] by multiply_left_division ?6 ?7
+Id : 9, {_}: multiply (left_inverse ?20) ?20 =>= identity [20] by left_inverse ?20
+Id : 22, {_}: left_division ?48 (multiply ?48 ?49) =>= ?49 [49, 48] by left_division_multiply ?48 ?49
+Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+Id : 5, {_}: left_division ?9 (multiply ?9 ?10) =>= ?10 [10, 9] by left_division_multiply ?9 ?10
+Id : 8, {_}: multiply ?18 (right_inverse ?18) =>= identity [18] by right_inverse ?18
+Id : 6, {_}: multiply (right_division ?12 ?13) ?13 =>= ?12 [13, 12] by multiply_right_division ?12 ?13
+Id : 10, {_}: multiply (multiply (multiply ?22 ?23) ?22) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by moufang3 ?22 ?23 ?24
+Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+Id : 7, {_}: right_division (multiply ?15 ?16) ?16 =>= ?15 [16, 15] by right_division_multiply ?15 ?16
+Id : 53, {_}: multiply ?115 (multiply ?116 (multiply ?115 identity)) =>= multiply (multiply ?115 ?116) ?115 [116, 115] by Super 3 with 10 at 2
+Id : 70, {_}: multiply ?115 (multiply ?116 ?115) =<= multiply (multiply ?115 ?116) ?115 [116, 115] by Demod 53 with 3 at 2,2,2
+Id : 889, {_}: right_division (multiply ?1099 (multiply ?1100 ?1099)) ?1099 =>= multiply ?1099 ?1100 [1100, 1099] by Super 7 with 70 at 1,2
+Id : 895, {_}: right_division (multiply ?1115 ?1116) ?1115 =<= multiply ?1115 (right_division ?1116 ?1115) [1116, 1115] by Super 889 with 6 at 2,1,2
+Id : 55, {_}: right_division (multiply ?122 (multiply ?123 (multiply ?122 ?124))) ?124 =>= multiply (multiply ?122 ?123) ?122 [124, 123, 122] by Super 7 with 10 at 1,2
+Id : 2553, {_}: right_division (multiply ?3478 (multiply ?3479 (multiply ?3478 ?3480))) ?3480 =>= multiply ?3478 (multiply ?3479 ?3478) [3480, 3479, 3478] by Demod 55 with 70 at 3
+Id : 647, {_}: multiply ?831 (multiply ?832 ?831) =<= multiply (multiply ?831 ?832) ?831 [832, 831] by Demod 53 with 3 at 2,2,2
+Id : 654, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= multiply identity ?850 [850] by Super 647 with 8 at 1,3
+Id : 677, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= ?850 [850] by Demod 654 with 2 at 3
+Id : 763, {_}: left_division ?991 ?991 =<= multiply (right_inverse ?991) ?991 [991] by Super 5 with 677 at 2,2
+Id : 24, {_}: left_division ?53 ?53 =>= identity [53] by Super 22 with 3 at 2,2
+Id : 789, {_}: identity =<= multiply (right_inverse ?991) ?991 [991] by Demod 763 with 24 at 2
+Id : 816, {_}: right_division identity ?1047 =>= right_inverse ?1047 [1047] by Super 7 with 789 at 1,2
+Id : 45, {_}: right_division identity ?99 =>= left_inverse ?99 [99] by Super 7 with 9 at 1,2
+Id : 843, {_}: left_inverse ?1047 =<= right_inverse ?1047 [1047] by Demod 816 with 45 at 2
+Id : 857, {_}: multiply ?18 (left_inverse ?18) =>= identity [18] by Demod 8 with 843 at 2,2
+Id : 2562, {_}: right_division (multiply ?3513 (multiply ?3514 identity)) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Super 2553 with 857 at 2,2,1,2
+Id : 2621, {_}: right_division (multiply ?3513 ?3514) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Demod 2562 with 3 at 2,1,2
+Id : 2806, {_}: right_division (multiply (left_inverse ?3781) (multiply ?3781 ?3782)) (left_inverse ?3781) =>= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Super 895 with 2621 at 2,3
+Id : 52, {_}: multiply ?111 (multiply ?112 (multiply ?111 (left_division (multiply (multiply ?111 ?112) ?111) ?113))) =>= ?113 [113, 112, 111] by Super 4 with 10 at 2
+Id : 963, {_}: multiply ?1216 (multiply ?1217 (multiply ?1216 (left_division (multiply ?1216 (multiply ?1217 ?1216)) ?1218))) =>= ?1218 [1218, 1217, 1216] by Demod 52 with 70 at 1,2,2,2,2
+Id : 970, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division (multiply ?1242 identity) ?1243))) =>= ?1243 [1243, 1242] by Super 963 with 9 at 2,1,2,2,2,2
+Id : 1030, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division ?1242 ?1243))) =>= ?1243 [1243, 1242] by Demod 970 with 3 at 1,2,2,2,2
+Id : 1031, {_}: multiply ?1242 (multiply (left_inverse ?1242) ?1243) =>= ?1243 [1243, 1242] by Demod 1030 with 4 at 2,2,2
+Id : 1164, {_}: left_division ?1548 ?1549 =<= multiply (left_inverse ?1548) ?1549 [1549, 1548] by Super 5 with 1031 at 2,2
+Id : 2852, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =<= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2806 with 1164 at 1,2
+Id : 2853, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =>= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2852 with 1164 at 3
+Id : 2854, {_}: right_division ?3782 (left_inverse ?3781) =<= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3781, 3782] by Demod 2853 with 5 at 1,2
+Id : 2855, {_}: right_division ?3782 (left_inverse ?3781) =>= multiply ?3782 ?3781 [3781, 3782] by Demod 2854 with 5 at 3
+Id : 1378, {_}: right_division (left_division ?1827 ?1828) ?1828 =>= left_inverse ?1827 [1828, 1827] by Super 7 with 1164 at 1,2
+Id : 28, {_}: left_division (right_division ?62 ?63) ?62 =>= ?63 [63, 62] by Super 5 with 6 at 2,2
+Id : 1384, {_}: right_division ?1844 ?1845 =<= left_inverse (right_division ?1845 ?1844) [1845, 1844] by Super 1378 with 28 at 1,2
+Id : 3643, {_}: multiply (multiply ?4879 ?4880) ?4881 =<= multiply ?4880 (multiply (left_division ?4880 ?4879) (multiply ?4880 ?4881)) [4881, 4880, 4879] by Super 56 with 4 at 1,1,2
+Id : 3648, {_}: multiply (multiply ?4897 ?4898) (left_division ?4898 ?4899) =>= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Super 3643 with 4 at 2,2,3
+Id : 2922, {_}: right_division (left_inverse ?3910) ?3911 =>= left_inverse (multiply ?3911 ?3910) [3911, 3910] by Super 1384 with 2855 at 1,3
+Id : 3008, {_}: left_inverse (multiply (left_inverse ?4021) ?4022) =>= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Super 2855 with 2922 at 2
+Id : 3027, {_}: left_inverse (left_division ?4021 ?4022) =<= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Demod 3008 with 1164 at 1,2
+Id : 3028, {_}: left_inverse (left_division ?4021 ?4022) =>= left_division ?4022 ?4021 [4022, 4021] by Demod 3027 with 1164 at 3
+Id : 3191, {_}: right_division ?4224 (left_division ?4225 ?4226) =<= multiply ?4224 (left_division ?4226 ?4225) [4226, 4225, 4224] by Super 2855 with 3028 at 2,2
+Id : 8019, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Demod 3648 with 3191 at 2
+Id : 3187, {_}: left_division (left_division ?4210 ?4211) ?4212 =<= multiply (left_division ?4211 ?4210) ?4212 [4212, 4211, 4210] by Super 1164 with 3028 at 1,3
+Id : 8020, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (left_division (left_division ?4897 ?4898) ?4899) [4899, 4898, 4897] by Demod 8019 with 3187 at 2,3
+Id : 8021, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =>= right_division ?4898 (left_division ?4899 (left_division ?4897 ?4898)) [4899, 4898, 4897] by Demod 8020 with 3191 at 3
+Id : 8034, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= left_inverse (right_division ?9767 (left_division ?9766 (left_division ?9768 ?9767))) [9768, 9767, 9766] by Super 1384 with 8021 at 1,3
+Id : 8099, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= right_division (left_division ?9766 (left_division ?9768 ?9767)) ?9767 [9768, 9767, 9766] by Demod 8034 with 1384 at 3
+Id : 23672, {_}: right_division (left_division ?25246 (left_inverse ?25247)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25247, 25246] by Super 2855 with 8099 at 2
+Id : 2932, {_}: right_division ?3937 (left_inverse ?3938) =>= multiply ?3937 ?3938 [3938, 3937] by Demod 2854 with 5 at 3
+Id : 46, {_}: left_division (left_inverse ?101) identity =>= ?101 [101] by Super 5 with 9 at 2,2
+Id : 40, {_}: left_division ?91 identity =>= right_inverse ?91 [91] by Super 5 with 8 at 2,2
+Id : 426, {_}: right_inverse (left_inverse ?101) =>= ?101 [101] by Demod 46 with 40 at 2
+Id : 860, {_}: left_inverse (left_inverse ?101) =>= ?101 [101] by Demod 426 with 843 at 2
+Id : 2936, {_}: right_division ?3949 ?3950 =<= multiply ?3949 (left_inverse ?3950) [3950, 3949] by Super 2932 with 860 at 2,2
+Id : 3077, {_}: left_division ?4125 (left_inverse ?4126) =>= right_division (left_inverse ?4125) ?4126 [4126, 4125] by Super 1164 with 2936 at 3
+Id : 3115, {_}: left_division ?4125 (left_inverse ?4126) =>= left_inverse (multiply ?4126 ?4125) [4126, 4125] by Demod 3077 with 2922 at 3
+Id : 23819, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23672 with 3115 at 1,2
+Id : 23820, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23819 with 2936 at 2,2
+Id : 23821, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25248, 25246, 25247] by Demod 23820 with 3187 at 3
+Id : 23822, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23821 with 2922 at 2
+Id : 23823, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23822 with 3115 at 1,1,3
+Id : 1167, {_}: multiply ?1556 (multiply (left_inverse ?1556) ?1557) =>= ?1557 [1557, 1556] by Demod 1030 with 4 at 2,2,2
+Id : 1177, {_}: multiply ?1584 ?1585 =<= left_division (left_inverse ?1584) ?1585 [1585, 1584] by Super 1167 with 4 at 2,2
+Id : 1414, {_}: multiply (right_division ?1873 ?1874) ?1875 =>= left_division (right_division ?1874 ?1873) ?1875 [1875, 1874, 1873] by Super 1177 with 1384 at 1,3
+Id : 23824, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25248, 25247] by Demod 23823 with 1414 at 1,2
+Id : 23825, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =>= left_division (multiply (multiply ?25247 ?25248) ?25246) ?25247 [25246, 25248, 25247] by Demod 23824 with 1177 at 1,3
+Id : 37248, {_}: left_division (multiply ?37773 ?37774) (right_division ?37773 ?37775) =<= left_division (multiply (multiply ?37773 ?37775) ?37774) ?37773 [37775, 37774, 37773] by Demod 23825 with 3028 at 2
+Id : 37265, {_}: left_division (multiply ?37844 ?37845) (right_division ?37844 (left_inverse ?37846)) =>= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Super 37248 with 2936 at 1,1,3
+Id : 37472, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Demod 37265 with 2855 at 2,2
+Id : 37473, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (left_division (right_division ?37846 ?37844) ?37845) ?37844 [37846, 37845, 37844] by Demod 37472 with 1414 at 1,3
+Id : 8041, {_}: right_division (multiply ?9794 ?9795) (left_division ?9796 ?9795) =>= right_division ?9795 (left_division ?9796 (left_division ?9794 ?9795)) [9796, 9795, 9794] by Demod 8020 with 3191 at 3
+Id : 8054, {_}: right_division (multiply ?9845 (left_inverse ?9846)) (left_inverse (multiply ?9846 ?9847)) =>= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Super 8041 with 3115 at 2,2
+Id : 8126, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Demod 8054 with 2855 at 2
+Id : 8127, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8126 with 2922 at 3
+Id : 8128, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8127 with 2936 at 1,2
+Id : 8129, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9846, 9845] by Demod 8128 with 3187 at 1,3
+Id : 8130, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9845, 9846] by Demod 8129 with 1414 at 2
+Id : 8131, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) [9847, 9845, 9846] by Demod 8130 with 3028 at 3
+Id : 8132, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_inverse (multiply ?9846 ?9845)) ?9847) [9847, 9845, 9846] by Demod 8131 with 3115 at 1,2,3
+Id : 24031, {_}: left_division (right_division ?25824 ?25825) (multiply ?25824 ?25826) =>= left_division ?25824 (multiply (multiply ?25824 ?25825) ?25826) [25826, 25825, 25824] by Demod 8132 with 1177 at 2,3
+Id : 24068, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =<= left_division ?25977 (multiply (multiply ?25977 (left_inverse ?25978)) ?25979) [25979, 25978, 25977] by Super 24031 with 2855 at 1,2
+Id : 24287, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (multiply (right_division ?25977 ?25978) ?25979) [25979, 25978, 25977] by Demod 24068 with 2936 at 1,2,3
+Id : 24288, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (left_division (right_division ?25978 ?25977) ?25979) [25979, 25978, 25977] by Demod 24287 with 1414 at 2,3
+Id : 47819, {_}: left_division ?49234 (left_division (right_division ?49235 ?49234) ?49236) =<= left_division (left_division (right_division ?49236 ?49234) ?49235) ?49234 [49236, 49235, 49234] by Demod 37473 with 24288 at 2
+Id : 1246, {_}: multiply (left_inverse ?1641) (multiply ?1642 (left_inverse ?1641)) =>= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Super 70 with 1164 at 1,3
+Id : 1310, {_}: left_division ?1641 (multiply ?1642 (left_inverse ?1641)) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1246 with 1164 at 2
+Id : 3056, {_}: left_division ?1641 (right_division ?1642 ?1641) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1310 with 2936 at 2,2
+Id : 3057, {_}: left_division ?1641 (right_division ?1642 ?1641) =>= right_division (left_division ?1641 ?1642) ?1641 [1642, 1641] by Demod 3056 with 2936 at 3
+Id : 47887, {_}: left_division ?49524 (left_division (right_division (right_division ?49525 (right_division ?49526 ?49524)) ?49524) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Super 47819 with 3057 at 1,3
+Id : 59, {_}: multiply (multiply ?136 ?137) ?138 =<= multiply ?137 (multiply (left_division ?137 ?136) (multiply ?137 ?138)) [138, 137, 136] by Super 56 with 4 at 1,1,2
+Id : 3632, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= multiply (left_division ?4830 ?4831) (multiply ?4830 ?4832) [4832, 4831, 4830] by Super 5 with 59 at 2,2
+Id : 7833, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= left_division (left_division ?4831 ?4830) (multiply ?4830 ?4832) [4832, 4831, 4830] by Demod 3632 with 3187 at 3
+Id : 7841, {_}: left_inverse (left_division ?9488 (multiply (multiply ?9489 ?9488) ?9490)) =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9489, 9488] by Super 3028 with 7833 at 1,2
+Id : 7910, {_}: left_division (multiply (multiply ?9489 ?9488) ?9490) ?9488 =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9488, 9489] by Demod 7841 with 3028 at 2
+Id : 22545, {_}: left_division (multiply (left_inverse ?23598) ?23599) (left_division ?23600 (left_inverse ?23598)) =>= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Super 3115 with 7910 at 2
+Id : 22628, {_}: left_division (left_division ?23598 ?23599) (left_division ?23600 (left_inverse ?23598)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22545 with 1164 at 1,2
+Id : 22629, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22628 with 3115 at 2,2
+Id : 22630, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23600, 23599, 23598] by Demod 22629 with 2936 at 1,2,1,3
+Id : 22631, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23599, 23600, 23598] by Demod 22630 with 3115 at 2
+Id : 22632, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22631 with 1414 at 2,1,3
+Id : 22633, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =<= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22632 with 3191 at 1,2
+Id : 22634, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =>= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23599, 23600, 23598] by Demod 22633 with 3191 at 1,3
+Id : 22635, {_}: right_division (left_division ?23599 ?23598) (multiply ?23598 ?23600) =<= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23600, 23598, 23599] by Demod 22634 with 1384 at 2
+Id : 33282, {_}: right_division (left_division ?33402 ?33403) (multiply ?33403 ?33404) =<= right_division (left_division ?33402 (right_division ?33403 ?33404)) ?33403 [33404, 33403, 33402] by Demod 22635 with 1384 at 3
+Id : 33363, {_}: right_division (left_division (left_inverse ?33737) ?33738) (multiply ?33738 ?33739) =>= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Super 33282 with 1177 at 1,3
+Id : 33649, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Demod 33363 with 1177 at 1,2
+Id : 2939, {_}: right_division ?3957 (right_division ?3958 ?3959) =<= multiply ?3957 (right_division ?3959 ?3958) [3959, 3958, 3957] by Super 2932 with 1384 at 2,2
+Id : 33650, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (right_division ?33737 (right_division ?33739 ?33738)) ?33738 [33739, 33738, 33737] by Demod 33649 with 2939 at 1,3
+Id : 48257, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Demod 47887 with 33650 at 1,2,2
+Id : 640, {_}: multiply (multiply ?22 (multiply ?23 ?22)) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by Demod 10 with 70 at 1,2
+Id : 1251, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =<= multiply ?1655 (multiply (left_inverse ?1656) (multiply ?1655 ?1657)) [1657, 1656, 1655] by Super 640 with 1164 at 2,1,2
+Id : 1306, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1251 with 1164 at 2,3
+Id : 5008, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1306 with 3191 at 1,2
+Id : 5009, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5008 with 3191 at 3
+Id : 5010, {_}: left_division (right_division (left_division ?1655 ?1656) ?1655) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5009 with 1414 at 2
+Id : 48258, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49526, 49525, 49524] by Demod 48257 with 5010 at 3
+Id : 3070, {_}: multiply (multiply (left_inverse ?4103) (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Super 640 with 2936 at 2,1,2
+Id : 3126, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3070 with 1164 at 1,2
+Id : 3127, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3126 with 1164 at 3
+Id : 3128, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3127 with 3057 at 1,2
+Id : 3129, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3128 with 1164 at 2,2,3
+Id : 3130, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3129 with 1414 at 2
+Id : 7047, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (right_division ?4104 (left_division ?4105 ?4103)) [4105, 4104, 4103] by Demod 3130 with 3191 at 2,3
+Id : 7063, {_}: left_division ?8435 (right_division ?8436 (left_division (left_inverse ?8437) ?8435)) =>= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Super 3115 with 7047 at 2
+Id : 7165, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Demod 7063 with 1177 at 2,2,2
+Id : 7166, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (right_division ?8437 (right_division (left_division ?8435 ?8436) ?8435)) [8437, 8436, 8435] by Demod 7165 with 2939 at 1,3
+Id : 7167, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =>= right_division (right_division (left_division ?8435 ?8436) ?8435) ?8437 [8437, 8436, 8435] by Demod 7166 with 1384 at 3
+Id : 21426, {_}: left_inverse (right_division (right_division (left_division ?22100 ?22101) ?22100) ?22102) =>= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22102, 22101, 22100] by Super 3028 with 7167 at 1,2
+Id : 21547, {_}: right_division ?22102 (right_division (left_division ?22100 ?22101) ?22100) =<= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22101, 22100, 22102] by Demod 21426 with 1384 at 2
+Id : 48259, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49525, 49526, 49524] by Demod 48258 with 21547 at 2,2
+Id : 48260, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49525, 49526, 49524] by Demod 48259 with 1414 at 1,2,3
+Id : 3073, {_}: left_division ?4114 (right_division ?4114 ?4115) =>= left_inverse ?4115 [4115, 4114] by Super 5 with 2936 at 2,2
+Id : 48261, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =<= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49524, 49525, 49526] by Demod 48260 with 3073 at 2
+Id : 48262, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48261 with 28 at 1,2,3
+Id : 48263, {_}: right_division ?49526 (left_division ?49526 (multiply ?49525 ?49524)) =<= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48262 with 1384 at 2
+Id : 52424, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= left_inverse (right_division ?54688 (left_division ?54688 (multiply ?54689 ?54690))) [54690, 54689, 54688] by Super 1384 with 48263 at 1,3
+Id : 52654, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= right_division (left_division ?54688 (multiply ?54689 ?54690)) ?54688 [54690, 54689, 54688] by Demod 52424 with 1384 at 3
+Id : 54963, {_}: right_division (left_division (left_inverse ?57654) ?57655) (right_division (left_inverse ?57654) ?57656) =>= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Super 2855 with 52654 at 2
+Id : 55156, {_}: right_division (multiply ?57654 ?57655) (right_division (left_inverse ?57654) ?57656) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 54963 with 1177 at 1,2
+Id : 55157, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55156 with 2922 at 2,2
+Id : 55158, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55157 with 3187 at 3
+Id : 55159, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55158 with 2855 at 2
+Id : 55160, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_inverse (multiply ?57654 (multiply ?57655 ?57656))) ?57654 [57656, 57655, 57654] by Demod 55159 with 3115 at 1,3
+Id : 55161, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= multiply (multiply ?57654 (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55160 with 1177 at 3
+Id : 55162, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =>= multiply ?57654 (multiply (multiply ?57655 ?57656) ?57654) [57656, 57655, 57654] by Demod 55161 with 70 at 3
+Id : 56911, {_}: multiply x (multiply (multiply y z) x) =?= multiply x (multiply (multiply y z) x) [] by Demod 1 with 55162 at 3
+Id : 1, {_}: multiply x (multiply (multiply y z) x) =<= multiply (multiply x y) (multiply z x) [] by prove_moufang4
+% SZS output end CNFRefutation for GRP205-1.p
+12861: solved GRP205-1.p in 14.652915 using kbo
+12861: status Unsatisfiable for GRP205-1.p
+NO CLASH, using fixed ground order
+12867: Facts:
+12867: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply ?3
+ (multiply
+ (multiply (multiply ?4 (inverse ?4))
+ (inverse (multiply ?2 ?3))) ?2)))
+ =>=
+ ?2
+ [4, 3, 2] by single_non_axiom ?2 ?3 ?4
+12867: Goal:
+12867: Id : 1, {_}:
+ multiply x
+ (inverse
+ (multiply y
+ (multiply
+ (multiply (multiply z (inverse z)) (inverse (multiply u y)))
+ x)))
+ =>=
+ u
+ [] by try_prove_this_axiom
+12867: Order:
+12867: nrkbo
+12867: Leaf order:
+12867: u 2 0 2 1,1,2,1,2,1,2,2
+12867: multiply 12 2 6 0,2
+12867: inverse 6 1 3 0,2,2
+12867: z 2 0 2 1,1,1,2,1,2,2
+12867: y 2 0 2 1,1,2,2
+12867: x 2 0 2 1,2
+NO CLASH, using fixed ground order
+12868: Facts:
+12868: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply ?3
+ (multiply
+ (multiply (multiply ?4 (inverse ?4))
+ (inverse (multiply ?2 ?3))) ?2)))
+ =>=
+ ?2
+ [4, 3, 2] by single_non_axiom ?2 ?3 ?4
+12868: Goal:
+12868: Id : 1, {_}:
+ multiply x
+ (inverse
+ (multiply y
+ (multiply
+ (multiply (multiply z (inverse z)) (inverse (multiply u y)))
+ x)))
+ =>=
+ u
+ [] by try_prove_this_axiom
+12868: Order:
+12868: kbo
+12868: Leaf order:
+12868: u 2 0 2 1,1,2,1,2,1,2,2
+12868: multiply 12 2 6 0,2
+12868: inverse 6 1 3 0,2,2
+12868: z 2 0 2 1,1,1,2,1,2,2
+12868: y 2 0 2 1,1,2,2
+12868: x 2 0 2 1,2
+NO CLASH, using fixed ground order
+12869: Facts:
+12869: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply ?3
+ (multiply
+ (multiply (multiply ?4 (inverse ?4))
+ (inverse (multiply ?2 ?3))) ?2)))
+ =>=
+ ?2
+ [4, 3, 2] by single_non_axiom ?2 ?3 ?4
+12869: Goal:
+12869: Id : 1, {_}:
+ multiply x
+ (inverse
+ (multiply y
+ (multiply
+ (multiply (multiply z (inverse z)) (inverse (multiply u y)))
+ x)))
+ =>=
+ u
+ [] by try_prove_this_axiom
+12869: Order:
+12869: lpo
+12869: Leaf order:
+12869: u 2 0 2 1,1,2,1,2,1,2,2
+12869: multiply 12 2 6 0,2
+12869: inverse 6 1 3 0,2,2
+12869: z 2 0 2 1,1,1,2,1,2,2
+12869: y 2 0 2 1,1,2,2
+12869: x 2 0 2 1,2
+% SZS status Timeout for GRP207-1.p
+Fatal error: exception Assert_failure("matitaprover.ml", 265, 46)
+NO CLASH, using fixed ground order
+12900: Facts:
+12900: Id : 2, {_}:
+ inverse
+ (multiply
+ (inverse
+ (multiply ?2
+ (inverse
+ (multiply (inverse ?3)
+ (inverse
+ (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
+ (multiply ?2 ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+12900: Goal:
+12900: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+12900: Order:
+12900: nrkbo
+12900: Leaf order:
+12900: inverse 7 1 0
+12900: c3 2 0 2 2,2
+12900: multiply 10 2 4 0,2
+12900: b3 2 0 2 2,1,2
+12900: a3 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+12901: Facts:
+12901: Id : 2, {_}:
+ inverse
+ (multiply
+ (inverse
+ (multiply ?2
+ (inverse
+ (multiply (inverse ?3)
+ (inverse
+ (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
+ (multiply ?2 ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+12901: Goal:
+12901: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+12901: Order:
+12901: kbo
+12901: Leaf order:
+12901: inverse 7 1 0
+12901: c3 2 0 2 2,2
+12901: multiply 10 2 4 0,2
+12901: b3 2 0 2 2,1,2
+12901: a3 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+12902: Facts:
+12902: Id : 2, {_}:
+ inverse
+ (multiply
+ (inverse
+ (multiply ?2
+ (inverse
+ (multiply (inverse ?3)
+ (inverse
+ (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
+ (multiply ?2 ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+12902: Goal:
+12902: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+12902: Order:
+12902: lpo
+12902: Leaf order:
+12902: inverse 7 1 0
+12902: c3 2 0 2 2,2
+12902: multiply 10 2 4 0,2
+12902: b3 2 0 2 2,1,2
+12902: a3 2 0 2 1,1,2
+% SZS status Timeout for GRP420-1.p
+NO CLASH, using fixed ground order
+12949: Facts:
+12949: Id : 2, {_}:
+ divide
+ (divide (divide ?2 ?2)
+ (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
+ ?4
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+12949: Id : 3, {_}:
+ multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
+ [8, 7, 6] by multiply ?6 ?7 ?8
+12949: Id : 4, {_}:
+ inverse ?10 =<= divide (divide ?11 ?11) ?10
+ [11, 10] by inverse ?10 ?11
+12949: Goal:
+12949: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+12949: Order:
+12949: nrkbo
+12949: Leaf order:
+12949: inverse 1 1 0
+12949: divide 13 2 0
+12949: c3 2 0 2 2,2
+12949: multiply 5 2 4 0,2
+12949: b3 2 0 2 2,1,2
+12949: a3 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+12950: Facts:
+12950: Id : 2, {_}:
+ divide
+ (divide (divide ?2 ?2)
+ (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
+ ?4
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+12950: Id : 3, {_}:
+ multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
+ [8, 7, 6] by multiply ?6 ?7 ?8
+12950: Id : 4, {_}:
+ inverse ?10 =<= divide (divide ?11 ?11) ?10
+ [11, 10] by inverse ?10 ?11
+12950: Goal:
+12950: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+12950: Order:
+12950: kbo
+12950: Leaf order:
+12950: inverse 1 1 0
+12950: divide 13 2 0
+12950: c3 2 0 2 2,2
+12950: multiply 5 2 4 0,2
+12950: b3 2 0 2 2,1,2
+12950: a3 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+12951: Facts:
+12951: Id : 2, {_}:
+ divide
+ (divide (divide ?2 ?2)
+ (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
+ ?4
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+12951: Id : 3, {_}:
+ multiply ?6 ?7 =?= divide ?6 (divide (divide ?8 ?8) ?7)
+ [8, 7, 6] by multiply ?6 ?7 ?8
+12951: Id : 4, {_}:
+ inverse ?10 =<= divide (divide ?11 ?11) ?10
+ [11, 10] by inverse ?10 ?11
+12951: Goal:
+12951: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+12951: Order:
+12951: lpo
+12951: Leaf order:
+12951: inverse 1 1 0
+12951: divide 13 2 0
+12951: c3 2 0 2 2,2
+12951: multiply 5 2 4 0,2
+12951: b3 2 0 2 2,1,2
+12951: a3 2 0 2 1,1,2
+Statistics :
+Max weight : 38
+Found proof, 2.410071s
+% SZS status Unsatisfiable for GRP453-1.p
+% SZS output start CNFRefutation for GRP453-1.p
+Id : 35, {_}: inverse ?90 =<= divide (divide ?91 ?91) ?90 [91, 90] by inverse ?90 ?91
+Id : 2, {_}: divide (divide (divide ?2 ?2) (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
+Id : 5, {_}: divide (divide (divide ?13 ?13) (divide ?13 (divide ?14 (divide (divide (divide ?13 ?13) ?13) ?15)))) ?15 =>= ?14 [15, 14, 13] by single_axiom ?13 ?14 ?15
+Id : 4, {_}: inverse ?10 =<= divide (divide ?11 ?11) ?10 [11, 10] by inverse ?10 ?11
+Id : 3, {_}: multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) [8, 7, 6] by multiply ?6 ?7 ?8
+Id : 29, {_}: multiply ?6 ?7 =<= divide ?6 (inverse ?7) [7, 6] by Demod 3 with 4 at 2,3
+Id : 6, {_}: divide (divide (divide ?17 ?17) (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Super 5 with 2 at 2,2,1,2
+Id : 142, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 6 with 4 at 1,2
+Id : 143, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 142 with 4 at 3
+Id : 144, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 143 with 4 at 1,2,2,1,3
+Id : 145, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (inverse ?17) ?19)))) [20, 19, 18, 17] by Demod 144 with 4 at 1,2,2,2,1,3
+Id : 36, {_}: inverse ?93 =<= divide (inverse (divide ?94 ?94)) ?93 [94, 93] by Super 35 with 4 at 1,3
+Id : 226, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (divide (divide ?529 ?529) (divide ?527 (inverse (divide (inverse ?526) ?528)))) [529, 528, 527, 526] by Super 145 with 36 at 2,2,1,3
+Id : 249, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (inverse (divide ?527 (inverse (divide (inverse ?526) ?528)))) [528, 527, 526] by Demod 226 with 4 at 1,3
+Id : 250, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (inverse (multiply ?527 (divide (inverse ?526) ?528))) [528, 527, 526] by Demod 249 with 29 at 1,1,3
+Id : 13, {_}: divide (multiply (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50))) ?50 =>= ?49 [50, 49, 48] by Super 2 with 3 at 1,2
+Id : 32, {_}: multiply (divide ?79 ?79) ?80 =>= inverse (inverse ?80) [80, 79] by Super 29 with 4 at 3
+Id : 479, {_}: divide (inverse (inverse (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 13 with 32 at 1,2
+Id : 480, {_}: divide (inverse (inverse (divide ?49 (divide (inverse (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 479 with 4 at 1,2,1,1,1,2
+Id : 481, {_}: divide (inverse (inverse (divide ?49 (inverse ?50)))) ?50 =>= ?49 [50, 49] by Demod 480 with 36 at 2,1,1,1,2
+Id : 482, {_}: divide (inverse (inverse (multiply ?49 ?50))) ?50 =>= ?49 [50, 49] by Demod 481 with 29 at 1,1,1,2
+Id : 888, {_}: divide (inverse (divide ?1873 ?1874)) ?1875 =<= inverse (inverse (multiply ?1874 (divide (inverse ?1873) ?1875))) [1875, 1874, 1873] by Demod 249 with 29 at 1,1,3
+Id : 903, {_}: divide (inverse (divide (divide ?1940 ?1940) ?1941)) ?1942 =>= inverse (inverse (multiply ?1941 (inverse ?1942))) [1942, 1941, 1940] by Super 888 with 36 at 2,1,1,3
+Id : 936, {_}: divide (inverse (inverse ?1941)) ?1942 =<= inverse (inverse (multiply ?1941 (inverse ?1942))) [1942, 1941] by Demod 903 with 4 at 1,1,2
+Id : 969, {_}: divide (inverse (inverse ?2088)) ?2089 =<= inverse (inverse (multiply ?2088 (inverse ?2089))) [2089, 2088] by Demod 903 with 4 at 1,1,2
+Id : 980, {_}: divide (inverse (inverse (divide ?2127 ?2127))) ?2128 =>= inverse (inverse (inverse (inverse (inverse ?2128)))) [2128, 2127] by Super 969 with 32 at 1,1,3
+Id : 223, {_}: inverse ?515 =<= divide (inverse (inverse (divide ?516 ?516))) ?515 [516, 515] by Super 4 with 36 at 1,3
+Id : 1009, {_}: inverse ?2128 =<= inverse (inverse (inverse (inverse (inverse ?2128)))) [2128] by Demod 980 with 223 at 2
+Id : 1026, {_}: multiply ?2199 (inverse (inverse (inverse (inverse ?2200)))) =>= divide ?2199 (inverse ?2200) [2200, 2199] by Super 29 with 1009 at 2,3
+Id : 1064, {_}: multiply ?2199 (inverse (inverse (inverse (inverse ?2200)))) =>= multiply ?2199 ?2200 [2200, 2199] by Demod 1026 with 29 at 3
+Id : 1096, {_}: divide (inverse (inverse ?2287)) (inverse (inverse (inverse ?2288))) =>= inverse (inverse (multiply ?2287 ?2288)) [2288, 2287] by Super 936 with 1064 at 1,1,3
+Id : 1169, {_}: multiply (inverse (inverse ?2287)) (inverse (inverse ?2288)) =>= inverse (inverse (multiply ?2287 ?2288)) [2288, 2287] by Demod 1096 with 29 at 2
+Id : 1211, {_}: divide (inverse (inverse (inverse (inverse ?2471)))) (inverse ?2472) =>= inverse (inverse (inverse (inverse (multiply ?2471 ?2472)))) [2472, 2471] by Super 936 with 1169 at 1,1,3
+Id : 1253, {_}: multiply (inverse (inverse (inverse (inverse ?2471)))) ?2472 =>= inverse (inverse (inverse (inverse (multiply ?2471 ?2472)))) [2472, 2471] by Demod 1211 with 29 at 2
+Id : 1506, {_}: divide (inverse (inverse (inverse (inverse (inverse (inverse (multiply ?3181 ?3182))))))) ?3182 =>= inverse (inverse (inverse (inverse ?3181))) [3182, 3181] by Super 482 with 1253 at 1,1,1,2
+Id : 1558, {_}: divide (inverse (inverse (multiply ?3181 ?3182))) ?3182 =>= inverse (inverse (inverse (inverse ?3181))) [3182, 3181] by Demod 1506 with 1009 at 1,2
+Id : 1559, {_}: ?3181 =<= inverse (inverse (inverse (inverse ?3181))) [3181] by Demod 1558 with 482 at 2
+Id : 1611, {_}: multiply ?3343 (inverse (inverse (inverse ?3344))) =>= divide ?3343 ?3344 [3344, 3343] by Super 29 with 1559 at 2,3
+Id : 1683, {_}: divide (inverse (inverse ?3483)) (inverse (inverse ?3484)) =>= inverse (inverse (divide ?3483 ?3484)) [3484, 3483] by Super 936 with 1611 at 1,1,3
+Id : 1717, {_}: multiply (inverse (inverse ?3483)) (inverse ?3484) =>= inverse (inverse (divide ?3483 ?3484)) [3484, 3483] by Demod 1683 with 29 at 2
+Id : 1782, {_}: divide (inverse (inverse (inverse (inverse (divide ?3605 ?3606))))) (inverse ?3606) =>= inverse (inverse ?3605) [3606, 3605] by Super 482 with 1717 at 1,1,1,2
+Id : 1824, {_}: multiply (inverse (inverse (inverse (inverse (divide ?3605 ?3606))))) ?3606 =>= inverse (inverse ?3605) [3606, 3605] by Demod 1782 with 29 at 2
+Id : 1825, {_}: multiply (divide ?3605 ?3606) ?3606 =>= inverse (inverse ?3605) [3606, 3605] by Demod 1824 with 1559 at 1,2
+Id : 1854, {_}: inverse (inverse ?3731) =<= divide (divide ?3731 (inverse (inverse (inverse ?3732)))) ?3732 [3732, 3731] by Super 1611 with 1825 at 2
+Id : 2653, {_}: inverse (inverse ?5844) =<= divide (multiply ?5844 (inverse (inverse ?5845))) ?5845 [5845, 5844] by Demod 1854 with 29 at 1,3
+Id : 224, {_}: multiply (inverse (inverse (divide ?518 ?518))) ?519 =>= inverse (inverse ?519) [519, 518] by Super 32 with 36 at 1,2
+Id : 2679, {_}: inverse (inverse (inverse (inverse (divide ?5935 ?5935)))) =?= divide (inverse (inverse (inverse (inverse ?5936)))) ?5936 [5936, 5935] by Super 2653 with 224 at 1,3
+Id : 2732, {_}: divide ?5935 ?5935 =?= divide (inverse (inverse (inverse (inverse ?5936)))) ?5936 [5936, 5935] by Demod 2679 with 1559 at 2
+Id : 2733, {_}: divide ?5935 ?5935 =?= divide ?5936 ?5936 [5936, 5935] by Demod 2732 with 1559 at 1,3
+Id : 2794, {_}: divide (inverse (divide ?6115 (divide (inverse ?6116) (divide (inverse ?6115) ?6117)))) ?6117 =?= inverse (divide ?6116 (divide ?6118 ?6118)) [6118, 6117, 6116, 6115] by Super 145 with 2733 at 2,1,3
+Id : 30, {_}: divide (inverse (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 2 with 4 at 1,2
+Id : 31, {_}: divide (inverse (divide ?2 (divide ?3 (divide (inverse ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 30 with 4 at 1,2,2,1,1,2
+Id : 2869, {_}: inverse ?6116 =<= inverse (divide ?6116 (divide ?6118 ?6118)) [6118, 6116] by Demod 2794 with 31 at 2
+Id : 2925, {_}: divide ?6471 (divide ?6472 ?6472) =>= inverse (inverse (inverse (inverse ?6471))) [6472, 6471] by Super 1559 with 2869 at 1,1,1,3
+Id : 2977, {_}: divide ?6471 (divide ?6472 ?6472) =>= ?6471 [6472, 6471] by Demod 2925 with 1559 at 3
+Id : 3050, {_}: divide (inverse (divide ?6728 ?6729)) (divide ?6730 ?6730) =>= inverse (inverse (multiply ?6729 (inverse ?6728))) [6730, 6729, 6728] by Super 250 with 2977 at 2,1,1,3
+Id : 3110, {_}: inverse (divide ?6728 ?6729) =<= inverse (inverse (multiply ?6729 (inverse ?6728))) [6729, 6728] by Demod 3050 with 2977 at 2
+Id : 3383, {_}: inverse (divide ?7439 ?7440) =<= divide (inverse (inverse ?7440)) ?7439 [7440, 7439] by Demod 3110 with 936 at 3
+Id : 1622, {_}: ?3381 =<= inverse (inverse (inverse (inverse ?3381))) [3381] by Demod 1558 with 482 at 2
+Id : 1636, {_}: multiply ?3417 (inverse ?3418) =<= inverse (inverse (divide (inverse (inverse ?3417)) ?3418)) [3418, 3417] by Super 1622 with 936 at 1,1,3
+Id : 3111, {_}: inverse (divide ?6728 ?6729) =<= divide (inverse (inverse ?6729)) ?6728 [6729, 6728] by Demod 3110 with 936 at 3
+Id : 3340, {_}: multiply ?3417 (inverse ?3418) =<= inverse (inverse (inverse (divide ?3418 ?3417))) [3418, 3417] by Demod 1636 with 3111 at 1,1,3
+Id : 3404, {_}: inverse (divide ?7516 (inverse (divide ?7517 ?7518))) =>= divide (multiply ?7518 (inverse ?7517)) ?7516 [7518, 7517, 7516] by Super 3383 with 3340 at 1,3
+Id : 3497, {_}: inverse (multiply ?7516 (divide ?7517 ?7518)) =<= divide (multiply ?7518 (inverse ?7517)) ?7516 [7518, 7517, 7516] by Demod 3404 with 29 at 1,2
+Id : 229, {_}: inverse ?541 =<= divide (inverse (divide ?542 ?542)) ?541 [542, 541] by Super 35 with 4 at 1,3
+Id : 236, {_}: inverse ?562 =<= divide (inverse (inverse (inverse (divide ?563 ?563)))) ?562 [563, 562] by Super 229 with 36 at 1,1,3
+Id : 3338, {_}: inverse ?562 =<= inverse (divide ?562 (inverse (divide ?563 ?563))) [563, 562] by Demod 236 with 3111 at 3
+Id : 3343, {_}: inverse ?562 =<= inverse (multiply ?562 (divide ?563 ?563)) [563, 562] by Demod 3338 with 29 at 1,3
+Id : 3051, {_}: multiply ?6732 (divide ?6733 ?6733) =>= inverse (inverse ?6732) [6733, 6732] by Super 1825 with 2977 at 1,2
+Id : 3711, {_}: inverse ?562 =<= inverse (inverse (inverse ?562)) [562] by Demod 3343 with 3051 at 1,3
+Id : 3714, {_}: multiply ?3343 (inverse ?3344) =>= divide ?3343 ?3344 [3344, 3343] by Demod 1611 with 3711 at 2,2
+Id : 4200, {_}: inverse (multiply ?8647 (divide ?8648 ?8649)) =>= divide (divide ?8649 ?8648) ?8647 [8649, 8648, 8647] by Demod 3497 with 3714 at 1,3
+Id : 3401, {_}: inverse (divide ?7505 (inverse (inverse ?7506))) =>= divide ?7506 ?7505 [7506, 7505] by Super 3383 with 1559 at 1,3
+Id : 3496, {_}: inverse (multiply ?7505 (inverse ?7506)) =>= divide ?7506 ?7505 [7506, 7505] by Demod 3401 with 29 at 1,2
+Id : 3715, {_}: inverse (divide ?7505 ?7506) =>= divide ?7506 ?7505 [7506, 7505] by Demod 3496 with 3714 at 1,2
+Id : 3725, {_}: divide (divide ?527 ?526) ?528 =<= inverse (inverse (multiply ?527 (divide (inverse ?526) ?528))) [528, 526, 527] by Demod 250 with 3715 at 1,2
+Id : 3337, {_}: inverse (divide ?50 (multiply ?49 ?50)) =>= ?49 [49, 50] by Demod 482 with 3111 at 2
+Id : 3721, {_}: divide (multiply ?49 ?50) ?50 =>= ?49 [50, 49] by Demod 3337 with 3715 at 2
+Id : 1860, {_}: multiply (divide ?3752 ?3753) ?3753 =>= inverse (inverse ?3752) [3753, 3752] by Demod 1824 with 1559 at 1,2
+Id : 1869, {_}: multiply (multiply ?3781 ?3782) (inverse ?3782) =>= inverse (inverse ?3781) [3782, 3781] by Super 1860 with 29 at 1,2
+Id : 3717, {_}: divide (multiply ?3781 ?3782) ?3782 =>= inverse (inverse ?3781) [3782, 3781] by Demod 1869 with 3714 at 2
+Id : 3737, {_}: inverse (inverse ?49) =>= ?49 [49] by Demod 3721 with 3717 at 2
+Id : 3738, {_}: divide (divide ?527 ?526) ?528 =<= multiply ?527 (divide (inverse ?526) ?528) [528, 526, 527] by Demod 3725 with 3737 at 3
+Id : 4230, {_}: inverse (divide (divide ?8777 ?8778) ?8779) =<= divide (divide ?8779 (inverse ?8778)) ?8777 [8779, 8778, 8777] by Super 4200 with 3738 at 1,2
+Id : 4280, {_}: divide ?8779 (divide ?8777 ?8778) =<= divide (divide ?8779 (inverse ?8778)) ?8777 [8778, 8777, 8779] by Demod 4230 with 3715 at 2
+Id : 4281, {_}: divide ?8779 (divide ?8777 ?8778) =<= divide (multiply ?8779 ?8778) ?8777 [8778, 8777, 8779] by Demod 4280 with 29 at 1,3
+Id : 4962, {_}: multiply (multiply ?10173 ?10174) ?10175 =<= divide ?10173 (divide (inverse ?10175) ?10174) [10175, 10174, 10173] by Super 29 with 4281 at 3
+Id : 4205, {_}: inverse (multiply ?8667 ?8668) =<= divide (divide (divide ?8669 ?8669) ?8668) ?8667 [8669, 8668, 8667] by Super 4200 with 2977 at 2,1,2
+Id : 4245, {_}: inverse (multiply ?8667 ?8668) =<= divide (inverse ?8668) ?8667 [8668, 8667] by Demod 4205 with 4 at 1,3
+Id : 5005, {_}: multiply (multiply ?10173 ?10174) ?10175 =<= divide ?10173 (inverse (multiply ?10174 ?10175)) [10175, 10174, 10173] by Demod 4962 with 4245 at 2,3
+Id : 5006, {_}: multiply (multiply ?10173 ?10174) ?10175 =>= multiply ?10173 (multiply ?10174 ?10175) [10175, 10174, 10173] by Demod 5005 with 29 at 3
+Id : 5130, {_}: multiply a3 (multiply b3 c3) =?= multiply a3 (multiply b3 c3) [] by Demod 1 with 5006 at 2
+Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
+% SZS output end CNFRefutation for GRP453-1.p
+12950: solved GRP453-1.p in 1.216075 using kbo
+12950: status Unsatisfiable for GRP453-1.p
+Fatal error: exception Assert_failure("matitaprover.ml", 265, 46)
+NO CLASH, using fixed ground order
+12960: Facts:
+12960: Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3
+12960: Id : 3, {_}:
+ meet ?5 (join ?6 ?7) =<= join (meet ?7 ?5) (meet ?6 ?5)
+ [7, 6, 5] by distribution ?5 ?6 ?7
+12960: Goal:
+12960: Id : 1, {_}:
+ join (join a b) c =>= join a (join b c)
+ [] by prove_associativity_of_join
+12960: Order:
+12960: nrkbo
+12960: Leaf order:
+12960: meet 4 2 0
+12960: c 2 0 2 2,2
+12960: join 7 2 4 0,2
+12960: b 2 0 2 2,1,2
+12960: a 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+12962: Facts:
+12962: Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3
+12962: Id : 3, {_}:
+ meet ?5 (join ?6 ?7) =?= join (meet ?7 ?5) (meet ?6 ?5)
+ [7, 6, 5] by distribution ?5 ?6 ?7
+12962: Goal:
+12962: Id : 1, {_}:
+ join (join a b) c =>= join a (join b c)
+ [] by prove_associativity_of_join
+12962: Order:
+12962: lpo
+12962: Leaf order:
+12962: meet 4 2 0
+12962: c 2 0 2 2,2
+12962: join 7 2 4 0,2
+12962: b 2 0 2 2,1,2
+12962: a 2 0 2 1,1,2
+12961: Facts:
+12961: Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3
+12961: Id : 3, {_}:
+ meet ?5 (join ?6 ?7) =<= join (meet ?7 ?5) (meet ?6 ?5)
+ [7, 6, 5] by distribution ?5 ?6 ?7
+12961: Goal:
+12961: Id : 1, {_}:
+ join (join a b) c =>= join a (join b c)
+ [] by prove_associativity_of_join
+12961: Order:
+12961: kbo
+12961: Leaf order:
+12961: meet 4 2 0
+12961: c 2 0 2 2,2
+12961: join 7 2 4 0,2
+12961: b 2 0 2 2,1,2
+12961: a 2 0 2 1,1,2
+Statistics :
+Max weight : 22
+Found proof, 37.088774s
+% SZS status Unsatisfiable for LAT007-1.p
+% SZS output start CNFRefutation for LAT007-1.p
+Id : 3, {_}: meet ?5 (join ?6 ?7) =<= join (meet ?7 ?5) (meet ?6 ?5) [7, 6, 5] by distribution ?5 ?6 ?7
+Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3
+Id : 7, {_}: meet ?18 (join ?19 ?20) =<= join (meet ?20 ?18) (meet ?19 ?18) [20, 19, 18] by distribution ?18 ?19 ?20
+Id : 8, {_}: meet (join ?22 ?23) (join ?22 ?24) =<= join (meet ?24 (join ?22 ?23)) ?22 [24, 23, 22] by Super 7 with 2 at 2,3
+Id : 122, {_}: meet (meet ?274 ?275) (meet ?275 (join ?276 ?274)) =>= meet ?274 ?275 [276, 275, 274] by Super 2 with 3 at 2,2
+Id : 132, {_}: meet (meet ?317 ?318) ?318 =>= meet ?317 ?318 [318, 317] by Super 122 with 2 at 2,2
+Id : 166, {_}: meet ?380 (join ?381 (meet ?382 ?380)) =<= join (meet ?382 ?380) (meet ?381 ?380) [382, 381, 380] by Super 3 with 132 at 1,3
+Id : 405, {_}: meet ?915 (join ?916 (meet ?917 ?915)) =>= meet ?915 (join ?916 ?917) [917, 916, 915] by Demod 166 with 3 at 3
+Id : 419, {_}: meet ?974 (meet ?974 (join ?975 ?976)) =?= meet ?974 (join (meet ?976 ?974) ?975) [976, 975, 974] by Super 405 with 3 at 2,2
+Id : 165, {_}: meet ?376 (join (meet ?377 ?376) ?378) =<= join (meet ?378 ?376) (meet ?377 ?376) [378, 377, 376] by Super 3 with 132 at 2,3
+Id : 187, {_}: meet ?376 (join (meet ?377 ?376) ?378) =>= meet ?376 (join ?377 ?378) [378, 377, 376] by Demod 165 with 3 at 3
+Id : 473, {_}: meet ?1062 (meet ?1062 (join ?1063 ?1064)) =>= meet ?1062 (join ?1064 ?1063) [1064, 1063, 1062] by Demod 419 with 187 at 3
+Id : 484, {_}: meet ?1111 ?1111 =<= meet ?1111 (join ?1112 ?1111) [1112, 1111] by Super 473 with 2 at 2,2
+Id : 590, {_}: meet (join ?1333 ?1334) (join ?1333 ?1334) =>= join (meet ?1334 ?1334) ?1333 [1334, 1333] by Super 8 with 484 at 1,3
+Id : 593, {_}: meet ?1344 ?1344 =>= ?1344 [1344] by Super 2 with 484 at 2
+Id : 2478, {_}: join ?1333 ?1334 =<= join (meet ?1334 ?1334) ?1333 [1334, 1333] by Demod 590 with 593 at 2
+Id : 2479, {_}: join ?1333 ?1334 =?= join ?1334 ?1333 [1334, 1333] by Demod 2478 with 593 at 1,3
+Id : 639, {_}: meet ?1436 (join ?1437 ?1436) =<= join ?1436 (meet ?1437 ?1436) [1437, 1436] by Super 3 with 593 at 1,3
+Id : 631, {_}: ?1111 =<= meet ?1111 (join ?1112 ?1111) [1112, 1111] by Demod 484 with 593 at 2
+Id : 669, {_}: ?1436 =<= join ?1436 (meet ?1437 ?1436) [1437, 1436] by Demod 639 with 631 at 2
+Id : 53, {_}: meet (join ?112 ?113) (join ?112 ?114) =<= join (meet ?114 (join ?112 ?113)) ?112 [114, 113, 112] by Super 7 with 2 at 2,3
+Id : 62, {_}: meet (join ?150 ?151) (join ?150 ?150) =>= join ?150 ?150 [151, 150] by Super 53 with 2 at 1,3
+Id : 57, {_}: meet (join (meet ?128 ?129) (meet ?130 ?129)) (join (meet ?128 ?129) ?131) =>= join (meet ?131 (meet ?129 (join ?130 ?128))) (meet ?128 ?129) [131, 130, 129, 128] by Super 53 with 3 at 2,1,3
+Id : 73, {_}: meet (meet ?129 (join ?130 ?128)) (join (meet ?128 ?129) ?131) =<= join (meet ?131 (meet ?129 (join ?130 ?128))) (meet ?128 ?129) [131, 128, 130, 129] by Demod 57 with 3 at 1,2
+Id : 642, {_}: meet (meet ?1444 (join ?1445 ?1444)) (join (meet ?1444 ?1444) ?1446) =>= join (meet ?1446 (meet ?1444 (join ?1445 ?1444))) ?1444 [1446, 1445, 1444] by Super 73 with 593 at 2,3
+Id : 657, {_}: meet ?1444 (join (meet ?1444 ?1444) ?1446) =<= join (meet ?1446 (meet ?1444 (join ?1445 ?1444))) ?1444 [1445, 1446, 1444] by Demod 642 with 631 at 1,2
+Id : 658, {_}: meet ?1444 (join ?1444 ?1446) =<= join (meet ?1446 (meet ?1444 (join ?1445 ?1444))) ?1444 [1445, 1446, 1444] by Demod 657 with 593 at 1,2,2
+Id : 659, {_}: meet ?1444 (join ?1444 ?1446) =<= join (meet ?1446 ?1444) ?1444 [1446, 1444] by Demod 658 with 631 at 2,1,3
+Id : 699, {_}: ?1517 =<= join (meet ?1518 ?1517) ?1517 [1518, 1517] by Demod 659 with 2 at 2
+Id : 711, {_}: ?1557 =<= join ?1557 ?1557 [1557] by Super 699 with 593 at 1,3
+Id : 744, {_}: meet (join ?150 ?151) ?150 =>= join ?150 ?150 [151, 150] by Demod 62 with 711 at 2,2
+Id : 745, {_}: meet (join ?150 ?151) ?150 =>= ?150 [151, 150] by Demod 744 with 711 at 3
+Id : 713, {_}: join ?1562 ?1563 =<= join ?1563 (join ?1562 ?1563) [1563, 1562] by Super 699 with 631 at 1,3
+Id : 1157, {_}: meet (join ?2329 ?2330) ?2330 =>= ?2330 [2330, 2329] by Super 745 with 713 at 1,2
+Id : 1688, {_}: meet ?3262 (join (join ?3263 ?3262) ?3264) =>= join (meet ?3264 ?3262) ?3262 [3264, 3263, 3262] by Super 3 with 1157 at 2,3
+Id : 660, {_}: ?1444 =<= join (meet ?1446 ?1444) ?1444 [1446, 1444] by Demod 659 with 2 at 2
+Id : 1738, {_}: meet ?3262 (join (join ?3263 ?3262) ?3264) =>= ?3262 [3264, 3263, 3262] by Demod 1688 with 660 at 3
+Id : 4104, {_}: join (join ?7363 ?7364) ?7365 =<= join (join (join ?7363 ?7364) ?7365) ?7364 [7365, 7364, 7363] by Super 669 with 1738 at 2,3
+Id : 9885, {_}: join (join ?18104 ?18105) ?18106 =<= join ?18105 (join (join ?18104 ?18105) ?18106) [18106, 18105, 18104] by Demod 4104 with 2479 at 3
+Id : 9889, {_}: join (join ?18120 ?18121) ?18122 =<= join ?18121 (join (join ?18121 ?18120) ?18122) [18122, 18121, 18120] by Super 9885 with 2479 at 1,2,3
+Id : 4118, {_}: meet ?7422 (join (join ?7423 ?7422) ?7424) =>= ?7422 [7424, 7423, 7422] by Demod 1688 with 660 at 3
+Id : 4122, {_}: meet ?7438 (join (join ?7438 ?7439) ?7440) =>= ?7438 [7440, 7439, 7438] by Super 4118 with 2479 at 1,2,2
+Id : 9604, {_}: join (join ?17475 ?17476) ?17477 =<= join (join (join ?17475 ?17476) ?17477) ?17475 [17477, 17476, 17475] by Super 669 with 4122 at 2,3
+Id : 9740, {_}: join (join ?17475 ?17476) ?17477 =<= join ?17475 (join (join ?17475 ?17476) ?17477) [17477, 17476, 17475] by Demod 9604 with 2479 at 3
+Id : 16688, {_}: join (join ?18120 ?18121) ?18122 =?= join (join ?18121 ?18120) ?18122 [18122, 18121, 18120] by Demod 9889 with 9740 at 3
+Id : 9, {_}: meet (join ?26 ?27) (join ?28 ?26) =<= join ?26 (meet ?28 (join ?26 ?27)) [28, 27, 26] by Super 7 with 2 at 1,3
+Id : 753, {_}: meet ?1599 (join ?1600 ?1600) =>= meet ?1600 ?1599 [1600, 1599] by Super 3 with 711 at 3
+Id : 773, {_}: meet ?1599 ?1600 =?= meet ?1600 ?1599 [1600, 1599] by Demod 753 with 711 at 2,2
+Id : 2380, {_}: meet (join ?4513 ?4514) (join ?4515 ?4513) =<= join ?4513 (meet (join ?4513 ?4514) ?4515) [4515, 4514, 4513] by Super 9 with 773 at 2,3
+Id : 2506, {_}: meet (join ?4784 ?4785) (join ?4786 ?4784) =<= join ?4784 (meet ?4786 (join ?4785 ?4784)) [4786, 4785, 4784] by Super 9 with 2479 at 2,2,3
+Id : 1153, {_}: meet (join ?2312 (join ?2313 ?2312)) (join ?2314 ?2312) =>= join ?2312 (meet ?2314 (join ?2313 ?2312)) [2314, 2313, 2312] by Super 9 with 713 at 2,2,3
+Id : 1191, {_}: meet (join ?2313 ?2312) (join ?2314 ?2312) =<= join ?2312 (meet ?2314 (join ?2313 ?2312)) [2314, 2312, 2313] by Demod 1153 with 713 at 1,2
+Id : 5434, {_}: meet (join ?4784 ?4785) (join ?4786 ?4784) =?= meet (join ?4785 ?4784) (join ?4786 ?4784) [4786, 4785, 4784] by Demod 2506 with 1191 at 3
+Id : 455, {_}: meet ?974 (meet ?974 (join ?975 ?976)) =>= meet ?974 (join ?976 ?975) [976, 975, 974] by Demod 419 with 187 at 3
+Id : 757, {_}: meet ?1611 (meet ?1611 ?1612) =?= meet ?1611 (join ?1612 ?1612) [1612, 1611] by Super 455 with 711 at 2,2,2
+Id : 767, {_}: meet ?1611 (meet ?1611 ?1612) =>= meet ?1611 ?1612 [1612, 1611] by Demod 757 with 711 at 2,3
+Id : 1239, {_}: meet (meet ?2426 ?2427) (join ?2426 ?2428) =<= join (meet ?2428 (meet ?2426 ?2427)) (meet ?2426 ?2427) [2428, 2427, 2426] by Super 3 with 767 at 2,3
+Id : 1275, {_}: meet (meet ?2426 ?2427) (join ?2426 ?2428) =>= meet ?2426 ?2427 [2428, 2427, 2426] by Demod 1239 with 660 at 3
+Id : 30976, {_}: meet (join ?55510 ?55511) (join (meet ?55510 ?55512) ?55511) =>= join ?55511 (meet ?55510 ?55512) [55512, 55511, 55510] by Super 1191 with 1275 at 2,3
+Id : 30986, {_}: meet (join ?55551 ?55552) (join (meet ?55553 ?55551) ?55552) =>= join ?55552 (meet ?55551 ?55553) [55553, 55552, 55551] by Super 30976 with 773 at 1,2,2
+Id : 3010, {_}: meet (join ?5441 ?5442) (join ?5443 ?5442) =<= join ?5442 (meet ?5443 (join ?5441 ?5442)) [5443, 5442, 5441] by Demod 1153 with 713 at 1,2
+Id : 3031, {_}: meet (join (meet ?5530 ?5531) ?5532) (join ?5531 ?5532) =>= join ?5532 (meet ?5531 (join ?5530 ?5532)) [5532, 5531, 5530] by Super 3010 with 187 at 2,3
+Id : 3109, {_}: meet (join ?5531 ?5532) (join (meet ?5530 ?5531) ?5532) =>= join ?5532 (meet ?5531 (join ?5530 ?5532)) [5530, 5532, 5531] by Demod 3031 with 773 at 2
+Id : 3110, {_}: meet (join ?5531 ?5532) (join (meet ?5530 ?5531) ?5532) =>= meet (join ?5530 ?5532) (join ?5531 ?5532) [5530, 5532, 5531] by Demod 3109 with 1191 at 3
+Id : 31246, {_}: meet (join ?55553 ?55552) (join ?55551 ?55552) =>= join ?55552 (meet ?55551 ?55553) [55551, 55552, 55553] by Demod 30986 with 3110 at 2
+Id : 31561, {_}: meet (join ?4784 ?4785) (join ?4786 ?4784) =>= join ?4784 (meet ?4786 ?4785) [4786, 4785, 4784] by Demod 5434 with 31246 at 3
+Id : 31569, {_}: join ?4513 (meet ?4515 ?4514) =<= join ?4513 (meet (join ?4513 ?4514) ?4515) [4514, 4515, 4513] by Demod 2380 with 31561 at 2
+Id : 31659, {_}: join ?56550 (meet (join ?56551 ?56552) ?56552) =?= join ?56550 (join ?56552 (meet ?56551 ?56550)) [56552, 56551, 56550] by Super 31569 with 31246 at 2,3
+Id : 31781, {_}: join ?56550 (meet ?56552 (join ?56551 ?56552)) =?= join ?56550 (join ?56552 (meet ?56551 ?56550)) [56551, 56552, 56550] by Demod 31659 with 773 at 2,2
+Id : 32533, {_}: join ?58368 ?58369 =<= join ?58368 (join ?58369 (meet ?58370 ?58368)) [58370, 58369, 58368] by Demod 31781 with 631 at 2,2
+Id : 32536, {_}: join (join ?58380 ?58381) ?58382 =<= join (join ?58380 ?58381) (join ?58382 ?58380) [58382, 58381, 58380] by Super 32533 with 2 at 2,2,3
+Id : 35660, {_}: join (join ?62824 ?62825) (join ?62825 ?62826) =>= join (join ?62825 ?62826) ?62824 [62826, 62825, 62824] by Super 2479 with 32536 at 3
+Id : 188, {_}: meet ?380 (join ?381 (meet ?382 ?380)) =>= meet ?380 (join ?381 ?382) [382, 381, 380] by Demod 166 with 3 at 3
+Id : 1695, {_}: meet ?3292 (join ?3293 ?3292) =<= meet ?3292 (join ?3293 (join ?3294 ?3292)) [3294, 3293, 3292] by Super 188 with 1157 at 2,2,2
+Id : 1732, {_}: ?3292 =<= meet ?3292 (join ?3293 (join ?3294 ?3292)) [3294, 3293, 3292] by Demod 1695 with 631 at 2
+Id : 3955, {_}: join ?7063 (join ?7064 ?7065) =<= join (join ?7063 (join ?7064 ?7065)) ?7065 [7065, 7064, 7063] by Super 669 with 1732 at 2,3
+Id : 9413, {_}: join ?17183 (join ?17184 ?17185) =<= join ?17185 (join ?17183 (join ?17184 ?17185)) [17185, 17184, 17183] by Demod 3955 with 2479 at 3
+Id : 9417, {_}: join ?17199 (join ?17200 ?17201) =<= join ?17201 (join ?17199 (join ?17201 ?17200)) [17201, 17200, 17199] by Super 9413 with 2479 at 2,2,3
+Id : 3974, {_}: ?7142 =<= meet ?7142 (join ?7143 (join ?7144 ?7142)) [7144, 7143, 7142] by Demod 1695 with 631 at 2
+Id : 3978, {_}: ?7158 =<= meet ?7158 (join ?7159 (join ?7158 ?7160)) [7160, 7159, 7158] by Super 3974 with 2479 at 2,2,3
+Id : 8662, {_}: join ?15620 (join ?15621 ?15622) =<= join (join ?15620 (join ?15621 ?15622)) ?15621 [15622, 15621, 15620] by Super 669 with 3978 at 2,3
+Id : 8767, {_}: join ?15620 (join ?15621 ?15622) =<= join ?15621 (join ?15620 (join ?15621 ?15622)) [15622, 15621, 15620] by Demod 8662 with 2479 at 3
+Id : 15553, {_}: join ?17199 (join ?17200 ?17201) =?= join ?17199 (join ?17201 ?17200) [17201, 17200, 17199] by Demod 9417 with 8767 at 3
+Id : 31782, {_}: join ?56550 ?56552 =<= join ?56550 (join ?56552 (meet ?56551 ?56550)) [56551, 56552, 56550] by Demod 31781 with 631 at 2,2
+Id : 35263, {_}: join ?62192 (join (meet ?62193 ?62192) ?62194) =>= join ?62192 ?62194 [62194, 62193, 62192] by Super 15553 with 31782 at 3
+Id : 35296, {_}: join (join ?62350 ?62351) (join ?62351 ?62352) =>= join (join ?62350 ?62351) ?62352 [62352, 62351, 62350] by Super 35263 with 631 at 1,2,2
+Id : 38052, {_}: join (join ?62824 ?62825) ?62826 =?= join (join ?62825 ?62826) ?62824 [62826, 62825, 62824] by Demod 35660 with 35296 at 2
+Id : 38125, {_}: join ?67897 (join ?67898 ?67899) =<= join (join ?67899 ?67897) ?67898 [67899, 67898, 67897] by Super 2479 with 38052 at 3
+Id : 38567, {_}: join ?18121 (join ?18122 ?18120) =<= join (join ?18121 ?18120) ?18122 [18120, 18122, 18121] by Demod 16688 with 38125 at 2
+Id : 38568, {_}: join ?18121 (join ?18122 ?18120) =?= join ?18120 (join ?18122 ?18121) [18120, 18122, 18121] by Demod 38567 with 38125 at 3
+Id : 39014, {_}: join c (join b a) =?= join c (join b a) [] by Demod 39013 with 2479 at 2,2
+Id : 39013, {_}: join c (join a b) =?= join c (join b a) [] by Demod 39012 with 38568 at 3
+Id : 39012, {_}: join c (join a b) =<= join a (join b c) [] by Demod 1 with 2479 at 2
+Id : 1, {_}: join (join a b) c =>= join a (join b c) [] by prove_associativity_of_join
+% SZS output end CNFRefutation for LAT007-1.p
+12961: solved LAT007-1.p in 17.645102 using kbo
+12961: status Unsatisfiable for LAT007-1.p
+NO CLASH, using fixed ground order
+12978: Facts:
+12978: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
+12978: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
+12978: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
+12978: Id : 5, {_}:
+ meet ?9 ?10 =?= meet ?10 ?9
+ [10, 9] by commutativity_of_meet ?9 ?10
+12978: Id : 6, {_}:
+ join ?12 ?13 =?= join ?13 ?12
+ [13, 12] by commutativity_of_join ?12 ?13
+12978: Id : 7, {_}:
+ meet (meet ?15 ?16) ?17 =?= meet ?15 (meet ?16 ?17)
+ [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
+12978: Id : 8, {_}:
+ join (join ?19 ?20) ?21 =?= join ?19 (join ?20 ?21)
+ [21, 20, 19] by associativity_of_join ?19 ?20 ?21
+12978: Id : 9, {_}:
+ complement (complement ?23) =>= ?23
+ [23] by complement_involution ?23
+12978: Id : 10, {_}:
+ join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
+ [26, 25] by join_complement ?25 ?26
+12978: Id : 11, {_}:
+ meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
+ [29, 28] by meet_complement ?28 ?29
+12978: Goal:
+12978: Id : 1, {_}:
+ join (complement (join (meet a (complement b)) (complement a)))
+ (join (meet a (complement b))
+ (join
+ (meet (complement a) (meet (join a (complement b)) (join a b)))
+ (meet (complement a)
+ (complement (meet (join a (complement b)) (join a b))))))
+ =>=
+ n1
+ [] by prove_e1
+12978: Order:
+12978: nrkbo
+12978: Leaf order:
+12978: n0 1 0 0
+12978: n1 2 0 1 3
+12978: join 20 2 8 0,2
+12978: meet 15 2 6 0,1,1,1,2
+12978: complement 18 1 9 0,1,2
+12978: b 6 0 6 1,2,1,1,1,2
+12978: a 9 0 9 1,1,1,1,2
+NO CLASH, using fixed ground order
+12979: Facts:
+12979: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
+12979: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
+12979: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
+12979: Id : 5, {_}:
+ meet ?9 ?10 =?= meet ?10 ?9
+ [10, 9] by commutativity_of_meet ?9 ?10
+12979: Id : 6, {_}:
+ join ?12 ?13 =?= join ?13 ?12
+ [13, 12] by commutativity_of_join ?12 ?13
+12979: Id : 7, {_}:
+ meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
+ [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
+12979: Id : 8, {_}:
+ join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
+ [21, 20, 19] by associativity_of_join ?19 ?20 ?21
+12979: Id : 9, {_}:
+ complement (complement ?23) =>= ?23
+ [23] by complement_involution ?23
+12979: Id : 10, {_}:
+ join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
+ [26, 25] by join_complement ?25 ?26
+12979: Id : 11, {_}:
+ meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
+ [29, 28] by meet_complement ?28 ?29
+12979: Goal:
+12979: Id : 1, {_}:
+ join (complement (join (meet a (complement b)) (complement a)))
+ (join (meet a (complement b))
+ (join
+ (meet (complement a) (meet (join a (complement b)) (join a b)))
+ (meet (complement a)
+ (complement (meet (join a (complement b)) (join a b))))))
+ =>=
+ n1
+ [] by prove_e1
+12979: Order:
+12979: kbo
+12979: Leaf order:
+12979: n0 1 0 0
+12979: n1 2 0 1 3
+12979: join 20 2 8 0,2
+12979: meet 15 2 6 0,1,1,1,2
+12979: complement 18 1 9 0,1,2
+12979: b 6 0 6 1,2,1,1,1,2
+12979: a 9 0 9 1,1,1,1,2
+NO CLASH, using fixed ground order
+12980: Facts:
+12980: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
+12980: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
+12980: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
+12980: Id : 5, {_}:
+ meet ?9 ?10 =?= meet ?10 ?9
+ [10, 9] by commutativity_of_meet ?9 ?10
+12980: Id : 6, {_}:
+ join ?12 ?13 =?= join ?13 ?12
+ [13, 12] by commutativity_of_join ?12 ?13
+12980: Id : 7, {_}:
+ meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
+ [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
+12980: Id : 8, {_}:
+ join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
+ [21, 20, 19] by associativity_of_join ?19 ?20 ?21
+12980: Id : 9, {_}:
+ complement (complement ?23) =>= ?23
+ [23] by complement_involution ?23
+12980: Id : 10, {_}:
+ join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
+ [26, 25] by join_complement ?25 ?26
+12980: Id : 11, {_}:
+ meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
+ [29, 28] by meet_complement ?28 ?29
+12980: Goal:
+12980: Id : 1, {_}:
+ join (complement (join (meet a (complement b)) (complement a)))
+ (join (meet a (complement b))
+ (join
+ (meet (complement a) (meet (join a (complement b)) (join a b)))
+ (meet (complement a)
+ (complement (meet (join a (complement b)) (join a b))))))
+ =>=
+ n1
+ [] by prove_e1
+12980: Order:
+12980: lpo
+12980: Leaf order:
+12980: n0 1 0 0
+12980: n1 2 0 1 3
+12980: join 20 2 8 0,2
+12980: meet 15 2 6 0,1,1,1,2
+12980: complement 18 1 9 0,1,2
+12980: b 6 0 6 1,2,1,1,1,2
+12980: a 9 0 9 1,1,1,1,2
+% SZS status Timeout for LAT016-1.p
+NO CLASH, using fixed ground order
+12998: Facts:
+12998: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+12998: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+NO CLASH, using fixed ground order
+12999: Facts:
+12999: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+12999: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+12999: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
+12999: Id : 5, {_}:
+ join ?9 ?10 =?= join ?10 ?9
+ [10, 9] by commutativity_of_join ?9 ?10
+12999: Id : 6, {_}:
+ meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14)
+ [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
+12999: Id : 7, {_}:
+ join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18)
+ [18, 17, 16] by associativity_of_join ?16 ?17 ?18
+12999: Id : 8, {_}:
+ join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
+ =>=
+ meet ?20 (join ?21 ?22)
+ [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
+NO CLASH, using fixed ground order
+13000: Facts:
+13000: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13000: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13000: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
+13000: Id : 5, {_}:
+ join ?9 ?10 =?= join ?10 ?9
+ [10, 9] by commutativity_of_join ?9 ?10
+13000: Id : 6, {_}:
+ meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14)
+ [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
+13000: Id : 7, {_}:
+ join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18)
+ [18, 17, 16] by associativity_of_join ?16 ?17 ?18
+13000: Id : 8, {_}:
+ join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
+ =>=
+ meet ?20 (join ?21 ?22)
+ [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
+13000: Id : 9, {_}:
+ meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
+ =>=
+ join ?24 (meet ?25 ?26)
+ [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
+13000: Id : 10, {_}: meet2 ?28 ?28 =>= ?28 [28] by idempotence_of_meet2 ?28
+13000: Id : 11, {_}:
+ meet2 ?30 ?31 =?= meet2 ?31 ?30
+ [31, 30] by commutativity_of_meet2 ?30 ?31
+13000: Id : 12, {_}:
+ meet2 (meet2 ?33 ?34) ?35 =>= meet2 ?33 (meet2 ?34 ?35)
+ [35, 34, 33] by associativity_of_meet2 ?33 ?34 ?35
+12998: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
+12999: Id : 9, {_}:
+ meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
+ =>=
+ join ?24 (meet ?25 ?26)
+ [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
+12998: Id : 5, {_}:
+ join ?9 ?10 =?= join ?10 ?9
+ [10, 9] by commutativity_of_join ?9 ?10
+13000: Id : 13, {_}:
+ join (meet2 ?37 (join ?38 ?39)) (meet2 ?37 ?38)
+ =>=
+ meet2 ?37 (join ?38 ?39)
+ [39, 38, 37] by quasi_lattice1_2 ?37 ?38 ?39
+13000: Id : 14, {_}:
+ meet2 (join ?41 (meet2 ?42 ?43)) (join ?41 ?42)
+ =>=
+ join ?41 (meet2 ?42 ?43)
+ [43, 42, 41] by quasi_lattice2_2 ?41 ?42 ?43
+13000: Goal:
+13000: Id : 1, {_}: meet a b =>= meet2 a b [] by prove_meets_equal
+13000: Order:
+13000: lpo
+13000: Leaf order:
+13000: join 19 2 0
+13000: meet2 14 2 1 0,3
+13000: meet 14 2 1 0,2
+13000: b 2 0 2 2,2
+13000: a 2 0 2 1,2
+12998: Id : 6, {_}:
+ meet (meet ?12 ?13) ?14 =?= meet ?12 (meet ?13 ?14)
+ [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
+12998: Id : 7, {_}:
+ join (join ?16 ?17) ?18 =?= join ?16 (join ?17 ?18)
+ [18, 17, 16] by associativity_of_join ?16 ?17 ?18
+12998: Id : 8, {_}:
+ join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
+ =>=
+ meet ?20 (join ?21 ?22)
+ [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
+12998: Id : 9, {_}:
+ meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
+ =>=
+ join ?24 (meet ?25 ?26)
+ [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
+12998: Id : 10, {_}: meet2 ?28 ?28 =>= ?28 [28] by idempotence_of_meet2 ?28
+12998: Id : 11, {_}:
+ meet2 ?30 ?31 =?= meet2 ?31 ?30
+ [31, 30] by commutativity_of_meet2 ?30 ?31
+12998: Id : 12, {_}:
+ meet2 (meet2 ?33 ?34) ?35 =?= meet2 ?33 (meet2 ?34 ?35)
+ [35, 34, 33] by associativity_of_meet2 ?33 ?34 ?35
+12998: Id : 13, {_}:
+ join (meet2 ?37 (join ?38 ?39)) (meet2 ?37 ?38)
+ =>=
+ meet2 ?37 (join ?38 ?39)
+ [39, 38, 37] by quasi_lattice1_2 ?37 ?38 ?39
+12998: Id : 14, {_}:
+ meet2 (join ?41 (meet2 ?42 ?43)) (join ?41 ?42)
+ =>=
+ join ?41 (meet2 ?42 ?43)
+ [43, 42, 41] by quasi_lattice2_2 ?41 ?42 ?43
+12998: Goal:
+12998: Id : 1, {_}: meet a b =>= meet2 a b [] by prove_meets_equal
+12998: Order:
+12998: nrkbo
+12998: Leaf order:
+12998: join 19 2 0
+12998: meet2 14 2 1 0,3
+12998: meet 14 2 1 0,2
+12998: b 2 0 2 2,2
+12998: a 2 0 2 1,2
+12999: Id : 10, {_}: meet2 ?28 ?28 =>= ?28 [28] by idempotence_of_meet2 ?28
+12999: Id : 11, {_}:
+ meet2 ?30 ?31 =?= meet2 ?31 ?30
+ [31, 30] by commutativity_of_meet2 ?30 ?31
+12999: Id : 12, {_}:
+ meet2 (meet2 ?33 ?34) ?35 =>= meet2 ?33 (meet2 ?34 ?35)
+ [35, 34, 33] by associativity_of_meet2 ?33 ?34 ?35
+12999: Id : 13, {_}:
+ join (meet2 ?37 (join ?38 ?39)) (meet2 ?37 ?38)
+ =>=
+ meet2 ?37 (join ?38 ?39)
+ [39, 38, 37] by quasi_lattice1_2 ?37 ?38 ?39
+12999: Id : 14, {_}:
+ meet2 (join ?41 (meet2 ?42 ?43)) (join ?41 ?42)
+ =>=
+ join ?41 (meet2 ?42 ?43)
+ [43, 42, 41] by quasi_lattice2_2 ?41 ?42 ?43
+12999: Goal:
+12999: Id : 1, {_}: meet a b =>= meet2 a b [] by prove_meets_equal
+12999: Order:
+12999: kbo
+12999: Leaf order:
+12999: join 19 2 0
+12999: meet2 14 2 1 0,3
+12999: meet 14 2 1 0,2
+12999: b 2 0 2 2,2
+12999: a 2 0 2 1,2
+% SZS status Timeout for LAT024-1.p
+NO CLASH, using fixed ground order
+13029: Facts:
+13029: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13029: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13029: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13029: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13029: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13029: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13029: Id : 8, {_}:
+ join ?18 (meet ?19 (meet ?18 ?20)) =>= ?18
+ [20, 19, 18] by tnl_1 ?18 ?19 ?20
+13029: Id : 9, {_}:
+ meet ?22 (join ?23 (join ?22 ?24)) =>= ?22
+ [24, 23, 22] by tnl_2 ?22 ?23 ?24
+13029: Id : 10, {_}: meet2 ?26 ?26 =>= ?26 [26] by idempotence_of_meet2 ?26
+13029: Id : 11, {_}:
+ meet2 ?28 (join ?28 ?29) =>= ?28
+ [29, 28] by absorption1_2 ?28 ?29
+13029: Id : 12, {_}:
+ join ?31 (meet2 ?31 ?32) =>= ?31
+ [32, 31] by absorption2_2 ?31 ?32
+13029: Id : 13, {_}:
+ meet2 ?34 ?35 =?= meet2 ?35 ?34
+ [35, 34] by commutativity_of_meet2 ?34 ?35
+13029: Id : 14, {_}:
+ join ?37 (meet2 ?38 (meet2 ?37 ?39)) =>= ?37
+ [39, 38, 37] by tnl_1_2 ?37 ?38 ?39
+13029: Id : 15, {_}:
+ meet2 ?41 (join ?42 (join ?41 ?43)) =>= ?41
+ [43, 42, 41] by tnl_2_2 ?41 ?42 ?43
+13029: Goal:
+13029: Id : 1, {_}: meet a b =>= meet2 a b [] by prove_meets_equal
+13029: Order:
+13029: nrkbo
+13029: Leaf order:
+13029: join 13 2 0
+13029: meet2 9 2 1 0,3
+13029: meet 9 2 1 0,2
+13029: b 2 0 2 2,2
+13029: a 2 0 2 1,2
+NO CLASH, using fixed ground order
+13030: Facts:
+13030: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13030: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13030: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13030: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13030: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13030: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13030: Id : 8, {_}:
+ join ?18 (meet ?19 (meet ?18 ?20)) =>= ?18
+ [20, 19, 18] by tnl_1 ?18 ?19 ?20
+13030: Id : 9, {_}:
+ meet ?22 (join ?23 (join ?22 ?24)) =>= ?22
+ [24, 23, 22] by tnl_2 ?22 ?23 ?24
+13030: Id : 10, {_}: meet2 ?26 ?26 =>= ?26 [26] by idempotence_of_meet2 ?26
+13030: Id : 11, {_}:
+ meet2 ?28 (join ?28 ?29) =>= ?28
+ [29, 28] by absorption1_2 ?28 ?29
+13030: Id : 12, {_}:
+ join ?31 (meet2 ?31 ?32) =>= ?31
+ [32, 31] by absorption2_2 ?31 ?32
+13030: Id : 13, {_}:
+ meet2 ?34 ?35 =?= meet2 ?35 ?34
+ [35, 34] by commutativity_of_meet2 ?34 ?35
+13030: Id : 14, {_}:
+ join ?37 (meet2 ?38 (meet2 ?37 ?39)) =>= ?37
+ [39, 38, 37] by tnl_1_2 ?37 ?38 ?39
+13030: Id : 15, {_}:
+ meet2 ?41 (join ?42 (join ?41 ?43)) =>= ?41
+ [43, 42, 41] by tnl_2_2 ?41 ?42 ?43
+13030: Goal:
+13030: Id : 1, {_}: meet a b =>= meet2 a b [] by prove_meets_equal
+13030: Order:
+13030: kbo
+13030: Leaf order:
+13030: join 13 2 0
+13030: meet2 9 2 1 0,3
+13030: meet 9 2 1 0,2
+13030: b 2 0 2 2,2
+13030: a 2 0 2 1,2
+NO CLASH, using fixed ground order
+13031: Facts:
+13031: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13031: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13031: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13031: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13031: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13031: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13031: Id : 8, {_}:
+ join ?18 (meet ?19 (meet ?18 ?20)) =>= ?18
+ [20, 19, 18] by tnl_1 ?18 ?19 ?20
+13031: Id : 9, {_}:
+ meet ?22 (join ?23 (join ?22 ?24)) =>= ?22
+ [24, 23, 22] by tnl_2 ?22 ?23 ?24
+13031: Id : 10, {_}: meet2 ?26 ?26 =>= ?26 [26] by idempotence_of_meet2 ?26
+13031: Id : 11, {_}:
+ meet2 ?28 (join ?28 ?29) =>= ?28
+ [29, 28] by absorption1_2 ?28 ?29
+13031: Id : 12, {_}:
+ join ?31 (meet2 ?31 ?32) =>= ?31
+ [32, 31] by absorption2_2 ?31 ?32
+13031: Id : 13, {_}:
+ meet2 ?34 ?35 =?= meet2 ?35 ?34
+ [35, 34] by commutativity_of_meet2 ?34 ?35
+13031: Id : 14, {_}:
+ join ?37 (meet2 ?38 (meet2 ?37 ?39)) =>= ?37
+ [39, 38, 37] by tnl_1_2 ?37 ?38 ?39
+13031: Id : 15, {_}:
+ meet2 ?41 (join ?42 (join ?41 ?43)) =>= ?41
+ [43, 42, 41] by tnl_2_2 ?41 ?42 ?43
+13031: Goal:
+13031: Id : 1, {_}: meet a b =>= meet2 a b [] by prove_meets_equal
+13031: Order:
+13031: lpo
+13031: Leaf order:
+13031: join 13 2 0
+13031: meet2 9 2 1 0,3
+13031: meet 9 2 1 0,2
+13031: b 2 0 2 2,2
+13031: a 2 0 2 1,2
+% SZS status Timeout for LAT025-1.p
+CLASH, statistics insufficient
+13057: Facts:
+13057: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13057: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13057: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13057: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13057: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13057: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13057: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13057: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13057: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+13057: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+13057: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+13057: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+13057: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+13057: Id : 15, {_}:
+ join ?38 (meet ?39 (join ?38 ?40))
+ =>=
+ meet (join ?38 ?39) (join ?38 ?40)
+ [40, 39, 38] by modular_law ?38 ?39 ?40
+13057: Goal:
+13057: Id : 1, {_}:
+ meet a (join b c) =<= join (meet a b) (meet a c)
+ [] by prove_distributivity
+13057: Order:
+13057: nrkbo
+13057: Leaf order:
+13057: n0 1 0 0
+13057: n1 1 0 0
+13057: complement 10 1 0
+13057: meet 17 2 3 0,2
+13057: join 18 2 2 0,2,2
+13057: c 2 0 2 2,2,2
+13057: b 2 0 2 1,2,2
+13057: a 3 0 3 1,2
+CLASH, statistics insufficient
+13058: Facts:
+13058: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13058: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13058: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13058: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13058: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13058: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13058: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13058: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13058: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+13058: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+13058: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+13058: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+13058: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+13058: Id : 15, {_}:
+ join ?38 (meet ?39 (join ?38 ?40))
+ =>=
+ meet (join ?38 ?39) (join ?38 ?40)
+ [40, 39, 38] by modular_law ?38 ?39 ?40
+13058: Goal:
+13058: Id : 1, {_}:
+ meet a (join b c) =<= join (meet a b) (meet a c)
+ [] by prove_distributivity
+13058: Order:
+13058: kbo
+13058: Leaf order:
+13058: n0 1 0 0
+13058: n1 1 0 0
+13058: complement 10 1 0
+13058: meet 17 2 3 0,2
+13058: join 18 2 2 0,2,2
+13058: c 2 0 2 2,2,2
+13058: b 2 0 2 1,2,2
+13058: a 3 0 3 1,2
+CLASH, statistics insufficient
+13059: Facts:
+13059: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13059: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13059: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13059: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13059: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13059: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13059: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13059: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13059: Id : 10, {_}:
+ complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+13059: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+13059: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+13059: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+13059: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+13059: Id : 15, {_}:
+ join ?38 (meet ?39 (join ?38 ?40))
+ =>=
+ meet (join ?38 ?39) (join ?38 ?40)
+ [40, 39, 38] by modular_law ?38 ?39 ?40
+13059: Goal:
+13059: Id : 1, {_}:
+ meet a (join b c) =<= join (meet a b) (meet a c)
+ [] by prove_distributivity
+13059: Order:
+13059: lpo
+13059: Leaf order:
+13059: n0 1 0 0
+13059: n1 1 0 0
+13059: complement 10 1 0
+13059: meet 17 2 3 0,2
+13059: join 18 2 2 0,2,2
+13059: c 2 0 2 2,2,2
+13059: b 2 0 2 1,2,2
+13059: a 3 0 3 1,2
+% SZS status Timeout for LAT046-1.p
+NO CLASH, using fixed ground order
+13087: Facts:
+NO CLASH, using fixed ground order
+13088: Facts:
+13088: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13088: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13088: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13088: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13088: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13088: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13088: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13088: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13088: Goal:
+13088: Id : 1, {_}:
+ join a (meet b (join a c)) =>= meet (join a b) (join a c)
+ [] by prove_modularity
+13088: Order:
+13088: kbo
+13088: Leaf order:
+13088: meet 11 2 2 0,2,2
+13088: join 13 2 4 0,2
+13088: c 2 0 2 2,2,2,2
+13088: b 2 0 2 1,2,2
+13088: a 4 0 4 1,2
+13087: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13087: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13087: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13087: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13087: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13087: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13087: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13087: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13087: Goal:
+13087: Id : 1, {_}:
+ join a (meet b (join a c)) =>= meet (join a b) (join a c)
+ [] by prove_modularity
+13087: Order:
+13087: nrkbo
+13087: Leaf order:
+13087: meet 11 2 2 0,2,2
+13087: join 13 2 4 0,2
+13087: c 2 0 2 2,2,2,2
+13087: b 2 0 2 1,2,2
+13087: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+13089: Facts:
+13089: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13089: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13089: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13089: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13089: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13089: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13089: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13089: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13089: Goal:
+13089: Id : 1, {_}:
+ join a (meet b (join a c)) =>= meet (join a b) (join a c)
+ [] by prove_modularity
+13089: Order:
+13089: lpo
+13089: Leaf order:
+13089: meet 11 2 2 0,2,2
+13089: join 13 2 4 0,2
+13089: c 2 0 2 2,2,2,2
+13089: b 2 0 2 1,2,2
+13089: a 4 0 4 1,2
+% SZS status Timeout for LAT047-1.p
+NO CLASH, using fixed ground order
+13105: Facts:
+13105: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13105: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13105: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13105: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13105: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13105: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13105: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13105: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13105: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+13105: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+13105: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+13105: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+13105: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+13105: Id : 15, {_}:
+ join (meet (complement ?38) (join ?38 ?39))
+ (join (complement ?39) (meet ?38 ?39))
+ =>=
+ n1
+ [39, 38] by weak_orthomodular_law ?38 ?39
+13105: Goal:
+13105: Id : 1, {_}:
+ join a (meet (complement a) (join a b)) =>= join a b
+ [] by prove_orthomodular_law
+13105: Order:
+13105: nrkbo
+13105: Leaf order:
+13105: n0 1 0 0
+13105: n1 2 0 0
+13105: meet 15 2 1 0,2,2
+13105: join 18 2 3 0,2
+13105: b 2 0 2 2,2,2,2
+13105: complement 13 1 1 0,1,2,2
+13105: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+13106: Facts:
+13106: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13106: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13106: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13106: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13106: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13106: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13106: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13106: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13106: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+13106: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+13106: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+13106: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+13106: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+13106: Id : 15, {_}:
+ join (meet (complement ?38) (join ?38 ?39))
+ (join (complement ?39) (meet ?38 ?39))
+ =>=
+ n1
+ [39, 38] by weak_orthomodular_law ?38 ?39
+13106: Goal:
+13106: Id : 1, {_}:
+ join a (meet (complement a) (join a b)) =>= join a b
+ [] by prove_orthomodular_law
+13106: Order:
+13106: kbo
+13106: Leaf order:
+13106: n0 1 0 0
+13106: n1 2 0 0
+13106: meet 15 2 1 0,2,2
+13106: join 18 2 3 0,2
+13106: b 2 0 2 2,2,2,2
+13106: complement 13 1 1 0,1,2,2
+13106: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+13107: Facts:
+13107: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13107: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13107: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13107: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13107: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13107: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13107: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13107: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13107: Id : 10, {_}:
+ complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+13107: Id : 11, {_}:
+ complement (meet ?29 ?30) =>= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+13107: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+13107: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+13107: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+13107: Id : 15, {_}:
+ join (meet (complement ?38) (join ?38 ?39))
+ (join (complement ?39) (meet ?38 ?39))
+ =>=
+ n1
+ [39, 38] by weak_orthomodular_law ?38 ?39
+13107: Goal:
+13107: Id : 1, {_}:
+ join a (meet (complement a) (join a b)) =>= join a b
+ [] by prove_orthomodular_law
+13107: Order:
+13107: lpo
+13107: Leaf order:
+13107: n0 1 0 0
+13107: n1 2 0 0
+13107: meet 15 2 1 0,2,2
+13107: join 18 2 3 0,2
+13107: b 2 0 2 2,2,2,2
+13107: complement 13 1 1 0,1,2,2
+13107: a 4 0 4 1,2
+% SZS status Timeout for LAT048-1.p
+NO CLASH, using fixed ground order
+13228: Facts:
+13228: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13228: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13228: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13228: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13228: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13228: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13228: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13228: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13228: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+13228: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+13228: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+13228: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+13228: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+13228: Goal:
+13228: Id : 1, {_}:
+ join (meet (complement a) (join a b))
+ (join (complement b) (meet a b))
+ =>=
+ n1
+ [] by prove_weak_orthomodular_law
+13228: Order:
+13228: nrkbo
+13228: Leaf order:
+13228: n0 1 0 0
+13228: n1 2 0 1 3
+13228: meet 14 2 2 0,1,2
+13228: join 15 2 3 0,2
+13228: b 3 0 3 2,2,1,2
+13228: complement 12 1 2 0,1,1,2
+13228: a 3 0 3 1,1,1,2
+NO CLASH, using fixed ground order
+13229: Facts:
+13229: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13229: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13229: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13229: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13229: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13229: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13229: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13229: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13229: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+13229: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+13229: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+13229: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+13229: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+13229: Goal:
+13229: Id : 1, {_}:
+ join (meet (complement a) (join a b))
+ (join (complement b) (meet a b))
+ =>=
+ n1
+ [] by prove_weak_orthomodular_law
+13229: Order:
+13229: kbo
+13229: Leaf order:
+13229: n0 1 0 0
+13229: n1 2 0 1 3
+13229: meet 14 2 2 0,1,2
+13229: join 15 2 3 0,2
+13229: b 3 0 3 2,2,1,2
+13229: complement 12 1 2 0,1,1,2
+13229: a 3 0 3 1,1,1,2
+NO CLASH, using fixed ground order
+13230: Facts:
+13230: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13230: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13230: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13230: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13230: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13230: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13230: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13230: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13230: Id : 10, {_}:
+ complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+13230: Id : 11, {_}:
+ complement (meet ?29 ?30) =>= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+13230: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+13230: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+13230: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+13230: Goal:
+13230: Id : 1, {_}:
+ join (meet (complement a) (join a b))
+ (join (complement b) (meet a b))
+ =>=
+ n1
+ [] by prove_weak_orthomodular_law
+13230: Order:
+13230: lpo
+13230: Leaf order:
+13230: n0 1 0 0
+13230: n1 2 0 1 3
+13230: meet 14 2 2 0,1,2
+13230: join 15 2 3 0,2
+13230: b 3 0 3 2,2,1,2
+13230: complement 12 1 2 0,1,1,2
+13230: a 3 0 3 1,1,1,2
+% SZS status Timeout for LAT049-1.p
+CLASH, statistics insufficient
+13579: Facts:
+13579: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13579: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13579: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13579: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13579: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13579: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13579: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13579: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13579: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+13579: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+13579: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+13579: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+13579: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+13579: Id : 15, {_}:
+ join ?38 (meet (complement ?38) (join ?38 ?39)) =>= join ?38 ?39
+ [39, 38] by orthomodular_law ?38 ?39
+13579: Goal:
+13579: Id : 1, {_}:
+ join a (meet b (join a c)) =>= meet (join a b) (join a c)
+ [] by prove_modular_law
+13579: Order:
+13579: nrkbo
+13579: Leaf order:
+13579: n0 1 0 0
+13579: n1 1 0 0
+13579: complement 11 1 0
+13579: meet 15 2 2 0,2,2
+13579: join 19 2 4 0,2
+13579: c 2 0 2 2,2,2,2
+13579: b 2 0 2 1,2,2
+13579: a 4 0 4 1,2
+CLASH, statistics insufficient
+13580: Facts:
+13580: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13580: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13580: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13580: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13580: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13580: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13580: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13580: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13580: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+13580: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+13580: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+13580: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+13580: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+13580: Id : 15, {_}:
+ join ?38 (meet (complement ?38) (join ?38 ?39)) =>= join ?38 ?39
+ [39, 38] by orthomodular_law ?38 ?39
+13580: Goal:
+13580: Id : 1, {_}:
+ join a (meet b (join a c)) =>= meet (join a b) (join a c)
+ [] by prove_modular_law
+13580: Order:
+13580: kbo
+13580: Leaf order:
+13580: n0 1 0 0
+13580: n1 1 0 0
+13580: complement 11 1 0
+13580: meet 15 2 2 0,2,2
+13580: join 19 2 4 0,2
+13580: c 2 0 2 2,2,2,2
+13580: b 2 0 2 1,2,2
+13580: a 4 0 4 1,2
+CLASH, statistics insufficient
+13582: Facts:
+13582: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13582: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13582: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13582: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13582: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13582: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13582: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13582: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13582: Id : 10, {_}:
+ complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+13582: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+13582: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+13582: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+13582: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+13582: Id : 15, {_}:
+ join ?38 (meet (complement ?38) (join ?38 ?39)) =>= join ?38 ?39
+ [39, 38] by orthomodular_law ?38 ?39
+13582: Goal:
+13582: Id : 1, {_}:
+ join a (meet b (join a c)) =>= meet (join a b) (join a c)
+ [] by prove_modular_law
+13582: Order:
+13582: lpo
+13582: Leaf order:
+13582: n0 1 0 0
+13582: n1 1 0 0
+13582: complement 11 1 0
+13582: meet 15 2 2 0,2,2
+13582: join 19 2 4 0,2
+13582: c 2 0 2 2,2,2,2
+13582: b 2 0 2 1,2,2
+13582: a 4 0 4 1,2
+% SZS status Timeout for LAT050-1.p
+CLASH, statistics insufficient
+13811: Facts:
+13811: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13811: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13811: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13811: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13811: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13811: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13811: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13811: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13811: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
+13811: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
+13811: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
+13811: Goal:
+13811: Id : 1, {_}:
+ complement (join a b) =<= meet (complement a) (complement b)
+ [] by prove_compatibility_law
+13811: Order:
+13811: nrkbo
+13811: Leaf order:
+13811: n0 1 0 0
+13811: n1 1 0 0
+13811: meet 11 2 1 0,3
+13811: complement 7 1 3 0,2
+13811: join 11 2 1 0,1,2
+13811: b 2 0 2 2,1,2
+13811: a 2 0 2 1,1,2
+CLASH, statistics insufficient
+13812: Facts:
+13812: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13812: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13812: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13812: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13812: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13812: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13812: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13812: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13812: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
+13812: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
+13812: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
+13812: Goal:
+13812: Id : 1, {_}:
+ complement (join a b) =<= meet (complement a) (complement b)
+ [] by prove_compatibility_law
+13812: Order:
+13812: kbo
+13812: Leaf order:
+13812: n0 1 0 0
+13812: n1 1 0 0
+13812: meet 11 2 1 0,3
+13812: complement 7 1 3 0,2
+13812: join 11 2 1 0,1,2
+13812: b 2 0 2 2,1,2
+13812: a 2 0 2 1,1,2
+CLASH, statistics insufficient
+13813: Facts:
+13813: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13813: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13813: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13813: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13813: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13813: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13813: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13813: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13813: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
+13813: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
+13813: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
+13813: Goal:
+13813: Id : 1, {_}:
+ complement (join a b) =>= meet (complement a) (complement b)
+ [] by prove_compatibility_law
+13813: Order:
+13813: lpo
+13813: Leaf order:
+13813: n0 1 0 0
+13813: n1 1 0 0
+13813: meet 11 2 1 0,3
+13813: complement 7 1 3 0,2
+13813: join 11 2 1 0,1,2
+13813: b 2 0 2 2,1,2
+13813: a 2 0 2 1,1,2
+% SZS status Timeout for LAT051-1.p
+CLASH, statistics insufficient
+13839: Facts:
+13839: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13839: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13839: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13839: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13839: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13839: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13839: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13839: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13839: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
+13839: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
+13839: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
+13839: Id : 13, {_}:
+ join ?32 (meet ?33 (join ?32 ?34))
+ =>=
+ meet (join ?32 ?33) (join ?32 ?34)
+ [34, 33, 32] by modular_law ?32 ?33 ?34
+13839: Goal:
+13839: Id : 1, {_}:
+ complement (join a b) =<= meet (complement a) (complement b)
+ [] by prove_compatibility_law
+13839: Order:
+13839: nrkbo
+13839: Leaf order:
+13839: n0 1 0 0
+13839: n1 1 0 0
+13839: meet 13 2 1 0,3
+13839: complement 7 1 3 0,2
+13839: join 15 2 1 0,1,2
+13839: b 2 0 2 2,1,2
+13839: a 2 0 2 1,1,2
+CLASH, statistics insufficient
+13840: Facts:
+13840: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13840: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13840: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13840: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13840: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13840: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13840: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13840: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13840: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
+13840: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
+13840: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
+13840: Id : 13, {_}:
+ join ?32 (meet ?33 (join ?32 ?34))
+ =>=
+ meet (join ?32 ?33) (join ?32 ?34)
+ [34, 33, 32] by modular_law ?32 ?33 ?34
+13840: Goal:
+13840: Id : 1, {_}:
+ complement (join a b) =<= meet (complement a) (complement b)
+ [] by prove_compatibility_law
+13840: Order:
+13840: kbo
+13840: Leaf order:
+13840: n0 1 0 0
+13840: n1 1 0 0
+13840: meet 13 2 1 0,3
+13840: complement 7 1 3 0,2
+13840: join 15 2 1 0,1,2
+13840: b 2 0 2 2,1,2
+13840: a 2 0 2 1,1,2
+CLASH, statistics insufficient
+13841: Facts:
+13841: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13841: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13841: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13841: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13841: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13841: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13841: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13841: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13841: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
+13841: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
+13841: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
+13841: Id : 13, {_}:
+ join ?32 (meet ?33 (join ?32 ?34))
+ =>=
+ meet (join ?32 ?33) (join ?32 ?34)
+ [34, 33, 32] by modular_law ?32 ?33 ?34
+13841: Goal:
+13841: Id : 1, {_}:
+ complement (join a b) =>= meet (complement a) (complement b)
+ [] by prove_compatibility_law
+13841: Order:
+13841: lpo
+13841: Leaf order:
+13841: n0 1 0 0
+13841: n1 1 0 0
+13841: meet 13 2 1 0,3
+13841: complement 7 1 3 0,2
+13841: join 15 2 1 0,1,2
+13841: b 2 0 2 2,1,2
+13841: a 2 0 2 1,1,2
+% SZS status Timeout for LAT052-1.p
+CLASH, statistics insufficient
+13871: Facts:
+13871: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13871: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13871: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13871: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13871: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13871: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13871: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13871: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13871: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+13871: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+13871: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+13871: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+13871: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+13871: Goal:
+13871: Id : 1, {_}:
+ join a
+ (meet (complement b)
+ (join (complement a)
+ (meet (complement b)
+ (join a (meet (complement b) (complement a))))))
+ =<=
+ join a
+ (meet (complement b)
+ (join (complement a)
+ (meet (complement b)
+ (join a
+ (meet (complement b)
+ (join (complement a) (meet (complement b) a)))))))
+ [] by prove_this
+13871: Order:
+13871: nrkbo
+13871: Leaf order:
+13871: n0 1 0 0
+13871: n1 1 0 0
+13871: join 19 2 7 0,2
+13871: meet 19 2 7 0,2,2
+13871: complement 21 1 11 0,1,2,2
+13871: b 7 0 7 1,1,2,2
+13871: a 9 0 9 1,2
+CLASH, statistics insufficient
+13872: Facts:
+13872: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13872: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13872: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13872: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13872: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13872: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13872: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13872: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13872: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+13872: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+13872: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+13872: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+13872: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+13872: Goal:
+13872: Id : 1, {_}:
+ join a
+ (meet (complement b)
+ (join (complement a)
+ (meet (complement b)
+ (join a (meet (complement b) (complement a))))))
+ =<=
+ join a
+ (meet (complement b)
+ (join (complement a)
+ (meet (complement b)
+ (join a
+ (meet (complement b)
+ (join (complement a) (meet (complement b) a)))))))
+ [] by prove_this
+13872: Order:
+13872: kbo
+13872: Leaf order:
+13872: n0 1 0 0
+13872: n1 1 0 0
+13872: join 19 2 7 0,2
+13872: meet 19 2 7 0,2,2
+13872: complement 21 1 11 0,1,2,2
+13872: b 7 0 7 1,1,2,2
+13872: a 9 0 9 1,2
+CLASH, statistics insufficient
+13873: Facts:
+13873: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13873: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13873: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13873: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13873: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13873: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13873: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13873: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13873: Id : 10, {_}:
+ complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+13873: Id : 11, {_}:
+ complement (meet ?29 ?30) =>= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+13873: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+13873: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+13873: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+13873: Goal:
+13873: Id : 1, {_}:
+ join a
+ (meet (complement b)
+ (join (complement a)
+ (meet (complement b)
+ (join a (meet (complement b) (complement a))))))
+ =<=
+ join a
+ (meet (complement b)
+ (join (complement a)
+ (meet (complement b)
+ (join a
+ (meet (complement b)
+ (join (complement a) (meet (complement b) a)))))))
+ [] by prove_this
+13873: Order:
+13873: lpo
+13873: Leaf order:
+13873: n0 1 0 0
+13873: n1 1 0 0
+13873: join 19 2 7 0,2
+13873: meet 19 2 7 0,2,2
+13873: complement 21 1 11 0,1,2,2
+13873: b 7 0 7 1,1,2,2
+13873: a 9 0 9 1,2
+% SZS status Timeout for LAT054-1.p
+CLASH, statistics insufficient
+13890: Facts:
+13890: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13890: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13890: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13890: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13890: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13890: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13890: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13890: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13890: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
+13890: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
+13890: Id : 12, {_}:
+ meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
+ [31, 30] by compatibility ?30 ?31
+13890: Goal:
+13890: Id : 1, {_}:
+ meet (join a (complement b))
+ (join (join (meet a b) (meet (complement a) b))
+ (meet (complement a) (complement b)))
+ =>=
+ join (meet a b) (meet (complement a) (complement b))
+ [] by prove_e51
+13890: Order:
+13890: nrkbo
+13890: Leaf order:
+13890: n0 1 0 0
+13890: n1 1 0 0
+13890: meet 17 2 6 0,2
+13890: join 15 2 4 0,1,2
+13890: complement 11 1 6 0,2,1,2
+13890: b 6 0 6 1,2,1,2
+13890: a 6 0 6 1,1,2
+CLASH, statistics insufficient
+13891: Facts:
+13891: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13891: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13891: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13891: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13891: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13891: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13891: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13891: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13891: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
+13891: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
+13891: Id : 12, {_}:
+ meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
+ [31, 30] by compatibility ?30 ?31
+13891: Goal:
+13891: Id : 1, {_}:
+ meet (join a (complement b))
+ (join (join (meet a b) (meet (complement a) b))
+ (meet (complement a) (complement b)))
+ =>=
+ join (meet a b) (meet (complement a) (complement b))
+ [] by prove_e51
+13891: Order:
+13891: kbo
+13891: Leaf order:
+13891: n0 1 0 0
+13891: n1 1 0 0
+13891: meet 17 2 6 0,2
+13891: join 15 2 4 0,1,2
+13891: complement 11 1 6 0,2,1,2
+13891: b 6 0 6 1,2,1,2
+13891: a 6 0 6 1,1,2
+CLASH, statistics insufficient
+13892: Facts:
+13892: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13892: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13892: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13892: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13892: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13892: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13892: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13892: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13892: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
+13892: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
+13892: Id : 12, {_}:
+ meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
+ [31, 30] by compatibility ?30 ?31
+13892: Goal:
+13892: Id : 1, {_}:
+ meet (join a (complement b))
+ (join (join (meet a b) (meet (complement a) b))
+ (meet (complement a) (complement b)))
+ =>=
+ join (meet a b) (meet (complement a) (complement b))
+ [] by prove_e51
+13892: Order:
+13892: lpo
+13892: Leaf order:
+13892: n0 1 0 0
+13892: n1 1 0 0
+13892: meet 17 2 6 0,2
+13892: join 15 2 4 0,1,2
+13892: complement 11 1 6 0,2,1,2
+13892: b 6 0 6 1,2,1,2
+13892: a 6 0 6 1,1,2
+% SZS status Timeout for LAT062-1.p
+CLASH, statistics insufficient
+13921: Facts:
+13921: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13921: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13921: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13921: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13921: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13921: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13921: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13921: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13921: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
+13921: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
+13921: Id : 12, {_}:
+ meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
+ [31, 30] by compatibility ?30 ?31
+13921: Goal:
+CLASH, statistics insufficient
+CLASH, statistics insufficient
+13921: Id : 1, {_}:
+ meet a (join b (meet a (join (complement a) (meet a b))))
+ =>=
+ meet a (join (complement a) (meet a b))
+ [] by prove_e62
+13921: Order:
+13921: nrkbo
+13921: Leaf order:
+13921: n0 1 0 0
+13921: n1 1 0 0
+13921: join 14 2 3 0,2,2
+13921: meet 16 2 5 0,2
+13921: complement 7 1 2 0,1,2,2,2,2
+13921: b 3 0 3 1,2,2
+13921: a 7 0 7 1,2
+13923: Facts:
+13923: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13923: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13923: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13923: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13923: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13923: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13923: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13923: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13923: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
+13923: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
+13923: Id : 12, {_}:
+ meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
+ [31, 30] by compatibility ?30 ?31
+13923: Goal:
+13923: Id : 1, {_}:
+ meet a (join b (meet a (join (complement a) (meet a b))))
+ =>=
+ meet a (join (complement a) (meet a b))
+ [] by prove_e62
+13923: Order:
+13923: lpo
+13923: Leaf order:
+13923: n0 1 0 0
+13923: n1 1 0 0
+13923: join 14 2 3 0,2,2
+13923: meet 16 2 5 0,2
+13923: complement 7 1 2 0,1,2,2,2,2
+13923: b 3 0 3 1,2,2
+13923: a 7 0 7 1,2
+13922: Facts:
+13922: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13922: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13922: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13922: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13922: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13922: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13922: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13922: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13922: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
+13922: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
+13922: Id : 12, {_}:
+ meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
+ [31, 30] by compatibility ?30 ?31
+13922: Goal:
+13922: Id : 1, {_}:
+ meet a (join b (meet a (join (complement a) (meet a b))))
+ =>=
+ meet a (join (complement a) (meet a b))
+ [] by prove_e62
+13922: Order:
+13922: kbo
+13922: Leaf order:
+13922: n0 1 0 0
+13922: n1 1 0 0
+13922: join 14 2 3 0,2,2
+13922: meet 16 2 5 0,2
+13922: complement 7 1 2 0,1,2,2,2,2
+13922: b 3 0 3 1,2,2
+13922: a 7 0 7 1,2
+% SZS status Timeout for LAT063-1.p
+NO CLASH, using fixed ground order
+13955: Facts:
+13955: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13955: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13955: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13955: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13955: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13955: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13955: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13955: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13955: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?28 (join (meet ?26 (join ?27 ?28)) (meet ?27 ?28))))
+ [28, 27, 26] by equation_H2 ?26 ?27 ?28
+13955: Goal:
+13955: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+13955: Order:
+13955: nrkbo
+13955: Leaf order:
+13955: join 17 2 4 0,2,2
+13955: meet 21 2 6 0,2
+13955: c 3 0 3 2,2,2,2
+13955: b 4 0 4 1,2,2
+13955: a 5 0 5 1,2
+NO CLASH, using fixed ground order
+13956: Facts:
+13956: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13956: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13956: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13956: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13956: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13956: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13956: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13956: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13956: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?28 (join (meet ?26 (join ?27 ?28)) (meet ?27 ?28))))
+ [28, 27, 26] by equation_H2 ?26 ?27 ?28
+13956: Goal:
+13956: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+13956: Order:
+13956: kbo
+13956: Leaf order:
+13956: join 17 2 4 0,2,2
+13956: meet 21 2 6 0,2
+13956: c 3 0 3 2,2,2,2
+13956: b 4 0 4 1,2,2
+13956: a 5 0 5 1,2
+NO CLASH, using fixed ground order
+13957: Facts:
+13957: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13957: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13957: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13957: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13957: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13957: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13957: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13957: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13957: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?28 (join (meet ?26 (join ?27 ?28)) (meet ?27 ?28))))
+ [28, 27, 26] by equation_H2 ?26 ?27 ?28
+13957: Goal:
+13957: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+13957: Order:
+13957: lpo
+13957: Leaf order:
+13957: join 17 2 4 0,2,2
+13957: meet 21 2 6 0,2
+13957: c 3 0 3 2,2,2,2
+13957: b 4 0 4 1,2,2
+13957: a 5 0 5 1,2
+% SZS status Timeout for LAT098-1.p
+NO CLASH, using fixed ground order
+13999: Facts:
+13999: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13999: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13999: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13999: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13999: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13999: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13999: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13999: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13999: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join (meet ?26 (join ?27 (meet ?26 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H6 ?26 ?27 ?28
+13999: Goal:
+13999: Id : 1, {_}:
+ meet a (join b (meet a (join c d)))
+ =<=
+ meet a (join b (meet (join a (meet b d)) (join c d)))
+ [] by prove_H4
+13999: Order:
+13999: nrkbo
+13999: Leaf order:
+13999: meet 20 2 5 0,2
+13999: join 18 2 5 0,2,2
+13999: d 3 0 3 2,2,2,2,2
+13999: c 2 0 2 1,2,2,2,2
+13999: b 3 0 3 1,2,2
+13999: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+14000: Facts:
+14000: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14000: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14000: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14000: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14000: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14000: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14000: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14000: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14000: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join (meet ?26 (join ?27 (meet ?26 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H6 ?26 ?27 ?28
+14000: Goal:
+14000: Id : 1, {_}:
+ meet a (join b (meet a (join c d)))
+ =<=
+ meet a (join b (meet (join a (meet b d)) (join c d)))
+ [] by prove_H4
+14000: Order:
+14000: kbo
+14000: Leaf order:
+14000: meet 20 2 5 0,2
+14000: join 18 2 5 0,2,2
+14000: d 3 0 3 2,2,2,2,2
+14000: c 2 0 2 1,2,2,2,2
+14000: b 3 0 3 1,2,2
+14000: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+14001: Facts:
+14001: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14001: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14001: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14001: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14001: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14001: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14001: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14001: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14001: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join (meet ?26 (join ?27 (meet ?26 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H6 ?26 ?27 ?28
+14001: Goal:
+14001: Id : 1, {_}:
+ meet a (join b (meet a (join c d)))
+ =<=
+ meet a (join b (meet (join a (meet b d)) (join c d)))
+ [] by prove_H4
+14001: Order:
+14001: lpo
+14001: Leaf order:
+14001: meet 20 2 5 0,2
+14001: join 18 2 5 0,2,2
+14001: d 3 0 3 2,2,2,2,2
+14001: c 2 0 2 1,2,2,2,2
+14001: b 3 0 3 1,2,2
+14001: a 4 0 4 1,2
+% SZS status Timeout for LAT100-1.p
+NO CLASH, using fixed ground order
+14017: Facts:
+14017: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14017: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14017: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14017: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14017: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14017: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14017: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14017: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14017: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join (meet ?26 (join ?27 (meet ?26 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H6 ?26 ?27 ?28
+14017: Goal:
+14017: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join a (meet b c))))
+ [] by prove_H10
+14017: Order:
+14017: nrkbo
+14017: Leaf order:
+14017: join 16 2 3 0,2,2
+14017: meet 20 2 5 0,2
+14017: c 3 0 3 2,2,2,2
+14017: b 3 0 3 1,2,2
+14017: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+14018: Facts:
+14018: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14018: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14018: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14018: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14018: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14018: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14018: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14018: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14018: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join (meet ?26 (join ?27 (meet ?26 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H6 ?26 ?27 ?28
+14018: Goal:
+14018: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join a (meet b c))))
+ [] by prove_H10
+14018: Order:
+14018: kbo
+14018: Leaf order:
+14018: join 16 2 3 0,2,2
+14018: meet 20 2 5 0,2
+14018: c 3 0 3 2,2,2,2
+14018: b 3 0 3 1,2,2
+14018: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+14019: Facts:
+14019: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14019: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14019: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14019: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14019: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14019: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14019: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14019: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14019: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join (meet ?26 (join ?27 (meet ?26 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H6 ?26 ?27 ?28
+14019: Goal:
+14019: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =>=
+ meet a (join b (meet c (join a (meet b c))))
+ [] by prove_H10
+14019: Order:
+14019: lpo
+14019: Leaf order:
+14019: join 16 2 3 0,2,2
+14019: meet 20 2 5 0,2
+14019: c 3 0 3 2,2,2,2
+14019: b 3 0 3 1,2,2
+14019: a 4 0 4 1,2
+% SZS status Timeout for LAT101-1.p
+NO CLASH, using fixed ground order
+14050: Facts:
+14050: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14050: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14050: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14050: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14050: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14050: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14050: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14050: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14050: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
+ [28, 27, 26] by equation_H7 ?26 ?27 ?28
+14050: Goal:
+14050: Id : 1, {_}:
+ meet a (join b (meet a (join c d)))
+ =<=
+ meet a (join b (meet (join a (meet b d)) (join c d)))
+ [] by prove_H4
+14050: Order:
+14050: nrkbo
+14050: Leaf order:
+14050: meet 20 2 5 0,2
+14050: join 18 2 5 0,2,2
+14050: d 3 0 3 2,2,2,2,2
+14050: c 2 0 2 1,2,2,2,2
+14050: b 3 0 3 1,2,2
+14050: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+14051: Facts:
+14051: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14051: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14051: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14051: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14051: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14051: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14051: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14051: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14051: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
+ [28, 27, 26] by equation_H7 ?26 ?27 ?28
+14051: Goal:
+14051: Id : 1, {_}:
+ meet a (join b (meet a (join c d)))
+ =<=
+ meet a (join b (meet (join a (meet b d)) (join c d)))
+ [] by prove_H4
+14051: Order:
+14051: kbo
+14051: Leaf order:
+14051: meet 20 2 5 0,2
+14051: join 18 2 5 0,2,2
+14051: d 3 0 3 2,2,2,2,2
+14051: c 2 0 2 1,2,2,2,2
+14051: b 3 0 3 1,2,2
+14051: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+14052: Facts:
+14052: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14052: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14052: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14052: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14052: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14052: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14052: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14052: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14052: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
+ [28, 27, 26] by equation_H7 ?26 ?27 ?28
+14052: Goal:
+14052: Id : 1, {_}:
+ meet a (join b (meet a (join c d)))
+ =<=
+ meet a (join b (meet (join a (meet b d)) (join c d)))
+ [] by prove_H4
+14052: Order:
+14052: lpo
+14052: Leaf order:
+14052: meet 20 2 5 0,2
+14052: join 18 2 5 0,2,2
+14052: d 3 0 3 2,2,2,2,2
+14052: c 2 0 2 1,2,2,2,2
+14052: b 3 0 3 1,2,2
+14052: a 4 0 4 1,2
+% SZS status Timeout for LAT102-1.p
+NO CLASH, using fixed ground order
+14140: Facts:
+14140: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14140: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14140: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14140: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14140: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14140: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14140: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14140: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14140: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?27 ?28))))
+ [28, 27, 26] by equation_H10 ?26 ?27 ?28
+14140: Goal:
+14140: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+14140: Order:
+14140: nrkbo
+14140: Leaf order:
+14140: join 16 2 4 0,2,2
+14140: meet 20 2 6 0,2
+14140: c 3 0 3 2,2,2,2
+14140: b 3 0 3 1,2,2
+14140: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+14141: Facts:
+14141: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14141: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14141: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14141: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14141: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14141: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14141: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14141: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14141: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?27 ?28))))
+ [28, 27, 26] by equation_H10 ?26 ?27 ?28
+14141: Goal:
+14141: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+14141: Order:
+14141: kbo
+14141: Leaf order:
+14141: join 16 2 4 0,2,2
+14141: meet 20 2 6 0,2
+14141: c 3 0 3 2,2,2,2
+14141: b 3 0 3 1,2,2
+14141: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+14142: Facts:
+14142: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14142: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14142: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14142: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14142: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14142: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14142: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14142: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14142: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?27 ?28))))
+ [28, 27, 26] by equation_H10 ?26 ?27 ?28
+14142: Goal:
+14142: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+14142: Order:
+14142: lpo
+14142: Leaf order:
+14142: join 16 2 4 0,2,2
+14142: meet 20 2 6 0,2
+14142: c 3 0 3 2,2,2,2
+14142: b 3 0 3 1,2,2
+14142: a 6 0 6 1,2
+% SZS status Timeout for LAT103-1.p
+NO CLASH, using fixed ground order
+14175: Facts:
+14175: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14175: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14175: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14175: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14175: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14175: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14175: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14175: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14175: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?26 (meet ?27 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H21 ?26 ?27 ?28
+14175: Goal:
+14175: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+14175: Order:
+14175: kbo
+14175: Leaf order:
+14175: join 17 2 4 0,2,2
+14175: meet 21 2 6 0,2
+14175: c 3 0 3 2,2,2,2
+14175: b 4 0 4 1,2,2
+14175: a 5 0 5 1,2
+NO CLASH, using fixed ground order
+14176: Facts:
+14176: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14176: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14176: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14176: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14176: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14176: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14176: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14176: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14176: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?26 (meet ?27 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H21 ?26 ?27 ?28
+14176: Goal:
+14176: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+14176: Order:
+14176: lpo
+14176: Leaf order:
+14176: join 17 2 4 0,2,2
+14176: meet 21 2 6 0,2
+14176: c 3 0 3 2,2,2,2
+14176: b 4 0 4 1,2,2
+14176: a 5 0 5 1,2
+NO CLASH, using fixed ground order
+14174: Facts:
+14174: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14174: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14174: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14174: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14174: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14174: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14174: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14174: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14174: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?26 (meet ?27 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H21 ?26 ?27 ?28
+14174: Goal:
+14174: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+14174: Order:
+14174: nrkbo
+14174: Leaf order:
+14174: join 17 2 4 0,2,2
+14174: meet 21 2 6 0,2
+14174: c 3 0 3 2,2,2,2
+14174: b 4 0 4 1,2,2
+14174: a 5 0 5 1,2
+% SZS status Timeout for LAT104-1.p
+NO CLASH, using fixed ground order
+14193: Facts:
+14193: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14193: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14193: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14193: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14193: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14193: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14193: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14193: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14193: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?26 (meet ?27 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H21 ?26 ?27 ?28
+14193: Goal:
+14193: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join a (meet b c))))
+ [] by prove_H10
+14193: Order:
+14193: nrkbo
+14193: Leaf order:
+14193: join 16 2 3 0,2,2
+14193: meet 20 2 5 0,2
+14193: c 3 0 3 2,2,2,2
+14193: b 3 0 3 1,2,2
+14193: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+14194: Facts:
+14194: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14194: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14194: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14194: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14194: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14194: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14194: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14194: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14194: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?26 (meet ?27 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H21 ?26 ?27 ?28
+14194: Goal:
+14194: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join a (meet b c))))
+ [] by prove_H10
+14194: Order:
+14194: kbo
+14194: Leaf order:
+14194: join 16 2 3 0,2,2
+14194: meet 20 2 5 0,2
+14194: c 3 0 3 2,2,2,2
+14194: b 3 0 3 1,2,2
+14194: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+14195: Facts:
+14195: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14195: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14195: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14195: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14195: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14195: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14195: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14195: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14195: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?26 (meet ?27 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H21 ?26 ?27 ?28
+14195: Goal:
+14195: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =>=
+ meet a (join b (meet c (join a (meet b c))))
+ [] by prove_H10
+14195: Order:
+14195: lpo
+14195: Leaf order:
+14195: join 16 2 3 0,2,2
+14195: meet 20 2 5 0,2
+14195: c 3 0 3 2,2,2,2
+14195: b 3 0 3 1,2,2
+14195: a 4 0 4 1,2
+% SZS status Timeout for LAT105-1.p
+NO CLASH, using fixed ground order
+14223: Facts:
+14223: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14223: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14223: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14223: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14223: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14223: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14223: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14223: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14223: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?28 (meet ?26 ?27)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H22 ?26 ?27 ?28
+14223: Goal:
+14223: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+14223: Order:
+14223: nrkbo
+14223: Leaf order:
+14223: join 17 2 4 0,2,2
+14223: meet 21 2 6 0,2
+14223: c 3 0 3 2,2,2,2
+14223: b 4 0 4 1,2,2
+14223: a 5 0 5 1,2
+NO CLASH, using fixed ground order
+14224: Facts:
+14224: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14224: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14224: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14224: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14224: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14224: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14224: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14224: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14224: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?28 (meet ?26 ?27)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H22 ?26 ?27 ?28
+14224: Goal:
+14224: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+14224: Order:
+14224: kbo
+14224: Leaf order:
+NO CLASH, using fixed ground order
+14225: Facts:
+14225: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14225: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14225: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14225: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14225: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14225: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14225: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14225: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14225: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?28 (meet ?26 ?27)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H22 ?26 ?27 ?28
+14225: Goal:
+14225: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+14225: Order:
+14225: lpo
+14225: Leaf order:
+14225: join 17 2 4 0,2,2
+14225: meet 21 2 6 0,2
+14225: c 3 0 3 2,2,2,2
+14225: b 4 0 4 1,2,2
+14225: a 5 0 5 1,2
+14224: join 17 2 4 0,2,2
+14224: meet 21 2 6 0,2
+14224: c 3 0 3 2,2,2,2
+14224: b 4 0 4 1,2,2
+14224: a 5 0 5 1,2
+% SZS status Timeout for LAT106-1.p
+NO CLASH, using fixed ground order
+14371: Facts:
+14371: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14371: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14371: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14371: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14371: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14371: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14371: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14371: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14371: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?28 (meet ?26 ?27)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H22 ?26 ?27 ?28
+14371: Goal:
+14371: Id : 1, {_}:
+ meet a (join (meet a b) (meet a c))
+ =<=
+ meet a (join (meet b (join a (meet b c))) (meet c (join a b)))
+ [] by prove_H17
+14371: Order:
+14371: nrkbo
+14371: Leaf order:
+14371: join 17 2 4 0,2,2
+14371: c 3 0 3 2,2,2,2
+14371: meet 22 2 7 0,2
+14371: b 4 0 4 2,1,2,2
+14371: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+14372: Facts:
+14372: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14372: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14372: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14372: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14372: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14372: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14372: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14372: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14372: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?28 (meet ?26 ?27)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H22 ?26 ?27 ?28
+14372: Goal:
+14372: Id : 1, {_}:
+ meet a (join (meet a b) (meet a c))
+ =<=
+ meet a (join (meet b (join a (meet b c))) (meet c (join a b)))
+ [] by prove_H17
+14372: Order:
+14372: kbo
+14372: Leaf order:
+14372: join 17 2 4 0,2,2
+14372: c 3 0 3 2,2,2,2
+14372: meet 22 2 7 0,2
+14372: b 4 0 4 2,1,2,2
+14372: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+14373: Facts:
+14373: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14373: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14373: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14373: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14373: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14373: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14373: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14373: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14373: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?28 (meet ?26 ?27)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H22 ?26 ?27 ?28
+14373: Goal:
+14373: Id : 1, {_}:
+ meet a (join (meet a b) (meet a c))
+ =>=
+ meet a (join (meet b (join a (meet b c))) (meet c (join a b)))
+ [] by prove_H17
+14373: Order:
+14373: lpo
+14373: Leaf order:
+14373: join 17 2 4 0,2,2
+14373: c 3 0 3 2,2,2,2
+14373: meet 22 2 7 0,2
+14373: b 4 0 4 2,1,2,2
+14373: a 6 0 6 1,2
+% SZS status Timeout for LAT107-1.p
+NO CLASH, using fixed ground order
+15801: Facts:
+15801: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+15801: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+15801: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+15801: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+15801: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+15801: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+15801: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+15801: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+15801: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
+ [29, 28, 27, 26] by equation_H31 ?26 ?27 ?28 ?29
+15801: Goal:
+15801: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+15801: Order:
+15801: nrkbo
+15801: Leaf order:
+15801: meet 21 2 5 0,2
+15801: join 17 2 5 0,2,2
+15801: d 2 0 2 2,2,2,2,2
+15801: c 3 0 3 1,2,2,2
+15801: b 3 0 3 1,2,2
+15801: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+15804: Facts:
+15804: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+15804: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+15804: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+15804: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+15804: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+15804: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+15804: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+15804: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+15804: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
+ [29, 28, 27, 26] by equation_H31 ?26 ?27 ?28 ?29
+15804: Goal:
+15804: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+15804: Order:
+15804: kbo
+15804: Leaf order:
+15804: meet 21 2 5 0,2
+15804: join 17 2 5 0,2,2
+15804: d 2 0 2 2,2,2,2,2
+15804: c 3 0 3 1,2,2,2
+15804: b 3 0 3 1,2,2
+15804: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+15805: Facts:
+15805: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+15805: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+15805: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+15805: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+15805: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+15805: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+15805: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+15805: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+15805: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
+ [29, 28, 27, 26] by equation_H31 ?26 ?27 ?28 ?29
+15805: Goal:
+15805: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =>=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+15805: Order:
+15805: lpo
+15805: Leaf order:
+15805: meet 21 2 5 0,2
+15805: join 17 2 5 0,2,2
+15805: d 2 0 2 2,2,2,2,2
+15805: c 3 0 3 1,2,2,2
+15805: b 3 0 3 1,2,2
+15805: a 4 0 4 1,2
+% SZS status Timeout for LAT108-1.p
+NO CLASH, using fixed ground order
+17324: Facts:
+17324: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+17324: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+17324: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+17324: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+17324: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+17324: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+17324: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+17324: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+17324: Id : 10, {_}:
+ meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
+ =?=
+ meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
+17324: Goal:
+17324: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+17324: Order:
+17324: lpo
+17324: Leaf order:
+17324: meet 19 2 5 0,2
+17324: join 19 2 5 0,2,2
+17324: d 2 0 2 2,2,2,2,2
+17324: c 3 0 3 1,2,2,2
+17324: b 3 0 3 1,2,2
+17324: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+17322: Facts:
+17322: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+17322: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+17322: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+17322: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+17322: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+17322: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+17322: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+17322: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+17322: Id : 10, {_}:
+ meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
+17322: Goal:
+17322: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+17322: Order:
+17322: nrkbo
+17322: Leaf order:
+17322: meet 19 2 5 0,2
+17322: join 19 2 5 0,2,2
+17322: d 2 0 2 2,2,2,2,2
+17322: c 3 0 3 1,2,2,2
+17322: b 3 0 3 1,2,2
+17322: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+17323: Facts:
+17323: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+17323: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+17323: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+17323: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+17323: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+17323: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+17323: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+17323: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+17323: Id : 10, {_}:
+ meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
+17323: Goal:
+17323: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+17323: Order:
+17323: kbo
+17323: Leaf order:
+17323: meet 19 2 5 0,2
+17323: join 19 2 5 0,2,2
+17323: d 2 0 2 2,2,2,2,2
+17323: c 3 0 3 1,2,2,2
+17323: b 3 0 3 1,2,2
+17323: a 4 0 4 1,2
+% SZS status Timeout for LAT109-1.p
+NO CLASH, using fixed ground order
+19002: Facts:
+19002: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19002: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19002: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19002: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19002: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19002: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19002: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19002: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19002: Id : 10, {_}:
+ meet ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H45 ?26 ?27 ?28 ?29
+19002: Goal:
+19002: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+19002: Order:
+19002: nrkbo
+19002: Leaf order:
+19002: meet 21 2 5 0,2
+19002: join 17 2 5 0,2,2
+19002: d 2 0 2 2,2,2,2,2
+19002: c 3 0 3 1,2,2,2
+19002: b 3 0 3 1,2,2
+19002: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+19008: Facts:
+19008: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19008: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19008: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19008: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19008: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19008: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19008: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19008: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19008: Id : 10, {_}:
+ meet ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H45 ?26 ?27 ?28 ?29
+19008: Goal:
+19008: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+19008: Order:
+19008: kbo
+19008: Leaf order:
+19008: meet 21 2 5 0,2
+19008: join 17 2 5 0,2,2
+19008: d 2 0 2 2,2,2,2,2
+19008: c 3 0 3 1,2,2,2
+19008: b 3 0 3 1,2,2
+19008: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+19009: Facts:
+19009: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19009: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19009: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19009: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19009: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19009: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19009: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19009: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19009: Id : 10, {_}:
+ meet ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =?=
+ meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H45 ?26 ?27 ?28 ?29
+19009: Goal:
+19009: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+19009: Order:
+19009: lpo
+19009: Leaf order:
+19009: meet 21 2 5 0,2
+19009: join 17 2 5 0,2,2
+19009: d 2 0 2 2,2,2,2,2
+19009: c 3 0 3 1,2,2,2
+19009: b 3 0 3 1,2,2
+19009: a 4 0 4 1,2
+% SZS status Timeout for LAT111-1.p
+NO CLASH, using fixed ground order
+19496: Facts:
+19496: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19496: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19496: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19496: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19496: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19496: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19496: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19496: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19496: Id : 10, {_}:
+ meet ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
+ =<=
+ meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
+ [29, 28, 27, 26] by equation_H47 ?26 ?27 ?28 ?29
+19496: Goal:
+19496: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+19496: Order:
+19496: nrkbo
+19496: Leaf order:
+19496: meet 21 2 5 0,2
+19496: join 17 2 5 0,2,2
+19496: d 2 0 2 2,2,2,2,2
+19496: c 3 0 3 1,2,2,2
+19496: b 3 0 3 1,2,2
+19496: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+19497: Facts:
+19497: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19497: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19497: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19497: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19497: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19497: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19497: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19497: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19497: Id : 10, {_}:
+ meet ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
+ =<=
+ meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
+ [29, 28, 27, 26] by equation_H47 ?26 ?27 ?28 ?29
+19497: Goal:
+19497: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+19497: Order:
+19497: kbo
+19497: Leaf order:
+19497: meet 21 2 5 0,2
+19497: join 17 2 5 0,2,2
+19497: d 2 0 2 2,2,2,2,2
+19497: c 3 0 3 1,2,2,2
+19497: b 3 0 3 1,2,2
+19497: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+19498: Facts:
+19498: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19498: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19498: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19498: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19498: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19498: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19498: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19498: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19498: Id : 10, {_}:
+ meet ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
+ =?=
+ meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
+ [29, 28, 27, 26] by equation_H47 ?26 ?27 ?28 ?29
+19498: Goal:
+19498: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =>=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+19498: Order:
+19498: lpo
+19498: Leaf order:
+19498: meet 21 2 5 0,2
+19498: join 17 2 5 0,2,2
+19498: d 2 0 2 2,2,2,2,2
+19498: c 3 0 3 1,2,2,2
+19498: b 3 0 3 1,2,2
+19498: a 4 0 4 1,2
+% SZS status Timeout for LAT112-1.p
+NO CLASH, using fixed ground order
+19529: Facts:
+19529: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19529: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19529: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19529: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19529: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19529: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19529: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19529: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19529: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
+ [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
+19529: Goal:
+19529: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+19529: Order:
+19529: nrkbo
+19529: Leaf order:
+19529: meet 19 2 5 0,2
+19529: join 19 2 5 0,2,2
+19529: d 2 0 2 2,2,2,2,2
+19529: c 3 0 3 1,2,2,2
+19529: b 3 0 3 1,2,2
+19529: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+19530: Facts:
+19530: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19530: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19530: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19530: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19530: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19530: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19530: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19530: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19530: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
+ [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
+19530: Goal:
+19530: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+19530: Order:
+19530: kbo
+19530: Leaf order:
+19530: meet 19 2 5 0,2
+19530: join 19 2 5 0,2,2
+19530: d 2 0 2 2,2,2,2,2
+19530: c 3 0 3 1,2,2,2
+19530: b 3 0 3 1,2,2
+19530: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+19531: Facts:
+19531: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19531: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19531: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19531: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19531: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19531: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19531: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19531: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19531: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
+ [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
+19531: Goal:
+19531: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+19531: Order:
+19531: lpo
+19531: Leaf order:
+19531: meet 19 2 5 0,2
+19531: join 19 2 5 0,2,2
+19531: d 2 0 2 2,2,2,2,2
+19531: c 3 0 3 1,2,2,2
+19531: b 3 0 3 1,2,2
+19531: a 4 0 4 1,2
+% SZS status Timeout for LAT113-1.p
+NO CLASH, using fixed ground order
+19568: Facts:
+19568: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19568: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19568: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19568: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19568: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19568: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19568: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19568: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19568: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
+ [28, 27, 26] by equation_H55 ?26 ?27 ?28
+19568: Goal:
+19568: Id : 1, {_}:
+ join (meet a b) (meet a (join b c))
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H56
+19568: Order:
+19568: kbo
+19568: Leaf order:
+19568: join 19 2 5 0,2
+19568: c 2 0 2 2,2,2,2
+19568: meet 17 2 5 0,1,2
+19568: b 5 0 5 2,1,2
+19568: a 5 0 5 1,1,2
+NO CLASH, using fixed ground order
+19567: Facts:
+19567: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19567: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19567: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19567: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19567: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19567: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19567: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19567: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19567: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
+ [28, 27, 26] by equation_H55 ?26 ?27 ?28
+19567: Goal:
+19567: Id : 1, {_}:
+ join (meet a b) (meet a (join b c))
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H56
+19567: Order:
+19567: nrkbo
+19567: Leaf order:
+19567: join 19 2 5 0,2
+19567: c 2 0 2 2,2,2,2
+19567: meet 17 2 5 0,1,2
+19567: b 5 0 5 2,1,2
+19567: a 5 0 5 1,1,2
+NO CLASH, using fixed ground order
+19569: Facts:
+19569: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19569: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19569: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19569: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19569: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19569: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19569: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19569: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19569: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
+ [28, 27, 26] by equation_H55 ?26 ?27 ?28
+19569: Goal:
+19569: Id : 1, {_}:
+ join (meet a b) (meet a (join b c))
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H56
+19569: Order:
+19569: lpo
+19569: Leaf order:
+19569: join 19 2 5 0,2
+19569: c 2 0 2 2,2,2,2
+19569: meet 17 2 5 0,1,2
+19569: b 5 0 5 2,1,2
+19569: a 5 0 5 1,1,2
+% SZS status Timeout for LAT114-1.p
+NO CLASH, using fixed ground order
+19631: Facts:
+19631: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19631: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19631: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19631: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19631: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19631: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19631: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19631: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19631: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
+ [28, 27, 26] by equation_H55 ?26 ?27 ?28
+19631: Goal:
+19631: Id : 1, {_}:
+ meet a (meet (join b c) (join b d))
+ =<=
+ meet a (join b (meet (join b d) (join c (meet a b))))
+ [] by prove_H59
+19631: Order:
+19631: nrkbo
+19631: Leaf order:
+19631: meet 17 2 5 0,2
+19631: d 2 0 2 2,2,2,2
+19631: join 19 2 5 0,1,2,2
+19631: c 2 0 2 2,1,2,2
+19631: b 5 0 5 1,1,2,2
+19631: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+19632: Facts:
+19632: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19632: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19632: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19632: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19632: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19632: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19632: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19632: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19632: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
+ [28, 27, 26] by equation_H55 ?26 ?27 ?28
+19632: Goal:
+19632: Id : 1, {_}:
+ meet a (meet (join b c) (join b d))
+ =<=
+ meet a (join b (meet (join b d) (join c (meet a b))))
+ [] by prove_H59
+19632: Order:
+19632: kbo
+19632: Leaf order:
+19632: meet 17 2 5 0,2
+19632: d 2 0 2 2,2,2,2
+19632: join 19 2 5 0,1,2,2
+19632: c 2 0 2 2,1,2,2
+19632: b 5 0 5 1,1,2,2
+19632: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+19633: Facts:
+19633: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19633: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19633: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19633: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19633: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19633: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19633: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19633: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19633: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =?=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
+ [28, 27, 26] by equation_H55 ?26 ?27 ?28
+19633: Goal:
+19633: Id : 1, {_}:
+ meet a (meet (join b c) (join b d))
+ =<=
+ meet a (join b (meet (join b d) (join c (meet a b))))
+ [] by prove_H59
+19633: Order:
+19633: lpo
+19633: Leaf order:
+19633: meet 17 2 5 0,2
+19633: d 2 0 2 2,2,2,2
+19633: join 19 2 5 0,1,2,2
+19633: c 2 0 2 2,1,2,2
+19633: b 5 0 5 1,1,2,2
+19633: a 3 0 3 1,2
+% SZS status Timeout for LAT115-1.p
+NO CLASH, using fixed ground order
+19650: Facts:
+19650: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19650: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19650: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19650: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19650: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19650: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+NO CLASH, using fixed ground order
+19651: Facts:
+19651: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19651: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19651: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19651: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19651: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19651: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19651: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19651: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19651: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
+ [28, 27, 26] by equation_H55 ?26 ?27 ?28
+19651: Goal:
+19651: Id : 1, {_}:
+ meet a (meet (join b c) (join b d))
+ =<=
+ meet a (join b (meet (join b c) (join d (meet a b))))
+ [] by prove_H60
+19651: Order:
+19651: kbo
+19651: Leaf order:
+19651: meet 17 2 5 0,2
+19651: d 2 0 2 2,2,2,2
+19651: join 19 2 5 0,1,2,2
+19651: c 2 0 2 2,1,2,2
+19651: b 5 0 5 1,1,2,2
+19651: a 3 0 3 1,2
+19650: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19650: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19650: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
+ [28, 27, 26] by equation_H55 ?26 ?27 ?28
+19650: Goal:
+19650: Id : 1, {_}:
+ meet a (meet (join b c) (join b d))
+ =<=
+ meet a (join b (meet (join b c) (join d (meet a b))))
+ [] by prove_H60
+19650: Order:
+19650: nrkbo
+19650: Leaf order:
+19650: meet 17 2 5 0,2
+19650: d 2 0 2 2,2,2,2
+19650: join 19 2 5 0,1,2,2
+19650: c 2 0 2 2,1,2,2
+19650: b 5 0 5 1,1,2,2
+19650: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+19652: Facts:
+19652: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19652: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19652: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19652: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19652: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19652: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19652: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19652: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19652: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =?=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
+ [28, 27, 26] by equation_H55 ?26 ?27 ?28
+19652: Goal:
+19652: Id : 1, {_}:
+ meet a (meet (join b c) (join b d))
+ =<=
+ meet a (join b (meet (join b c) (join d (meet a b))))
+ [] by prove_H60
+19652: Order:
+19652: lpo
+19652: Leaf order:
+19652: meet 17 2 5 0,2
+19652: d 2 0 2 2,2,2,2
+19652: join 19 2 5 0,1,2,2
+19652: c 2 0 2 2,1,2,2
+19652: b 5 0 5 1,1,2,2
+19652: a 3 0 3 1,2
+% SZS status Timeout for LAT116-1.p
+NO CLASH, using fixed ground order
+19680: Facts:
+19680: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19680: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19680: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19680: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19680: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19680: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19680: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19680: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19680: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 ?29))
+ =<=
+ meet ?26 (join ?27 (meet ?26 (join (meet ?26 ?27) (meet ?28 ?29))))
+ [29, 28, 27, 26] by equation_H65 ?26 ?27 ?28 ?29
+19680: Goal:
+19680: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+19680: Order:
+19680: nrkbo
+19680: Leaf order:
+19680: meet 20 2 5 0,2
+19680: join 16 2 4 0,2,2
+19680: c 3 0 3 2,2,2
+19680: b 3 0 3 1,2,2
+19680: a 5 0 5 1,2
+NO CLASH, using fixed ground order
+19681: Facts:
+19681: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19681: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19681: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19681: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19681: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19681: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19681: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19681: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19681: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 ?29))
+ =<=
+ meet ?26 (join ?27 (meet ?26 (join (meet ?26 ?27) (meet ?28 ?29))))
+ [29, 28, 27, 26] by equation_H65 ?26 ?27 ?28 ?29
+19681: Goal:
+19681: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+19681: Order:
+19681: kbo
+19681: Leaf order:
+19681: meet 20 2 5 0,2
+19681: join 16 2 4 0,2,2
+19681: c 3 0 3 2,2,2
+19681: b 3 0 3 1,2,2
+19681: a 5 0 5 1,2
+NO CLASH, using fixed ground order
+19682: Facts:
+19682: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19682: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19682: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19682: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19682: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19682: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19682: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19682: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19682: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 ?29))
+ =<=
+ meet ?26 (join ?27 (meet ?26 (join (meet ?26 ?27) (meet ?28 ?29))))
+ [29, 28, 27, 26] by equation_H65 ?26 ?27 ?28 ?29
+19682: Goal:
+19682: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+19682: Order:
+19682: lpo
+19682: Leaf order:
+19682: meet 20 2 5 0,2
+19682: join 16 2 4 0,2,2
+19682: c 3 0 3 2,2,2
+19682: b 3 0 3 1,2,2
+19682: a 5 0 5 1,2
+% SZS status Timeout for LAT117-1.p
+NO CLASH, using fixed ground order
+19698: Facts:
+19698: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19698: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19698: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19698: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19698: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19698: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19698: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19698: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19698: Id : 10, {_}:
+ meet ?26 (join (meet ?27 (join ?26 ?28)) (meet ?28 (join ?26 ?27)))
+ =>=
+ join (meet ?26 ?27) (meet ?26 ?28)
+ [28, 27, 26] by equation_H82 ?26 ?27 ?28
+19698: Goal:
+19698: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+19698: Order:
+19698: nrkbo
+19698: Leaf order:
+19698: join 17 2 4 0,2,2
+19698: meet 20 2 6 0,2
+19698: c 3 0 3 2,2,2,2
+19698: b 4 0 4 1,2,2
+19698: a 5 0 5 1,2
+NO CLASH, using fixed ground order
+19699: Facts:
+19699: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19699: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19699: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19699: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19699: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19699: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19699: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19699: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19699: Id : 10, {_}:
+ meet ?26 (join (meet ?27 (join ?26 ?28)) (meet ?28 (join ?26 ?27)))
+ =>=
+ join (meet ?26 ?27) (meet ?26 ?28)
+ [28, 27, 26] by equation_H82 ?26 ?27 ?28
+19699: Goal:
+19699: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+19699: Order:
+19699: kbo
+19699: Leaf order:
+19699: join 17 2 4 0,2,2
+19699: meet 20 2 6 0,2
+19699: c 3 0 3 2,2,2,2
+19699: b 4 0 4 1,2,2
+19699: a 5 0 5 1,2
+NO CLASH, using fixed ground order
+19700: Facts:
+19700: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19700: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19700: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19700: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19700: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19700: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19700: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19700: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19700: Id : 10, {_}:
+ meet ?26 (join (meet ?27 (join ?26 ?28)) (meet ?28 (join ?26 ?27)))
+ =>=
+ join (meet ?26 ?27) (meet ?26 ?28)
+ [28, 27, 26] by equation_H82 ?26 ?27 ?28
+19700: Goal:
+19700: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+19700: Order:
+19700: lpo
+19700: Leaf order:
+19700: join 17 2 4 0,2,2
+19700: meet 20 2 6 0,2
+19700: c 3 0 3 2,2,2,2
+19700: b 4 0 4 1,2,2
+19700: a 5 0 5 1,2
+% SZS status Timeout for LAT119-1.p
+NO CLASH, using fixed ground order
+19732: Facts:
+19732: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19732: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19732: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19732: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19732: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19732: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19732: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19732: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19732: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?27 ?28))))
+ [28, 27, 26] by equation_H10_dual ?26 ?27 ?28
+19732: Goal:
+19732: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H58
+19732: Order:
+19732: nrkbo
+19732: Leaf order:
+19732: meet 16 2 4 0,2
+19732: join 18 2 4 0,2,2
+19732: c 2 0 2 2,2,2
+19732: b 4 0 4 1,2,2
+19732: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+19733: Facts:
+19733: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19733: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19733: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19733: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19733: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19733: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19733: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19733: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19733: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?27 ?28))))
+ [28, 27, 26] by equation_H10_dual ?26 ?27 ?28
+19733: Goal:
+19733: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H58
+19733: Order:
+19733: kbo
+19733: Leaf order:
+19733: meet 16 2 4 0,2
+19733: join 18 2 4 0,2,2
+19733: c 2 0 2 2,2,2
+19733: b 4 0 4 1,2,2
+19733: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+19734: Facts:
+19734: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19734: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19734: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19734: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19734: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19734: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19734: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19734: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19734: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =?=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?27 ?28))))
+ [28, 27, 26] by equation_H10_dual ?26 ?27 ?28
+19734: Goal:
+19734: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H58
+19734: Order:
+19734: lpo
+19734: Leaf order:
+19734: meet 16 2 4 0,2
+19734: join 18 2 4 0,2,2
+19734: c 2 0 2 2,2,2
+19734: b 4 0 4 1,2,2
+19734: a 4 0 4 1,2
+% SZS status Timeout for LAT120-1.p
+NO CLASH, using fixed ground order
+19750: Facts:
+19750: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19750: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19750: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19750: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19750: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19750: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19750: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19750: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19750: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?26 ?27)
+ (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
+ [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
+19750: Goal:
+19750: Id : 1, {_}:
+ join a (meet b (join a c))
+ =<=
+ join a (meet b (join c (meet a (join c b))))
+ [] by prove_H55
+19750: Order:
+19750: nrkbo
+19750: Leaf order:
+19750: meet 16 2 3 0,2,2
+19750: join 20 2 5 0,2
+19750: c 3 0 3 2,2,2,2
+19750: b 3 0 3 1,2,2
+19750: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+19751: Facts:
+19751: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19751: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19751: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19751: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19751: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19751: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19751: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19751: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19751: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?26 ?27)
+ (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
+ [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
+19751: Goal:
+19751: Id : 1, {_}:
+ join a (meet b (join a c))
+ =<=
+ join a (meet b (join c (meet a (join c b))))
+ [] by prove_H55
+19751: Order:
+19751: kbo
+19751: Leaf order:
+19751: meet 16 2 3 0,2,2
+19751: join 20 2 5 0,2
+19751: c 3 0 3 2,2,2,2
+19751: b 3 0 3 1,2,2
+19751: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+19752: Facts:
+19752: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19752: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19752: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19752: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19752: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19752: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19752: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19752: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19752: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?26 ?27)
+ (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
+ [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
+19752: Goal:
+19752: Id : 1, {_}:
+ join a (meet b (join a c))
+ =>=
+ join a (meet b (join c (meet a (join c b))))
+ [] by prove_H55
+19752: Order:
+19752: lpo
+19752: Leaf order:
+19752: meet 16 2 3 0,2,2
+19752: join 20 2 5 0,2
+19752: c 3 0 3 2,2,2,2
+19752: b 3 0 3 1,2,2
+19752: a 4 0 4 1,2
+% SZS status Timeout for LAT121-1.p
+NO CLASH, using fixed ground order
+19779: Facts:
+19779: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19779: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19779: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19779: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19779: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19779: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19779: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19779: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19779: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?27 (meet ?26 (join ?27 ?28)))
+ (join ?28 (meet ?26 ?27)))
+ [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
+19779: Goal:
+19779: Id : 1, {_}:
+ join a (meet b (join a c))
+ =<=
+ join a (meet b (join c (meet a (join c b))))
+ [] by prove_H55
+19779: Order:
+19779: nrkbo
+19779: Leaf order:
+19779: meet 16 2 3 0,2,2
+19779: join 20 2 5 0,2
+19779: c 3 0 3 2,2,2,2
+19779: b 3 0 3 1,2,2
+19779: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+19780: Facts:
+19780: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19780: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19780: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19780: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19780: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19780: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19780: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19780: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19780: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?27 (meet ?26 (join ?27 ?28)))
+ (join ?28 (meet ?26 ?27)))
+ [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
+19780: Goal:
+19780: Id : 1, {_}:
+ join a (meet b (join a c))
+ =<=
+ join a (meet b (join c (meet a (join c b))))
+ [] by prove_H55
+19780: Order:
+19780: kbo
+19780: Leaf order:
+19780: meet 16 2 3 0,2,2
+19780: join 20 2 5 0,2
+19780: c 3 0 3 2,2,2,2
+19780: b 3 0 3 1,2,2
+19780: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+19781: Facts:
+19781: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19781: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19781: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19781: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19781: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19781: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19781: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19781: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19781: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?27 (meet ?26 (join ?27 ?28)))
+ (join ?28 (meet ?26 ?27)))
+ [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
+19781: Goal:
+19781: Id : 1, {_}:
+ join a (meet b (join a c))
+ =>=
+ join a (meet b (join c (meet a (join c b))))
+ [] by prove_H55
+19781: Order:
+19781: lpo
+19781: Leaf order:
+19781: meet 16 2 3 0,2,2
+19781: join 20 2 5 0,2
+19781: c 3 0 3 2,2,2,2
+19781: b 3 0 3 1,2,2
+19781: a 4 0 4 1,2
+% SZS status Timeout for LAT122-1.p
+NO CLASH, using fixed ground order
+19798: Facts:
+19798: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19798: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19798: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19798: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19798: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19798: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19798: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19798: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19798: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?27 (meet ?28 (join ?26 ?27)))
+ (join ?28 (meet ?26 ?27)))
+ [28, 27, 26] by equation_H22_dual ?26 ?27 ?28
+19798: Goal:
+19798: Id : 1, {_}:
+ join a (meet b (join a c))
+ =<=
+ join a (meet b (join c (meet a (join c b))))
+ [] by prove_H55
+19798: Order:
+19798: nrkbo
+19798: Leaf order:
+19798: meet 16 2 3 0,2,2
+19798: join 20 2 5 0,2
+19798: c 3 0 3 2,2,2,2
+19798: b 3 0 3 1,2,2
+19798: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+19799: Facts:
+19799: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19799: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19799: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19799: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19799: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19799: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19799: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19799: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19799: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?27 (meet ?28 (join ?26 ?27)))
+ (join ?28 (meet ?26 ?27)))
+ [28, 27, 26] by equation_H22_dual ?26 ?27 ?28
+19799: Goal:
+19799: Id : 1, {_}:
+ join a (meet b (join a c))
+ =<=
+ join a (meet b (join c (meet a (join c b))))
+ [] by prove_H55
+19799: Order:
+19799: kbo
+19799: Leaf order:
+19799: meet 16 2 3 0,2,2
+19799: join 20 2 5 0,2
+19799: c 3 0 3 2,2,2,2
+19799: b 3 0 3 1,2,2
+19799: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+19800: Facts:
+19800: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19800: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19800: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19800: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19800: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19800: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19800: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19800: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19800: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?27 (meet ?28 (join ?26 ?27)))
+ (join ?28 (meet ?26 ?27)))
+ [28, 27, 26] by equation_H22_dual ?26 ?27 ?28
+19800: Goal:
+19800: Id : 1, {_}:
+ join a (meet b (join a c))
+ =>=
+ join a (meet b (join c (meet a (join c b))))
+ [] by prove_H55
+19800: Order:
+19800: lpo
+19800: Leaf order:
+19800: meet 16 2 3 0,2,2
+19800: join 20 2 5 0,2
+19800: c 3 0 3 2,2,2,2
+19800: b 3 0 3 1,2,2
+19800: a 4 0 4 1,2
+% SZS status Timeout for LAT123-1.p
+NO CLASH, using fixed ground order
+19842: Facts:
+19842: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19842: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19842: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19842: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19842: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19842: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19842: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19842: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19842: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 (join ?28 ?29)))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet (join ?26 ?29) (join ?27 ?29))))
+ [29, 28, 27, 26] by equation_H32_dual ?26 ?27 ?28 ?29
+19842: Goal:
+19842: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+19842: Order:
+19842: nrkbo
+19842: Leaf order:
+19842: meet 17 2 5 0,2
+19842: join 20 2 4 0,2,2
+19842: c 3 0 3 2,2,2
+19842: b 3 0 3 1,2,2
+19842: a 5 0 5 1,2
+NO CLASH, using fixed ground order
+19843: Facts:
+19843: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19843: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19843: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19843: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19843: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19843: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19843: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19843: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19843: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 (join ?28 ?29)))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet (join ?26 ?29) (join ?27 ?29))))
+ [29, 28, 27, 26] by equation_H32_dual ?26 ?27 ?28 ?29
+19843: Goal:
+19843: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+19843: Order:
+19843: kbo
+19843: Leaf order:
+19843: meet 17 2 5 0,2
+19843: join 20 2 4 0,2,2
+19843: c 3 0 3 2,2,2
+19843: b 3 0 3 1,2,2
+19843: a 5 0 5 1,2
+NO CLASH, using fixed ground order
+19844: Facts:
+19844: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19844: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19844: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19844: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19844: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19844: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19844: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19844: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19844: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 (join ?28 ?29)))
+ =?=
+ join ?26 (meet ?27 (join ?28 (meet (join ?26 ?29) (join ?27 ?29))))
+ [29, 28, 27, 26] by equation_H32_dual ?26 ?27 ?28 ?29
+19844: Goal:
+19844: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+19844: Order:
+19844: lpo
+19844: Leaf order:
+19844: meet 17 2 5 0,2
+19844: join 20 2 4 0,2,2
+19844: c 3 0 3 2,2,2
+19844: b 3 0 3 1,2,2
+19844: a 5 0 5 1,2
+% SZS status Timeout for LAT124-1.p
+NO CLASH, using fixed ground order
+19863: Facts:
+19863: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19863: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19863: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19863: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19863: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19863: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19863: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19863: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19863: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 ?29))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?27 (join ?29 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H34_dual ?26 ?27 ?28 ?29
+19863: Goal:
+19863: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+19863: Order:
+19863: nrkbo
+19863: Leaf order:
+19863: meet 18 2 5 0,2
+19863: join 18 2 4 0,2,2
+19863: c 3 0 3 2,2,2
+19863: b 3 0 3 1,2,2
+19863: a 5 0 5 1,2
+NO CLASH, using fixed ground order
+19864: Facts:
+19864: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19864: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19864: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19864: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19864: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19864: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19864: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19864: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19864: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 ?29))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?27 (join ?29 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H34_dual ?26 ?27 ?28 ?29
+19864: Goal:
+19864: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+19864: Order:
+19864: kbo
+19864: Leaf order:
+19864: meet 18 2 5 0,2
+19864: join 18 2 4 0,2,2
+19864: c 3 0 3 2,2,2
+19864: b 3 0 3 1,2,2
+19864: a 5 0 5 1,2
+NO CLASH, using fixed ground order
+19865: Facts:
+19865: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19865: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19865: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19865: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19865: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19865: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19865: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19865: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19865: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 ?29))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?27 (join ?29 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H34_dual ?26 ?27 ?28 ?29
+19865: Goal:
+19865: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+19865: Order:
+19865: lpo
+19865: Leaf order:
+19865: meet 18 2 5 0,2
+19865: join 18 2 4 0,2,2
+19865: c 3 0 3 2,2,2
+19865: b 3 0 3 1,2,2
+19865: a 5 0 5 1,2
+% SZS status Timeout for LAT125-1.p
+NO CLASH, using fixed ground order
+19895: Facts:
+19895: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19895: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19895: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19895: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19895: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19895: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19895: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19895: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19895: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?28))))
+ [29, 28, 27, 26] by equation_H39_dual ?26 ?27 ?28 ?29
+19895: Goal:
+19895: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+19895: Order:
+19895: kbo
+19895: Leaf order:
+19895: meet 18 2 5 0,2
+19895: join 18 2 4 0,2,2
+19895: c 3 0 3 2,2,2
+19895: b 3 0 3 1,2,2
+19895: a 5 0 5 1,2
+NO CLASH, using fixed ground order
+19894: Facts:
+19894: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19894: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19894: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19894: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19894: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19894: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19894: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19894: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19894: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?28))))
+ [29, 28, 27, 26] by equation_H39_dual ?26 ?27 ?28 ?29
+19894: Goal:
+19894: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+19894: Order:
+19894: nrkbo
+19894: Leaf order:
+19894: meet 18 2 5 0,2
+19894: join 18 2 4 0,2,2
+19894: c 3 0 3 2,2,2
+19894: b 3 0 3 1,2,2
+19894: a 5 0 5 1,2
+NO CLASH, using fixed ground order
+19896: Facts:
+19896: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19896: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19896: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19896: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19896: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19896: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19896: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19896: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19896: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =?=
+ join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?28))))
+ [29, 28, 27, 26] by equation_H39_dual ?26 ?27 ?28 ?29
+19896: Goal:
+19896: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+19896: Order:
+19896: lpo
+19896: Leaf order:
+19896: meet 18 2 5 0,2
+19896: join 18 2 4 0,2,2
+19896: c 3 0 3 2,2,2
+19896: b 3 0 3 1,2,2
+19896: a 5 0 5 1,2
+% SZS status Timeout for LAT126-1.p
+NO CLASH, using fixed ground order
+19924: Facts:
+19924: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19924: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19924: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19924: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19924: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19924: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19924: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19924: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19924: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 ?27))))
+ [28, 27, 26] by equation_H55_dual ?26 ?27 ?28
+19924: Goal:
+19924: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+19924: Order:
+19924: nrkbo
+19924: Leaf order:
+19924: join 16 2 4 0,2,2
+19924: meet 20 2 6 0,2
+19924: c 3 0 3 2,2,2,2
+19924: b 3 0 3 1,2,2
+19924: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+19925: Facts:
+19925: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19925: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19925: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19925: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19925: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19925: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19925: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19925: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19925: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 ?27))))
+ [28, 27, 26] by equation_H55_dual ?26 ?27 ?28
+19925: Goal:
+19925: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+19925: Order:
+19925: kbo
+19925: Leaf order:
+19925: join 16 2 4 0,2,2
+19925: meet 20 2 6 0,2
+19925: c 3 0 3 2,2,2,2
+19925: b 3 0 3 1,2,2
+19925: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+19926: Facts:
+19926: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19926: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19926: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19926: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19926: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19926: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19926: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19926: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19926: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 ?27))))
+ [28, 27, 26] by equation_H55_dual ?26 ?27 ?28
+19926: Goal:
+19926: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+19926: Order:
+19926: lpo
+19926: Leaf order:
+19926: join 16 2 4 0,2,2
+19926: meet 20 2 6 0,2
+19926: c 3 0 3 2,2,2,2
+19926: b 3 0 3 1,2,2
+19926: a 6 0 6 1,2
+% SZS status Timeout for LAT127-1.p
+NO CLASH, using fixed ground order
+20053: Facts:
+20053: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20053: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20053: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20053: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20053: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20053: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20053: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20053: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20053: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
+ [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
+20053: Goal:
+20053: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+20053: Order:
+20053: nrkbo
+20053: Leaf order:
+20053: join 17 2 4 0,2,2
+20053: meet 19 2 6 0,2
+20053: c 3 0 3 2,2,2,2
+20053: b 4 0 4 1,2,2
+20053: a 5 0 5 1,2
+NO CLASH, using fixed ground order
+20054: Facts:
+20054: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20054: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20054: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20054: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20054: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20054: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20054: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20054: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20054: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
+ [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
+20054: Goal:
+20054: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+20054: Order:
+20054: kbo
+20054: Leaf order:
+20054: join 17 2 4 0,2,2
+20054: meet 19 2 6 0,2
+20054: c 3 0 3 2,2,2,2
+20054: b 4 0 4 1,2,2
+20054: a 5 0 5 1,2
+NO CLASH, using fixed ground order
+20055: Facts:
+20055: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20055: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20055: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20055: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20055: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20055: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20055: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20055: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20055: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
+ [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
+20055: Goal:
+20055: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+20055: Order:
+20055: lpo
+20055: Leaf order:
+20055: join 17 2 4 0,2,2
+20055: meet 19 2 6 0,2
+20055: c 3 0 3 2,2,2,2
+20055: b 4 0 4 1,2,2
+20055: a 5 0 5 1,2
+% SZS status Timeout for LAT128-1.p
+NO CLASH, using fixed ground order
+20071: Facts:
+20071: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20071: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20071: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20071: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20071: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20071: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20071: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20071: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20071: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
+ [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
+20071: Goal:
+20071: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join a (meet b c))))
+ [] by prove_H10
+20071: Order:
+20071: nrkbo
+20071: Leaf order:
+20071: join 16 2 3 0,2,2
+20071: meet 18 2 5 0,2
+20071: c 3 0 3 2,2,2,2
+20071: b 3 0 3 1,2,2
+20071: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+20072: Facts:
+20072: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20072: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20072: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20072: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20072: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20072: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20072: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20072: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20072: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
+ [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
+20072: Goal:
+20072: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join a (meet b c))))
+ [] by prove_H10
+20072: Order:
+20072: kbo
+20072: Leaf order:
+20072: join 16 2 3 0,2,2
+20072: meet 18 2 5 0,2
+20072: c 3 0 3 2,2,2,2
+20072: b 3 0 3 1,2,2
+20072: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+20073: Facts:
+20073: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20073: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20073: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20073: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20073: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20073: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20073: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20073: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20073: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
+ [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
+20073: Goal:
+20073: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =>=
+ meet a (join b (meet c (join a (meet b c))))
+ [] by prove_H10
+20073: Order:
+20073: lpo
+20073: Leaf order:
+20073: join 16 2 3 0,2,2
+20073: meet 18 2 5 0,2
+20073: c 3 0 3 2,2,2,2
+20073: b 3 0 3 1,2,2
+20073: a 4 0 4 1,2
+% SZS status Timeout for LAT129-1.p
+NO CLASH, using fixed ground order
+20105: Facts:
+20105: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20105: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20105: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20105: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20105: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20105: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20105: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20105: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20105: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
+ [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
+20105: Goal:
+20105: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet a c))))
+ [] by prove_H39
+20105: Order:
+20105: nrkbo
+20105: Leaf order:
+20105: meet 17 2 5 0,2
+20105: join 17 2 4 0,2,2
+20105: d 2 0 2 2,2,2,2,2
+20105: c 3 0 3 1,2,2,2
+20105: b 2 0 2 1,2,2
+20105: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+20106: Facts:
+20106: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20106: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20106: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20106: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20106: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20106: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20106: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20106: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20106: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
+ [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
+20106: Goal:
+20106: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet a c))))
+ [] by prove_H39
+20106: Order:
+20106: kbo
+20106: Leaf order:
+20106: meet 17 2 5 0,2
+20106: join 17 2 4 0,2,2
+20106: d 2 0 2 2,2,2,2,2
+20106: c 3 0 3 1,2,2,2
+20106: b 2 0 2 1,2,2
+20106: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+20107: Facts:
+20107: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20107: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20107: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20107: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20107: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20107: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20107: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20107: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20107: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
+ [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
+20107: Goal:
+20107: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =>=
+ meet a (join b (meet c (join d (meet a c))))
+ [] by prove_H39
+20107: Order:
+20107: lpo
+20107: Leaf order:
+20107: meet 17 2 5 0,2
+20107: join 17 2 4 0,2,2
+20107: d 2 0 2 2,2,2,2,2
+20107: c 3 0 3 1,2,2,2
+20107: b 2 0 2 1,2,2
+20107: a 4 0 4 1,2
+% SZS status Timeout for LAT130-1.p
+NO CLASH, using fixed ground order
+20123: Facts:
+20123: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20123: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20123: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20123: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20123: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20123: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20123: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20123: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20123: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
+ [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
+20123: Goal:
+20123: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+20123: Order:
+20123: nrkbo
+20123: Leaf order:
+20123: meet 17 2 5 0,2
+20123: join 18 2 5 0,2,2
+20123: d 2 0 2 2,2,2,2,2
+20123: c 3 0 3 1,2,2,2
+20123: b 3 0 3 1,2,2
+20123: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+20124: Facts:
+20124: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20124: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20124: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20124: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20124: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20124: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20124: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20124: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20124: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
+ [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
+20124: Goal:
+20124: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+20124: Order:
+20124: kbo
+20124: Leaf order:
+20124: meet 17 2 5 0,2
+20124: join 18 2 5 0,2,2
+20124: d 2 0 2 2,2,2,2,2
+20124: c 3 0 3 1,2,2,2
+20124: b 3 0 3 1,2,2
+20124: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+20125: Facts:
+20125: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20125: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20125: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20125: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20125: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20125: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20125: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20125: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20125: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
+ [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
+20125: Goal:
+20125: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =>=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+20125: Order:
+20125: lpo
+20125: Leaf order:
+20125: meet 17 2 5 0,2
+20125: join 18 2 5 0,2,2
+20125: d 2 0 2 2,2,2,2,2
+20125: c 3 0 3 1,2,2,2
+20125: b 3 0 3 1,2,2
+20125: a 4 0 4 1,2
+% SZS status Timeout for LAT131-1.p
+NO CLASH, using fixed ground order
+20152: Facts:
+20152: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20152: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20152: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20152: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20152: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20152: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20152: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20152: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20152: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ meet (join ?26 (meet ?28 (join ?26 ?27)))
+ (join ?26 (meet ?27 (join ?26 ?28)))
+ [28, 27, 26] by equation_H69_dual ?26 ?27 ?28
+20152: Goal:
+20152: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+20152: Order:
+20152: nrkbo
+20152: Leaf order:
+20152: meet 18 2 5 0,2
+20152: join 19 2 5 0,2,2
+20152: d 2 0 2 2,2,2,2,2
+20152: c 3 0 3 1,2,2,2
+20152: b 3 0 3 1,2,2
+20152: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+20153: Facts:
+20153: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20153: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20153: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20153: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20153: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20153: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20153: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20153: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20153: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ meet (join ?26 (meet ?28 (join ?26 ?27)))
+ (join ?26 (meet ?27 (join ?26 ?28)))
+ [28, 27, 26] by equation_H69_dual ?26 ?27 ?28
+20153: Goal:
+20153: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+20153: Order:
+20153: kbo
+20153: Leaf order:
+20153: meet 18 2 5 0,2
+20153: join 19 2 5 0,2,2
+20153: d 2 0 2 2,2,2,2,2
+20153: c 3 0 3 1,2,2,2
+20153: b 3 0 3 1,2,2
+20153: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+20154: Facts:
+20154: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20154: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20154: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20154: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20154: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20154: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20154: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20154: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20154: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ meet (join ?26 (meet ?28 (join ?26 ?27)))
+ (join ?26 (meet ?27 (join ?26 ?28)))
+ [28, 27, 26] by equation_H69_dual ?26 ?27 ?28
+20154: Goal:
+20154: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =>=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+20154: Order:
+20154: lpo
+20154: Leaf order:
+20154: meet 18 2 5 0,2
+20154: join 19 2 5 0,2,2
+20154: d 2 0 2 2,2,2,2,2
+20154: c 3 0 3 1,2,2,2
+20154: b 3 0 3 1,2,2
+20154: a 4 0 4 1,2
+% SZS status Timeout for LAT132-1.p
+NO CLASH, using fixed ground order
+20170: Facts:
+20170: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20170: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20170: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20170: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20170: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20170: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20170: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20170: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20170: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
+ [28, 27, 26] by equation_H55 ?26 ?27 ?28
+20170: Goal:
+20170: Id : 1, {_}:
+ join a (meet b (join a c))
+ =<=
+ join a (meet (join a (meet b (join a c))) (join c (meet a b)))
+ [] by prove_H6_dual
+20170: Order:
+20170: nrkbo
+20170: Leaf order:
+20170: meet 16 2 4 0,2,2
+20170: join 20 2 6 0,2
+20170: c 3 0 3 2,2,2,2
+20170: b 3 0 3 1,2,2
+20170: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+20171: Facts:
+20171: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20171: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20171: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20171: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20171: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20171: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20171: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20171: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20171: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
+ [28, 27, 26] by equation_H55 ?26 ?27 ?28
+20171: Goal:
+20171: Id : 1, {_}:
+ join a (meet b (join a c))
+ =<=
+ join a (meet (join a (meet b (join a c))) (join c (meet a b)))
+ [] by prove_H6_dual
+20171: Order:
+20171: kbo
+20171: Leaf order:
+20171: meet 16 2 4 0,2,2
+20171: join 20 2 6 0,2
+20171: c 3 0 3 2,2,2,2
+20171: b 3 0 3 1,2,2
+20171: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+20172: Facts:
+20172: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20172: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20172: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20172: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20172: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20172: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20172: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20172: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20172: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =?=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
+ [28, 27, 26] by equation_H55 ?26 ?27 ?28
+20172: Goal:
+20172: Id : 1, {_}:
+ join a (meet b (join a c))
+ =<=
+ join a (meet (join a (meet b (join a c))) (join c (meet a b)))
+ [] by prove_H6_dual
+20172: Order:
+20172: lpo
+20172: Leaf order:
+20172: meet 16 2 4 0,2,2
+20172: join 20 2 6 0,2
+20172: c 3 0 3 2,2,2,2
+20172: b 3 0 3 1,2,2
+20172: a 6 0 6 1,2
+% SZS status Timeout for LAT133-1.p
+NO CLASH, using fixed ground order
+20205: Facts:
+20205: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20205: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20205: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20205: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20205: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20205: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20205: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20205: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20205: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26 (meet (join ?26 ?27) (join (meet ?26 ?27) ?28))
+ [28, 27, 26] by equation_H61 ?26 ?27 ?28
+20205: Goal:
+20205: Id : 1, {_}:
+ meet (join a b) (join a c)
+ =<=
+ join a (meet (join b (meet c (join a b))) (join c (meet a b)))
+ [] by prove_H22_dual
+20205: Order:
+20205: kbo
+20205: Leaf order:
+20205: meet 16 2 4 0,2
+20205: c 3 0 3 2,2,2
+20205: join 20 2 6 0,1,2
+20205: b 4 0 4 2,1,2
+20205: a 5 0 5 1,1,2
+NO CLASH, using fixed ground order
+20204: Facts:
+20204: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20204: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20204: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20204: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20204: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20204: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20204: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20204: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20204: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26 (meet (join ?26 ?27) (join (meet ?26 ?27) ?28))
+ [28, 27, 26] by equation_H61 ?26 ?27 ?28
+20204: Goal:
+20204: Id : 1, {_}:
+ meet (join a b) (join a c)
+ =<=
+ join a (meet (join b (meet c (join a b))) (join c (meet a b)))
+ [] by prove_H22_dual
+20204: Order:
+20204: nrkbo
+20204: Leaf order:
+20204: meet 16 2 4 0,2
+20204: c 3 0 3 2,2,2
+20204: join 20 2 6 0,1,2
+20204: b 4 0 4 2,1,2
+20204: a 5 0 5 1,1,2
+NO CLASH, using fixed ground order
+20206: Facts:
+20206: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20206: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20206: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20206: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20206: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20206: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20206: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20206: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20206: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26 (meet (join ?26 ?27) (join (meet ?26 ?27) ?28))
+ [28, 27, 26] by equation_H61 ?26 ?27 ?28
+20206: Goal:
+20206: Id : 1, {_}:
+ meet (join a b) (join a c)
+ =<=
+ join a (meet (join b (meet c (join a b))) (join c (meet a b)))
+ [] by prove_H22_dual
+20206: Order:
+20206: lpo
+20206: Leaf order:
+20206: meet 16 2 4 0,2
+20206: c 3 0 3 2,2,2
+20206: join 20 2 6 0,1,2
+20206: b 4 0 4 2,1,2
+20206: a 5 0 5 1,1,2
+% SZS status Timeout for LAT134-1.p
+NO CLASH, using fixed ground order
+20243: Facts:
+20243: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20243: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20243: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20243: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20243: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20243: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20243: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20243: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20243: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
+ [28, 27, 26] by equation_H68 ?26 ?27 ?28
+20243: Goal:
+20243: Id : 1, {_}:
+ join a (meet b (join c (meet a d)))
+ =<=
+ join a (meet b (join c (meet d (join a c))))
+ [] by prove_H39_dual
+20243: Order:
+20243: nrkbo
+20243: Leaf order:
+20243: join 17 2 5 0,2
+20243: meet 17 2 4 0,2,2
+20243: d 2 0 2 2,2,2,2,2
+20243: c 3 0 3 1,2,2,2
+20243: b 2 0 2 1,2,2
+20243: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+20244: Facts:
+20244: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20244: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20244: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20244: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20244: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20244: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20244: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20244: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20244: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
+ [28, 27, 26] by equation_H68 ?26 ?27 ?28
+20244: Goal:
+20244: Id : 1, {_}:
+ join a (meet b (join c (meet a d)))
+ =<=
+ join a (meet b (join c (meet d (join a c))))
+ [] by prove_H39_dual
+20244: Order:
+20244: kbo
+20244: Leaf order:
+20244: join 17 2 5 0,2
+20244: meet 17 2 4 0,2,2
+20244: d 2 0 2 2,2,2,2,2
+20244: c 3 0 3 1,2,2,2
+20244: b 2 0 2 1,2,2
+20244: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+20245: Facts:
+20245: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20245: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20245: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20245: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20245: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20245: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20245: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20245: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20245: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
+ [28, 27, 26] by equation_H68 ?26 ?27 ?28
+20245: Goal:
+20245: Id : 1, {_}:
+ join a (meet b (join c (meet a d)))
+ =>=
+ join a (meet b (join c (meet d (join a c))))
+ [] by prove_H39_dual
+20245: Order:
+20245: lpo
+20245: Leaf order:
+20245: join 17 2 5 0,2
+20245: meet 17 2 4 0,2,2
+20245: d 2 0 2 2,2,2,2,2
+20245: c 3 0 3 1,2,2,2
+20245: b 2 0 2 1,2,2
+20245: a 4 0 4 1,2
+% SZS status Timeout for LAT135-1.p
+NO CLASH, using fixed ground order
+20272: Facts:
+20272: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20272: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20272: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20272: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20272: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20272: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20272: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20272: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20272: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ join (meet ?26 (join ?28 (meet ?26 ?27)))
+ (meet ?26 (join ?27 (meet ?26 ?28)))
+ [28, 27, 26] by equation_H69 ?26 ?27 ?28
+20272: Goal:
+20272: Id : 1, {_}:
+ join a (meet b (join c (meet a d)))
+ =<=
+ join a (meet b (join c (meet d (join a c))))
+ [] by prove_H39_dual
+20272: Order:
+20272: nrkbo
+20272: Leaf order:
+20272: join 18 2 5 0,2
+20272: meet 18 2 4 0,2,2
+20272: d 2 0 2 2,2,2,2,2
+20272: c 3 0 3 1,2,2,2
+20272: b 2 0 2 1,2,2
+20272: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+20273: Facts:
+20273: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20273: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20273: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20273: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20273: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20273: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20273: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20273: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20273: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ join (meet ?26 (join ?28 (meet ?26 ?27)))
+ (meet ?26 (join ?27 (meet ?26 ?28)))
+ [28, 27, 26] by equation_H69 ?26 ?27 ?28
+20273: Goal:
+20273: Id : 1, {_}:
+ join a (meet b (join c (meet a d)))
+ =<=
+ join a (meet b (join c (meet d (join a c))))
+ [] by prove_H39_dual
+20273: Order:
+20273: kbo
+20273: Leaf order:
+20273: join 18 2 5 0,2
+20273: meet 18 2 4 0,2,2
+20273: d 2 0 2 2,2,2,2,2
+20273: c 3 0 3 1,2,2,2
+20273: b 2 0 2 1,2,2
+20273: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+20274: Facts:
+20274: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20274: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20274: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20274: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20274: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20274: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20274: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20274: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20274: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ join (meet ?26 (join ?28 (meet ?26 ?27)))
+ (meet ?26 (join ?27 (meet ?26 ?28)))
+ [28, 27, 26] by equation_H69 ?26 ?27 ?28
+20274: Goal:
+20274: Id : 1, {_}:
+ join a (meet b (join c (meet a d)))
+ =>=
+ join a (meet b (join c (meet d (join a c))))
+ [] by prove_H39_dual
+20274: Order:
+20274: lpo
+20274: Leaf order:
+20274: join 18 2 5 0,2
+20274: meet 18 2 4 0,2,2
+20274: d 2 0 2 2,2,2,2,2
+20274: c 3 0 3 1,2,2,2
+20274: b 2 0 2 1,2,2
+20274: a 4 0 4 1,2
+% SZS status Timeout for LAT136-1.p
+NO CLASH, using fixed ground order
+20301: Facts:
+20301: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20301: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20301: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20301: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20301: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20301: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20301: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20301: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20301: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ join (meet ?26 (join ?28 (meet ?26 ?27)))
+ (meet ?26 (join ?27 (meet ?26 ?28)))
+ [28, 27, 26] by equation_H69 ?26 ?27 ?28
+20301: Goal:
+20301: Id : 1, {_}:
+ join a (meet b (join c (meet a d)))
+ =<=
+ join a (meet b (join c (meet d (join c (meet a b)))))
+ [] by prove_H40_dual
+20301: Order:
+20301: nrkbo
+20301: Leaf order:
+20301: join 18 2 5 0,2
+20301: meet 19 2 5 0,2,2
+20301: d 2 0 2 2,2,2,2,2
+20301: c 3 0 3 1,2,2,2
+20301: b 3 0 3 1,2,2
+20301: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+20302: Facts:
+20302: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20302: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20302: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20302: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20302: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20302: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20302: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20302: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20302: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ join (meet ?26 (join ?28 (meet ?26 ?27)))
+ (meet ?26 (join ?27 (meet ?26 ?28)))
+ [28, 27, 26] by equation_H69 ?26 ?27 ?28
+20302: Goal:
+20302: Id : 1, {_}:
+ join a (meet b (join c (meet a d)))
+ =<=
+ join a (meet b (join c (meet d (join c (meet a b)))))
+ [] by prove_H40_dual
+20302: Order:
+20302: kbo
+20302: Leaf order:
+20302: join 18 2 5 0,2
+20302: meet 19 2 5 0,2,2
+20302: d 2 0 2 2,2,2,2,2
+20302: c 3 0 3 1,2,2,2
+20302: b 3 0 3 1,2,2
+20302: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+20303: Facts:
+20303: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20303: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20303: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20303: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20303: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20303: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20303: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20303: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20303: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ join (meet ?26 (join ?28 (meet ?26 ?27)))
+ (meet ?26 (join ?27 (meet ?26 ?28)))
+ [28, 27, 26] by equation_H69 ?26 ?27 ?28
+20303: Goal:
+20303: Id : 1, {_}:
+ join a (meet b (join c (meet a d)))
+ =<=
+ join a (meet b (join c (meet d (join c (meet a b)))))
+ [] by prove_H40_dual
+20303: Order:
+20303: lpo
+20303: Leaf order:
+20303: join 18 2 5 0,2
+20303: meet 19 2 5 0,2,2
+20303: d 2 0 2 2,2,2,2,2
+20303: c 3 0 3 1,2,2,2
+20303: b 3 0 3 1,2,2
+20303: a 4 0 4 1,2
+% SZS status Timeout for LAT137-1.p
+NO CLASH, using fixed ground order
+20331: Facts:
+20331: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20331: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20331: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20331: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20331: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20331: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20331: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20331: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20331: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26 (join (meet ?26 ?27) (meet (join ?26 ?27) ?28))
+ [28, 27, 26] by equation_H61_dual ?26 ?27 ?28
+20331: Goal:
+20331: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+20331: Order:
+20331: nrkbo
+20331: Leaf order:
+20331: join 16 2 4 0,2,2
+20331: meet 20 2 6 0,2
+20331: c 3 0 3 2,2,2,2
+20331: b 3 0 3 1,2,2
+20331: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+20332: Facts:
+20332: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20332: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20332: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20332: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20332: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20332: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20332: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20332: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20332: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26 (join (meet ?26 ?27) (meet (join ?26 ?27) ?28))
+ [28, 27, 26] by equation_H61_dual ?26 ?27 ?28
+20332: Goal:
+20332: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+20332: Order:
+20332: kbo
+20332: Leaf order:
+20332: join 16 2 4 0,2,2
+20332: meet 20 2 6 0,2
+20332: c 3 0 3 2,2,2,2
+20332: b 3 0 3 1,2,2
+20332: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+20333: Facts:
+20333: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+20333: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+20333: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+20333: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+20333: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+20333: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+20333: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+20333: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+20333: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26 (join (meet ?26 ?27) (meet (join ?26 ?27) ?28))
+ [28, 27, 26] by equation_H61_dual ?26 ?27 ?28
+20333: Goal:
+20333: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+20333: Order:
+20333: lpo
+20333: Leaf order:
+20333: join 16 2 4 0,2,2
+20333: meet 20 2 6 0,2
+20333: c 3 0 3 2,2,2,2
+20333: b 3 0 3 1,2,2
+20333: a 6 0 6 1,2
+% SZS status Timeout for LAT171-1.p
+NO CLASH, using fixed ground order
+20686: Facts:
+20686: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+20686: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+20686: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+20686: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+20686: Id : 6, {_}: implies x y =>= implies y z [] by lemma_antecedent
+20686: Goal:
+20686: Id : 1, {_}: implies x z =>= truth [] by prove_wajsberg_lemma
+20686: Order:
+20686: nrkbo
+20686: Leaf order:
+20686: y 2 0 0
+20686: not 2 1 0
+20686: truth 4 0 1 3
+20686: implies 16 2 1 0,2
+20686: z 2 0 1 2,2
+20686: x 2 0 1 1,2
+NO CLASH, using fixed ground order
+20687: Facts:
+20687: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+20687: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+20687: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+20687: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+20687: Id : 6, {_}: implies x y =>= implies y z [] by lemma_antecedent
+20687: Goal:
+20687: Id : 1, {_}: implies x z =>= truth [] by prove_wajsberg_lemma
+20687: Order:
+20687: kbo
+20687: Leaf order:
+20687: y 2 0 0
+20687: not 2 1 0
+20687: truth 4 0 1 3
+20687: implies 16 2 1 0,2
+20687: z 2 0 1 2,2
+20687: x 2 0 1 1,2
+NO CLASH, using fixed ground order
+20688: Facts:
+20688: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+20688: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+20688: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+20688: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+20688: Id : 6, {_}: implies x y =>= implies y z [] by lemma_antecedent
+20688: Goal:
+20688: Id : 1, {_}: implies x z =>= truth [] by prove_wajsberg_lemma
+20688: Order:
+20688: lpo
+20688: Leaf order:
+20688: y 2 0 0
+20688: not 2 1 0
+20688: truth 4 0 1 3
+20688: implies 16 2 1 0,2
+20688: z 2 0 1 2,2
+20688: x 2 0 1 1,2
+% SZS status Timeout for LCL136-1.p
+NO CLASH, using fixed ground order
+20715: Facts:
+20715: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+20715: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+20715: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+20715: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+20715: Goal:
+20715: Id : 1, {_}:
+ implies (implies (implies x y) y)
+ (implies (implies y z) (implies x z))
+ =>=
+ truth
+ [] by prove_wajsberg_lemma
+20715: Order:
+20715: nrkbo
+20715: Leaf order:
+20715: not 2 1 0
+20715: truth 4 0 1 3
+20715: z 2 0 2 2,1,2,2
+20715: implies 19 2 6 0,2
+20715: y 3 0 3 2,1,1,2
+20715: x 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+20716: Facts:
+20716: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+20716: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+20716: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+20716: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+20716: Goal:
+20716: Id : 1, {_}:
+ implies (implies (implies x y) y)
+ (implies (implies y z) (implies x z))
+ =>=
+ truth
+ [] by prove_wajsberg_lemma
+20716: Order:
+20716: kbo
+20716: Leaf order:
+20716: not 2 1 0
+20716: truth 4 0 1 3
+20716: z 2 0 2 2,1,2,2
+20716: implies 19 2 6 0,2
+20716: y 3 0 3 2,1,1,2
+20716: x 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+20717: Facts:
+20717: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+20717: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+20717: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+20717: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+20717: Goal:
+20717: Id : 1, {_}:
+ implies (implies (implies x y) y)
+ (implies (implies y z) (implies x z))
+ =>=
+ truth
+ [] by prove_wajsberg_lemma
+20717: Order:
+20717: lpo
+20717: Leaf order:
+20717: not 2 1 0
+20717: truth 4 0 1 3
+20717: z 2 0 2 2,1,2,2
+20717: implies 19 2 6 0,2
+20717: y 3 0 3 2,1,1,2
+20717: x 2 0 2 1,1,1,2
+% SZS status Timeout for LCL137-1.p
+NO CLASH, using fixed ground order
+20733: Facts:
+20733: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+20733: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+20733: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+20733: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+20733: Id : 6, {_}:
+ or ?14 ?15 =<= implies (not ?14) ?15
+ [15, 14] by or_definition ?14 ?15
+20733: Id : 7, {_}:
+ or (or ?17 ?18) ?19 =?= or ?17 (or ?18 ?19)
+ [19, 18, 17] by or_associativity ?17 ?18 ?19
+20733: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
+20733: Id : 9, {_}:
+ and ?24 ?25 =<= not (or (not ?24) (not ?25))
+ [25, 24] by and_definition ?24 ?25
+20733: Id : 10, {_}:
+ and (and ?27 ?28) ?29 =?= and ?27 (and ?28 ?29)
+ [29, 28, 27] by and_associativity ?27 ?28 ?29
+20733: Id : 11, {_}:
+ and ?31 ?32 =?= and ?32 ?31
+ [32, 31] by and_commutativity ?31 ?32
+20733: Goal:
+20733: Id : 1, {_}:
+ not (or (and x (or x x)) (and x x))
+ =<=
+ and (not x) (or (or (not x) (not x)) (and (not x) (not x)))
+ [] by prove_wajsberg_theorem
+20733: Order:
+20733: nrkbo
+20733: Leaf order:
+20733: implies 14 2 0
+20733: truth 3 0 0
+20733: not 12 1 6 0,2
+20733: and 11 2 4 0,1,1,2
+20733: or 12 2 4 0,1,2
+20733: x 10 0 10 1,1,1,2
+NO CLASH, using fixed ground order
+20734: Facts:
+20734: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+20734: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+20734: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+20734: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+20734: Id : 6, {_}:
+ or ?14 ?15 =<= implies (not ?14) ?15
+ [15, 14] by or_definition ?14 ?15
+20734: Id : 7, {_}:
+ or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
+ [19, 18, 17] by or_associativity ?17 ?18 ?19
+20734: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
+20734: Id : 9, {_}:
+ and ?24 ?25 =<= not (or (not ?24) (not ?25))
+ [25, 24] by and_definition ?24 ?25
+20734: Id : 10, {_}:
+ and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
+ [29, 28, 27] by and_associativity ?27 ?28 ?29
+20734: Id : 11, {_}:
+ and ?31 ?32 =?= and ?32 ?31
+ [32, 31] by and_commutativity ?31 ?32
+20734: Goal:
+NO CLASH, using fixed ground order
+20735: Facts:
+20735: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+20735: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+20735: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+20735: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+20735: Id : 6, {_}:
+ or ?14 ?15 =>= implies (not ?14) ?15
+ [15, 14] by or_definition ?14 ?15
+20735: Id : 7, {_}:
+ or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
+ [19, 18, 17] by or_associativity ?17 ?18 ?19
+20735: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
+20735: Id : 9, {_}:
+ and ?24 ?25 =<= not (or (not ?24) (not ?25))
+ [25, 24] by and_definition ?24 ?25
+20735: Id : 10, {_}:
+ and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
+ [29, 28, 27] by and_associativity ?27 ?28 ?29
+20735: Id : 11, {_}:
+ and ?31 ?32 =?= and ?32 ?31
+ [32, 31] by and_commutativity ?31 ?32
+20735: Goal:
+20735: Id : 1, {_}:
+ not (or (and x (or x x)) (and x x))
+ =<=
+ and (not x) (or (or (not x) (not x)) (and (not x) (not x)))
+ [] by prove_wajsberg_theorem
+20735: Order:
+20735: lpo
+20735: Leaf order:
+20735: implies 14 2 0
+20735: truth 3 0 0
+20735: not 12 1 6 0,2
+20735: and 11 2 4 0,1,1,2
+20735: or 12 2 4 0,1,2
+20735: x 10 0 10 1,1,1,2
+20734: Id : 1, {_}:
+ not (or (and x (or x x)) (and x x))
+ =<=
+ and (not x) (or (or (not x) (not x)) (and (not x) (not x)))
+ [] by prove_wajsberg_theorem
+20734: Order:
+20734: kbo
+20734: Leaf order:
+20734: implies 14 2 0
+20734: truth 3 0 0
+20734: not 12 1 6 0,2
+20734: and 11 2 4 0,1,1,2
+20734: or 12 2 4 0,1,2
+20734: x 10 0 10 1,1,1,2
+% SZS status Timeout for LCL165-1.p
+NO CLASH, using fixed ground order
+20763: Facts:
+20763: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+20763: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+20763: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+20763: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+20763: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+20763: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+20763: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+20763: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+20763: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+20763: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+20763: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+20763: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+20763: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+20763: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+20763: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+20763: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+20763: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+20763: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+20763: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+20763: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+20763: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+20763: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+20763: Goal:
+20763: Id : 1, {_}:
+ associator x y (add u v)
+ =<=
+ add (associator x y u) (associator x y v)
+ [] by prove_linearised_form1
+20763: Order:
+20763: kbo
+20763: Leaf order:
+20763: commutator 1 2 0
+20763: additive_inverse 22 1 0
+20763: multiply 40 2 0
+20763: additive_identity 8 0 0
+20763: associator 4 3 3 0,2
+20763: add 26 2 2 0,3,2
+20763: v 2 0 2 2,3,2
+20763: u 2 0 2 1,3,2
+20763: y 3 0 3 2,2
+20763: x 3 0 3 1,2
+NO CLASH, using fixed ground order
+20762: Facts:
+20762: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+20762: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+20762: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+20762: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+20762: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+20762: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+20762: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+20762: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+20762: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+20762: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+20762: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+20762: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+20762: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+20762: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+20762: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+20762: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+20762: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+20762: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+20762: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+20762: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+20762: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+20762: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+20762: Goal:
+20762: Id : 1, {_}:
+ associator x y (add u v)
+ =<=
+ add (associator x y u) (associator x y v)
+ [] by prove_linearised_form1
+20762: Order:
+20762: nrkbo
+20762: Leaf order:
+20762: commutator 1 2 0
+20762: additive_inverse 22 1 0
+20762: multiply 40 2 0
+20762: additive_identity 8 0 0
+20762: associator 4 3 3 0,2
+20762: add 26 2 2 0,3,2
+20762: v 2 0 2 2,3,2
+20762: u 2 0 2 1,3,2
+20762: y 3 0 3 2,2
+20762: x 3 0 3 1,2
+NO CLASH, using fixed ground order
+20764: Facts:
+20764: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+20764: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+20764: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+20764: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+20764: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+20764: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+20764: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+20764: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+20764: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+20764: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+20764: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+20764: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+20764: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+20764: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+20764: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+20764: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+20764: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+20764: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+20764: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+20764: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+20764: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+20764: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+20764: Goal:
+20764: Id : 1, {_}:
+ associator x y (add u v)
+ =<=
+ add (associator x y u) (associator x y v)
+ [] by prove_linearised_form1
+20764: Order:
+20764: lpo
+20764: Leaf order:
+20764: commutator 1 2 0
+20764: additive_inverse 22 1 0
+20764: multiply 40 2 0
+20764: additive_identity 8 0 0
+20764: associator 4 3 3 0,2
+20764: add 26 2 2 0,3,2
+20764: v 2 0 2 2,3,2
+20764: u 2 0 2 1,3,2
+20764: y 3 0 3 2,2
+20764: x 3 0 3 1,2
+% SZS status Timeout for RNG019-7.p
+NO CLASH, using fixed ground order
+20780: Facts:
+20780: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+20780: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+20780: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+20780: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+20780: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+20780: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+20780: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+20780: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+20780: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+20780: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+20780: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+20780: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+20780: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+20780: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+20780: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+20780: Goal:
+20780: Id : 1, {_}:
+ associator x (add u v) y
+ =<=
+ add (associator x u y) (associator x v y)
+ [] by prove_linearised_form2
+20780: Order:
+20780: nrkbo
+20780: Leaf order:
+20780: commutator 1 2 0
+20780: additive_inverse 6 1 0
+20780: multiply 22 2 0
+20780: additive_identity 8 0 0
+20780: associator 4 3 3 0,2
+20780: y 3 0 3 3,2
+20780: add 18 2 2 0,2,2
+20780: v 2 0 2 2,2,2
+20780: u 2 0 2 1,2,2
+20780: x 3 0 3 1,2
+NO CLASH, using fixed ground order
+20781: Facts:
+20781: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+20781: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+20781: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+20781: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+20781: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+20781: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+20781: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+20781: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+20781: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+20781: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+20781: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+20781: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+20781: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+20781: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+20781: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+20781: Goal:
+20781: Id : 1, {_}:
+ associator x (add u v) y
+ =<=
+ add (associator x u y) (associator x v y)
+ [] by prove_linearised_form2
+20781: Order:
+20781: kbo
+20781: Leaf order:
+20781: commutator 1 2 0
+20781: additive_inverse 6 1 0
+20781: multiply 22 2 0
+20781: additive_identity 8 0 0
+20781: associator 4 3 3 0,2
+20781: y 3 0 3 3,2
+20781: add 18 2 2 0,2,2
+20781: v 2 0 2 2,2,2
+20781: u 2 0 2 1,2,2
+20781: x 3 0 3 1,2
+NO CLASH, using fixed ground order
+20782: Facts:
+20782: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+20782: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+20782: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+20782: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+20782: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+20782: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+20782: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+20782: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+20782: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+20782: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+20782: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+20782: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+20782: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+20782: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+20782: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+20782: Goal:
+20782: Id : 1, {_}:
+ associator x (add u v) y
+ =<=
+ add (associator x u y) (associator x v y)
+ [] by prove_linearised_form2
+20782: Order:
+20782: lpo
+20782: Leaf order:
+20782: commutator 1 2 0
+20782: additive_inverse 6 1 0
+20782: multiply 22 2 0
+20782: additive_identity 8 0 0
+20782: associator 4 3 3 0,2
+20782: y 3 0 3 3,2
+20782: add 18 2 2 0,2,2
+20782: v 2 0 2 2,2,2
+20782: u 2 0 2 1,2,2
+20782: x 3 0 3 1,2
+% SZS status Timeout for RNG020-6.p
+NO CLASH, using fixed ground order
+20815: Facts:
+20815: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+20815: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+20815: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+20815: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+20815: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+20815: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+20815: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+20815: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+20815: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+20815: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+20815: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+20815: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+20815: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+NO CLASH, using fixed ground order
+20816: Facts:
+20816: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+20816: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+20816: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+20816: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+NO CLASH, using fixed ground order
+20817: Facts:
+20817: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+20817: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+20816: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+20817: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+20816: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+20817: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+20817: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+20816: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+20817: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+20817: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+20816: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+20817: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+20816: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+20815: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+20816: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+20815: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+20816: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+20816: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+20815: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+20816: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+20815: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+20816: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+20815: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+20816: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+20815: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+20816: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+20815: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+20815: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+20815: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+20815: Goal:
+20815: Id : 1, {_}:
+ associator x (add u v) y
+ =<=
+ add (associator x u y) (associator x v y)
+ [] by prove_linearised_form2
+20815: Order:
+20815: nrkbo
+20815: Leaf order:
+20815: commutator 1 2 0
+20815: additive_inverse 22 1 0
+20815: multiply 40 2 0
+20815: additive_identity 8 0 0
+20815: associator 4 3 3 0,2
+20815: y 3 0 3 3,2
+20815: add 26 2 2 0,2,2
+20815: v 2 0 2 2,2,2
+20815: u 2 0 2 1,2,2
+20815: x 3 0 3 1,2
+20817: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+20816: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+20816: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+20816: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+20816: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+20816: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+20816: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+20816: Goal:
+20816: Id : 1, {_}:
+ associator x (add u v) y
+ =<=
+ add (associator x u y) (associator x v y)
+ [] by prove_linearised_form2
+20816: Order:
+20816: kbo
+20816: Leaf order:
+20816: commutator 1 2 0
+20816: additive_inverse 22 1 0
+20816: multiply 40 2 0
+20816: additive_identity 8 0 0
+20816: associator 4 3 3 0,2
+20816: y 3 0 3 3,2
+20816: add 26 2 2 0,2,2
+20816: v 2 0 2 2,2,2
+20816: u 2 0 2 1,2,2
+20816: x 3 0 3 1,2
+20817: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+20817: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+20817: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+20817: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+20817: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+20817: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+20817: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+20817: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+20817: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+20817: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+20817: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+20817: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+20817: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+20817: Goal:
+20817: Id : 1, {_}:
+ associator x (add u v) y
+ =<=
+ add (associator x u y) (associator x v y)
+ [] by prove_linearised_form2
+20817: Order:
+20817: lpo
+20817: Leaf order:
+20817: commutator 1 2 0
+20817: additive_inverse 22 1 0
+20817: multiply 40 2 0
+20817: additive_identity 8 0 0
+20817: associator 4 3 3 0,2
+20817: y 3 0 3 3,2
+20817: add 26 2 2 0,2,2
+20817: v 2 0 2 2,2,2
+20817: u 2 0 2 1,2,2
+20817: x 3 0 3 1,2
+% SZS status Timeout for RNG020-7.p
+NO CLASH, using fixed ground order
+20843: Facts:
+20843: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+20843: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+20843: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+20843: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+20843: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+20843: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+20843: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+20843: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+20843: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+20843: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+20843: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+20843: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+20843: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+20843: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+20843: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+20843: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+20843: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+20843: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+20843: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+20843: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+20843: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+20843: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+20843: Goal:
+20843: Id : 1, {_}:
+ associator (add u v) x y
+ =<=
+ add (associator u x y) (associator v x y)
+ [] by prove_linearised_form3
+20843: Order:
+20843: kbo
+20843: Leaf order:
+20843: commutator 1 2 0
+20843: additive_inverse 22 1 0
+20843: multiply 40 2 0
+20843: additive_identity 8 0 0
+20843: associator 4 3 3 0,2
+20843: y 3 0 3 3,2
+20843: x 3 0 3 2,2
+20843: add 26 2 2 0,1,2
+20843: v 2 0 2 2,1,2
+20843: u 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+20842: Facts:
+20842: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+20842: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+20842: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+20842: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+20842: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+20842: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+20842: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+20842: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+20842: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+20842: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+20842: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+20842: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+20842: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+20842: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+20842: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+20842: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+20842: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+20842: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+20842: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+20842: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+20842: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+20842: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+20842: Goal:
+20842: Id : 1, {_}:
+ associator (add u v) x y
+ =<=
+ add (associator u x y) (associator v x y)
+ [] by prove_linearised_form3
+20842: Order:
+20842: nrkbo
+20842: Leaf order:
+20842: commutator 1 2 0
+20842: additive_inverse 22 1 0
+20842: multiply 40 2 0
+20842: additive_identity 8 0 0
+20842: associator 4 3 3 0,2
+20842: y 3 0 3 3,2
+20842: x 3 0 3 2,2
+20842: add 26 2 2 0,1,2
+20842: v 2 0 2 2,1,2
+20842: u 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+20844: Facts:
+20844: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+20844: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+20844: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+20844: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+20844: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+20844: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+20844: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+20844: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+20844: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+20844: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+20844: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+20844: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+20844: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+20844: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+20844: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+20844: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+20844: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+20844: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+20844: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+20844: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+20844: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+20844: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+20844: Goal:
+20844: Id : 1, {_}:
+ associator (add u v) x y
+ =<=
+ add (associator u x y) (associator v x y)
+ [] by prove_linearised_form3
+20844: Order:
+20844: lpo
+20844: Leaf order:
+20844: commutator 1 2 0
+20844: additive_inverse 22 1 0
+20844: multiply 40 2 0
+20844: additive_identity 8 0 0
+20844: associator 4 3 3 0,2
+20844: y 3 0 3 3,2
+20844: x 3 0 3 2,2
+20844: add 26 2 2 0,1,2
+20844: v 2 0 2 2,1,2
+20844: u 2 0 2 1,1,2
+% SZS status Timeout for RNG021-7.p
+NO CLASH, using fixed ground order
+20871: Facts:
+20871: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+20871: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+20871: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+20871: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+20871: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+20871: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+20871: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+20871: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+20871: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+20871: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+20871: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+20871: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+20871: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+20871: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+20871: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+20871: Goal:
+20871: Id : 1, {_}:
+ add (associator x y z) (associator x z y) =>= additive_identity
+ [] by prove_equation
+20871: Order:
+20871: nrkbo
+20871: Leaf order:
+20871: commutator 1 2 0
+20871: additive_inverse 6 1 0
+20871: multiply 22 2 0
+20871: additive_identity 9 0 1 3
+20871: add 17 2 1 0,2
+20871: associator 3 3 2 0,1,2
+20871: z 2 0 2 3,1,2
+20871: y 2 0 2 2,1,2
+20871: x 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+20872: Facts:
+20872: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+20872: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+20872: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+20872: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+20872: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+20872: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+20872: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+20872: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+20872: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+20872: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+20872: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+20872: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+20872: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+20872: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+20872: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+20872: Goal:
+20872: Id : 1, {_}:
+ add (associator x y z) (associator x z y) =>= additive_identity
+ [] by prove_equation
+20872: Order:
+20872: kbo
+20872: Leaf order:
+20872: commutator 1 2 0
+20872: additive_inverse 6 1 0
+20872: multiply 22 2 0
+20872: additive_identity 9 0 1 3
+20872: add 17 2 1 0,2
+20872: associator 3 3 2 0,1,2
+20872: z 2 0 2 3,1,2
+20872: y 2 0 2 2,1,2
+20872: x 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+20873: Facts:
+20873: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+20873: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+20873: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+20873: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+20873: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+20873: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+20873: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+20873: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+20873: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+20873: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+20873: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+20873: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+20873: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+20873: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+20873: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+20873: Goal:
+20873: Id : 1, {_}:
+ add (associator x y z) (associator x z y) =>= additive_identity
+ [] by prove_equation
+20873: Order:
+20873: lpo
+20873: Leaf order:
+20873: commutator 1 2 0
+20873: additive_inverse 6 1 0
+20873: multiply 22 2 0
+20873: additive_identity 9 0 1 3
+20873: add 17 2 1 0,2
+20873: associator 3 3 2 0,1,2
+20873: z 2 0 2 3,1,2
+20873: y 2 0 2 2,1,2
+20873: x 2 0 2 1,1,2
+% SZS status Timeout for RNG025-4.p
+NO CLASH, using fixed ground order
+20890: Facts:
+20890: Id : 2, {_}:
+ add ?2 ?3 =?= add ?3 ?2
+ [3, 2] by commutativity_for_addition ?2 ?3
+20890: Id : 3, {_}:
+ add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7
+ [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
+20890: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
+20890: Id : 5, {_}:
+ add ?11 additive_identity =>= ?11
+ [11] by right_additive_identity ?11
+20890: Id : 6, {_}:
+ multiply additive_identity ?13 =>= additive_identity
+ [13] by left_multiplicative_zero ?13
+20890: Id : 7, {_}:
+ multiply ?15 additive_identity =>= additive_identity
+ [15] by right_multiplicative_zero ?15
+20890: Id : 8, {_}:
+ add (additive_inverse ?17) ?17 =>= additive_identity
+ [17] by left_additive_inverse ?17
+20890: Id : 9, {_}:
+ add ?19 (additive_inverse ?19) =>= additive_identity
+ [19] by right_additive_inverse ?19
+20890: Id : 10, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+20890: Id : 11, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+20890: Id : 12, {_}:
+ additive_inverse (additive_inverse ?29) =>= ?29
+ [29] by additive_inverse_additive_inverse ?29
+20890: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+20890: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+20890: Id : 15, {_}:
+ associator ?37 ?38 (add ?39 ?40)
+ =<=
+ add (associator ?37 ?38 ?39) (associator ?37 ?38 ?40)
+ [40, 39, 38, 37] by linearised_associator1 ?37 ?38 ?39 ?40
+20890: Id : 16, {_}:
+ associator ?42 (add ?43 ?44) ?45
+ =<=
+ add (associator ?42 ?43 ?45) (associator ?42 ?44 ?45)
+ [45, 44, 43, 42] by linearised_associator2 ?42 ?43 ?44 ?45
+20890: Id : 17, {_}:
+ associator (add ?47 ?48) ?49 ?50
+ =<=
+ add (associator ?47 ?49 ?50) (associator ?48 ?49 ?50)
+ [50, 49, 48, 47] by linearised_associator3 ?47 ?48 ?49 ?50
+NO CLASH, using fixed ground order
+20891: Facts:
+20891: Id : 2, {_}:
+ add ?2 ?3 =?= add ?3 ?2
+ [3, 2] by commutativity_for_addition ?2 ?3
+20891: Id : 3, {_}:
+ add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
+ [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
+20891: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
+20891: Id : 5, {_}:
+ add ?11 additive_identity =>= ?11
+ [11] by right_additive_identity ?11
+20891: Id : 6, {_}:
+ multiply additive_identity ?13 =>= additive_identity
+ [13] by left_multiplicative_zero ?13
+20891: Id : 7, {_}:
+ multiply ?15 additive_identity =>= additive_identity
+ [15] by right_multiplicative_zero ?15
+20891: Id : 8, {_}:
+ add (additive_inverse ?17) ?17 =>= additive_identity
+ [17] by left_additive_inverse ?17
+20891: Id : 9, {_}:
+ add ?19 (additive_inverse ?19) =>= additive_identity
+ [19] by right_additive_inverse ?19
+NO CLASH, using fixed ground order
+20892: Facts:
+20892: Id : 2, {_}:
+ add ?2 ?3 =?= add ?3 ?2
+ [3, 2] by commutativity_for_addition ?2 ?3
+20892: Id : 3, {_}:
+ add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
+ [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
+20892: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
+20892: Id : 5, {_}:
+ add ?11 additive_identity =>= ?11
+ [11] by right_additive_identity ?11
+20892: Id : 6, {_}:
+ multiply additive_identity ?13 =>= additive_identity
+ [13] by left_multiplicative_zero ?13
+20892: Id : 7, {_}:
+ multiply ?15 additive_identity =>= additive_identity
+ [15] by right_multiplicative_zero ?15
+20892: Id : 8, {_}:
+ add (additive_inverse ?17) ?17 =>= additive_identity
+ [17] by left_additive_inverse ?17
+20892: Id : 9, {_}:
+ add ?19 (additive_inverse ?19) =>= additive_identity
+ [19] by right_additive_inverse ?19
+20892: Id : 10, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+20891: Id : 10, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+20890: Id : 18, {_}:
+ commutator ?52 ?53
+ =<=
+ add (multiply ?53 ?52) (additive_inverse (multiply ?52 ?53))
+ [53, 52] by commutator ?52 ?53
+20890: Goal:
+20892: Id : 11, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+20890: Id : 1, {_}:
+ add (associator a b c) (associator a c b) =>= additive_identity
+ [] by prove_flexible_law
+20890: Order:
+20890: nrkbo
+20890: Leaf order:
+20892: Id : 12, {_}:
+ additive_inverse (additive_inverse ?29) =>= ?29
+ [29] by additive_inverse_additive_inverse ?29
+20892: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+20892: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+20892: Id : 15, {_}:
+ associator ?37 ?38 (add ?39 ?40)
+ =>=
+ add (associator ?37 ?38 ?39) (associator ?37 ?38 ?40)
+ [40, 39, 38, 37] by linearised_associator1 ?37 ?38 ?39 ?40
+20892: Id : 16, {_}:
+ associator ?42 (add ?43 ?44) ?45
+ =>=
+ add (associator ?42 ?43 ?45) (associator ?42 ?44 ?45)
+ [45, 44, 43, 42] by linearised_associator2 ?42 ?43 ?44 ?45
+20892: Id : 17, {_}:
+ associator (add ?47 ?48) ?49 ?50
+ =>=
+ add (associator ?47 ?49 ?50) (associator ?48 ?49 ?50)
+ [50, 49, 48, 47] by linearised_associator3 ?47 ?48 ?49 ?50
+20892: Id : 18, {_}:
+ commutator ?52 ?53
+ =<=
+ add (multiply ?53 ?52) (additive_inverse (multiply ?52 ?53))
+ [53, 52] by commutator ?52 ?53
+20892: Goal:
+20892: Id : 1, {_}:
+ add (associator a b c) (associator a c b) =>= additive_identity
+ [] by prove_flexible_law
+20892: Order:
+20892: lpo
+20892: Leaf order:
+20892: commutator 1 2 0
+20892: additive_inverse 5 1 0
+20892: multiply 18 2 0
+20892: additive_identity 9 0 1 3
+20892: add 22 2 1 0,2
+20892: associator 11 3 2 0,1,2
+20892: c 2 0 2 3,1,2
+20892: b 2 0 2 2,1,2
+20892: a 2 0 2 1,1,2
+20891: Id : 11, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+20890: commutator 1 2 0
+20890: additive_inverse 5 1 0
+20890: multiply 18 2 0
+20890: additive_identity 9 0 1 3
+20890: add 22 2 1 0,2
+20890: associator 11 3 2 0,1,2
+20890: c 2 0 2 3,1,2
+20890: b 2 0 2 2,1,2
+20890: a 2 0 2 1,1,2
+20891: Id : 12, {_}:
+ additive_inverse (additive_inverse ?29) =>= ?29
+ [29] by additive_inverse_additive_inverse ?29
+20891: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+20891: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+20891: Id : 15, {_}:
+ associator ?37 ?38 (add ?39 ?40)
+ =<=
+ add (associator ?37 ?38 ?39) (associator ?37 ?38 ?40)
+ [40, 39, 38, 37] by linearised_associator1 ?37 ?38 ?39 ?40
+20891: Id : 16, {_}:
+ associator ?42 (add ?43 ?44) ?45
+ =<=
+ add (associator ?42 ?43 ?45) (associator ?42 ?44 ?45)
+ [45, 44, 43, 42] by linearised_associator2 ?42 ?43 ?44 ?45
+20891: Id : 17, {_}:
+ associator (add ?47 ?48) ?49 ?50
+ =<=
+ add (associator ?47 ?49 ?50) (associator ?48 ?49 ?50)
+ [50, 49, 48, 47] by linearised_associator3 ?47 ?48 ?49 ?50
+20891: Id : 18, {_}:
+ commutator ?52 ?53
+ =<=
+ add (multiply ?53 ?52) (additive_inverse (multiply ?52 ?53))
+ [53, 52] by commutator ?52 ?53
+20891: Goal:
+20891: Id : 1, {_}:
+ add (associator a b c) (associator a c b) =>= additive_identity
+ [] by prove_flexible_law
+20891: Order:
+20891: kbo
+20891: Leaf order:
+20891: commutator 1 2 0
+20891: additive_inverse 5 1 0
+20891: multiply 18 2 0
+20891: additive_identity 9 0 1 3
+20891: add 22 2 1 0,2
+20891: associator 11 3 2 0,1,2
+20891: c 2 0 2 3,1,2
+20891: b 2 0 2 2,1,2
+20891: a 2 0 2 1,1,2
+% SZS status Timeout for RNG025-8.p
+NO CLASH, using fixed ground order
+20920: Facts:
+20920: Id : 2, {_}:
+ multiply (additive_inverse ?2) (additive_inverse ?3)
+ =>=
+ multiply ?2 ?3
+ [3, 2] by product_of_inverses ?2 ?3
+20920: Id : 3, {_}:
+ multiply (additive_inverse ?5) ?6
+ =<=
+ additive_inverse (multiply ?5 ?6)
+ [6, 5] by inverse_product1 ?5 ?6
+20920: Id : 4, {_}:
+ multiply ?8 (additive_inverse ?9)
+ =<=
+ additive_inverse (multiply ?8 ?9)
+ [9, 8] by inverse_product2 ?8 ?9
+20920: Id : 5, {_}:
+ multiply ?11 (add ?12 (additive_inverse ?13))
+ =<=
+ add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
+ [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
+20920: Id : 6, {_}:
+ multiply (add ?15 (additive_inverse ?16)) ?17
+ =<=
+ add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
+ [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
+20920: Id : 7, {_}:
+ multiply (additive_inverse ?19) (add ?20 ?21)
+ =<=
+ add (additive_inverse (multiply ?19 ?20))
+ (additive_inverse (multiply ?19 ?21))
+ [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
+20920: Id : 8, {_}:
+ multiply (add ?23 ?24) (additive_inverse ?25)
+ =<=
+ add (additive_inverse (multiply ?23 ?25))
+ (additive_inverse (multiply ?24 ?25))
+ [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
+20920: Id : 9, {_}:
+ add ?27 ?28 =?= add ?28 ?27
+ [28, 27] by commutativity_for_addition ?27 ?28
+20920: Id : 10, {_}:
+ add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32
+ [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
+20920: Id : 11, {_}:
+ add additive_identity ?34 =>= ?34
+ [34] by left_additive_identity ?34
+20920: Id : 12, {_}:
+ add ?36 additive_identity =>= ?36
+ [36] by right_additive_identity ?36
+20920: Id : 13, {_}:
+ multiply additive_identity ?38 =>= additive_identity
+ [38] by left_multiplicative_zero ?38
+20920: Id : 14, {_}:
+ multiply ?40 additive_identity =>= additive_identity
+ [40] by right_multiplicative_zero ?40
+20920: Id : 15, {_}:
+ add (additive_inverse ?42) ?42 =>= additive_identity
+ [42] by left_additive_inverse ?42
+20920: Id : 16, {_}:
+ add ?44 (additive_inverse ?44) =>= additive_identity
+ [44] by right_additive_inverse ?44
+20920: Id : 17, {_}:
+ multiply ?46 (add ?47 ?48)
+ =<=
+ add (multiply ?46 ?47) (multiply ?46 ?48)
+ [48, 47, 46] by distribute1 ?46 ?47 ?48
+20920: Id : 18, {_}:
+ multiply (add ?50 ?51) ?52
+ =<=
+ add (multiply ?50 ?52) (multiply ?51 ?52)
+ [52, 51, 50] by distribute2 ?50 ?51 ?52
+20920: Id : 19, {_}:
+ additive_inverse (additive_inverse ?54) =>= ?54
+ [54] by additive_inverse_additive_inverse ?54
+20920: Id : 20, {_}:
+ multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57)
+ [57, 56] by right_alternative ?56 ?57
+20920: Id : 21, {_}:
+ multiply (multiply ?59 ?59) ?60 =?= multiply ?59 (multiply ?59 ?60)
+ [60, 59] by left_alternative ?59 ?60
+20920: Id : 22, {_}:
+ associator ?62 ?63 (add ?64 ?65)
+ =<=
+ add (associator ?62 ?63 ?64) (associator ?62 ?63 ?65)
+ [65, 64, 63, 62] by linearised_associator1 ?62 ?63 ?64 ?65
+20920: Id : 23, {_}:
+ associator ?67 (add ?68 ?69) ?70
+ =<=
+ add (associator ?67 ?68 ?70) (associator ?67 ?69 ?70)
+ [70, 69, 68, 67] by linearised_associator2 ?67 ?68 ?69 ?70
+20920: Id : 24, {_}:
+ associator (add ?72 ?73) ?74 ?75
+ =<=
+ add (associator ?72 ?74 ?75) (associator ?73 ?74 ?75)
+ [75, 74, 73, 72] by linearised_associator3 ?72 ?73 ?74 ?75
+20920: Id : 25, {_}:
+ commutator ?77 ?78
+ =<=
+ add (multiply ?78 ?77) (additive_inverse (multiply ?77 ?78))
+ [78, 77] by commutator ?77 ?78
+20920: Goal:
+20920: Id : 1, {_}:
+ add (associator a b c) (associator a c b) =>= additive_identity
+ [] by prove_flexible_law
+20920: Order:
+20920: nrkbo
+20920: Leaf order:
+20920: commutator 1 2 0
+20920: multiply 36 2 0 add
+20920: additive_inverse 21 1 0
+20920: additive_identity 9 0 1 3
+20920: add 30 2 1 0,2
+20920: associator 11 3 2 0,1,2
+20920: c 2 0 2 3,1,2
+20920: b 2 0 2 2,1,2
+20920: a 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+20921: Facts:
+20921: Id : 2, {_}:
+ multiply (additive_inverse ?2) (additive_inverse ?3)
+ =>=
+ multiply ?2 ?3
+ [3, 2] by product_of_inverses ?2 ?3
+20921: Id : 3, {_}:
+ multiply (additive_inverse ?5) ?6
+ =<=
+ additive_inverse (multiply ?5 ?6)
+ [6, 5] by inverse_product1 ?5 ?6
+20921: Id : 4, {_}:
+ multiply ?8 (additive_inverse ?9)
+ =<=
+ additive_inverse (multiply ?8 ?9)
+ [9, 8] by inverse_product2 ?8 ?9
+20921: Id : 5, {_}:
+ multiply ?11 (add ?12 (additive_inverse ?13))
+ =<=
+ add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
+ [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
+20921: Id : 6, {_}:
+ multiply (add ?15 (additive_inverse ?16)) ?17
+ =<=
+ add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
+ [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
+20921: Id : 7, {_}:
+ multiply (additive_inverse ?19) (add ?20 ?21)
+ =<=
+ add (additive_inverse (multiply ?19 ?20))
+ (additive_inverse (multiply ?19 ?21))
+ [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
+20921: Id : 8, {_}:
+ multiply (add ?23 ?24) (additive_inverse ?25)
+ =<=
+ add (additive_inverse (multiply ?23 ?25))
+ (additive_inverse (multiply ?24 ?25))
+ [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
+20921: Id : 9, {_}:
+ add ?27 ?28 =?= add ?28 ?27
+ [28, 27] by commutativity_for_addition ?27 ?28
+20921: Id : 10, {_}:
+ add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
+ [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
+20921: Id : 11, {_}:
+ add additive_identity ?34 =>= ?34
+ [34] by left_additive_identity ?34
+20921: Id : 12, {_}:
+ add ?36 additive_identity =>= ?36
+ [36] by right_additive_identity ?36
+20921: Id : 13, {_}:
+ multiply additive_identity ?38 =>= additive_identity
+ [38] by left_multiplicative_zero ?38
+20921: Id : 14, {_}:
+ multiply ?40 additive_identity =>= additive_identity
+ [40] by right_multiplicative_zero ?40
+20921: Id : 15, {_}:
+ add (additive_inverse ?42) ?42 =>= additive_identity
+ [42] by left_additive_inverse ?42
+20921: Id : 16, {_}:
+ add ?44 (additive_inverse ?44) =>= additive_identity
+ [44] by right_additive_inverse ?44
+20921: Id : 17, {_}:
+ multiply ?46 (add ?47 ?48)
+ =<=
+ add (multiply ?46 ?47) (multiply ?46 ?48)
+ [48, 47, 46] by distribute1 ?46 ?47 ?48
+20921: Id : 18, {_}:
+ multiply (add ?50 ?51) ?52
+ =<=
+ add (multiply ?50 ?52) (multiply ?51 ?52)
+ [52, 51, 50] by distribute2 ?50 ?51 ?52
+20921: Id : 19, {_}:
+ additive_inverse (additive_inverse ?54) =>= ?54
+ [54] by additive_inverse_additive_inverse ?54
+20921: Id : 20, {_}:
+ multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
+ [57, 56] by right_alternative ?56 ?57
+20921: Id : 21, {_}:
+ multiply (multiply ?59 ?59) ?60 =>= multiply ?59 (multiply ?59 ?60)
+ [60, 59] by left_alternative ?59 ?60
+20921: Id : 22, {_}:
+ associator ?62 ?63 (add ?64 ?65)
+ =<=
+ add (associator ?62 ?63 ?64) (associator ?62 ?63 ?65)
+ [65, 64, 63, 62] by linearised_associator1 ?62 ?63 ?64 ?65
+20921: Id : 23, {_}:
+ associator ?67 (add ?68 ?69) ?70
+ =<=
+ add (associator ?67 ?68 ?70) (associator ?67 ?69 ?70)
+ [70, 69, 68, 67] by linearised_associator2 ?67 ?68 ?69 ?70
+20921: Id : 24, {_}:
+ associator (add ?72 ?73) ?74 ?75
+ =<=
+ add (associator ?72 ?74 ?75) (associator ?73 ?74 ?75)
+ [75, 74, 73, 72] by linearised_associator3 ?72 ?73 ?74 ?75
+20921: Id : 25, {_}:
+ commutator ?77 ?78
+ =<=
+ add (multiply ?78 ?77) (additive_inverse (multiply ?77 ?78))
+ [78, 77] by commutator ?77 ?78
+20921: Goal:
+20921: Id : 1, {_}:
+ add (associator a b c) (associator a c b) =>= additive_identity
+ [] by prove_flexible_law
+20921: Order:
+20921: kbo
+20921: Leaf order:
+20921: commutator 1 2 0
+20921: multiply 36 2 0 add
+20921: additive_inverse 21 1 0
+20921: additive_identity 9 0 1 3
+20921: add 30 2 1 0,2
+20921: associator 11 3 2 0,1,2
+20921: c 2 0 2 3,1,2
+20921: b 2 0 2 2,1,2
+20921: a 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+20922: Facts:
+20922: Id : 2, {_}:
+ multiply (additive_inverse ?2) (additive_inverse ?3)
+ =>=
+ multiply ?2 ?3
+ [3, 2] by product_of_inverses ?2 ?3
+20922: Id : 3, {_}:
+ multiply (additive_inverse ?5) ?6
+ =<=
+ additive_inverse (multiply ?5 ?6)
+ [6, 5] by inverse_product1 ?5 ?6
+20922: Id : 4, {_}:
+ multiply ?8 (additive_inverse ?9)
+ =<=
+ additive_inverse (multiply ?8 ?9)
+ [9, 8] by inverse_product2 ?8 ?9
+20922: Id : 5, {_}:
+ multiply ?11 (add ?12 (additive_inverse ?13))
+ =<=
+ add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
+ [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
+20922: Id : 6, {_}:
+ multiply (add ?15 (additive_inverse ?16)) ?17
+ =<=
+ add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
+ [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
+20922: Id : 7, {_}:
+ multiply (additive_inverse ?19) (add ?20 ?21)
+ =<=
+ add (additive_inverse (multiply ?19 ?20))
+ (additive_inverse (multiply ?19 ?21))
+ [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
+20922: Id : 8, {_}:
+ multiply (add ?23 ?24) (additive_inverse ?25)
+ =<=
+ add (additive_inverse (multiply ?23 ?25))
+ (additive_inverse (multiply ?24 ?25))
+ [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
+20922: Id : 9, {_}:
+ add ?27 ?28 =?= add ?28 ?27
+ [28, 27] by commutativity_for_addition ?27 ?28
+20922: Id : 10, {_}:
+ add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
+ [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
+20922: Id : 11, {_}:
+ add additive_identity ?34 =>= ?34
+ [34] by left_additive_identity ?34
+20922: Id : 12, {_}:
+ add ?36 additive_identity =>= ?36
+ [36] by right_additive_identity ?36
+20922: Id : 13, {_}:
+ multiply additive_identity ?38 =>= additive_identity
+ [38] by left_multiplicative_zero ?38
+20922: Id : 14, {_}:
+ multiply ?40 additive_identity =>= additive_identity
+ [40] by right_multiplicative_zero ?40
+20922: Id : 15, {_}:
+ add (additive_inverse ?42) ?42 =>= additive_identity
+ [42] by left_additive_inverse ?42
+20922: Id : 16, {_}:
+ add ?44 (additive_inverse ?44) =>= additive_identity
+ [44] by right_additive_inverse ?44
+20922: Id : 17, {_}:
+ multiply ?46 (add ?47 ?48)
+ =<=
+ add (multiply ?46 ?47) (multiply ?46 ?48)
+ [48, 47, 46] by distribute1 ?46 ?47 ?48
+20922: Id : 18, {_}:
+ multiply (add ?50 ?51) ?52
+ =<=
+ add (multiply ?50 ?52) (multiply ?51 ?52)
+ [52, 51, 50] by distribute2 ?50 ?51 ?52
+20922: Id : 19, {_}:
+ additive_inverse (additive_inverse ?54) =>= ?54
+ [54] by additive_inverse_additive_inverse ?54
+20922: Id : 20, {_}:
+ multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
+ [57, 56] by right_alternative ?56 ?57
+20922: Id : 21, {_}:
+ multiply (multiply ?59 ?59) ?60 =>= multiply ?59 (multiply ?59 ?60)
+ [60, 59] by left_alternative ?59 ?60
+20922: Id : 22, {_}:
+ associator ?62 ?63 (add ?64 ?65)
+ =>=
+ add (associator ?62 ?63 ?64) (associator ?62 ?63 ?65)
+ [65, 64, 63, 62] by linearised_associator1 ?62 ?63 ?64 ?65
+20922: Id : 23, {_}:
+ associator ?67 (add ?68 ?69) ?70
+ =>=
+ add (associator ?67 ?68 ?70) (associator ?67 ?69 ?70)
+ [70, 69, 68, 67] by linearised_associator2 ?67 ?68 ?69 ?70
+20922: Id : 24, {_}:
+ associator (add ?72 ?73) ?74 ?75
+ =>=
+ add (associator ?72 ?74 ?75) (associator ?73 ?74 ?75)
+ [75, 74, 73, 72] by linearised_associator3 ?72 ?73 ?74 ?75
+20922: Id : 25, {_}:
+ commutator ?77 ?78
+ =<=
+ add (multiply ?78 ?77) (additive_inverse (multiply ?77 ?78))
+ [78, 77] by commutator ?77 ?78
+20922: Goal:
+20922: Id : 1, {_}:
+ add (associator a b c) (associator a c b) =>= additive_identity
+ [] by prove_flexible_law
+20922: Order:
+20922: lpo
+20922: Leaf order:
+20922: commutator 1 2 0
+20922: multiply 36 2 0 add
+20922: additive_inverse 21 1 0
+20922: additive_identity 9 0 1 3
+20922: add 30 2 1 0,2
+20922: associator 11 3 2 0,1,2
+20922: c 2 0 2 3,1,2
+20922: b 2 0 2 2,1,2
+20922: a 2 0 2 1,1,2
+% SZS status Timeout for RNG025-9.p
+NO CLASH, using fixed ground order
+20954: Facts:
+20954: Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3
+20954: Id : 3, {_}:
+ multiply ?5 (add ?6 ?7) =<= add (multiply ?6 ?5) (multiply ?7 ?5)
+ [7, 6, 5] by multiply_add_property ?5 ?6 ?7
+20954: Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9
+20954: Id : 5, {_}:
+ pixley ?11 ?12 ?13
+ =<=
+ add (multiply ?11 (inverse ?12))
+ (add (multiply ?11 ?13) (multiply (inverse ?12) ?13))
+ [13, 12, 11] by pixley_defn ?11 ?12 ?13
+20954: Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16
+20954: Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19
+20954: Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22
+20954: Goal:
+20954: Id : 1, {_}:
+ add a (multiply b c) =<= multiply (add a b) (add a c)
+ [] by prove_add_multiply_property
+20954: Order:
+20954: nrkbo
+20954: Leaf order:
+20954: pixley 4 3 0
+20954: n1 1 0 0
+20954: inverse 3 1 0
+20954: add 9 2 3 0,2
+20954: multiply 9 2 2 0,2,2
+20954: c 2 0 2 2,2,2
+20954: b 2 0 2 1,2,2
+20954: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+20955: Facts:
+20955: Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3
+20955: Id : 3, {_}:
+ multiply ?5 (add ?6 ?7) =<= add (multiply ?6 ?5) (multiply ?7 ?5)
+ [7, 6, 5] by multiply_add_property ?5 ?6 ?7
+20955: Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9
+20955: Id : 5, {_}:
+ pixley ?11 ?12 ?13
+ =<=
+ add (multiply ?11 (inverse ?12))
+ (add (multiply ?11 ?13) (multiply (inverse ?12) ?13))
+ [13, 12, 11] by pixley_defn ?11 ?12 ?13
+20955: Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16
+20955: Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19
+20955: Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22
+20955: Goal:
+20955: Id : 1, {_}:
+ add a (multiply b c) =<= multiply (add a b) (add a c)
+ [] by prove_add_multiply_property
+20955: Order:
+20955: kbo
+20955: Leaf order:
+20955: pixley 4 3 0
+20955: n1 1 0 0
+20955: inverse 3 1 0
+20955: add 9 2 3 0,2
+20955: multiply 9 2 2 0,2,2
+20955: c 2 0 2 2,2,2
+20955: b 2 0 2 1,2,2
+20955: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+20956: Facts:
+20956: Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3
+20956: Id : 3, {_}:
+ multiply ?5 (add ?6 ?7) =?= add (multiply ?6 ?5) (multiply ?7 ?5)
+ [7, 6, 5] by multiply_add_property ?5 ?6 ?7
+20956: Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9
+20956: Id : 5, {_}:
+ pixley ?11 ?12 ?13
+ =<=
+ add (multiply ?11 (inverse ?12))
+ (add (multiply ?11 ?13) (multiply (inverse ?12) ?13))
+ [13, 12, 11] by pixley_defn ?11 ?12 ?13
+20956: Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16
+20956: Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19
+20956: Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22
+20956: Goal:
+20956: Id : 1, {_}:
+ add a (multiply b c) =<= multiply (add a b) (add a c)
+ [] by prove_add_multiply_property
+20956: Order:
+20956: lpo
+20956: Leaf order:
+20956: pixley 4 3 0
+20956: n1 1 0 0
+20956: inverse 3 1 0
+20956: add 9 2 3 0,2
+20956: multiply 9 2 2 0,2,2
+20956: c 2 0 2 2,2,2
+20956: b 2 0 2 1,2,2
+20956: a 3 0 3 1,2
+Statistics :
+Max weight : 22
+Found proof, 38.942991s
+% SZS status Unsatisfiable for BOO023-1.p
+% SZS output start CNFRefutation for BOO023-1.p
+Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22
+Id : 12, {_}: multiply ?33 (add ?34 ?35) =<= add (multiply ?34 ?33) (multiply ?35 ?33) [35, 34, 33] by multiply_add_property ?33 ?34 ?35
+Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16
+Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9
+Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19
+Id : 5, {_}: pixley ?11 ?12 ?13 =<= add (multiply ?11 (inverse ?12)) (add (multiply ?11 ?13) (multiply (inverse ?12) ?13)) [13, 12, 11] by pixley_defn ?11 ?12 ?13
+Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3
+Id : 3, {_}: multiply ?5 (add ?6 ?7) =<= add (multiply ?6 ?5) (multiply ?7 ?5) [7, 6, 5] by multiply_add_property ?5 ?6 ?7
+Id : 19, {_}: pixley ?11 ?12 ?13 =<= add (multiply ?11 (inverse ?12)) (multiply ?13 (add ?11 (inverse ?12))) [13, 12, 11] by Demod 5 with 3 at 2,3
+Id : 485, {_}: multiply (pixley ?939 ?940 ?941) (multiply ?941 (add ?939 (inverse ?940))) =>= multiply ?941 (add ?939 (inverse ?940)) [941, 940, 939] by Super 2 with 19 at 1,2
+Id : 505, {_}: multiply ?1017 (multiply ?1018 (add ?1017 (inverse ?1018))) =>= multiply ?1018 (add ?1017 (inverse ?1018)) [1018, 1017] by Super 485 with 7 at 1,2
+Id : 21, {_}: pixley ?58 ?59 ?60 =<= add (multiply ?58 (inverse ?59)) (multiply ?60 (add ?58 (inverse ?59))) [60, 59, 58] by Demod 5 with 3 at 2,3
+Id : 22, {_}: pixley ?62 ?62 ?63 =<= add (multiply ?62 (inverse ?62)) (multiply ?63 n1) [63, 62] by Super 21 with 4 at 2,2,3
+Id : 413, {_}: ?825 =<= add (multiply ?826 (inverse ?826)) (multiply ?825 n1) [826, 825] by Demod 22 with 6 at 2
+Id : 16, {_}: multiply n1 (inverse ?49) =>= inverse ?49 [49] by Super 2 with 4 at 1,2
+Id : 428, {_}: ?870 =<= add (inverse n1) (multiply ?870 n1) [870] by Super 413 with 16 at 1,3
+Id : 14, {_}: multiply ?41 (add (add ?42 ?41) ?43) =>= add ?41 (multiply ?43 ?41) [43, 42, 41] by Super 12 with 2 at 1,3
+Id : 548, {_}: ?1062 =<= add (inverse n1) (multiply ?1062 n1) [1062] by Super 413 with 16 at 1,3
+Id : 593, {_}: add ?1120 n1 =?= add (inverse n1) n1 [1120] by Super 548 with 2 at 2,3
+Id : 553, {_}: add ?1072 n1 =?= add (inverse n1) n1 [1072] by Super 548 with 2 at 2,3
+Id : 607, {_}: add ?1148 n1 =?= add ?1149 n1 [1149, 1148] by Super 593 with 553 at 3
+Id : 13, {_}: multiply ?37 (add ?38 (add ?39 ?37)) =>= add (multiply ?38 ?37) ?37 [39, 38, 37] by Super 12 with 2 at 2,3
+Id : 408, {_}: ?63 =<= add (multiply ?62 (inverse ?62)) (multiply ?63 n1) [62, 63] by Demod 22 with 6 at 2
+Id : 412, {_}: multiply (multiply ?822 n1) (add ?823 ?822) =<= add (multiply ?823 (multiply ?822 n1)) (multiply ?822 n1) [823, 822] by Super 13 with 408 at 2,2,2
+Id : 274, {_}: multiply (multiply ?502 (add ?503 ?504)) (multiply ?504 ?502) =>= multiply ?504 ?502 [504, 503, 502] by Super 2 with 3 at 1,2
+Id : 284, {_}: multiply (multiply ?542 n1) (multiply (inverse ?543) ?542) =>= multiply (inverse ?543) ?542 [543, 542] by Super 274 with 4 at 2,1,2
+Id : 173, {_}: multiply (inverse ?334) (add ?335 n1) =<= add (multiply ?335 (inverse ?334)) (inverse ?334) [335, 334] by Super 3 with 16 at 2,3
+Id : 1514, {_}: multiply ?2669 (multiply ?2670 (add ?2669 (inverse ?2670))) =>= multiply ?2670 (add ?2669 (inverse ?2670)) [2670, 2669] by Super 485 with 7 at 1,2
+Id : 672, {_}: multiply (multiply ?1271 n1) (multiply (inverse ?1272) ?1271) =>= multiply (inverse ?1272) ?1271 [1272, 1271] by Super 274 with 4 at 2,1,2
+Id : 688, {_}: multiply n1 (multiply (inverse ?1320) (add ?1321 n1)) =>= multiply (inverse ?1320) (add ?1321 n1) [1321, 1320] by Super 672 with 2 at 1,2
+Id : 199, {_}: multiply (inverse ?371) (add ?372 n1) =<= add (multiply ?372 (inverse ?371)) (inverse ?371) [372, 371] by Super 3 with 16 at 2,3
+Id : 210, {_}: multiply (inverse ?404) (add (add ?405 (inverse ?404)) n1) =>= add (inverse ?404) (inverse ?404) [405, 404] by Super 199 with 2 at 1,3
+Id : 966, {_}: add (inverse ?404) (multiply n1 (inverse ?404)) =>= add (inverse ?404) (inverse ?404) [404] by Demod 210 with 14 at 2
+Id : 174, {_}: multiply (inverse ?337) (add n1 ?338) =<= add (inverse ?337) (multiply ?338 (inverse ?337)) [338, 337] by Super 3 with 16 at 1,3
+Id : 967, {_}: multiply (inverse ?404) (add n1 n1) =?= add (inverse ?404) (inverse ?404) [404] by Demod 966 with 174 at 2
+Id : 982, {_}: multiply n1 (add (inverse ?1904) (inverse ?1904)) =>= multiply (inverse ?1904) (add n1 n1) [1904] by Super 688 with 967 at 2,2
+Id : 1530, {_}: multiply (inverse n1) (multiply (inverse n1) (add n1 n1)) =>= multiply n1 (add (inverse n1) (inverse n1)) [] by Super 1514 with 982 at 2,2
+Id : 1554, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= multiply n1 (add (inverse n1) (inverse n1)) [] by Demod 1530 with 967 at 2,2
+Id : 1555, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= multiply (inverse n1) (add n1 n1) [] by Demod 1554 with 982 at 3
+Id : 1556, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= add (inverse n1) (inverse n1) [] by Demod 1555 with 967 at 3
+Id : 1568, {_}: pixley (inverse n1) n1 (inverse n1) =<= add (multiply (inverse n1) (inverse n1)) (add (inverse n1) (inverse n1)) [] by Super 19 with 1556 at 2,3
+Id : 1597, {_}: inverse n1 =<= add (multiply (inverse n1) (inverse n1)) (add (inverse n1) (inverse n1)) [] by Demod 1568 with 8 at 2
+Id : 1814, {_}: multiply (inverse n1) (inverse n1) =<= add (multiply (multiply (inverse n1) (inverse n1)) (inverse n1)) (inverse n1) [] by Super 13 with 1597 at 2,2
+Id : 1906, {_}: multiply (inverse n1) (inverse n1) =<= multiply (inverse n1) (add (multiply (inverse n1) (inverse n1)) n1) [] by Demod 1814 with 173 at 3
+Id : 1990, {_}: multiply (inverse n1) (inverse n1) =<= multiply (inverse n1) (add ?3163 n1) [3163] by Super 1906 with 607 at 2,3
+Id : 2009, {_}: multiply (inverse n1) (inverse n1) =>= add (inverse n1) (inverse n1) [] by Super 1990 with 967 at 3
+Id : 2048, {_}: multiply (inverse n1) (add (inverse n1) n1) =<= add (add (inverse n1) (inverse n1)) (inverse n1) [] by Super 173 with 2009 at 1,3
+Id : 1928, {_}: multiply (inverse n1) (inverse n1) =<= multiply (inverse n1) (add ?3128 n1) [3128] by Super 1906 with 607 at 2,3
+Id : 2040, {_}: add (inverse n1) (inverse n1) =<= multiply (inverse n1) (add ?3128 n1) [3128] by Demod 1928 with 2009 at 2
+Id : 2082, {_}: add (inverse n1) (inverse n1) =<= add (add (inverse n1) (inverse n1)) (inverse n1) [] by Demod 2048 with 2040 at 2
+Id : 2135, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= add (inverse n1) (multiply (inverse n1) (inverse n1)) [] by Super 14 with 2082 at 2,2
+Id : 2186, {_}: add (inverse n1) (inverse n1) =<= add (inverse n1) (multiply (inverse n1) (inverse n1)) [] by Demod 2135 with 1556 at 2
+Id : 2187, {_}: add (inverse n1) (inverse n1) =<= multiply (inverse n1) (add n1 (inverse n1)) [] by Demod 2186 with 174 at 3
+Id : 2188, {_}: add (inverse n1) (inverse n1) =>= multiply (inverse n1) n1 [] by Demod 2187 with 4 at 2,3
+Id : 2041, {_}: inverse n1 =<= add (add (inverse n1) (inverse n1)) (add (inverse n1) (inverse n1)) [] by Demod 1597 with 2009 at 1,3
+Id : 2225, {_}: inverse n1 =<= add (multiply (inverse n1) n1) (add (inverse n1) (inverse n1)) [] by Demod 2041 with 2188 at 1,3
+Id : 2226, {_}: inverse n1 =<= add (multiply (inverse n1) n1) (multiply (inverse n1) n1) [] by Demod 2225 with 2188 at 2,3
+Id : 2235, {_}: inverse n1 =<= multiply n1 (add (inverse n1) (inverse n1)) [] by Demod 2226 with 3 at 3
+Id : 2236, {_}: inverse n1 =<= multiply (inverse n1) (add n1 n1) [] by Demod 2235 with 982 at 3
+Id : 2237, {_}: inverse n1 =<= add (inverse n1) (inverse n1) [] by Demod 2236 with 967 at 3
+Id : 2238, {_}: inverse n1 =<= multiply (inverse n1) n1 [] by Demod 2237 with 2188 at 3
+Id : 2244, {_}: add (inverse n1) (inverse n1) =>= inverse n1 [] by Demod 2188 with 2238 at 3
+Id : 2259, {_}: multiply (inverse n1) (add ?3306 (inverse n1)) =>= add (multiply ?3306 (inverse n1)) (inverse n1) [3306] by Super 13 with 2244 at 2,2,2
+Id : 2294, {_}: multiply (inverse n1) (add ?3306 (inverse n1)) =>= multiply (inverse n1) (add ?3306 n1) [3306] by Demod 2259 with 173 at 3
+Id : 2232, {_}: multiply (inverse n1) n1 =<= multiply (inverse n1) (add ?3128 n1) [3128] by Demod 2040 with 2188 at 2
+Id : 2243, {_}: inverse n1 =<= multiply (inverse n1) (add ?3128 n1) [3128] by Demod 2232 with 2238 at 2
+Id : 2295, {_}: multiply (inverse n1) (add ?3306 (inverse n1)) =>= inverse n1 [3306] by Demod 2294 with 2243 at 3
+Id : 2419, {_}: multiply (multiply (add ?3405 (inverse n1)) n1) (inverse n1) =>= multiply (inverse n1) (add ?3405 (inverse n1)) [3405] by Super 284 with 2295 at 2,2
+Id : 3205, {_}: multiply (multiply (add ?4259 (inverse n1)) n1) (inverse n1) =>= inverse n1 [4259] by Demod 2419 with 2295 at 3
+Id : 3222, {_}: multiply (multiply n1 n1) (inverse n1) =>= inverse n1 [] by Super 3205 with 4 at 1,1,2
+Id : 3294, {_}: multiply (inverse n1) (add (multiply n1 n1) ?4332) =>= add (inverse n1) (multiply ?4332 (inverse n1)) [4332] by Super 3 with 3222 at 1,3
+Id : 3323, {_}: multiply (inverse n1) (add (multiply n1 n1) ?4332) =>= multiply (inverse n1) (add n1 ?4332) [4332] by Demod 3294 with 174 at 3
+Id : 24, {_}: pixley (add ?69 (inverse ?70)) ?70 ?71 =<= add (inverse ?70) (multiply ?71 (add (add ?69 (inverse ?70)) (inverse ?70))) [71, 70, 69] by Super 21 with 2 at 1,3
+Id : 2249, {_}: pixley (add (inverse n1) (inverse n1)) n1 ?3289 =<= add (inverse n1) (multiply ?3289 (add (inverse n1) (inverse n1))) [3289] by Super 24 with 2244 at 1,2,2,3
+Id : 2310, {_}: pixley (inverse n1) n1 ?3289 =<= add (inverse n1) (multiply ?3289 (add (inverse n1) (inverse n1))) [3289] by Demod 2249 with 2244 at 1,2
+Id : 2311, {_}: pixley (inverse n1) n1 ?3289 =<= add (inverse n1) (multiply ?3289 (inverse n1)) [3289] by Demod 2310 with 2244 at 2,2,3
+Id : 2312, {_}: pixley (inverse n1) n1 ?3289 =<= multiply (inverse n1) (add n1 ?3289) [3289] by Demod 2311 with 174 at 3
+Id : 3528, {_}: multiply (inverse n1) (add (multiply n1 n1) ?4508) =>= pixley (inverse n1) n1 ?4508 [4508] by Demod 3323 with 2312 at 3
+Id : 3542, {_}: multiply (inverse n1) (multiply n1 (add n1 ?4535)) =>= pixley (inverse n1) n1 (multiply ?4535 n1) [4535] by Super 3528 with 3 at 2,2
+Id : 2258, {_}: pixley (inverse n1) n1 ?3304 =<= add (multiply (inverse n1) (inverse n1)) (multiply ?3304 (inverse n1)) [3304] by Super 19 with 2244 at 2,2,3
+Id : 2766, {_}: pixley (inverse n1) n1 ?3924 =<= multiply (inverse n1) (add (inverse n1) ?3924) [3924] by Demod 2258 with 3 at 3
+Id : 2784, {_}: pixley (inverse n1) n1 (multiply ?3959 n1) =>= multiply (inverse n1) ?3959 [3959] by Super 2766 with 428 at 2,3
+Id : 4047, {_}: multiply (inverse n1) (multiply n1 (add n1 ?5164)) =>= multiply (inverse n1) ?5164 [5164] by Demod 3542 with 2784 at 3
+Id : 4052, {_}: multiply (inverse n1) (multiply n1 n1) =>= multiply (inverse n1) (inverse n1) [] by Super 4047 with 4 at 2,2,2
+Id : 2233, {_}: multiply (inverse n1) (inverse n1) =>= multiply (inverse n1) n1 [] by Demod 2009 with 2188 at 3
+Id : 2242, {_}: multiply (inverse n1) (inverse n1) =>= inverse n1 [] by Demod 2233 with 2238 at 3
+Id : 4088, {_}: multiply (inverse n1) (multiply n1 n1) =>= inverse n1 [] by Demod 4052 with 2242 at 3
+Id : 4118, {_}: multiply (multiply n1 n1) (add (inverse n1) n1) =>= add (inverse n1) (multiply n1 n1) [] by Super 412 with 4088 at 1,3
+Id : 1137, {_}: multiply (multiply ?2152 n1) (add ?2152 ?2153) =<= add (multiply ?2152 n1) (multiply ?2153 (multiply ?2152 n1)) [2153, 2152] by Super 14 with 408 at 1,2,2
+Id : 411, {_}: multiply ?820 (multiply ?820 n1) =>= multiply ?820 n1 [820] by Super 2 with 408 at 1,2
+Id : 1151, {_}: multiply (multiply ?2193 n1) (add ?2193 ?2193) =>= add (multiply ?2193 n1) (multiply ?2193 n1) [2193] by Super 1137 with 411 at 2,3
+Id : 1282, {_}: multiply (multiply ?2412 n1) (add ?2412 ?2412) =>= multiply n1 (add ?2412 ?2412) [2412] by Demod 1151 with 3 at 3
+Id : 1286, {_}: multiply (multiply n1 n1) (add ?2420 n1) =>= multiply n1 (add n1 n1) [2420] by Super 1282 with 607 at 2,2
+Id : 4147, {_}: multiply n1 (add n1 n1) =<= add (inverse n1) (multiply n1 n1) [] by Demod 4118 with 1286 at 2
+Id : 4148, {_}: multiply n1 (add n1 n1) =>= n1 [] by Demod 4147 with 428 at 3
+Id : 4590, {_}: multiply (add n1 n1) (add n1 ?5598) =>= add n1 (multiply ?5598 (add n1 n1)) [5598] by Super 3 with 4148 at 1,3
+Id : 4186, {_}: multiply n1 (add n1 n1) =>= n1 [] by Demod 4147 with 428 at 3
+Id : 4194, {_}: multiply n1 (add ?5284 n1) =>= n1 [5284] by Super 4186 with 607 at 2,2
+Id : 4313, {_}: n1 =<= add n1 (multiply n1 n1) [] by Super 14 with 4194 at 2
+Id : 4601, {_}: multiply (add n1 n1) n1 =<= add n1 (multiply (multiply n1 n1) (add n1 n1)) [] by Super 4590 with 4313 at 2,2
+Id : 4648, {_}: n1 =<= add n1 (multiply (multiply n1 n1) (add n1 n1)) [] by Demod 4601 with 2 at 2
+Id : 1187, {_}: multiply (multiply ?2193 n1) (add ?2193 ?2193) =>= multiply n1 (add ?2193 ?2193) [2193] by Demod 1151 with 3 at 3
+Id : 4649, {_}: n1 =<= add n1 (multiply n1 (add n1 n1)) [] by Demod 4648 with 1187 at 2,3
+Id : 4650, {_}: n1 =<= add n1 n1 [] by Demod 4649 with 4194 at 2,3
+Id : 4692, {_}: add ?5677 n1 =>= n1 [5677] by Super 607 with 4650 at 3
+Id : 5124, {_}: multiply ?6342 n1 =<= add ?6342 (multiply n1 ?6342) [6342] by Super 14 with 4692 at 2,2
+Id : 4670, {_}: multiply n1 (add (inverse ?1904) (inverse ?1904)) =>= multiply (inverse ?1904) n1 [1904] by Demod 982 with 4650 at 2,3
+Id : 4669, {_}: multiply (inverse ?404) n1 =<= add (inverse ?404) (inverse ?404) [404] by Demod 967 with 4650 at 2,2
+Id : 4674, {_}: multiply n1 (multiply (inverse ?1904) n1) =>= multiply (inverse ?1904) n1 [1904] by Demod 4670 with 4669 at 2,2
+Id : 5136, {_}: multiply (multiply (inverse ?6367) n1) n1 =<= add (multiply (inverse ?6367) n1) (multiply (inverse ?6367) n1) [6367] by Super 5124 with 4674 at 2,3
+Id : 5182, {_}: multiply (multiply (inverse ?6367) n1) n1 =<= multiply n1 (add (inverse ?6367) (inverse ?6367)) [6367] by Demod 5136 with 3 at 3
+Id : 5183, {_}: multiply (multiply (inverse ?6367) n1) n1 =>= multiply n1 (multiply (inverse ?6367) n1) [6367] by Demod 5182 with 4669 at 2,3
+Id : 5184, {_}: multiply (multiply (inverse ?6367) n1) n1 =>= multiply (inverse ?6367) n1 [6367] by Demod 5183 with 4674 at 3
+Id : 5206, {_}: multiply (inverse ?6424) n1 =<= add (inverse n1) (multiply (inverse ?6424) n1) [6424] by Super 428 with 5184 at 2,3
+Id : 5244, {_}: multiply (inverse ?6424) n1 =>= inverse ?6424 [6424] by Demod 5206 with 428 at 3
+Id : 5308, {_}: inverse ?6512 =<= add (inverse n1) (inverse ?6512) [6512] by Super 428 with 5244 at 2,3
+Id : 5370, {_}: pixley (inverse n1) ?6557 ?6558 =<= add (multiply (inverse n1) (inverse ?6557)) (multiply ?6558 (inverse ?6557)) [6558, 6557] by Super 19 with 5308 at 2,2,3
+Id : 7459, {_}: pixley (inverse n1) ?8766 ?8767 =<= multiply (inverse ?8766) (add (inverse n1) ?8767) [8767, 8766] by Demod 5370 with 3 at 3
+Id : 5371, {_}: inverse (inverse n1) =>= n1 [] by Super 4 with 5308 at 2
+Id : 7482, {_}: pixley (inverse n1) (inverse n1) ?8832 =<= multiply n1 (add (inverse n1) ?8832) [8832] by Super 7459 with 5371 at 1,3
+Id : 7542, {_}: ?8832 =<= multiply n1 (add (inverse n1) ?8832) [8832] by Demod 7482 with 6 at 2
+Id : 5466, {_}: pixley ?6672 (inverse n1) ?6673 =<= add (multiply ?6672 (inverse (inverse n1))) (multiply ?6673 (add ?6672 n1)) [6673, 6672] by Super 19 with 5371 at 2,2,2,3
+Id : 5516, {_}: pixley ?6672 (inverse n1) ?6673 =<= add (multiply ?6672 n1) (multiply ?6673 (add ?6672 n1)) [6673, 6672] by Demod 5466 with 5371 at 2,1,3
+Id : 5517, {_}: pixley ?6672 (inverse n1) ?6673 =<= add (multiply ?6672 n1) (multiply ?6673 n1) [6673, 6672] by Demod 5516 with 4692 at 2,2,3
+Id : 5854, {_}: pixley ?6987 (inverse n1) ?6988 =<= multiply n1 (add ?6987 ?6988) [6988, 6987] by Demod 5517 with 3 at 3
+Id : 5871, {_}: pixley (inverse n1) (inverse n1) (multiply ?7040 n1) =>= multiply n1 ?7040 [7040] by Super 5854 with 428 at 2,3
+Id : 5916, {_}: multiply ?7040 n1 =?= multiply n1 ?7040 [7040] by Demod 5871 with 6 at 2
+Id : 5518, {_}: pixley ?6672 (inverse n1) ?6673 =<= multiply n1 (add ?6672 ?6673) [6673, 6672] by Demod 5517 with 3 at 3
+Id : 5837, {_}: multiply ?6926 (pixley ?6926 (inverse n1) (inverse n1)) =>= multiply n1 (add ?6926 (inverse n1)) [6926] by Super 505 with 5518 at 2,2
+Id : 5906, {_}: multiply ?6926 ?6926 =?= multiply n1 (add ?6926 (inverse n1)) [6926] by Demod 5837 with 7 at 2,2
+Id : 5907, {_}: multiply ?6926 ?6926 =?= pixley ?6926 (inverse n1) (inverse n1) [6926] by Demod 5906 with 5518 at 3
+Id : 5908, {_}: multiply ?6926 ?6926 =>= ?6926 [6926] by Demod 5907 with 7 at 3
+Id : 7131, {_}: multiply ?8481 (add ?8482 ?8481) =>= add (multiply ?8482 ?8481) ?8481 [8482, 8481] by Super 3 with 5908 at 2,3
+Id : 5066, {_}: multiply ?6275 n1 =<= add ?6275 (multiply n1 ?6275) [6275] by Super 14 with 4692 at 2,2
+Id : 6609, {_}: multiply ?7988 n1 =<= add ?7988 (multiply ?7988 n1) [7988] by Super 5066 with 5916 at 2,3
+Id : 7156, {_}: multiply (multiply ?8553 n1) (multiply ?8553 n1) =<= add (multiply ?8553 (multiply ?8553 n1)) (multiply ?8553 n1) [8553] by Super 7131 with 6609 at 2,2
+Id : 7254, {_}: multiply ?8553 n1 =<= add (multiply ?8553 (multiply ?8553 n1)) (multiply ?8553 n1) [8553] by Demod 7156 with 5908 at 2
+Id : 7255, {_}: multiply ?8553 n1 =<= multiply (multiply ?8553 n1) (add ?8553 ?8553) [8553] by Demod 7254 with 412 at 3
+Id : 5833, {_}: multiply (multiply ?2193 n1) (add ?2193 ?2193) =>= pixley ?2193 (inverse n1) ?2193 [2193] by Demod 1187 with 5518 at 3
+Id : 5835, {_}: multiply (multiply ?2193 n1) (add ?2193 ?2193) =>= ?2193 [2193] by Demod 5833 with 8 at 3
+Id : 7256, {_}: multiply ?8553 n1 =>= ?8553 [8553] by Demod 7255 with 5835 at 3
+Id : 7273, {_}: ?7040 =<= multiply n1 ?7040 [7040] by Demod 5916 with 7256 at 2
+Id : 7543, {_}: ?8832 =<= add (inverse n1) ?8832 [8832] by Demod 7542 with 7273 at 3
+Id : 7582, {_}: multiply (inverse n1) (multiply ?8919 (inverse ?8919)) =?= multiply ?8919 (add (inverse n1) (inverse ?8919)) [8919] by Super 505 with 7543 at 2,2,2
+Id : 5473, {_}: multiply ?6687 (multiply (inverse n1) (add ?6687 n1)) =?= multiply (inverse n1) (add ?6687 (inverse (inverse n1))) [6687] by Super 505 with 5371 at 2,2,2,2
+Id : 5499, {_}: multiply ?6687 (multiply (inverse n1) n1) =<= multiply (inverse n1) (add ?6687 (inverse (inverse n1))) [6687] by Demod 5473 with 4692 at 2,2,2
+Id : 5500, {_}: multiply ?6687 (multiply (inverse n1) n1) =?= multiply (inverse n1) (add ?6687 n1) [6687] by Demod 5499 with 5371 at 2,2,3
+Id : 5501, {_}: multiply ?6687 (inverse n1) =<= multiply (inverse n1) (add ?6687 n1) [6687] by Demod 5500 with 5244 at 2,2
+Id : 5502, {_}: multiply ?6687 (inverse n1) =?= multiply (inverse n1) n1 [6687] by Demod 5501 with 4692 at 2,3
+Id : 5503, {_}: multiply ?6687 (inverse n1) =>= inverse n1 [6687] by Demod 5502 with 5244 at 3
+Id : 5615, {_}: multiply (inverse n1) (add n1 ?6752) =>= add (inverse n1) (inverse n1) [6752] by Super 174 with 5503 at 2,3
+Id : 5636, {_}: pixley (inverse n1) n1 ?6752 =?= add (inverse n1) (inverse n1) [6752] by Demod 5615 with 2312 at 2
+Id : 5285, {_}: inverse ?404 =<= add (inverse ?404) (inverse ?404) [404] by Demod 4669 with 5244 at 2
+Id : 5637, {_}: pixley (inverse n1) n1 ?6752 =>= inverse n1 [6752] by Demod 5636 with 5285 at 3
+Id : 5782, {_}: inverse n1 =<= multiply (inverse n1) ?3959 [3959] by Demod 2784 with 5637 at 2
+Id : 7613, {_}: inverse n1 =<= multiply ?8919 (add (inverse n1) (inverse ?8919)) [8919] by Demod 7582 with 5782 at 2
+Id : 7614, {_}: inverse n1 =<= multiply ?8919 (inverse ?8919) [8919] by Demod 7613 with 7543 at 2,3
+Id : 7674, {_}: multiply (inverse ?8984) (add ?8984 ?8985) =?= add (inverse n1) (multiply ?8985 (inverse ?8984)) [8985, 8984] by Super 3 with 7614 at 1,3
+Id : 7731, {_}: multiply (inverse ?8984) (add ?8984 ?8985) =>= multiply ?8985 (inverse ?8984) [8985, 8984] by Demod 7674 with 7543 at 3
+Id : 289, {_}: multiply (multiply ?563 (multiply (inverse ?564) (add ?565 n1))) (multiply (inverse ?564) ?563) =>= multiply (inverse ?564) ?563 [565, 564, 563] by Super 274 with 173 at 2,1,2
+Id : 8394, {_}: multiply (multiply ?563 (multiply (inverse ?564) n1)) (multiply (inverse ?564) ?563) =>= multiply (inverse ?564) ?563 [564, 563] by Demod 289 with 4692 at 2,2,1,2
+Id : 8406, {_}: multiply (multiply ?9773 (inverse ?9774)) (multiply (inverse ?9774) ?9773) =>= multiply (inverse ?9774) ?9773 [9774, 9773] by Demod 8394 with 7256 at 2,1,2
+Id : 8444, {_}: multiply (inverse n1) (multiply (inverse ?9877) ?9877) =>= multiply (inverse ?9877) ?9877 [9877] by Super 8406 with 7614 at 1,2
+Id : 8534, {_}: inverse n1 =<= multiply (inverse ?9877) ?9877 [9877] by Demod 8444 with 5782 at 2
+Id : 8551, {_}: multiply ?9925 (add ?9926 (inverse ?9925)) =>= add (multiply ?9926 ?9925) (inverse n1) [9926, 9925] by Super 3 with 8534 at 2,3
+Id : 367, {_}: multiply ?731 (add (add ?732 ?731) ?733) =>= add ?731 (multiply ?733 ?731) [733, 732, 731] by Super 12 with 2 at 1,3
+Id : 379, {_}: multiply ?780 n1 =<= add ?780 (multiply (inverse (add ?781 ?780)) ?780) [781, 780] by Super 367 with 4 at 2,2
+Id : 7285, {_}: ?780 =<= add ?780 (multiply (inverse (add ?781 ?780)) ?780) [781, 780] by Demod 379 with 7256 at 2
+Id : 7585, {_}: ?8927 =<= add ?8927 (multiply (inverse ?8927) ?8927) [8927] by Super 7285 with 7543 at 1,1,2,3
+Id : 8670, {_}: ?8927 =<= add ?8927 (inverse n1) [8927] by Demod 7585 with 8534 at 2,3
+Id : 9041, {_}: multiply ?9925 (add ?9926 (inverse ?9925)) =>= multiply ?9926 ?9925 [9926, 9925] by Demod 8551 with 8670 at 3
+Id : 172, {_}: pixley n1 ?331 ?332 =<= add (inverse ?331) (multiply ?332 (add n1 (inverse ?331))) [332, 331] by Super 19 with 16 at 1,3
+Id : 9053, {_}: pixley n1 ?10412 ?10412 =<= add (inverse ?10412) (multiply n1 ?10412) [10412] by Super 172 with 9041 at 2,3
+Id : 9135, {_}: n1 =<= add (inverse ?10412) (multiply n1 ?10412) [10412] by Demod 9053 with 7 at 2
+Id : 9136, {_}: n1 =<= add (inverse ?10412) ?10412 [10412] by Demod 9135 with 7273 at 2,3
+Id : 9201, {_}: pixley (inverse (inverse ?10589)) ?10589 ?10590 =<= add (multiply (inverse (inverse ?10589)) (inverse ?10589)) (multiply ?10590 n1) [10590, 10589] by Super 19 with 9136 at 2,2,3
+Id : 9238, {_}: pixley (inverse (inverse ?10589)) ?10589 ?10590 =?= add (inverse n1) (multiply ?10590 n1) [10590, 10589] by Demod 9201 with 8534 at 1,3
+Id : 9239, {_}: pixley (inverse (inverse ?10589)) ?10589 ?10590 =>= add (inverse n1) ?10590 [10590, 10589] by Demod 9238 with 7256 at 2,3
+Id : 9240, {_}: pixley (inverse (inverse ?10589)) ?10589 ?10590 =>= ?10590 [10590, 10589] by Demod 9239 with 7543 at 3
+Id : 10446, {_}: ?12102 =<= inverse (inverse ?12102) [12102] by Super 7 with 9240 at 2
+Id : 10555, {_}: multiply (inverse ?12273) (add ?12274 ?12273) =>= multiply ?12274 (inverse ?12273) [12274, 12273] by Super 9041 with 10446 at 2,2,2
+Id : 11456, {_}: pixley (add ?13531 (inverse ?13532)) ?13532 (inverse (inverse ?13532)) =<= add (inverse ?13532) (multiply (add ?13531 (inverse ?13532)) (inverse (inverse ?13532))) [13532, 13531] by Super 24 with 10555 at 2,3
+Id : 11548, {_}: pixley (add ?13531 (inverse ?13532)) ?13532 ?13532 =<= add (inverse ?13532) (multiply (add ?13531 (inverse ?13532)) (inverse (inverse ?13532))) [13532, 13531] by Demod 11456 with 10446 at 3,2
+Id : 8892, {_}: multiply (inverse ?10244) (add ?10244 ?10245) =>= multiply ?10245 (inverse ?10244) [10245, 10244] by Demod 7674 with 7543 at 3
+Id : 7580, {_}: multiply ?8914 (add ?8915 ?8914) =?= add (multiply (inverse n1) ?8914) ?8914 [8915, 8914] by Super 13 with 7543 at 2,2
+Id : 5958, {_}: multiply ?7147 (add ?7148 ?7147) =>= add (multiply ?7148 ?7147) ?7147 [7148, 7147] by Super 3 with 5908 at 2,3
+Id : 7619, {_}: add (multiply ?8915 ?8914) ?8914 =?= add (multiply (inverse n1) ?8914) ?8914 [8914, 8915] by Demod 7580 with 5958 at 2
+Id : 7620, {_}: add (multiply ?8915 ?8914) ?8914 =>= add (inverse n1) ?8914 [8914, 8915] by Demod 7619 with 5782 at 1,3
+Id : 7775, {_}: add (multiply ?9114 ?9115) ?9115 =>= ?9115 [9115, 9114] by Demod 7620 with 7543 at 3
+Id : 7621, {_}: add (multiply ?8915 ?8914) ?8914 =>= ?8914 [8914, 8915] by Demod 7620 with 7543 at 3
+Id : 7749, {_}: multiply ?7147 (add ?7148 ?7147) =>= ?7147 [7148, 7147] by Demod 5958 with 7621 at 3
+Id : 7792, {_}: add ?9167 (add ?9168 ?9167) =>= add ?9168 ?9167 [9168, 9167] by Super 7775 with 7749 at 1,2
+Id : 8900, {_}: multiply (inverse ?10265) (add ?10266 ?10265) =<= multiply (add ?10266 ?10265) (inverse ?10265) [10266, 10265] by Super 8892 with 7792 at 2,2
+Id : 11444, {_}: multiply ?10266 (inverse ?10265) =<= multiply (add ?10266 ?10265) (inverse ?10265) [10265, 10266] by Demod 8900 with 10555 at 2
+Id : 11549, {_}: pixley (add ?13531 (inverse ?13532)) ?13532 ?13532 =?= add (inverse ?13532) (multiply ?13531 (inverse (inverse ?13532))) [13532, 13531] by Demod 11548 with 11444 at 2,3
+Id : 11550, {_}: add ?13531 (inverse ?13532) =<= add (inverse ?13532) (multiply ?13531 (inverse (inverse ?13532))) [13532, 13531] by Demod 11549 with 7 at 2
+Id : 11551, {_}: add ?13531 (inverse ?13532) =<= add (inverse ?13532) (multiply ?13531 ?13532) [13532, 13531] by Demod 11550 with 10446 at 2,2,3
+Id : 11841, {_}: multiply (inverse (inverse ?13951)) (add ?13952 (inverse ?13951)) =>= multiply (multiply ?13952 ?13951) (inverse (inverse ?13951)) [13952, 13951] by Super 7731 with 11551 at 2,2
+Id : 11918, {_}: multiply ?13952 (inverse (inverse ?13951)) =<= multiply (multiply ?13952 ?13951) (inverse (inverse ?13951)) [13951, 13952] by Demod 11841 with 10555 at 2
+Id : 11919, {_}: multiply ?13952 (inverse (inverse ?13951)) =<= multiply (multiply ?13952 ?13951) ?13951 [13951, 13952] by Demod 11918 with 10446 at 2,3
+Id : 11920, {_}: multiply ?13952 ?13951 =<= multiply (multiply ?13952 ?13951) ?13951 [13951, 13952] by Demod 11919 with 10446 at 2,2
+Id : 12244, {_}: multiply ?14434 (add ?14435 (multiply ?14436 ?14434)) =>= add (multiply ?14435 ?14434) (multiply ?14436 ?14434) [14436, 14435, 14434] by Super 3 with 11920 at 2,3
+Id : 29011, {_}: multiply ?35505 (add ?35506 (multiply ?35507 ?35505)) =>= multiply ?35505 (add ?35506 ?35507) [35507, 35506, 35505] by Demod 12244 with 3 at 3
+Id : 29060, {_}: multiply ?35715 (add ?35716 (inverse n1)) =?= multiply ?35715 (add ?35716 (inverse ?35715)) [35716, 35715] by Super 29011 with 8534 at 2,2,2
+Id : 11860, {_}: add ?14021 (inverse ?14022) =<= add (inverse ?14022) (multiply ?14021 ?14022) [14022, 14021] by Demod 11550 with 10446 at 2,2,3
+Id : 11890, {_}: add n1 (inverse ?14122) =<= add (inverse ?14122) ?14122 [14122] by Super 11860 with 7273 at 2,3
+Id : 11943, {_}: add n1 (inverse ?14122) =>= n1 [14122] by Demod 11890 with 9136 at 3
+Id : 11977, {_}: pixley n1 ?331 ?332 =<= add (inverse ?331) (multiply ?332 n1) [332, 331] by Demod 172 with 11943 at 2,2,3
+Id : 11984, {_}: pixley n1 ?331 ?332 =<= add (inverse ?331) ?332 [332, 331] by Demod 11977 with 7256 at 2,3
+Id : 11991, {_}: add ?13531 (inverse ?13532) =<= pixley n1 ?13532 (multiply ?13531 ?13532) [13532, 13531] by Demod 11551 with 11984 at 3
+Id : 12023, {_}: add n1 (inverse ?14257) =>= n1 [14257] by Demod 11890 with 9136 at 3
+Id : 12028, {_}: add n1 ?14267 =>= n1 [14267] by Super 12023 with 10446 at 2,2
+Id : 12137, {_}: multiply ?14331 (add n1 ?14332) =?= add ?14331 (multiply ?14332 ?14331) [14332, 14331] by Super 14 with 12028 at 1,2,2
+Id : 12188, {_}: multiply ?14331 n1 =<= add ?14331 (multiply ?14332 ?14331) [14332, 14331] by Demod 12137 with 12028 at 2,2
+Id : 12598, {_}: ?14940 =<= add ?14940 (multiply ?14941 ?14940) [14941, 14940] by Demod 12188 with 7256 at 2
+Id : 409, {_}: multiply (multiply ?814 n1) (add ?814 ?815) =<= add (multiply ?814 n1) (multiply ?815 (multiply ?814 n1)) [815, 814] by Super 14 with 408 at 1,2,2
+Id : 7278, {_}: multiply ?814 (add ?814 ?815) =<= add (multiply ?814 n1) (multiply ?815 (multiply ?814 n1)) [815, 814] by Demod 409 with 7256 at 1,2
+Id : 7279, {_}: multiply ?814 (add ?814 ?815) =<= add ?814 (multiply ?815 (multiply ?814 n1)) [815, 814] by Demod 7278 with 7256 at 1,3
+Id : 7280, {_}: multiply ?814 (add ?814 ?815) =>= add ?814 (multiply ?815 ?814) [815, 814] by Demod 7279 with 7256 at 2,2,3
+Id : 12189, {_}: ?14331 =<= add ?14331 (multiply ?14332 ?14331) [14332, 14331] by Demod 12188 with 7256 at 2
+Id : 12573, {_}: multiply ?814 (add ?814 ?815) =>= ?814 [815, 814] by Demod 7280 with 12189 at 3
+Id : 12624, {_}: add ?15025 ?15026 =<= add (add ?15025 ?15026) ?15025 [15026, 15025] by Super 12598 with 12573 at 2,3
+Id : 12720, {_}: multiply ?15175 (add (inverse ?15175) ?15176) =<= multiply (add (inverse ?15175) ?15176) ?15175 [15176, 15175] by Super 9041 with 12624 at 2,2
+Id : 12767, {_}: multiply ?15175 (pixley n1 ?15175 ?15176) =<= multiply (add (inverse ?15175) ?15176) ?15175 [15176, 15175] by Demod 12720 with 11984 at 2,2
+Id : 12768, {_}: multiply ?15175 (pixley n1 ?15175 ?15176) =<= multiply (pixley n1 ?15175 ?15176) ?15175 [15176, 15175] by Demod 12767 with 11984 at 1,3
+Id : 8552, {_}: multiply ?9928 (add (inverse ?9928) ?9929) =>= add (inverse n1) (multiply ?9929 ?9928) [9929, 9928] by Super 3 with 8534 at 1,3
+Id : 8614, {_}: multiply ?9928 (add (inverse ?9928) ?9929) =>= multiply ?9929 ?9928 [9929, 9928] by Demod 8552 with 7543 at 3
+Id : 11985, {_}: multiply ?9928 (pixley n1 ?9928 ?9929) =>= multiply ?9929 ?9928 [9929, 9928] by Demod 8614 with 11984 at 2,2
+Id : 12769, {_}: multiply ?15176 ?15175 =<= multiply (pixley n1 ?15175 ?15176) ?15175 [15175, 15176] by Demod 12768 with 11985 at 2
+Id : 15132, {_}: add (pixley n1 ?18424 ?18425) (inverse ?18424) =>= pixley n1 ?18424 (multiply ?18425 ?18424) [18425, 18424] by Super 11991 with 12769 at 3,3
+Id : 15170, {_}: add (pixley n1 ?18424 ?18425) (inverse ?18424) =>= add ?18425 (inverse ?18424) [18425, 18424] by Demod 15132 with 11991 at 3
+Id : 12729, {_}: add ?15203 ?15204 =<= add (add ?15203 ?15204) ?15203 [15204, 15203] by Super 12598 with 12573 at 2,3
+Id : 12745, {_}: add (inverse ?15249) ?15250 =<= add (pixley n1 ?15249 ?15250) (inverse ?15249) [15250, 15249] by Super 12729 with 11984 at 1,3
+Id : 12826, {_}: pixley n1 ?15249 ?15250 =<= add (pixley n1 ?15249 ?15250) (inverse ?15249) [15250, 15249] by Demod 12745 with 11984 at 2
+Id : 23185, {_}: pixley n1 ?18424 ?18425 =<= add ?18425 (inverse ?18424) [18425, 18424] by Demod 15170 with 12826 at 2
+Id : 29209, {_}: multiply ?35715 (pixley n1 n1 ?35716) =?= multiply ?35715 (add ?35716 (inverse ?35715)) [35716, 35715] by Demod 29060 with 23185 at 2,2
+Id : 29210, {_}: multiply ?35715 (pixley n1 n1 ?35716) =?= multiply ?35715 (pixley n1 ?35715 ?35716) [35716, 35715] by Demod 29209 with 23185 at 2,3
+Id : 29211, {_}: multiply ?35715 ?35716 =<= multiply ?35715 (pixley n1 ?35715 ?35716) [35716, 35715] by Demod 29210 with 6 at 2,2
+Id : 29212, {_}: multiply ?35715 ?35716 =?= multiply ?35716 ?35715 [35716, 35715] by Demod 29211 with 11985 at 3
+Id : 11904, {_}: add ?14161 (inverse (inverse ?14162)) =<= add ?14162 (multiply ?14161 (inverse ?14162)) [14162, 14161] by Super 11860 with 10446 at 1,3
+Id : 11970, {_}: add ?14161 ?14162 =<= add ?14162 (multiply ?14161 (inverse ?14162)) [14162, 14161] by Demod 11904 with 10446 at 2,2
+Id : 15099, {_}: add (pixley n1 (inverse ?18302) ?18303) ?18302 =>= add ?18302 (multiply ?18303 (inverse ?18302)) [18303, 18302] by Super 11970 with 12769 at 2,3
+Id : 15201, {_}: add (pixley n1 (inverse ?18302) ?18303) ?18302 =>= add ?18303 ?18302 [18303, 18302] by Demod 15099 with 11970 at 3
+Id : 10547, {_}: pixley n1 (inverse ?12250) ?12251 =<= add (inverse (inverse ?12250)) (multiply ?12251 (add n1 ?12250)) [12251, 12250] by Super 172 with 10446 at 2,2,2,3
+Id : 10574, {_}: pixley n1 (inverse ?12250) ?12251 =<= add ?12250 (multiply ?12251 (add n1 ?12250)) [12251, 12250] by Demod 10547 with 10446 at 1,3
+Id : 17614, {_}: pixley n1 (inverse ?12250) ?12251 =<= add ?12250 (multiply ?12251 n1) [12251, 12250] by Demod 10574 with 12028 at 2,2,3
+Id : 17615, {_}: pixley n1 (inverse ?12250) ?12251 =>= add ?12250 ?12251 [12251, 12250] by Demod 17614 with 7256 at 2,3
+Id : 23377, {_}: add (add ?18302 ?18303) ?18302 =>= add ?18303 ?18302 [18303, 18302] by Demod 15201 with 17615 at 1,2
+Id : 23378, {_}: add ?18302 ?18303 =?= add ?18303 ?18302 [18303, 18302] by Demod 23377 with 12624 at 2
+Id : 363, {_}: multiply (add (add ?713 ?714) ?715) (add ?716 ?714) =<= add (multiply ?716 (add (add ?713 ?714) ?715)) (add ?714 (multiply ?715 ?714)) [716, 715, 714, 713] by Super 3 with 14 at 2,3
+Id : 33202, {_}: multiply (add (add ?713 ?714) ?715) (add ?716 ?714) =>= add (multiply ?716 (add (add ?713 ?714) ?715)) ?714 [716, 715, 714, 713] by Demod 363 with 12189 at 2,3
+Id : 33249, {_}: multiply (add (add ?41120 ?41121) ?41122) (add ?41123 ?41121) =>= add ?41121 (multiply ?41123 (add (add ?41120 ?41121) ?41122)) [41123, 41122, 41121, 41120] by Demod 33202 with 23378 at 3
+Id : 7276, {_}: multiply ?2193 (add ?2193 ?2193) =>= ?2193 [2193] by Demod 5835 with 7256 at 1,2
+Id : 7300, {_}: add (multiply ?2193 ?2193) ?2193 =>= ?2193 [2193] by Demod 7276 with 5958 at 2
+Id : 7301, {_}: add ?2193 ?2193 =>= ?2193 [2193] by Demod 7300 with 5908 at 1,2
+Id : 33300, {_}: multiply (add ?41374 ?41375) (add ?41376 ?41375) =<= add ?41375 (multiply ?41376 (add (add ?41374 ?41375) (add ?41374 ?41375))) [41376, 41375, 41374] by Super 33249 with 7301 at 1,2
+Id : 33433, {_}: multiply (add ?41374 ?41375) (add ?41376 ?41375) =>= add ?41375 (multiply ?41376 (add ?41374 ?41375)) [41376, 41375, 41374] by Demod 33300 with 7301 at 2,2,3
+Id : 42671, {_}: multiply ?52830 (add ?52831 ?52832) =<= add (multiply ?52830 ?52831) (multiply ?52832 ?52830) [52832, 52831, 52830] by Super 3 with 29212 at 1,3
+Id : 42679, {_}: multiply (add ?52859 ?52860) (add ?52861 ?52860) =>= add (multiply (add ?52859 ?52860) ?52861) ?52860 [52861, 52860, 52859] by Super 42671 with 7749 at 2,3
+Id : 42859, {_}: multiply (add ?52859 ?52860) (add ?52861 ?52860) =>= add ?52860 (multiply (add ?52859 ?52860) ?52861) [52861, 52860, 52859] by Demod 42679 with 23378 at 3
+Id : 58778, {_}: add ?52860 (multiply ?52861 (add ?52859 ?52860)) =?= add ?52860 (multiply (add ?52859 ?52860) ?52861) [52859, 52861, 52860] by Demod 42859 with 33433 at 2
+Id : 42225, {_}: multiply ?51978 (add ?51979 ?51980) =<= add (multiply ?51979 ?51978) (multiply ?51978 ?51980) [51980, 51979, 51978] by Super 3 with 29212 at 2,3
+Id : 56980, {_}: multiply (add ?78761 ?78762) (add ?78762 ?78763) =>= add ?78762 (multiply (add ?78761 ?78762) ?78763) [78763, 78762, 78761] by Super 42225 with 7749 at 1,3
+Id : 57032, {_}: multiply (add ?78985 ?78986) (add ?78985 ?78987) =>= add ?78985 (multiply (add ?78986 ?78985) ?78987) [78987, 78986, 78985] by Super 56980 with 23378 at 1,2
+Id : 42307, {_}: multiply (add ?52335 ?52336) (add ?52335 ?52337) =>= add ?52335 (multiply (add ?52335 ?52336) ?52337) [52337, 52336, 52335] by Super 42225 with 12573 at 1,3
+Id : 69246, {_}: add ?78985 (multiply (add ?78985 ?78986) ?78987) =?= add ?78985 (multiply (add ?78986 ?78985) ?78987) [78987, 78986, 78985] by Demod 57032 with 42307 at 2
+Id : 42691, {_}: multiply (add ?52915 ?52916) (add ?52917 ?52915) =>= add (multiply (add ?52915 ?52916) ?52917) ?52915 [52917, 52916, 52915] by Super 42671 with 12573 at 2,3
+Id : 42878, {_}: multiply (add ?52915 ?52916) (add ?52917 ?52915) =>= add ?52915 (multiply (add ?52915 ?52916) ?52917) [52917, 52916, 52915] by Demod 42691 with 23378 at 3
+Id : 33277, {_}: multiply (add ?41259 ?41260) (add ?41261 ?41259) =<= add ?41259 (multiply ?41261 (add (add ?41259 ?41259) ?41260)) [41261, 41260, 41259] by Super 33249 with 7301 at 1,1,2
+Id : 33397, {_}: multiply (add ?41259 ?41260) (add ?41261 ?41259) =>= add ?41259 (multiply ?41261 (add ?41259 ?41260)) [41261, 41260, 41259] by Demod 33277 with 7301 at 1,2,2,3
+Id : 59822, {_}: add ?52915 (multiply ?52917 (add ?52915 ?52916)) =?= add ?52915 (multiply (add ?52915 ?52916) ?52917) [52916, 52917, 52915] by Demod 42878 with 33397 at 2
+Id : 49363, {_}: multiply (add ?63432 ?63433) (add ?63433 ?63434) =>= add ?63433 (multiply ?63432 (add ?63433 ?63434)) [63434, 63433, 63432] by Super 29212 with 33397 at 3
+Id : 42295, {_}: multiply (add ?52279 ?52280) (add ?52280 ?52281) =>= add ?52280 (multiply (add ?52279 ?52280) ?52281) [52281, 52280, 52279] by Super 42225 with 7749 at 1,3
+Id : 65944, {_}: add ?95703 (multiply (add ?95704 ?95703) ?95705) =?= add ?95703 (multiply ?95704 (add ?95703 ?95705)) [95705, 95704, 95703] by Demod 49363 with 42295 at 2
+Id : 12345, {_}: multiply ?14434 (add ?14435 (multiply ?14436 ?14434)) =>= multiply ?14434 (add ?14435 ?14436) [14436, 14435, 14434] by Demod 12244 with 3 at 3
+Id : 66007, {_}: add ?95981 (multiply (add ?95982 ?95981) (multiply ?95983 ?95982)) =>= add ?95981 (multiply ?95982 (add ?95981 ?95983)) [95983, 95982, 95981] by Super 65944 with 12345 at 2,3
+Id : 12571, {_}: multiply ?41 (add (add ?42 ?41) ?43) =>= ?41 [43, 42, 41] by Demod 14 with 12189 at 3
+Id : 12574, {_}: multiply (multiply ?14855 ?14856) (add ?14856 ?14857) =>= multiply ?14855 ?14856 [14857, 14856, 14855] by Super 12571 with 12189 at 1,2,2
+Id : 32599, {_}: multiply (add ?39770 ?39771) (multiply ?39772 ?39770) =>= multiply ?39772 ?39770 [39772, 39771, 39770] by Super 29212 with 12574 at 3
+Id : 66421, {_}: add ?95981 (multiply ?95983 ?95982) =<= add ?95981 (multiply ?95982 (add ?95981 ?95983)) [95982, 95983, 95981] by Demod 66007 with 32599 at 2,2
+Id : 74546, {_}: add ?52915 (multiply ?52916 ?52917) =<= add ?52915 (multiply (add ?52915 ?52916) ?52917) [52917, 52916, 52915] by Demod 59822 with 66421 at 2
+Id : 74547, {_}: add ?78985 (multiply ?78986 ?78987) =<= add ?78985 (multiply (add ?78986 ?78985) ?78987) [78987, 78986, 78985] by Demod 69246 with 74546 at 2
+Id : 74549, {_}: add ?52860 (multiply ?52861 (add ?52859 ?52860)) =>= add ?52860 (multiply ?52859 ?52861) [52859, 52861, 52860] by Demod 58778 with 74547 at 3
+Id : 75087, {_}: add a (multiply c b) =?= add a (multiply c b) [] by Demod 57307 with 74549 at 3
+Id : 57307, {_}: add a (multiply c b) =<= add a (multiply b (add c a)) [] by Demod 57306 with 33433 at 3
+Id : 57306, {_}: add a (multiply c b) =<= multiply (add c a) (add b a) [] by Demod 57305 with 29212 at 3
+Id : 57305, {_}: add a (multiply c b) =<= multiply (add b a) (add c a) [] by Demod 57304 with 23378 at 2,3
+Id : 57304, {_}: add a (multiply c b) =<= multiply (add b a) (add a c) [] by Demod 57303 with 23378 at 1,3
+Id : 57303, {_}: add a (multiply c b) =<= multiply (add a b) (add a c) [] by Demod 1 with 29212 at 2,2
+Id : 1, {_}: add a (multiply b c) =<= multiply (add a b) (add a c) [] by prove_add_multiply_property
+% SZS output end CNFRefutation for BOO023-1.p
+20955: solved BOO023-1.p in 19.273203 using kbo
+20955: status Unsatisfiable for BOO023-1.p
+NO CLASH, using fixed ground order
+21165: Facts:
+NO CLASH, using fixed ground order
+21166: Facts:
+21166: Id : 2, {_}:
+ multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
+ =>=
+ multiply ?2 ?3 (multiply ?4 ?5 ?6)
+ [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
+21166: Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
+21166: Id : 4, {_}:
+ multiply ?11 ?11 ?12 =>= ?11
+ [12, 11] by ternary_multiply_2 ?11 ?12
+21166: Id : 5, {_}:
+ multiply (inverse ?14) ?14 ?15 =>= ?15
+ [15, 14] by left_inverse ?14 ?15
+21166: Id : 6, {_}:
+ multiply ?17 ?18 (inverse ?18) =>= ?17
+ [18, 17] by right_inverse ?17 ?18
+21166: Goal:
+21166: Id : 1, {_}:
+ multiply (multiply a (inverse a) b)
+ (inverse (multiply (multiply c d e) f (multiply c d g)))
+ (multiply d (multiply g f e) c)
+ =>=
+ b
+ [] by prove_single_axiom
+21166: Order:
+21166: kbo
+21166: Leaf order:
+21166: g 2 0 2 3,3,1,2,2
+21166: f 2 0 2 2,1,2,2
+21166: e 2 0 2 3,1,1,2,2
+21166: d 3 0 3 2,1,1,2,2
+21166: c 3 0 3 1,1,1,2,2
+21166: multiply 16 3 7 0,2
+21166: b 2 0 2 3,1,2
+21166: inverse 4 1 2 0,2,1,2
+21166: a 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+21167: Facts:
+21167: Id : 2, {_}:
+ multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
+ =>=
+ multiply ?2 ?3 (multiply ?4 ?5 ?6)
+ [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
+21167: Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
+21167: Id : 4, {_}:
+ multiply ?11 ?11 ?12 =>= ?11
+ [12, 11] by ternary_multiply_2 ?11 ?12
+21167: Id : 5, {_}:
+ multiply (inverse ?14) ?14 ?15 =>= ?15
+ [15, 14] by left_inverse ?14 ?15
+21167: Id : 6, {_}:
+ multiply ?17 ?18 (inverse ?18) =>= ?17
+ [18, 17] by right_inverse ?17 ?18
+21167: Goal:
+21167: Id : 1, {_}:
+ multiply (multiply a (inverse a) b)
+ (inverse (multiply (multiply c d e) f (multiply c d g)))
+ (multiply d (multiply g f e) c)
+ =>=
+ b
+ [] by prove_single_axiom
+21167: Order:
+21167: lpo
+21167: Leaf order:
+21167: g 2 0 2 3,3,1,2,2
+21167: f 2 0 2 2,1,2,2
+21167: e 2 0 2 3,1,1,2,2
+21167: d 3 0 3 2,1,1,2,2
+21167: c 3 0 3 1,1,1,2,2
+21167: multiply 16 3 7 0,2
+21167: b 2 0 2 3,1,2
+21167: inverse 4 1 2 0,2,1,2
+21167: a 2 0 2 1,1,2
+21165: Id : 2, {_}:
+ multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
+ =>=
+ multiply ?2 ?3 (multiply ?4 ?5 ?6)
+ [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
+21165: Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
+21165: Id : 4, {_}:
+ multiply ?11 ?11 ?12 =>= ?11
+ [12, 11] by ternary_multiply_2 ?11 ?12
+21165: Id : 5, {_}:
+ multiply (inverse ?14) ?14 ?15 =>= ?15
+ [15, 14] by left_inverse ?14 ?15
+21165: Id : 6, {_}:
+ multiply ?17 ?18 (inverse ?18) =>= ?17
+ [18, 17] by right_inverse ?17 ?18
+21165: Goal:
+21165: Id : 1, {_}:
+ multiply (multiply a (inverse a) b)
+ (inverse (multiply (multiply c d e) f (multiply c d g)))
+ (multiply d (multiply g f e) c)
+ =>=
+ b
+ [] by prove_single_axiom
+21165: Order:
+21165: nrkbo
+21165: Leaf order:
+21165: g 2 0 2 3,3,1,2,2
+21165: f 2 0 2 2,1,2,2
+21165: e 2 0 2 3,1,1,2,2
+21165: d 3 0 3 2,1,1,2,2
+21165: c 3 0 3 1,1,1,2,2
+21165: multiply 16 3 7 0,2
+21165: b 2 0 2 3,1,2
+21165: inverse 4 1 2 0,2,1,2
+21165: a 2 0 2 1,1,2
+Statistics :
+Max weight : 24
+Found proof, 10.936664s
+% SZS status Unsatisfiable for BOO034-1.p
+% SZS output start CNFRefutation for BOO034-1.p
+Id : 5, {_}: multiply (inverse ?14) ?14 ?15 =>= ?15 [15, 14] by left_inverse ?14 ?15
+Id : 4, {_}: multiply ?11 ?11 ?12 =>= ?11 [12, 11] by ternary_multiply_2 ?11 ?12
+Id : 6, {_}: multiply ?17 ?18 (inverse ?18) =>= ?17 [18, 17] by right_inverse ?17 ?18
+Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
+Id : 2, {_}: multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6) =>= multiply ?2 ?3 (multiply ?4 ?5 ?6) [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
+Id : 12, {_}: multiply (multiply ?48 ?49 ?50) ?51 ?49 =?= multiply ?48 ?49 (multiply ?50 ?51 ?49) [51, 50, 49, 48] by Super 2 with 3 at 3,2
+Id : 13, {_}: multiply ?53 ?54 (multiply ?55 ?53 ?56) =?= multiply ?55 ?53 (multiply ?53 ?54 ?56) [56, 55, 54, 53] by Super 2 with 3 at 1,2
+Id : 920, {_}: multiply (multiply ?2937 ?2938 ?2939) ?2937 ?2938 =?= multiply ?2939 ?2937 (multiply ?2937 ?2938 ?2938) [2939, 2938, 2937] by Super 12 with 13 at 3
+Id : 1359, {_}: multiply (multiply ?4051 ?4052 ?4053) ?4051 ?4052 =>= multiply ?4053 ?4051 ?4052 [4053, 4052, 4051] by Demod 920 with 3 at 3,3
+Id : 1364, {_}: multiply ?4070 ?4070 ?4071 =?= multiply (inverse ?4071) ?4070 ?4071 [4071, 4070] by Super 1359 with 6 at 1,2
+Id : 1413, {_}: ?4070 =<= multiply (inverse ?4071) ?4070 ?4071 [4071, 4070] by Demod 1364 with 4 at 2
+Id : 1453, {_}: multiply (multiply ?4288 ?4289 (inverse ?4289)) ?4290 ?4289 =>= multiply ?4288 ?4289 ?4290 [4290, 4289, 4288] by Super 12 with 1413 at 3,3
+Id : 1476, {_}: multiply ?4288 ?4290 ?4289 =?= multiply ?4288 ?4289 ?4290 [4289, 4290, 4288] by Demod 1453 with 6 at 1,2
+Id : 519, {_}: multiply (multiply ?1786 ?1787 ?1788) ?1789 ?1787 =?= multiply ?1786 ?1787 (multiply ?1788 ?1789 ?1787) [1789, 1788, 1787, 1786] by Super 2 with 3 at 3,2
+Id : 659, {_}: multiply (multiply ?2172 ?2173 ?2174) ?2174 ?2173 =>= multiply ?2172 ?2173 ?2174 [2174, 2173, 2172] by Super 519 with 4 at 3,3
+Id : 664, {_}: multiply ?2191 (inverse ?2192) ?2192 =?= multiply ?2191 ?2192 (inverse ?2192) [2192, 2191] by Super 659 with 6 at 1,2
+Id : 701, {_}: multiply ?2191 (inverse ?2192) ?2192 =>= ?2191 [2192, 2191] by Demod 664 with 6 at 3
+Id : 1371, {_}: multiply ?4106 ?4106 (inverse ?4107) =?= multiply ?4107 ?4106 (inverse ?4107) [4107, 4106] by Super 1359 with 701 at 1,2
+Id : 1415, {_}: ?4106 =<= multiply ?4107 ?4106 (inverse ?4107) [4107, 4106] by Demod 1371 with 4 at 2
+Id : 1522, {_}: multiply ?4441 ?4442 (multiply ?4443 ?4441 (inverse ?4441)) =>= multiply ?4443 ?4441 ?4442 [4443, 4442, 4441] by Super 13 with 1415 at 3,3
+Id : 1536, {_}: multiply ?4441 ?4442 ?4443 =?= multiply ?4443 ?4441 ?4442 [4443, 4442, 4441] by Demod 1522 with 6 at 3,2
+Id : 727, {_}: inverse (inverse ?2329) =>= ?2329 [2329] by Super 5 with 701 at 2
+Id : 761, {_}: multiply ?2420 (inverse ?2420) ?2421 =>= ?2421 [2421, 2420] by Super 5 with 727 at 1,2
+Id : 40424, {_}: b === b [] by Demod 40423 with 6 at 2
+Id : 40423, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply g f e))) =>= b [] by Demod 40422 with 1476 at 3,1,3,2
+Id : 40422, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply g e f))) =>= b [] by Demod 40421 with 1536 at 3,1,3,2
+Id : 40421, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply f g e))) =>= b [] by Demod 40420 with 1476 at 3,1,3,2
+Id : 40420, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply f e g))) =>= b [] by Demod 40419 with 1536 at 3,1,3,2
+Id : 40419, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply e g f))) =>= b [] by Demod 40418 with 1476 at 3,1,3,2
+Id : 40418, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply e f g))) =>= b [] by Demod 40417 with 1476 at 1,3,2
+Id : 40417, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d (multiply e f g) c)) =>= b [] by Demod 40416 with 1476 at 2
+Id : 40416, {_}: multiply b (inverse (multiply d (multiply e f g) c)) (multiply d c (multiply g f e)) =>= b [] by Demod 40415 with 1536 at 2
+Id : 40415, {_}: multiply (multiply d c (multiply g f e)) b (inverse (multiply d (multiply e f g) c)) =>= b [] by Demod 40414 with 1536 at 1,3,2
+Id : 40414, {_}: multiply (multiply d c (multiply g f e)) b (inverse (multiply c d (multiply e f g))) =>= b [] by Demod 40413 with 761 at 2,2
+Id : 40413, {_}: multiply (multiply d c (multiply g f e)) (multiply a (inverse a) b) (inverse (multiply c d (multiply e f g))) =>= b [] by Demod 40412 with 1476 at 1,2
+Id : 40412, {_}: multiply (multiply d (multiply g f e) c) (multiply a (inverse a) b) (inverse (multiply c d (multiply e f g))) =>= b [] by Demod 40411 with 1476 at 2
+Id : 40411, {_}: multiply (multiply d (multiply g f e) c) (inverse (multiply c d (multiply e f g))) (multiply a (inverse a) b) =>= b [] by Demod 40410 with 1536 at 2
+Id : 40410, {_}: multiply (multiply a (inverse a) b) (multiply d (multiply g f e) c) (inverse (multiply c d (multiply e f g))) =>= b [] by Demod 11 with 1476 at 2
+Id : 11, {_}: multiply (multiply a (inverse a) b) (inverse (multiply c d (multiply e f g))) (multiply d (multiply g f e) c) =>= b [] by Demod 1 with 2 at 1,2,2
+Id : 1, {_}: multiply (multiply a (inverse a) b) (inverse (multiply (multiply c d e) f (multiply c d g))) (multiply d (multiply g f e) c) =>= b [] by prove_single_axiom
+% SZS output end CNFRefutation for BOO034-1.p
+21165: solved BOO034-1.p in 10.220638 using nrkbo
+21165: status Unsatisfiable for BOO034-1.p
+CLASH, statistics insufficient
+21378: Facts:
+21378: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+21378: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
+21378: Goal:
+21378: Id : 1, {_}:
+ apply (apply ?1 (f ?1)) (g ?1)
+ =<=
+ apply (g ?1) (apply (apply (f ?1) (f ?1)) (g ?1))
+ [1] by prove_u_combinator ?1
+21378: Order:
+21378: nrkbo
+21378: Leaf order:
+21378: k 1 0 0
+21378: s 1 0 0
+21378: g 3 1 3 0,2,2
+21378: apply 13 2 5 0,2
+21378: f 3 1 3 0,2,1,2
+CLASH, statistics insufficient
+21379: Facts:
+21379: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+21379: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
+21379: Goal:
+21379: Id : 1, {_}:
+ apply (apply ?1 (f ?1)) (g ?1)
+ =<=
+ apply (g ?1) (apply (apply (f ?1) (f ?1)) (g ?1))
+ [1] by prove_u_combinator ?1
+21379: Order:
+21379: kbo
+21379: Leaf order:
+21379: k 1 0 0
+21379: s 1 0 0
+21379: g 3 1 3 0,2,2
+21379: apply 13 2 5 0,2
+21379: f 3 1 3 0,2,1,2
+CLASH, statistics insufficient
+21380: Facts:
+21380: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+21380: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
+21380: Goal:
+21380: Id : 1, {_}:
+ apply (apply ?1 (f ?1)) (g ?1)
+ =<=
+ apply (g ?1) (apply (apply (f ?1) (f ?1)) (g ?1))
+ [1] by prove_u_combinator ?1
+21380: Order:
+21380: lpo
+21380: Leaf order:
+21380: k 1 0 0
+21380: s 1 0 0
+21380: g 3 1 3 0,2,2
+21380: apply 13 2 5 0,2
+21380: f 3 1 3 0,2,1,2
+% SZS status Timeout for COL004-1.p
+NO CLASH, using fixed ground order
+21607: Facts:
+21607: Id : 2, {_}:
+ apply (apply (apply s ?2) ?3) ?4
+ =?=
+ apply (apply ?2 ?4) (apply ?3 ?4)
+ [4, 3, 2] by s_definition ?2 ?3 ?4
+21607: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+21607: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply s
+ (apply k
+ (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
+ (apply (apply s (apply (apply s (apply k s)) k))
+ (apply k
+ (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
+ [] by strong_fixed_point
+21607: Goal:
+21607: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+21607: Order:
+21607: nrkbo
+21607: Leaf order:
+21607: k 13 0 0
+21607: s 11 0 0
+21607: apply 32 2 3 0,2
+21607: fixed_pt 3 0 3 2,2
+21607: strong_fixed_point 3 0 2 1,2
+NO CLASH, using fixed ground order
+21608: Facts:
+21608: Id : 2, {_}:
+ apply (apply (apply s ?2) ?3) ?4
+ =?=
+ apply (apply ?2 ?4) (apply ?3 ?4)
+ [4, 3, 2] by s_definition ?2 ?3 ?4
+21608: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+21608: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply s
+ (apply k
+ (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
+ (apply (apply s (apply (apply s (apply k s)) k))
+ (apply k
+ (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
+ [] by strong_fixed_point
+21608: Goal:
+21608: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+21608: Order:
+21608: kbo
+21608: Leaf order:
+21608: k 13 0 0
+21608: s 11 0 0
+21608: apply 32 2 3 0,2
+21608: fixed_pt 3 0 3 2,2
+21608: strong_fixed_point 3 0 2 1,2
+NO CLASH, using fixed ground order
+21609: Facts:
+21609: Id : 2, {_}:
+ apply (apply (apply s ?2) ?3) ?4
+ =?=
+ apply (apply ?2 ?4) (apply ?3 ?4)
+ [4, 3, 2] by s_definition ?2 ?3 ?4
+21609: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+21609: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply s
+ (apply k
+ (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
+ (apply (apply s (apply (apply s (apply k s)) k))
+ (apply k
+ (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
+ [] by strong_fixed_point
+21609: Goal:
+21609: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+21609: Order:
+21609: lpo
+21609: Leaf order:
+21609: k 13 0 0
+21609: s 11 0 0
+21609: apply 32 2 3 0,2
+21609: fixed_pt 3 0 3 2,2
+21609: strong_fixed_point 3 0 2 1,2
+% SZS status Timeout for COL006-6.p
+CLASH, statistics insufficient
+21625: Facts:
+21625: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+21625: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+21625: Id : 4, {_}:
+ apply (apply t ?11) ?12 =>= apply ?12 ?11
+ [12, 11] by t_definition ?11 ?12
+21625: Goal:
+21625: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+21625: Order:
+21625: nrkbo
+21625: Leaf order:
+21625: t 1 0 0
+21625: b 1 0 0
+21625: s 1 0 0
+21625: apply 17 2 3 0,2
+21625: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+21626: Facts:
+21626: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+21626: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+21626: Id : 4, {_}:
+ apply (apply t ?11) ?12 =>= apply ?12 ?11
+ [12, 11] by t_definition ?11 ?12
+21626: Goal:
+21626: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+21626: Order:
+21626: kbo
+21626: Leaf order:
+21626: t 1 0 0
+21626: b 1 0 0
+21626: s 1 0 0
+21626: apply 17 2 3 0,2
+21626: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+21627: Facts:
+21627: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+21627: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+21627: Id : 4, {_}:
+ apply (apply t ?11) ?12 =?= apply ?12 ?11
+ [12, 11] by t_definition ?11 ?12
+21627: Goal:
+21627: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+21627: Order:
+21627: lpo
+21627: Leaf order:
+21627: t 1 0 0
+21627: b 1 0 0
+21627: s 1 0 0
+21627: apply 17 2 3 0,2
+21627: f 3 1 3 0,2,2
+% SZS status Timeout for COL036-1.p
+CLASH, statistics insufficient
+21654: Facts:
+21654: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+CLASH, statistics insufficient
+21655: Facts:
+21655: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+21655: Id : 3, {_}:
+ apply (apply t ?7) ?8 =>= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+21655: Goal:
+21655: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (apply (h ?1) (g ?1)) (f ?1)
+ [1] by prove_f_combinator ?1
+21655: Order:
+21655: kbo
+21655: Leaf order:
+21655: t 1 0 0
+21655: b 1 0 0
+21655: h 2 1 2 0,2,2
+21655: g 2 1 2 0,2,1,2
+21655: apply 13 2 5 0,2
+21655: f 2 1 2 0,2,1,1,2
+21654: Id : 3, {_}:
+ apply (apply t ?7) ?8 =>= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+21654: Goal:
+21654: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (apply (h ?1) (g ?1)) (f ?1)
+ [1] by prove_f_combinator ?1
+21654: Order:
+21654: nrkbo
+21654: Leaf order:
+21654: t 1 0 0
+21654: b 1 0 0
+21654: h 2 1 2 0,2,2
+21654: g 2 1 2 0,2,1,2
+21654: apply 13 2 5 0,2
+21654: f 2 1 2 0,2,1,1,2
+CLASH, statistics insufficient
+21656: Facts:
+21656: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+21656: Id : 3, {_}:
+ apply (apply t ?7) ?8 =?= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+21656: Goal:
+21656: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (apply (h ?1) (g ?1)) (f ?1)
+ [1] by prove_f_combinator ?1
+21656: Order:
+21656: lpo
+21656: Leaf order:
+21656: t 1 0 0
+21656: b 1 0 0
+21656: h 2 1 2 0,2,2
+21656: g 2 1 2 0,2,1,2
+21656: apply 13 2 5 0,2
+21656: f 2 1 2 0,2,1,1,2
+Goal subsumed
+Statistics :
+Max weight : 100
+Found proof, 5.123186s
+% SZS status Unsatisfiable for COL063-1.p
+% SZS output start CNFRefutation for COL063-1.p
+Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
+Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
+Id : 3189, {_}: apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) === apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) [] by Super 3184 with 3 at 2
+Id : 3184, {_}: apply (apply ?10590 (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590))))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590))))) =>= apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590)))) [10590] by Super 3164 with 3 at 2,2
+Id : 3164, {_}: apply (apply ?10539 (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (apply (apply ?10540 (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) =>= apply (apply (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) [10540, 10539] by Super 442 with 2 at 2
+Id : 442, {_}: apply (apply (apply ?1394 (apply ?1395 (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (apply ?1396 (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) =>= apply (apply (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395))))) (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) [1396, 1395, 1394] by Super 277 with 2 at 1,1,2
+Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (apply (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) [901, 900] by Super 29 with 2 at 1,2
+Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (apply (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) [87, 86, 85] by Super 13 with 3 at 1,1,2
+Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (apply (h (apply (apply b ?33) (apply (apply b ?34) ?35))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (f (apply (apply b ?33) (apply (apply b ?34) ?35))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
+Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (apply (h (apply (apply b ?18) ?19)) (g (apply (apply b ?18) ?19))) (f (apply (apply b ?18) ?19)) [19, 18] by Super 1 with 2 at 1,1,2
+Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (h ?1) (g ?1)) (f ?1) [1] by prove_f_combinator ?1
+% SZS output end CNFRefutation for COL063-1.p
+21654: solved COL063-1.p in 5.12832 using nrkbo
+21654: status Unsatisfiable for COL063-1.p
+NO CLASH, using fixed ground order
+21661: Facts:
+21661: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+21661: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+21661: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+21661: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+21661: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+21661: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+21661: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+21661: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+21661: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+21661: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+21661: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+21661: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+21661: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+21661: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+21661: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+21661: Goal:
+21661: Id : 1, {_}:
+ a
+ =<=
+ multiply (least_upper_bound a identity)
+ (greatest_lower_bound a identity)
+ [] by prove_p19
+21661: Order:
+21661: nrkbo
+21661: Leaf order:
+21661: inverse 1 1 0
+21661: multiply 19 2 1 0,3
+21661: greatest_lower_bound 14 2 1 0,2,3
+21661: least_upper_bound 14 2 1 0,1,3
+21661: identity 4 0 2 2,1,3
+21661: a 3 0 3 2
+NO CLASH, using fixed ground order
+21662: Facts:
+21662: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+21662: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+21662: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+21662: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+21662: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+21662: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+21662: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+21662: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+21662: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+21662: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+21662: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+21662: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+21662: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+21662: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+21662: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+21662: Goal:
+21662: Id : 1, {_}:
+ a
+ =<=
+ multiply (least_upper_bound a identity)
+ (greatest_lower_bound a identity)
+ [] by prove_p19
+21662: Order:
+21662: kbo
+21662: Leaf order:
+21662: inverse 1 1 0
+21662: multiply 19 2 1 0,3
+21662: greatest_lower_bound 14 2 1 0,2,3
+21662: least_upper_bound 14 2 1 0,1,3
+21662: identity 4 0 2 2,1,3
+21662: a 3 0 3 2
+NO CLASH, using fixed ground order
+21663: Facts:
+21663: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+21663: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+21663: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+21663: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+21663: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+21663: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+21663: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+21663: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+21663: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+21663: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+21663: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+21663: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+21663: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+21663: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+21663: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+21663: Goal:
+21663: Id : 1, {_}:
+ a
+ =<=
+ multiply (least_upper_bound a identity)
+ (greatest_lower_bound a identity)
+ [] by prove_p19
+21663: Order:
+21663: lpo
+21663: Leaf order:
+21663: inverse 1 1 0
+21663: multiply 19 2 1 0,3
+21663: greatest_lower_bound 14 2 1 0,2,3
+21663: least_upper_bound 14 2 1 0,1,3
+21663: identity 4 0 2 2,1,3
+21663: a 3 0 3 2
+% SZS status Timeout for GRP167-3.p
+NO CLASH, using fixed ground order
+21683: Facts:
+21683: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+21683: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+21683: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+21683: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+21683: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+21683: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+21683: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+21683: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+21683: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+21683: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+21683: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+21683: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+21683: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+21683: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+21683: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+21683: Goal:
+21683: Id : 1, {_}:
+ inverse (least_upper_bound a b)
+ =<=
+ greatest_lower_bound (inverse a) (inverse b)
+ [] by prove_p10
+21683: Order:
+21683: nrkbo
+21683: Leaf order:
+21683: multiply 18 2 0
+21683: identity 2 0 0
+21683: greatest_lower_bound 14 2 1 0,3
+21683: inverse 4 1 3 0,2
+21683: least_upper_bound 14 2 1 0,1,2
+21683: b 2 0 2 2,1,2
+21683: a 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+21684: Facts:
+21684: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+21684: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+21684: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+21684: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+21684: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+21684: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+21684: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+21684: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+21684: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+21684: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+21684: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+21684: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+NO CLASH, using fixed ground order
+21685: Facts:
+21685: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+21685: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+21685: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+21685: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+21685: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+21685: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+21685: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+21685: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+21685: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+21685: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+21685: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+21685: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+21685: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+21685: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+21685: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+21685: Goal:
+21685: Id : 1, {_}:
+ inverse (least_upper_bound a b)
+ =>=
+ greatest_lower_bound (inverse a) (inverse b)
+ [] by prove_p10
+21685: Order:
+21685: lpo
+21685: Leaf order:
+21685: multiply 18 2 0
+21685: identity 2 0 0
+21685: greatest_lower_bound 14 2 1 0,3
+21685: inverse 4 1 3 0,2
+21685: least_upper_bound 14 2 1 0,1,2
+21685: b 2 0 2 2,1,2
+21685: a 2 0 2 1,1,2
+21684: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+21684: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+21684: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+21684: Goal:
+21684: Id : 1, {_}:
+ inverse (least_upper_bound a b)
+ =<=
+ greatest_lower_bound (inverse a) (inverse b)
+ [] by prove_p10
+21684: Order:
+21684: kbo
+21684: Leaf order:
+21684: multiply 18 2 0
+21684: identity 2 0 0
+21684: greatest_lower_bound 14 2 1 0,3
+21684: inverse 4 1 3 0,2
+21684: least_upper_bound 14 2 1 0,1,2
+21684: b 2 0 2 2,1,2
+21684: a 2 0 2 1,1,2
+% SZS status Timeout for GRP179-1.p
+NO CLASH, using fixed ground order
+21733: Facts:
+21733: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+21733: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+21733: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+21733: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+21733: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+21733: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+21733: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+21733: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+21733: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+21733: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+21733: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+21733: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+21733: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+21733: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+21733: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+21733: Goal:
+21733: Id : 1, {_}:
+ least_upper_bound (inverse a) identity
+ =<=
+ inverse (greatest_lower_bound a identity)
+ [] by prove_p18
+21733: Order:
+21733: kbo
+21733: Leaf order:
+21733: multiply 18 2 0
+21733: greatest_lower_bound 14 2 1 0,1,3
+21733: least_upper_bound 14 2 1 0,2
+21733: identity 4 0 2 2,2
+21733: inverse 3 1 2 0,1,2
+21733: a 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+21732: Facts:
+21732: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+21732: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+21732: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+21732: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+21732: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+21732: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+21732: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+21732: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+21732: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+21732: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+21732: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+21732: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+21732: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+21732: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+21732: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+21732: Goal:
+21732: Id : 1, {_}:
+ least_upper_bound (inverse a) identity
+ =<=
+ inverse (greatest_lower_bound a identity)
+ [] by prove_p18
+21732: Order:
+21732: nrkbo
+21732: Leaf order:
+21732: multiply 18 2 0
+21732: greatest_lower_bound 14 2 1 0,1,3
+21732: least_upper_bound 14 2 1 0,2
+21732: identity 4 0 2 2,2
+21732: inverse 3 1 2 0,1,2
+21732: a 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+21734: Facts:
+21734: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+21734: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+21734: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+21734: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+21734: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+21734: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+21734: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+21734: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+21734: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+21734: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+21734: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+21734: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+21734: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+21734: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+21734: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+21734: Goal:
+21734: Id : 1, {_}:
+ least_upper_bound (inverse a) identity
+ =<=
+ inverse (greatest_lower_bound a identity)
+ [] by prove_p18
+21734: Order:
+21734: lpo
+21734: Leaf order:
+21734: multiply 18 2 0
+21734: greatest_lower_bound 14 2 1 0,1,3
+21734: least_upper_bound 14 2 1 0,2
+21734: identity 4 0 2 2,2
+21734: inverse 3 1 2 0,1,2
+21734: a 2 0 2 1,1,2
+% SZS status Timeout for GRP179-2.p
+NO CLASH, using fixed ground order
+21751: Facts:
+21751: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+21751: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+21751: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+21751: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+21751: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+21751: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+21751: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+21751: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+21751: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+21751: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+21751: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+21751: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+21751: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+21751: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+21751: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+21751: Goal:
+21751: Id : 1, {_}:
+ multiply a (multiply (inverse (greatest_lower_bound a b)) b)
+ =>=
+ least_upper_bound a b
+ [] by prove_p11
+21751: Order:
+21751: nrkbo
+21751: Leaf order:
+21751: identity 2 0 0
+21751: least_upper_bound 14 2 1 0,3
+21751: multiply 20 2 2 0,2
+21751: inverse 2 1 1 0,1,2,2
+21751: greatest_lower_bound 14 2 1 0,1,1,2,2
+21751: b 3 0 3 2,1,1,2,2
+21751: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+21752: Facts:
+21752: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+21752: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+21752: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+21752: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+21752: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+21752: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+21752: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+21752: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+21752: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+21752: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+21752: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+21752: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+21752: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+21752: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+21752: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+21752: Goal:
+21752: Id : 1, {_}:
+ multiply a (multiply (inverse (greatest_lower_bound a b)) b)
+ =>=
+ least_upper_bound a b
+ [] by prove_p11
+21752: Order:
+21752: kbo
+21752: Leaf order:
+21752: identity 2 0 0
+21752: least_upper_bound 14 2 1 0,3
+21752: multiply 20 2 2 0,2
+21752: inverse 2 1 1 0,1,2,2
+21752: greatest_lower_bound 14 2 1 0,1,1,2,2
+21752: b 3 0 3 2,1,1,2,2
+21752: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+21753: Facts:
+21753: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+21753: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+21753: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+21753: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+21753: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+21753: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+21753: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+21753: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+21753: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+21753: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+21753: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+21753: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+21753: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+21753: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+21753: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+21753: Goal:
+21753: Id : 1, {_}:
+ multiply a (multiply (inverse (greatest_lower_bound a b)) b)
+ =>=
+ least_upper_bound a b
+ [] by prove_p11
+21753: Order:
+21753: lpo
+21753: Leaf order:
+21753: identity 2 0 0
+21753: least_upper_bound 14 2 1 0,3
+21753: multiply 20 2 2 0,2
+21753: inverse 2 1 1 0,1,2,2
+21753: greatest_lower_bound 14 2 1 0,1,1,2,2
+21753: b 3 0 3 2,1,1,2,2
+21753: a 3 0 3 1,2
+% SZS status Timeout for GRP180-1.p
+NO CLASH, using fixed ground order
+21783: Facts:
+21783: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+21783: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+21783: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+21783: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+21783: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+21783: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+21783: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+21783: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+21783: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+21783: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+21783: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+21783: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+21783: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+21783: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+21783: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+21783: Id : 17, {_}: inverse identity =>= identity [] by p20_1
+21783: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20_2 ?51
+21783: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p20_3 ?53 ?54
+21783: Goal:
+21783: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =>=
+ identity
+ [] by prove_p20
+21783: Order:
+21783: nrkbo
+21783: Leaf order:
+21783: multiply 20 2 0
+21783: inverse 8 1 1 0,2,2
+21783: greatest_lower_bound 15 2 2 0,2
+21783: least_upper_bound 14 2 1 0,1,2
+21783: identity 7 0 3 2,1,2
+21783: a 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+21785: Facts:
+21785: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+21785: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+21785: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+21785: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+21785: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+21785: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+21785: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+21785: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+21785: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+21785: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+21785: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+21785: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+21785: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+21785: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+21785: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+21785: Id : 17, {_}: inverse identity =>= identity [] by p20_1
+21785: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20_2 ?51
+21785: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =>= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p20_3 ?53 ?54
+21785: Goal:
+21785: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =>=
+ identity
+ [] by prove_p20
+21785: Order:
+21785: lpo
+21785: Leaf order:
+21785: multiply 20 2 0
+21785: inverse 8 1 1 0,2,2
+21785: greatest_lower_bound 15 2 2 0,2
+21785: least_upper_bound 14 2 1 0,1,2
+21785: identity 7 0 3 2,1,2
+21785: a 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+21784: Facts:
+21784: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+21784: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+21784: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+21784: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+21784: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+21784: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+21784: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+21784: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+21784: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+21784: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+21784: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+21784: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+21784: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+21784: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+21784: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+21784: Id : 17, {_}: inverse identity =>= identity [] by p20_1
+21784: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20_2 ?51
+21784: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p20_3 ?53 ?54
+21784: Goal:
+21784: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =>=
+ identity
+ [] by prove_p20
+21784: Order:
+21784: kbo
+21784: Leaf order:
+21784: multiply 20 2 0
+21784: inverse 8 1 1 0,2,2
+21784: greatest_lower_bound 15 2 2 0,2
+21784: least_upper_bound 14 2 1 0,1,2
+21784: identity 7 0 3 2,1,2
+21784: a 2 0 2 1,1,2
+% SZS status Timeout for GRP183-2.p
+NO CLASH, using fixed ground order
+21802: Facts:
+21802: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+21802: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+21802: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+21802: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+21802: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+21802: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+21802: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+21802: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+21802: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+21802: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+21802: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+21802: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+21802: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+21802: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+21802: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+21802: Goal:
+21802: Id : 1, {_}:
+ least_upper_bound (multiply a b) identity
+ =<=
+ multiply a (inverse (greatest_lower_bound a (inverse b)))
+ [] by prove_p23
+21802: Order:
+21802: nrkbo
+21802: Leaf order:
+21802: greatest_lower_bound 14 2 1 0,1,2,3
+21802: inverse 3 1 2 0,2,3
+21802: least_upper_bound 14 2 1 0,2
+21802: identity 3 0 1 2,2
+21802: multiply 20 2 2 0,1,2
+21802: b 2 0 2 2,1,2
+21802: a 3 0 3 1,1,2
+NO CLASH, using fixed ground order
+21803: Facts:
+21803: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+21803: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+21803: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+21803: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+21803: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+21803: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+21803: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+21803: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+21803: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+21803: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+21803: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+21803: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+21803: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+21803: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+21803: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+21803: Goal:
+21803: Id : 1, {_}:
+ least_upper_bound (multiply a b) identity
+ =<=
+ multiply a (inverse (greatest_lower_bound a (inverse b)))
+ [] by prove_p23
+21803: Order:
+21803: kbo
+21803: Leaf order:
+21803: greatest_lower_bound 14 2 1 0,1,2,3
+21803: inverse 3 1 2 0,2,3
+21803: least_upper_bound 14 2 1 0,2
+21803: identity 3 0 1 2,2
+21803: multiply 20 2 2 0,1,2
+21803: b 2 0 2 2,1,2
+21803: a 3 0 3 1,1,2
+NO CLASH, using fixed ground order
+21804: Facts:
+21804: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+21804: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+21804: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+21804: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+21804: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+21804: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+21804: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+21804: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+21804: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+21804: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+21804: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+21804: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+21804: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+21804: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+21804: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+21804: Goal:
+21804: Id : 1, {_}:
+ least_upper_bound (multiply a b) identity
+ =<=
+ multiply a (inverse (greatest_lower_bound a (inverse b)))
+ [] by prove_p23
+21804: Order:
+21804: lpo
+21804: Leaf order:
+21804: greatest_lower_bound 14 2 1 0,1,2,3
+21804: inverse 3 1 2 0,2,3
+21804: least_upper_bound 14 2 1 0,2
+21804: identity 3 0 1 2,2
+21804: multiply 20 2 2 0,1,2
+21804: b 2 0 2 2,1,2
+21804: a 3 0 3 1,1,2
+% SZS status Timeout for GRP186-1.p
+NO CLASH, using fixed ground order
+21831: Facts:
+21831: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
+21831: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
+21831: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
+21831: Id : 5, {_}:
+ meet ?9 ?10 =?= meet ?10 ?9
+ [10, 9] by commutativity_of_meet ?9 ?10
+21831: Id : 6, {_}:
+ join ?12 ?13 =?= join ?13 ?12
+ [13, 12] by commutativity_of_join ?12 ?13
+21831: Id : 7, {_}:
+ meet (meet ?15 ?16) ?17 =?= meet ?15 (meet ?16 ?17)
+ [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
+21831: Id : 8, {_}:
+ join (join ?19 ?20) ?21 =?= join ?19 (join ?20 ?21)
+ [21, 20, 19] by associativity_of_join ?19 ?20 ?21
+21831: Id : 9, {_}:
+ complement (complement ?23) =>= ?23
+ [23] by complement_involution ?23
+21831: Id : 10, {_}:
+ join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
+ [26, 25] by join_complement ?25 ?26
+21831: Id : 11, {_}:
+ meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
+ [29, 28] by meet_complement ?28 ?29
+21831: Goal:
+21831: Id : 1, {_}:
+ join a
+ (join
+ (meet (complement a) (meet (join a (complement b)) (join a b)))
+ (meet (complement a)
+ (join (meet (complement a) b)
+ (meet (complement a) (complement b)))))
+ =>=
+ n1
+ [] by prove_e2
+21831: Order:
+21831: nrkbo
+21831: Leaf order:
+21831: n0 1 0 0
+21831: n1 2 0 1 3
+21831: meet 14 2 5 0,1,2,2
+21831: join 17 2 5 0,2
+21831: b 4 0 4 1,2,1,2,1,2,2
+21831: complement 15 1 6 0,1,1,2,2
+21831: a 7 0 7 1,2
+NO CLASH, using fixed ground order
+21832: Facts:
+21832: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
+21832: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
+21832: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
+21832: Id : 5, {_}:
+ meet ?9 ?10 =?= meet ?10 ?9
+ [10, 9] by commutativity_of_meet ?9 ?10
+21832: Id : 6, {_}:
+ join ?12 ?13 =?= join ?13 ?12
+ [13, 12] by commutativity_of_join ?12 ?13
+21832: Id : 7, {_}:
+ meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
+ [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
+21832: Id : 8, {_}:
+ join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
+ [21, 20, 19] by associativity_of_join ?19 ?20 ?21
+21832: Id : 9, {_}:
+ complement (complement ?23) =>= ?23
+ [23] by complement_involution ?23
+21832: Id : 10, {_}:
+ join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
+ [26, 25] by join_complement ?25 ?26
+21832: Id : 11, {_}:
+ meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
+ [29, 28] by meet_complement ?28 ?29
+21832: Goal:
+21832: Id : 1, {_}:
+ join a
+ (join
+ (meet (complement a) (meet (join a (complement b)) (join a b)))
+ (meet (complement a)
+ (join (meet (complement a) b)
+ (meet (complement a) (complement b)))))
+ =>=
+ n1
+ [] by prove_e2
+21832: Order:
+21832: kbo
+21832: Leaf order:
+21832: n0 1 0 0
+21832: n1 2 0 1 3
+21832: meet 14 2 5 0,1,2,2
+21832: join 17 2 5 0,2
+21832: b 4 0 4 1,2,1,2,1,2,2
+21832: complement 15 1 6 0,1,1,2,2
+21832: a 7 0 7 1,2
+NO CLASH, using fixed ground order
+21833: Facts:
+21833: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
+21833: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
+21833: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
+21833: Id : 5, {_}:
+ meet ?9 ?10 =?= meet ?10 ?9
+ [10, 9] by commutativity_of_meet ?9 ?10
+21833: Id : 6, {_}:
+ join ?12 ?13 =?= join ?13 ?12
+ [13, 12] by commutativity_of_join ?12 ?13
+21833: Id : 7, {_}:
+ meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
+ [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
+21833: Id : 8, {_}:
+ join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
+ [21, 20, 19] by associativity_of_join ?19 ?20 ?21
+21833: Id : 9, {_}:
+ complement (complement ?23) =>= ?23
+ [23] by complement_involution ?23
+21833: Id : 10, {_}:
+ join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
+ [26, 25] by join_complement ?25 ?26
+21833: Id : 11, {_}:
+ meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
+ [29, 28] by meet_complement ?28 ?29
+21833: Goal:
+21833: Id : 1, {_}:
+ join a
+ (join
+ (meet (complement a) (meet (join a (complement b)) (join a b)))
+ (meet (complement a)
+ (join (meet (complement a) b)
+ (meet (complement a) (complement b)))))
+ =>=
+ n1
+ [] by prove_e2
+21833: Order:
+21833: lpo
+21833: Leaf order:
+21833: n0 1 0 0
+21833: n1 2 0 1 3
+21833: meet 14 2 5 0,1,2,2
+21833: join 17 2 5 0,2
+21833: b 4 0 4 1,2,1,2,1,2,2
+21833: complement 15 1 6 0,1,1,2,2
+21833: a 7 0 7 1,2
+% SZS status Timeout for LAT017-1.p
+NO CLASH, using fixed ground order
+21853: Facts:
+21853: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+21853: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+21853: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
+21853: Id : 5, {_}:
+ join ?9 ?10 =?= join ?10 ?9
+ [10, 9] by commutativity_of_join ?9 ?10
+21853: Id : 6, {_}:
+ meet (meet ?12 ?13) ?14 =?= meet ?12 (meet ?13 ?14)
+ [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
+21853: Id : 7, {_}:
+ join (join ?16 ?17) ?18 =?= join ?16 (join ?17 ?18)
+ [18, 17, 16] by associativity_of_join ?16 ?17 ?18
+21853: Id : 8, {_}:
+ join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
+ =>=
+ meet ?20 (join ?21 ?22)
+ [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
+21853: Id : 9, {_}:
+ meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
+ =>=
+ join ?24 (meet ?25 ?26)
+ [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
+21853: Id : 10, {_}:
+ join (meet (join (meet ?28 ?29) ?30) ?29) (meet ?30 ?28)
+ =>=
+ meet (join (meet (join ?28 ?29) ?30) ?29) (join ?30 ?28)
+ [30, 29, 28] by self_dual_distributivity ?28 ?29 ?30
+21853: Goal:
+21853: Id : 1, {_}:
+ meet a (join b c) =<= join (meet a b) (meet a c)
+ [] by prove_distributivity
+21853: Order:
+21853: nrkbo
+21853: Leaf order:
+21853: meet 21 2 3 0,2
+21853: join 20 2 2 0,2,2
+21853: c 2 0 2 2,2,2
+21853: b 2 0 2 1,2,2
+21853: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+21854: Facts:
+21854: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+21854: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+21854: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
+21854: Id : 5, {_}:
+ join ?9 ?10 =?= join ?10 ?9
+ [10, 9] by commutativity_of_join ?9 ?10
+21854: Id : 6, {_}:
+ meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14)
+ [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
+21854: Id : 7, {_}:
+ join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18)
+ [18, 17, 16] by associativity_of_join ?16 ?17 ?18
+21854: Id : 8, {_}:
+ join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
+ =>=
+ meet ?20 (join ?21 ?22)
+ [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
+21854: Id : 9, {_}:
+ meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
+ =>=
+ join ?24 (meet ?25 ?26)
+ [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
+21854: Id : 10, {_}:
+ join (meet (join (meet ?28 ?29) ?30) ?29) (meet ?30 ?28)
+ =>=
+ meet (join (meet (join ?28 ?29) ?30) ?29) (join ?30 ?28)
+ [30, 29, 28] by self_dual_distributivity ?28 ?29 ?30
+21854: Goal:
+21854: Id : 1, {_}:
+ meet a (join b c) =<= join (meet a b) (meet a c)
+ [] by prove_distributivity
+21854: Order:
+21854: kbo
+21854: Leaf order:
+21854: meet 21 2 3 0,2
+21854: join 20 2 2 0,2,2
+21854: c 2 0 2 2,2,2
+21854: b 2 0 2 1,2,2
+21854: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+21855: Facts:
+21855: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+21855: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+21855: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
+21855: Id : 5, {_}:
+ join ?9 ?10 =?= join ?10 ?9
+ [10, 9] by commutativity_of_join ?9 ?10
+21855: Id : 6, {_}:
+ meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14)
+ [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
+21855: Id : 7, {_}:
+ join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18)
+ [18, 17, 16] by associativity_of_join ?16 ?17 ?18
+21855: Id : 8, {_}:
+ join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
+ =>=
+ meet ?20 (join ?21 ?22)
+ [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
+21855: Id : 9, {_}:
+ meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
+ =>=
+ join ?24 (meet ?25 ?26)
+ [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
+21855: Id : 10, {_}:
+ join (meet (join (meet ?28 ?29) ?30) ?29) (meet ?30 ?28)
+ =>=
+ meet (join (meet (join ?28 ?29) ?30) ?29) (join ?30 ?28)
+ [30, 29, 28] by self_dual_distributivity ?28 ?29 ?30
+21855: Goal:
+21855: Id : 1, {_}:
+ meet a (join b c) =<= join (meet a b) (meet a c)
+ [] by prove_distributivity
+21855: Order:
+21855: lpo
+21855: Leaf order:
+21855: meet 21 2 3 0,2
+21855: join 20 2 2 0,2,2
+21855: c 2 0 2 2,2,2
+21855: b 2 0 2 1,2,2
+21855: a 3 0 3 1,2
+% SZS status Timeout for LAT020-1.p
+NO CLASH, using fixed ground order
+21955: Facts:
+21955: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+21955: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+21955: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+21955: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+21955: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+21955: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+21955: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+21955: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+21955: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+21955: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+21955: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+21955: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+21955: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+21955: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+21955: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+21955: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+21955: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+21955: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+21955: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+21955: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+21955: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+21955: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+21955: Goal:
+21955: Id : 1, {_}:
+ add (associator x y z) (associator x z y) =>= additive_identity
+ [] by prove_equation
+21955: Order:
+21955: nrkbo
+21955: Leaf order:
+21955: commutator 1 2 0
+21955: additive_inverse 22 1 0
+21955: multiply 40 2 0
+21955: additive_identity 9 0 1 3
+21955: add 25 2 1 0,2
+21955: associator 3 3 2 0,1,2
+21955: z 2 0 2 3,1,2
+21955: y 2 0 2 2,1,2
+21955: x 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+21956: Facts:
+21956: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+21956: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+21956: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+21956: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+21956: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+21956: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+21956: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+21956: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+21956: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+21956: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+21956: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+21956: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+21956: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+21956: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+21956: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+21956: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+21956: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+21956: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+21956: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+21956: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+21956: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+21956: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+21956: Goal:
+21956: Id : 1, {_}:
+ add (associator x y z) (associator x z y) =>= additive_identity
+ [] by prove_equation
+21956: Order:
+21956: kbo
+21956: Leaf order:
+21956: commutator 1 2 0
+21956: additive_inverse 22 1 0
+21956: multiply 40 2 0
+21956: additive_identity 9 0 1 3
+21956: add 25 2 1 0,2
+21956: associator 3 3 2 0,1,2
+21956: z 2 0 2 3,1,2
+21956: y 2 0 2 2,1,2
+21956: x 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+21957: Facts:
+21957: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+21957: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+21957: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+21957: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+21957: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+21957: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+21957: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+21957: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+21957: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+21957: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+21957: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+21957: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+21957: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+21957: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+21957: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+21957: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+21957: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+21957: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+21957: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+21957: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+21957: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+21957: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+21957: Goal:
+21957: Id : 1, {_}:
+ add (associator x y z) (associator x z y) =>= additive_identity
+ [] by prove_equation
+21957: Order:
+21957: lpo
+21957: Leaf order:
+21957: commutator 1 2 0
+21957: additive_inverse 22 1 0
+21957: multiply 40 2 0
+21957: additive_identity 9 0 1 3
+21957: add 25 2 1 0,2
+21957: associator 3 3 2 0,1,2
+21957: z 2 0 2 3,1,2
+21957: y 2 0 2 2,1,2
+21957: x 2 0 2 1,1,2
+% SZS status Timeout for RNG025-5.p
+NO CLASH, using fixed ground order
+21975: Facts:
+21975: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+21975: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+21975: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+21975: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+21975: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+21975: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+21975: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+21975: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+21975: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+21975: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+21975: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+21975: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+21975: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+21975: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+21975: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+21975: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+21975: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+21975: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+21975: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+21975: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+21975: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+21975: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+21975: Goal:
+21975: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
+21975: Order:
+21975: nrkbo
+21975: Leaf order:
+21975: commutator 1 2 0
+21975: additive_inverse 22 1 0
+21975: multiply 40 2 0
+21975: add 24 2 0
+21975: additive_identity 9 0 1 3
+21975: associator 2 3 1 0,2
+21975: y 1 0 1 2,2
+21975: x 2 0 2 1,2
+NO CLASH, using fixed ground order
+21976: Facts:
+21976: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+21976: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+21976: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+21976: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+21976: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+21976: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+21976: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+21976: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+21976: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+21976: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+21976: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+21976: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+21976: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+21976: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+21976: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+21976: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+21976: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+21976: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+21976: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+21976: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+21976: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+21976: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+21976: Goal:
+21976: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
+21976: Order:
+21976: kbo
+21976: Leaf order:
+21976: commutator 1 2 0
+21976: additive_inverse 22 1 0
+21976: multiply 40 2 0
+21976: add 24 2 0
+21976: additive_identity 9 0 1 3
+21976: associator 2 3 1 0,2
+21976: y 1 0 1 2,2
+21976: x 2 0 2 1,2
+NO CLASH, using fixed ground order
+21977: Facts:
+21977: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+21977: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+21977: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+21977: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+21977: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+21977: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+21977: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+21977: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+21977: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+21977: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+21977: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+21977: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+21977: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+21977: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+21977: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+21977: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+21977: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+21977: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+21977: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+21977: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+21977: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+21977: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+21977: Goal:
+21977: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
+21977: Order:
+21977: lpo
+21977: Leaf order:
+21977: commutator 1 2 0
+21977: additive_inverse 22 1 0
+21977: multiply 40 2 0
+21977: add 24 2 0
+21977: additive_identity 9 0 1 3
+21977: associator 2 3 1 0,2
+21977: y 1 0 1 2,2
+21977: x 2 0 2 1,2
+% SZS status Timeout for RNG025-7.p
+CLASH, statistics insufficient
+22004: Facts:
+22004: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+CLASH, statistics insufficient
+22005: Facts:
+22005: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+22005: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
+22005: Goal:
+22005: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+22005: Order:
+22005: kbo
+22005: Leaf order:
+22005: k 1 0 0
+22005: s 1 0 0
+22005: apply 11 2 3 0,2
+22005: f 3 1 3 0,2,2
+22004: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
+22004: Goal:
+22004: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+22004: Order:
+22004: nrkbo
+22004: Leaf order:
+22004: k 1 0 0
+22004: s 1 0 0
+22004: apply 11 2 3 0,2
+22004: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+22006: Facts:
+22006: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+22006: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
+22006: Goal:
+22006: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+22006: Order:
+22006: lpo
+22006: Leaf order:
+22006: k 1 0 0
+22006: s 1 0 0
+22006: apply 11 2 3 0,2
+22006: f 3 1 3 0,2,2
+% SZS status Timeout for COL006-1.p
+NO CLASH, using fixed ground order
+22027: Facts:
+22027: Id : 2, {_}:
+ apply (apply (apply s ?2) ?3) ?4
+ =?=
+ apply (apply ?2 ?4) (apply ?3 ?4)
+ [4, 3, 2] by s_definition ?2 ?3 ?4
+22027: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+NO CLASH, using fixed ground order
+22028: Facts:
+22028: Id : 2, {_}:
+ apply (apply (apply s ?2) ?3) ?4
+ =?=
+ apply (apply ?2 ?4) (apply ?3 ?4)
+ [4, 3, 2] by s_definition ?2 ?3 ?4
+22028: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+22028: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply s
+ (apply k
+ (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
+ (apply (apply s (apply k (apply (apply s s) (apply s k))))
+ (apply (apply s (apply k s)) k))
+ [] by strong_fixed_point
+22028: Goal:
+22028: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+22028: Order:
+22028: kbo
+22028: Leaf order:
+22028: k 10 0 0
+22028: s 11 0 0
+22028: apply 29 2 3 0,2
+22028: fixed_pt 3 0 3 2,2
+22028: strong_fixed_point 3 0 2 1,2
+22027: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply s
+ (apply k
+ (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
+ (apply (apply s (apply k (apply (apply s s) (apply s k))))
+ (apply (apply s (apply k s)) k))
+ [] by strong_fixed_point
+22027: Goal:
+22027: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+22027: Order:
+22027: nrkbo
+22027: Leaf order:
+22027: k 10 0 0
+22027: s 11 0 0
+22027: apply 29 2 3 0,2
+22027: fixed_pt 3 0 3 2,2
+22027: strong_fixed_point 3 0 2 1,2
+NO CLASH, using fixed ground order
+22029: Facts:
+22029: Id : 2, {_}:
+ apply (apply (apply s ?2) ?3) ?4
+ =?=
+ apply (apply ?2 ?4) (apply ?3 ?4)
+ [4, 3, 2] by s_definition ?2 ?3 ?4
+22029: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+22029: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply s
+ (apply k
+ (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
+ (apply (apply s (apply k (apply (apply s s) (apply s k))))
+ (apply (apply s (apply k s)) k))
+ [] by strong_fixed_point
+22029: Goal:
+22029: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+22029: Order:
+22029: lpo
+22029: Leaf order:
+22029: k 10 0 0
+22029: s 11 0 0
+22029: apply 29 2 3 0,2
+22029: fixed_pt 3 0 3 2,2
+22029: strong_fixed_point 3 0 2 1,2
+% SZS status Timeout for COL006-5.p
+NO CLASH, using fixed ground order
+22056: Facts:
+22056: Id : 2, {_}:
+ apply (apply (apply s ?2) ?3) ?4
+ =?=
+ apply (apply ?2 ?4) (apply ?3 ?4)
+ [4, 3, 2] by s_definition ?2 ?3 ?4
+22056: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+22056: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply s
+ (apply k
+ (apply (apply (apply s s) (apply (apply s k) k))
+ (apply (apply s s) (apply s k)))))
+ (apply (apply s (apply k s)) k)
+ [] by strong_fixed_point
+22056: Goal:
+22056: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+22056: Order:
+22056: nrkbo
+22056: Leaf order:
+22056: k 7 0 0
+22056: s 10 0 0
+22056: apply 25 2 3 0,2
+22056: fixed_pt 3 0 3 2,2
+22056: strong_fixed_point 3 0 2 1,2
+NO CLASH, using fixed ground order
+22057: Facts:
+22057: Id : 2, {_}:
+ apply (apply (apply s ?2) ?3) ?4
+ =?=
+ apply (apply ?2 ?4) (apply ?3 ?4)
+ [4, 3, 2] by s_definition ?2 ?3 ?4
+22057: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+22057: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply s
+ (apply k
+ (apply (apply (apply s s) (apply (apply s k) k))
+ (apply (apply s s) (apply s k)))))
+ (apply (apply s (apply k s)) k)
+ [] by strong_fixed_point
+22057: Goal:
+22057: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+22057: Order:
+22057: kbo
+22057: Leaf order:
+22057: k 7 0 0
+22057: s 10 0 0
+22057: apply 25 2 3 0,2
+22057: fixed_pt 3 0 3 2,2
+22057: strong_fixed_point 3 0 2 1,2
+NO CLASH, using fixed ground order
+22058: Facts:
+22058: Id : 2, {_}:
+ apply (apply (apply s ?2) ?3) ?4
+ =?=
+ apply (apply ?2 ?4) (apply ?3 ?4)
+ [4, 3, 2] by s_definition ?2 ?3 ?4
+22058: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+22058: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply s
+ (apply k
+ (apply (apply (apply s s) (apply (apply s k) k))
+ (apply (apply s s) (apply s k)))))
+ (apply (apply s (apply k s)) k)
+ [] by strong_fixed_point
+22058: Goal:
+22058: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+22058: Order:
+22058: lpo
+22058: Leaf order:
+22058: k 7 0 0
+22058: s 10 0 0
+22058: apply 25 2 3 0,2
+22058: fixed_pt 3 0 3 2,2
+22058: strong_fixed_point 3 0 2 1,2
+% SZS status Timeout for COL006-7.p
+NO CLASH, using fixed ground order
+22074: Facts:
+22074: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+22074: Id : 3, {_}:
+ apply (apply (apply n ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?8) ?7) ?8
+ [8, 7, 6] by n_definition ?6 ?7 ?8
+22074: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply n
+ (apply (apply b b)
+ (apply (apply n (apply (apply b b) n)) n))) n)) b)) b
+ [] by strong_fixed_point
+22074: Goal:
+22074: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+22074: Order:
+22074: nrkbo
+22074: Leaf order:
+22074: n 6 0 0
+22074: b 9 0 0
+22074: apply 26 2 3 0,2
+22074: fixed_pt 3 0 3 2,2
+22074: strong_fixed_point 3 0 2 1,2
+NO CLASH, using fixed ground order
+22075: Facts:
+22075: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+22075: Id : 3, {_}:
+ apply (apply (apply n ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?8) ?7) ?8
+ [8, 7, 6] by n_definition ?6 ?7 ?8
+22075: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply n
+ (apply (apply b b)
+ (apply (apply n (apply (apply b b) n)) n))) n)) b)) b
+ [] by strong_fixed_point
+22075: Goal:
+22075: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+22075: Order:
+22075: kbo
+22075: Leaf order:
+22075: n 6 0 0
+22075: b 9 0 0
+22075: apply 26 2 3 0,2
+22075: fixed_pt 3 0 3 2,2
+22075: strong_fixed_point 3 0 2 1,2
+NO CLASH, using fixed ground order
+22076: Facts:
+22076: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+22076: Id : 3, {_}:
+ apply (apply (apply n ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?8) ?7) ?8
+ [8, 7, 6] by n_definition ?6 ?7 ?8
+22076: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply n
+ (apply (apply b b)
+ (apply (apply n (apply (apply b b) n)) n))) n)) b)) b
+ [] by strong_fixed_point
+22076: Goal:
+22076: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+22076: Order:
+22076: lpo
+22076: Leaf order:
+22076: n 6 0 0
+22076: b 9 0 0
+22076: apply 26 2 3 0,2
+22076: fixed_pt 3 0 3 2,2
+22076: strong_fixed_point 3 0 2 1,2
+% SZS status Timeout for COL044-6.p
+NO CLASH, using fixed ground order
+22116: Facts:
+22116: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+22116: Id : 3, {_}:
+ apply (apply (apply n ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?8) ?7) ?8
+ [8, 7, 6] by n_definition ?6 ?7 ?8
+22116: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply n
+ (apply (apply b b)
+ (apply (apply n (apply n (apply b b))) n))) n)) b)) b
+ [] by strong_fixed_point
+22116: Goal:
+22116: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+22116: Order:
+22116: nrkbo
+22116: Leaf order:
+22116: n 6 0 0
+22116: b 9 0 0
+22116: apply 26 2 3 0,2
+22116: fixed_pt 3 0 3 2,2
+22116: strong_fixed_point 3 0 2 1,2
+NO CLASH, using fixed ground order
+22117: Facts:
+22117: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+22117: Id : 3, {_}:
+ apply (apply (apply n ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?8) ?7) ?8
+ [8, 7, 6] by n_definition ?6 ?7 ?8
+22117: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply n
+ (apply (apply b b)
+ (apply (apply n (apply n (apply b b))) n))) n)) b)) b
+ [] by strong_fixed_point
+22117: Goal:
+22117: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+22117: Order:
+22117: kbo
+22117: Leaf order:
+22117: n 6 0 0
+22117: b 9 0 0
+22117: apply 26 2 3 0,2
+22117: fixed_pt 3 0 3 2,2
+22117: strong_fixed_point 3 0 2 1,2
+NO CLASH, using fixed ground order
+22118: Facts:
+22118: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+22118: Id : 3, {_}:
+ apply (apply (apply n ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?8) ?7) ?8
+ [8, 7, 6] by n_definition ?6 ?7 ?8
+22118: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply n
+ (apply (apply b b)
+ (apply (apply n (apply n (apply b b))) n))) n)) b)) b
+ [] by strong_fixed_point
+22118: Goal:
+22118: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+22118: Order:
+22118: lpo
+22118: Leaf order:
+22118: n 6 0 0
+22118: b 9 0 0
+22118: apply 26 2 3 0,2
+22118: fixed_pt 3 0 3 2,2
+22118: strong_fixed_point 3 0 2 1,2
+% SZS status Timeout for COL044-7.p
+CLASH, statistics insufficient
+22135: Facts:
+22135: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+22135: Id : 3, {_}:
+ apply (apply t ?7) ?8 =>= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+22135: Goal:
+22135: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (apply (h ?1) (f ?1)) (g ?1)
+ [1] by prove_v_combinator ?1
+22135: Order:
+22135: nrkbo
+22135: Leaf order:
+22135: t 1 0 0
+22135: b 1 0 0
+22135: h 2 1 2 0,2,2
+22135: g 2 1 2 0,2,1,2
+22135: apply 13 2 5 0,2
+22135: f 2 1 2 0,2,1,1,2
+CLASH, statistics insufficient
+22136: Facts:
+22136: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+22136: Id : 3, {_}:
+ apply (apply t ?7) ?8 =>= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+22136: Goal:
+22136: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (apply (h ?1) (f ?1)) (g ?1)
+ [1] by prove_v_combinator ?1
+22136: Order:
+22136: kbo
+22136: Leaf order:
+22136: t 1 0 0
+22136: b 1 0 0
+22136: h 2 1 2 0,2,2
+22136: g 2 1 2 0,2,1,2
+22136: apply 13 2 5 0,2
+22136: f 2 1 2 0,2,1,1,2
+CLASH, statistics insufficient
+22137: Facts:
+22137: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+22137: Id : 3, {_}:
+ apply (apply t ?7) ?8 =?= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+22137: Goal:
+22137: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (apply (h ?1) (f ?1)) (g ?1)
+ [1] by prove_v_combinator ?1
+22137: Order:
+22137: lpo
+22137: Leaf order:
+22137: t 1 0 0
+22137: b 1 0 0
+22137: h 2 1 2 0,2,2
+22137: g 2 1 2 0,2,1,2
+22137: apply 13 2 5 0,2
+22137: f 2 1 2 0,2,1,1,2
+Goal subsumed
+Statistics :
+Max weight : 124
+Found proof, 35.273110s
+% SZS status Unsatisfiable for COL064-1.p
+% SZS output start CNFRefutation for COL064-1.p
+Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
+Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
+Id : 10997, {_}: apply (apply (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) === apply (apply (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) [] by Super 10996 with 3 at 2
+Id : 10996, {_}: apply (apply ?37685 (g (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t))))) (apply (h (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t))))) =>= apply (apply (h (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t)))) [37685] by Super 3193 with 2 at 2
+Id : 3193, {_}: apply (apply (apply ?10612 (apply ?10613 (g (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))))) (h (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))) =>= apply (apply (h (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))) [10613, 10612] by Super 3188 with 2 at 1,1,2
+Id : 3188, {_}: apply (apply (apply ?10602 (g (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t))))) (h (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t)))) =>= apply (apply (h (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t)))) [10602] by Super 3164 with 3 at 2
+Id : 3164, {_}: apply (apply ?10539 (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (apply (apply ?10540 (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) =>= apply (apply (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) [10540, 10539] by Super 442 with 2 at 2
+Id : 442, {_}: apply (apply (apply ?1394 (apply ?1395 (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (apply ?1396 (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) =>= apply (apply (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395))))) (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) [1396, 1395, 1394] by Super 277 with 2 at 1,1,2
+Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (apply (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) [901, 900] by Super 29 with 2 at 1,2
+Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (apply (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) [87, 86, 85] by Super 13 with 3 at 1,1,2
+Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (apply (h (apply (apply b ?33) (apply (apply b ?34) ?35))) (f (apply (apply b ?33) (apply (apply b ?34) ?35)))) (g (apply (apply b ?33) (apply (apply b ?34) ?35))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
+Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (apply (h (apply (apply b ?18) ?19)) (f (apply (apply b ?18) ?19))) (g (apply (apply b ?18) ?19)) [19, 18] by Super 1 with 2 at 1,1,2
+Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (h ?1) (f ?1)) (g ?1) [1] by prove_v_combinator ?1
+% SZS output end CNFRefutation for COL064-1.p
+22135: solved COL064-1.p in 35.146196 using nrkbo
+22135: status Unsatisfiable for COL064-1.p
+CLASH, statistics insufficient
+22153: Facts:
+22153: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+22153: Id : 3, {_}:
+ apply (apply t ?7) ?8 =>= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+22153: Goal:
+22153: Id : 1, {_}:
+ apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1)
+ =>=
+ apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1))
+ [1] by prove_g_combinator ?1
+22153: Order:
+22153: nrkbo
+22153: Leaf order:
+22153: t 1 0 0
+22153: b 1 0 0
+22153: i 2 1 2 0,2,2
+22153: h 2 1 2 0,2,1,2
+22153: g 2 1 2 0,2,1,1,2
+22153: apply 15 2 7 0,2
+22153: f 2 1 2 0,2,1,1,1,2
+CLASH, statistics insufficient
+22154: Facts:
+22154: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+22154: Id : 3, {_}:
+ apply (apply t ?7) ?8 =>= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+22154: Goal:
+22154: Id : 1, {_}:
+ apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1)
+ =>=
+ apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1))
+ [1] by prove_g_combinator ?1
+22154: Order:
+22154: kbo
+22154: Leaf order:
+22154: t 1 0 0
+22154: b 1 0 0
+22154: i 2 1 2 0,2,2
+22154: h 2 1 2 0,2,1,2
+22154: g 2 1 2 0,2,1,1,2
+22154: apply 15 2 7 0,2
+22154: f 2 1 2 0,2,1,1,1,2
+CLASH, statistics insufficient
+22155: Facts:
+22155: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+22155: Id : 3, {_}:
+ apply (apply t ?7) ?8 =?= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+22155: Goal:
+22155: Id : 1, {_}:
+ apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1)
+ =>=
+ apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1))
+ [1] by prove_g_combinator ?1
+22155: Order:
+22155: lpo
+22155: Leaf order:
+22155: t 1 0 0
+22155: b 1 0 0
+22155: i 2 1 2 0,2,2
+22155: h 2 1 2 0,2,1,2
+22155: g 2 1 2 0,2,1,1,2
+22155: apply 15 2 7 0,2
+22155: f 2 1 2 0,2,1,1,1,2
+% SZS status Timeout for COL065-1.p
+CLASH, statistics insufficient
+22171: Facts:
+22171: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22171: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22171: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22171: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22171: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22171: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22171: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22171: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22171: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22171: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22171: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22171: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22171: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22171: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22171: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22171: Id : 17, {_}:
+ greatest_lower_bound a c =>= greatest_lower_bound b c
+ [] by p12_1
+22171: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_2
+22171: Goal:
+22171: Id : 1, {_}: a =>= b [] by prove_p12
+22171: Order:
+22171: nrkbo
+22171: Leaf order:
+22171: c 4 0 0
+22171: least_upper_bound 15 2 0
+22171: greatest_lower_bound 15 2 0
+22171: inverse 1 1 0
+22171: multiply 18 2 0
+22171: identity 2 0 0
+22171: b 3 0 1 3
+22171: a 3 0 1 2
+CLASH, statistics insufficient
+22172: Facts:
+22172: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22172: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22172: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22172: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22172: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22172: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22172: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22172: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22172: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22172: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22172: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22172: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22172: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22172: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22172: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22172: Id : 17, {_}:
+ greatest_lower_bound a c =>= greatest_lower_bound b c
+ [] by p12_1
+22172: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_2
+22172: Goal:
+22172: Id : 1, {_}: a =>= b [] by prove_p12
+22172: Order:
+22172: kbo
+22172: Leaf order:
+22172: c 4 0 0
+22172: least_upper_bound 15 2 0
+22172: greatest_lower_bound 15 2 0
+22172: inverse 1 1 0
+22172: multiply 18 2 0
+22172: identity 2 0 0
+22172: b 3 0 1 3
+22172: a 3 0 1 2
+CLASH, statistics insufficient
+22173: Facts:
+22173: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22173: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22173: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22173: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22173: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22173: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22173: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22173: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22173: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22173: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22173: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22173: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22173: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22173: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22173: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22173: Id : 17, {_}:
+ greatest_lower_bound a c =>= greatest_lower_bound b c
+ [] by p12_1
+22173: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_2
+22173: Goal:
+22173: Id : 1, {_}: a =>= b [] by prove_p12
+22173: Order:
+22173: lpo
+22173: Leaf order:
+22173: c 4 0 0
+22173: least_upper_bound 15 2 0
+22173: greatest_lower_bound 15 2 0
+22173: inverse 1 1 0
+22173: multiply 18 2 0
+22173: identity 2 0 0
+22173: b 3 0 1 3
+22173: a 3 0 1 2
+% SZS status Timeout for GRP181-1.p
+CLASH, statistics insufficient
+22201: Facts:
+22201: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22201: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22201: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22201: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22201: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22201: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22201: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22201: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22201: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22201: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22201: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22201: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22201: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22201: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22201: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22201: Id : 17, {_}: inverse identity =>= identity [] by p12_1
+22201: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12_2 ?51
+22201: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p12_3 ?53 ?54
+22201: Id : 20, {_}:
+ greatest_lower_bound a c =>= greatest_lower_bound b c
+ [] by p12_4
+22201: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_5
+22201: Goal:
+22201: Id : 1, {_}: a =>= b [] by prove_p12
+22201: Order:
+22201: kbo
+22201: Leaf order:
+22201: c 4 0 0
+22201: least_upper_bound 15 2 0
+22201: greatest_lower_bound 15 2 0
+22201: inverse 7 1 0
+22201: multiply 20 2 0
+22201: identity 4 0 0
+22201: b 3 0 1 3
+22201: a 3 0 1 2
+CLASH, statistics insufficient
+22202: Facts:
+22202: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22202: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22202: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22202: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22202: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22202: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22202: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22202: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22202: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22202: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22202: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22202: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22202: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22202: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22202: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22202: Id : 17, {_}: inverse identity =>= identity [] by p12_1
+22202: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12_2 ?51
+22202: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p12_3 ?53 ?54
+22202: Id : 20, {_}:
+ greatest_lower_bound a c =>= greatest_lower_bound b c
+ [] by p12_4
+22202: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_5
+22202: Goal:
+22202: Id : 1, {_}: a =>= b [] by prove_p12
+22202: Order:
+22202: lpo
+22202: Leaf order:
+22202: c 4 0 0
+22202: least_upper_bound 15 2 0
+22202: greatest_lower_bound 15 2 0
+22202: inverse 7 1 0
+22202: multiply 20 2 0
+22202: identity 4 0 0
+22202: b 3 0 1 3
+22202: a 3 0 1 2
+CLASH, statistics insufficient
+22200: Facts:
+22200: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22200: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22200: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22200: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22200: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22200: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22200: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22200: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22200: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22200: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22200: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22200: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22200: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22200: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22200: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22200: Id : 17, {_}: inverse identity =>= identity [] by p12_1
+22200: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12_2 ?51
+22200: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p12_3 ?53 ?54
+22200: Id : 20, {_}:
+ greatest_lower_bound a c =>= greatest_lower_bound b c
+ [] by p12_4
+22200: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_5
+22200: Goal:
+22200: Id : 1, {_}: a =>= b [] by prove_p12
+22200: Order:
+22200: nrkbo
+22200: Leaf order:
+22200: c 4 0 0
+22200: least_upper_bound 15 2 0
+22200: greatest_lower_bound 15 2 0
+22200: inverse 7 1 0
+22200: multiply 20 2 0
+22200: identity 4 0 0
+22200: b 3 0 1 3
+22200: a 3 0 1 2
+% SZS status Timeout for GRP181-2.p
+NO CLASH, using fixed ground order
+22218: Facts:
+22218: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22218: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22218: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22218: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22218: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22218: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22218: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22218: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22218: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22218: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22218: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22218: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22218: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22218: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22218: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22218: Id : 17, {_}:
+ greatest_lower_bound (least_upper_bound a (inverse a))
+ (least_upper_bound b (inverse b))
+ =>=
+ identity
+ [] by p33_1
+22218: Goal:
+22218: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_p33
+22218: Order:
+22218: nrkbo
+22218: Leaf order:
+22218: least_upper_bound 15 2 0
+22218: greatest_lower_bound 14 2 0
+22218: inverse 3 1 0
+22218: identity 3 0 0
+22218: multiply 20 2 2 0,2
+22218: b 4 0 2 2,2
+22218: a 4 0 2 1,2
+NO CLASH, using fixed ground order
+22219: Facts:
+22219: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22219: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22219: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22219: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22219: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22219: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22219: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22219: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22219: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22219: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22219: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22219: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22219: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22219: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22219: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22219: Id : 17, {_}:
+ greatest_lower_bound (least_upper_bound a (inverse a))
+ (least_upper_bound b (inverse b))
+ =>=
+ identity
+ [] by p33_1
+22219: Goal:
+22219: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_p33
+22219: Order:
+22219: kbo
+22219: Leaf order:
+22219: least_upper_bound 15 2 0
+22219: greatest_lower_bound 14 2 0
+22219: inverse 3 1 0
+22219: identity 3 0 0
+22219: multiply 20 2 2 0,2
+22219: b 4 0 2 2,2
+22219: a 4 0 2 1,2
+NO CLASH, using fixed ground order
+22220: Facts:
+22220: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22220: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22220: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22220: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22220: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22220: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22220: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22220: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22220: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22220: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22220: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22220: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22220: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22220: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22220: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22220: Id : 17, {_}:
+ greatest_lower_bound (least_upper_bound a (inverse a))
+ (least_upper_bound b (inverse b))
+ =>=
+ identity
+ [] by p33_1
+22220: Goal:
+22220: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_p33
+22220: Order:
+22220: lpo
+22220: Leaf order:
+22220: least_upper_bound 15 2 0
+22220: greatest_lower_bound 14 2 0
+22220: inverse 3 1 0
+22220: identity 3 0 0
+22220: multiply 20 2 2 0,2
+22220: b 4 0 2 2,2
+22220: a 4 0 2 1,2
+% SZS status Timeout for GRP187-1.p
+NO CLASH, using fixed ground order
+22280: Facts:
+22280: Id : 2, {_}:
+ multiply
+ (inverse
+ (multiply
+ (inverse
+ (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
+ (multiply (inverse (multiply ?4 ?5))
+ (multiply ?4
+ (inverse
+ (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
+ ?7
+ =>=
+ ?6
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22280: Goal:
+22280: Id : 1, {_}:
+ multiply (inverse a1) a1 =>= multiply (inverse b1) b1
+ [] by prove_these_axioms_1
+22280: Order:
+22280: nrkbo
+22280: Leaf order:
+22280: b1 2 0 2 1,1,3
+22280: multiply 12 2 2 0,2
+22280: inverse 9 1 2 0,1,2
+22280: a1 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+22281: Facts:
+22281: Id : 2, {_}:
+ multiply
+ (inverse
+ (multiply
+ (inverse
+ (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
+ (multiply (inverse (multiply ?4 ?5))
+ (multiply ?4
+ (inverse
+ (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
+ ?7
+ =>=
+ ?6
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22281: Goal:
+22281: Id : 1, {_}:
+ multiply (inverse a1) a1 =>= multiply (inverse b1) b1
+ [] by prove_these_axioms_1
+22281: Order:
+22281: kbo
+22281: Leaf order:
+22281: b1 2 0 2 1,1,3
+22281: multiply 12 2 2 0,2
+22281: inverse 9 1 2 0,1,2
+22281: a1 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+22282: Facts:
+22282: Id : 2, {_}:
+ multiply
+ (inverse
+ (multiply
+ (inverse
+ (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
+ (multiply (inverse (multiply ?4 ?5))
+ (multiply ?4
+ (inverse
+ (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
+ ?7
+ =>=
+ ?6
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22282: Goal:
+22282: Id : 1, {_}:
+ multiply (inverse a1) a1 =>= multiply (inverse b1) b1
+ [] by prove_these_axioms_1
+22282: Order:
+22282: lpo
+22282: Leaf order:
+22282: b1 2 0 2 1,1,3
+22282: multiply 12 2 2 0,2
+22282: inverse 9 1 2 0,1,2
+22282: a1 2 0 2 1,1,2
+% SZS status Timeout for GRP505-1.p
+NO CLASH, using fixed ground order
+22298: Facts:
+22298: Id : 2, {_}:
+ multiply
+ (inverse
+ (multiply
+ (inverse
+ (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
+ (multiply (inverse (multiply ?4 ?5))
+ (multiply ?4
+ (inverse
+ (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
+ ?7
+ =>=
+ ?6
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22298: Goal:
+22298: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+22298: Order:
+22298: nrkbo
+22298: Leaf order:
+22298: inverse 7 1 0
+22298: c3 2 0 2 2,2
+22298: multiply 14 2 4 0,2
+22298: b3 2 0 2 2,1,2
+22298: a3 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+22299: Facts:
+22299: Id : 2, {_}:
+ multiply
+ (inverse
+ (multiply
+ (inverse
+ (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
+ (multiply (inverse (multiply ?4 ?5))
+ (multiply ?4
+ (inverse
+ (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
+ ?7
+ =>=
+ ?6
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22299: Goal:
+22299: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+22299: Order:
+22299: kbo
+22299: Leaf order:
+22299: inverse 7 1 0
+22299: c3 2 0 2 2,2
+22299: multiply 14 2 4 0,2
+22299: b3 2 0 2 2,1,2
+22299: a3 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+22300: Facts:
+22300: Id : 2, {_}:
+ multiply
+ (inverse
+ (multiply
+ (inverse
+ (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
+ (multiply (inverse (multiply ?4 ?5))
+ (multiply ?4
+ (inverse
+ (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
+ ?7
+ =>=
+ ?6
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22300: Goal:
+22300: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+22300: Order:
+22300: lpo
+22300: Leaf order:
+22300: inverse 7 1 0
+22300: c3 2 0 2 2,2
+22300: multiply 14 2 4 0,2
+22300: b3 2 0 2 2,1,2
+22300: a3 2 0 2 1,1,2
+% SZS status Timeout for GRP507-1.p
+NO CLASH, using fixed ground order
+22343: Facts:
+22343: Id : 2, {_}:
+ multiply
+ (inverse
+ (multiply
+ (inverse
+ (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
+ (multiply (inverse (multiply ?4 ?5))
+ (multiply ?4
+ (inverse
+ (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
+ ?7
+ =>=
+ ?6
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22343: Goal:
+22343: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_these_axioms_4
+22343: Order:
+22343: nrkbo
+22343: Leaf order:
+22343: inverse 7 1 0
+22343: multiply 12 2 2 0,2
+22343: b 2 0 2 2,2
+22343: a 2 0 2 1,2
+NO CLASH, using fixed ground order
+22344: Facts:
+22344: Id : 2, {_}:
+ multiply
+ (inverse
+ (multiply
+ (inverse
+ (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
+ (multiply (inverse (multiply ?4 ?5))
+ (multiply ?4
+ (inverse
+ (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
+ ?7
+ =>=
+ ?6
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22344: Goal:
+22344: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_these_axioms_4
+22344: Order:
+22344: kbo
+22344: Leaf order:
+22344: inverse 7 1 0
+22344: multiply 12 2 2 0,2
+22344: b 2 0 2 2,2
+22344: a 2 0 2 1,2
+NO CLASH, using fixed ground order
+22345: Facts:
+22345: Id : 2, {_}:
+ multiply
+ (inverse
+ (multiply
+ (inverse
+ (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
+ (multiply (inverse (multiply ?4 ?5))
+ (multiply ?4
+ (inverse
+ (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
+ ?7
+ =>=
+ ?6
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22345: Goal:
+22345: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_these_axioms_4
+22345: Order:
+22345: lpo
+22345: Leaf order:
+22345: inverse 7 1 0
+22345: multiply 12 2 2 0,2
+22345: b 2 0 2 2,2
+22345: a 2 0 2 1,2
+% SZS status Timeout for GRP508-1.p
+NO CLASH, using fixed ground order
+22381: Facts:
+22381: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+22381: Goal:
+22381: Id : 1, {_}: meet a a =>= a [] by prove_normal_axioms_1
+22381: Order:
+22381: nrkbo
+22381: Leaf order:
+22381: join 20 2 0
+22381: meet 19 2 1 0,2
+22381: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+22382: Facts:
+22382: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+22382: Goal:
+22382: Id : 1, {_}: meet a a =>= a [] by prove_normal_axioms_1
+22382: Order:
+22382: kbo
+22382: Leaf order:
+22382: join 20 2 0
+22382: meet 19 2 1 0,2
+22382: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+22383: Facts:
+22383: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+22383: Goal:
+22383: Id : 1, {_}: meet a a =>= a [] by prove_normal_axioms_1
+22383: Order:
+22383: lpo
+22383: Leaf order:
+22383: join 20 2 0
+22383: meet 19 2 1 0,2
+22383: a 3 0 3 1,2
+% SZS status Timeout for LAT080-1.p
+NO CLASH, using fixed ground order
+22413: Facts:
+22413: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+22413: Goal:
+22413: Id : 1, {_}: join a a =>= a [] by prove_normal_axioms_4
+22413: Order:
+22413: nrkbo
+22413: Leaf order:
+22413: meet 18 2 0
+22413: join 21 2 1 0,2
+22413: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+22414: Facts:
+22414: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+22414: Goal:
+22414: Id : 1, {_}: join a a =>= a [] by prove_normal_axioms_4
+22414: Order:
+22414: kbo
+22414: Leaf order:
+22414: meet 18 2 0
+22414: join 21 2 1 0,2
+22414: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+22415: Facts:
+22415: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+22415: Goal:
+22415: Id : 1, {_}: join a a =>= a [] by prove_normal_axioms_4
+22415: Order:
+22415: lpo
+22415: Leaf order:
+22415: meet 18 2 0
+22415: join 21 2 1 0,2
+22415: a 3 0 3 1,2
+% SZS status Timeout for LAT083-1.p
+NO CLASH, using fixed ground order
+22432: Facts:
+22432: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22432: Goal:
+22432: Id : 1, {_}: meet a a =>= a [] by prove_wal_axioms_1
+22432: Order:
+22432: nrkbo
+22432: Leaf order:
+22432: join 18 2 0
+22432: meet 19 2 1 0,2
+22432: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+22434: Facts:
+22434: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22434: Goal:
+22434: Id : 1, {_}: meet a a =>= a [] by prove_wal_axioms_1
+22434: Order:
+22434: lpo
+22434: Leaf order:
+22434: join 18 2 0
+22434: meet 19 2 1 0,2
+22434: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+22433: Facts:
+22433: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22433: Goal:
+22433: Id : 1, {_}: meet a a =>= a [] by prove_wal_axioms_1
+22433: Order:
+22433: kbo
+22433: Leaf order:
+22433: join 18 2 0
+22433: meet 19 2 1 0,2
+22433: a 3 0 3 1,2
+% SZS status Timeout for LAT092-1.p
+NO CLASH, using fixed ground order
+22466: Facts:
+22466: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22466: Goal:
+22466: Id : 1, {_}: meet b a =>= meet a b [] by prove_wal_axioms_2
+22466: Order:
+22466: nrkbo
+22466: Leaf order:
+22466: join 18 2 0
+22466: meet 20 2 2 0,2
+22466: a 2 0 2 2,2
+22466: b 2 0 2 1,2
+NO CLASH, using fixed ground order
+22467: Facts:
+22467: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22467: Goal:
+22467: Id : 1, {_}: meet b a =>= meet a b [] by prove_wal_axioms_2
+22467: Order:
+22467: kbo
+22467: Leaf order:
+22467: join 18 2 0
+22467: meet 20 2 2 0,2
+22467: a 2 0 2 2,2
+22467: b 2 0 2 1,2
+NO CLASH, using fixed ground order
+22468: Facts:
+22468: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22468: Goal:
+22468: Id : 1, {_}: meet b a =>= meet a b [] by prove_wal_axioms_2
+22468: Order:
+22468: lpo
+22468: Leaf order:
+22468: join 18 2 0
+22468: meet 20 2 2 0,2
+22468: a 2 0 2 2,2
+22468: b 2 0 2 1,2
+% SZS status Timeout for LAT093-1.p
+NO CLASH, using fixed ground order
+22493: Facts:
+22493: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22493: Goal:
+22493: Id : 1, {_}: join a a =>= a [] by prove_wal_axioms_3
+22493: Order:
+22493: nrkbo
+22493: Leaf order:
+22493: meet 18 2 0
+22493: join 19 2 1 0,2
+22493: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+22494: Facts:
+22494: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22494: Goal:
+22494: Id : 1, {_}: join a a =>= a [] by prove_wal_axioms_3
+22494: Order:
+22494: kbo
+22494: Leaf order:
+22494: meet 18 2 0
+22494: join 19 2 1 0,2
+22494: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+22495: Facts:
+22495: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22495: Goal:
+22495: Id : 1, {_}: join a a =>= a [] by prove_wal_axioms_3
+22495: Order:
+22495: lpo
+22495: Leaf order:
+22495: meet 18 2 0
+22495: join 19 2 1 0,2
+22495: a 3 0 3 1,2
+% SZS status Timeout for LAT094-1.p
+NO CLASH, using fixed ground order
+22522: Facts:
+22522: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22522: Goal:
+22522: Id : 1, {_}: join b a =>= join a b [] by prove_wal_axioms_4
+22522: Order:
+22522: nrkbo
+22522: Leaf order:
+22522: meet 18 2 0
+22522: join 20 2 2 0,2
+22522: a 2 0 2 2,2
+22522: b 2 0 2 1,2
+NO CLASH, using fixed ground order
+22523: Facts:
+22523: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22523: Goal:
+22523: Id : 1, {_}: join b a =>= join a b [] by prove_wal_axioms_4
+22523: Order:
+22523: kbo
+22523: Leaf order:
+22523: meet 18 2 0
+22523: join 20 2 2 0,2
+22523: a 2 0 2 2,2
+22523: b 2 0 2 1,2
+NO CLASH, using fixed ground order
+22524: Facts:
+22524: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22524: Goal:
+22524: Id : 1, {_}: join b a =>= join a b [] by prove_wal_axioms_4
+22524: Order:
+22524: lpo
+22524: Leaf order:
+22524: meet 18 2 0
+22524: join 20 2 2 0,2
+22524: a 2 0 2 2,2
+22524: b 2 0 2 1,2
+% SZS status Timeout for LAT095-1.p
+NO CLASH, using fixed ground order
+22540: Facts:
+22540: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22540: Goal:
+22540: Id : 1, {_}:
+ meet (meet (join a b) (join c b)) b =>= b
+ [] by prove_wal_axioms_5
+22540: Order:
+22540: nrkbo
+22540: Leaf order:
+22540: meet 20 2 2 0,2
+22540: c 1 0 1 1,2,1,2
+22540: join 20 2 2 0,1,1,2
+22540: b 4 0 4 2,1,1,2
+22540: a 1 0 1 1,1,1,2
+NO CLASH, using fixed ground order
+22541: Facts:
+22541: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22541: Goal:
+22541: Id : 1, {_}:
+ meet (meet (join a b) (join c b)) b =>= b
+ [] by prove_wal_axioms_5
+22541: Order:
+22541: kbo
+22541: Leaf order:
+22541: meet 20 2 2 0,2
+22541: c 1 0 1 1,2,1,2
+22541: join 20 2 2 0,1,1,2
+22541: b 4 0 4 2,1,1,2
+22541: a 1 0 1 1,1,1,2
+NO CLASH, using fixed ground order
+22542: Facts:
+22542: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22542: Goal:
+22542: Id : 1, {_}:
+ meet (meet (join a b) (join c b)) b =>= b
+ [] by prove_wal_axioms_5
+22542: Order:
+22542: lpo
+22542: Leaf order:
+22542: meet 20 2 2 0,2
+22542: c 1 0 1 1,2,1,2
+22542: join 20 2 2 0,1,1,2
+22542: b 4 0 4 2,1,1,2
+22542: a 1 0 1 1,1,1,2
+% SZS status Timeout for LAT096-1.p
+NO CLASH, using fixed ground order
+22569: Facts:
+22569: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22569: Goal:
+22569: Id : 1, {_}:
+ join (join (meet a b) (meet c b)) b =>= b
+ [] by prove_wal_axioms_6
+22569: Order:
+22569: nrkbo
+22569: Leaf order:
+22569: join 20 2 2 0,2
+22569: c 1 0 1 1,2,1,2
+22569: meet 20 2 2 0,1,1,2
+22569: b 4 0 4 2,1,1,2
+22569: a 1 0 1 1,1,1,2
+NO CLASH, using fixed ground order
+22570: Facts:
+22570: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22570: Goal:
+22570: Id : 1, {_}:
+ join (join (meet a b) (meet c b)) b =>= b
+ [] by prove_wal_axioms_6
+22570: Order:
+22570: kbo
+22570: Leaf order:
+22570: join 20 2 2 0,2
+22570: c 1 0 1 1,2,1,2
+22570: meet 20 2 2 0,1,1,2
+22570: b 4 0 4 2,1,1,2
+22570: a 1 0 1 1,1,1,2
+NO CLASH, using fixed ground order
+22571: Facts:
+22571: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+22571: Goal:
+22571: Id : 1, {_}:
+ join (join (meet a b) (meet c b)) b =>= b
+ [] by prove_wal_axioms_6
+22571: Order:
+22571: lpo
+22571: Leaf order:
+22571: join 20 2 2 0,2
+22571: c 1 0 1 1,2,1,2
+22571: meet 20 2 2 0,1,1,2
+22571: b 4 0 4 2,1,1,2
+22571: a 1 0 1 1,1,1,2
+% SZS status Timeout for LAT097-1.p
+NO CLASH, using fixed ground order
+22740: Facts:
+22740: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+22740: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+22740: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+22740: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+22740: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+22740: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+22740: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+22740: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+22740: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 ?29))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
+22740: Goal:
+22740: Id : 1, {_}:
+ meet a (join b (meet a (meet c d)))
+ =<=
+ meet a (join b (meet c (meet d (join a (meet b d)))))
+ [] by prove_H28
+22740: Order:
+22740: nrkbo
+22740: Leaf order:
+22740: join 16 2 3 0,2,2
+22740: meet 21 2 7 0,2
+22740: d 3 0 3 2,2,2,2,2
+22740: c 2 0 2 1,2,2,2,2
+22740: b 3 0 3 1,2,2
+22740: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+22742: Facts:
+22742: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+22742: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+22742: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+22742: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+22742: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+22742: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+22742: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+22742: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+22742: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 ?29))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
+22742: Goal:
+22742: Id : 1, {_}:
+ meet a (join b (meet a (meet c d)))
+ =>=
+ meet a (join b (meet c (meet d (join a (meet b d)))))
+ [] by prove_H28
+22742: Order:
+22742: lpo
+22742: Leaf order:
+22742: join 16 2 3 0,2,2
+22742: meet 21 2 7 0,2
+22742: d 3 0 3 2,2,2,2,2
+22742: c 2 0 2 1,2,2,2,2
+22742: b 3 0 3 1,2,2
+22742: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+22741: Facts:
+22741: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+22741: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+22741: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+22741: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+22741: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+22741: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+22741: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+22741: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+22741: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 ?29))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
+22741: Goal:
+22741: Id : 1, {_}:
+ meet a (join b (meet a (meet c d)))
+ =<=
+ meet a (join b (meet c (meet d (join a (meet b d)))))
+ [] by prove_H28
+22741: Order:
+22741: kbo
+22741: Leaf order:
+22741: join 16 2 3 0,2,2
+22741: meet 21 2 7 0,2
+22741: d 3 0 3 2,2,2,2,2
+22741: c 2 0 2 1,2,2,2,2
+22741: b 3 0 3 1,2,2
+22741: a 4 0 4 1,2
+% SZS status Timeout for LAT146-1.p
+NO CLASH, using fixed ground order
+22773: Facts:
+22773: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+22773: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+22773: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+22773: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+22773: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+22773: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+22773: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+22773: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+22773: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 ?29))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
+22773: Goal:
+22773: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
+ [] by prove_H7
+22773: Order:
+22773: nrkbo
+22773: Leaf order:
+22773: join 17 2 4 0,2,2
+22773: meet 20 2 6 0,2
+22773: c 2 0 2 2,2,2,2
+22773: b 4 0 4 1,2,2
+22773: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+22774: Facts:
+22774: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+22774: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+22774: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+22774: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+22774: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+22774: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+22774: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+22774: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+22774: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 ?29))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
+22774: Goal:
+22774: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
+ [] by prove_H7
+22774: Order:
+22774: kbo
+22774: Leaf order:
+22774: join 17 2 4 0,2,2
+22774: meet 20 2 6 0,2
+22774: c 2 0 2 2,2,2,2
+22774: b 4 0 4 1,2,2
+22774: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+22775: Facts:
+22775: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+22775: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+22775: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+22775: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+22775: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+22775: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+22775: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+22775: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+22775: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 ?29))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
+22775: Goal:
+22775: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
+ [] by prove_H7
+22775: Order:
+22775: lpo
+22775: Leaf order:
+22775: join 17 2 4 0,2,2
+22775: meet 20 2 6 0,2
+22775: c 2 0 2 2,2,2,2
+22775: b 4 0 4 1,2,2
+22775: a 6 0 6 1,2
+% SZS status Timeout for LAT148-1.p
+NO CLASH, using fixed ground order
+22791: Facts:
+22791: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+22791: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+22791: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+22791: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+22791: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+22791: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+22791: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+22791: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+22791: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
+ [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
+22791: Goal:
+22791: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+22791: Order:
+22791: nrkbo
+22791: Leaf order:
+22791: join 18 2 4 0,2,2
+22791: meet 20 2 6 0,2
+22791: c 3 0 3 2,2,2,2
+22791: b 3 0 3 1,2,2
+22791: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+22792: Facts:
+22792: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+22792: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+22792: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+22792: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+22792: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+22792: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+22792: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+22792: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+22792: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
+ [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
+22792: Goal:
+22792: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+22792: Order:
+22792: kbo
+22792: Leaf order:
+22792: join 18 2 4 0,2,2
+22792: meet 20 2 6 0,2
+22792: c 3 0 3 2,2,2,2
+22792: b 3 0 3 1,2,2
+22792: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+22793: Facts:
+22793: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+22793: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+22793: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+22793: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+22793: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+22793: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+22793: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+22793: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+22793: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =?=
+ meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
+ [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
+22793: Goal:
+22793: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+22793: Order:
+22793: lpo
+22793: Leaf order:
+22793: join 18 2 4 0,2,2
+22793: meet 20 2 6 0,2
+22793: c 3 0 3 2,2,2,2
+22793: b 3 0 3 1,2,2
+22793: a 6 0 6 1,2
+% SZS status Timeout for LAT156-1.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+22830: Facts:
+22830: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+22830: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+22830: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+22830: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+22830: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+22830: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+22830: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+22830: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+22830: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (join (meet ?28 ?29) (meet ?28 (join ?26 ?27))))
+ [29, 28, 27, 26] by equation_H52 ?26 ?27 ?28 ?29
+22830: Goal:
+22830: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (join (meet a c) (meet c d)))
+ [] by prove_H51
+22830: Order:
+22830: kbo
+22830: Leaf order:
+22830: meet 19 2 5 0,2
+22830: join 18 2 4 0,2,2
+22830: d 2 0 2 2,2,2,2,2
+22830: c 3 0 3 1,2,2,2
+22830: b 2 0 2 1,2,2
+22830: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+22831: Facts:
+22831: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+22831: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+22831: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+22831: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+22831: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+22831: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+22831: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+22831: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+22831: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =?=
+ meet ?26 (join ?27 (join (meet ?28 ?29) (meet ?28 (join ?26 ?27))))
+ [29, 28, 27, 26] by equation_H52 ?26 ?27 ?28 ?29
+22831: Goal:
+22831: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (join (meet a c) (meet c d)))
+ [] by prove_H51
+22831: Order:
+22831: lpo
+22831: Leaf order:
+22831: meet 19 2 5 0,2
+22831: join 18 2 4 0,2,2
+22831: d 2 0 2 2,2,2,2,2
+22831: c 3 0 3 1,2,2,2
+22831: b 2 0 2 1,2,2
+22831: a 4 0 4 1,2
+22829: Facts:
+22829: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+22829: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+22829: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+22829: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+22829: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+22829: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+22829: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+22829: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+22829: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (join (meet ?28 ?29) (meet ?28 (join ?26 ?27))))
+ [29, 28, 27, 26] by equation_H52 ?26 ?27 ?28 ?29
+22829: Goal:
+22829: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (join (meet a c) (meet c d)))
+ [] by prove_H51
+22829: Order:
+22829: nrkbo
+22829: Leaf order:
+22829: meet 19 2 5 0,2
+22829: join 18 2 4 0,2,2
+22829: d 2 0 2 2,2,2,2,2
+22829: c 3 0 3 1,2,2,2
+22829: b 2 0 2 1,2,2
+22829: a 4 0 4 1,2
+% SZS status Timeout for LAT160-1.p
+NO CLASH, using fixed ground order
+22849: Facts:
+22849: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+22849: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+22849: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+22849: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+22849: Id : 6, {_}:
+ or ?14 ?15 =<= implies (not ?14) ?15
+ [15, 14] by or_definition ?14 ?15
+22849: Id : 7, {_}:
+ or (or ?17 ?18) ?19 =?= or ?17 (or ?18 ?19)
+ [19, 18, 17] by or_associativity ?17 ?18 ?19
+22849: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
+22849: Id : 9, {_}:
+ and ?24 ?25 =<= not (or (not ?24) (not ?25))
+ [25, 24] by and_definition ?24 ?25
+22849: Id : 10, {_}:
+ and (and ?27 ?28) ?29 =?= and ?27 (and ?28 ?29)
+ [29, 28, 27] by and_associativity ?27 ?28 ?29
+22849: Id : 11, {_}:
+ and ?31 ?32 =?= and ?32 ?31
+ [32, 31] by and_commutativity ?31 ?32
+22849: Id : 12, {_}:
+ xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
+ [35, 34] by xor_definition ?34 ?35
+22849: Id : 13, {_}:
+ xor ?37 ?38 =?= xor ?38 ?37
+ [38, 37] by xor_commutativity ?37 ?38
+22849: Id : 14, {_}:
+ and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
+ [41, 40] by and_star_definition ?40 ?41
+22849: Id : 15, {_}:
+ and_star (and_star ?43 ?44) ?45 =?= and_star ?43 (and_star ?44 ?45)
+ [45, 44, 43] by and_star_associativity ?43 ?44 ?45
+22849: Id : 16, {_}:
+ and_star ?47 ?48 =?= and_star ?48 ?47
+ [48, 47] by and_star_commutativity ?47 ?48
+22849: Id : 17, {_}: not truth =>= falsehood [] by false_definition
+22849: Goal:
+22849: Id : 1, {_}:
+ and_star (xor (and_star (xor truth x) y) truth) y
+ =>=
+ and_star (xor (and_star (xor truth y) x) truth) x
+ [] by prove_alternative_wajsberg_axiom
+22849: Order:
+22849: nrkbo
+22849: Leaf order:
+22849: falsehood 1 0 0
+22849: and 9 2 0
+22849: or 10 2 0
+22849: not 12 1 0
+22849: implies 14 2 0
+22849: and_star 11 2 4 0,2
+22849: y 3 0 3 2,1,1,2
+22849: xor 7 2 4 0,1,2
+22849: x 3 0 3 2,1,1,1,2
+22849: truth 8 0 4 1,1,1,1,2
+NO CLASH, using fixed ground order
+22850: Facts:
+22850: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+22850: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+22850: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+22850: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+22850: Id : 6, {_}:
+ or ?14 ?15 =<= implies (not ?14) ?15
+ [15, 14] by or_definition ?14 ?15
+22850: Id : 7, {_}:
+ or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
+ [19, 18, 17] by or_associativity ?17 ?18 ?19
+22850: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
+22850: Id : 9, {_}:
+ and ?24 ?25 =<= not (or (not ?24) (not ?25))
+ [25, 24] by and_definition ?24 ?25
+22850: Id : 10, {_}:
+ and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
+ [29, 28, 27] by and_associativity ?27 ?28 ?29
+22850: Id : 11, {_}:
+ and ?31 ?32 =?= and ?32 ?31
+ [32, 31] by and_commutativity ?31 ?32
+22850: Id : 12, {_}:
+ xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
+ [35, 34] by xor_definition ?34 ?35
+22850: Id : 13, {_}:
+ xor ?37 ?38 =?= xor ?38 ?37
+ [38, 37] by xor_commutativity ?37 ?38
+22850: Id : 14, {_}:
+ and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
+ [41, 40] by and_star_definition ?40 ?41
+22850: Id : 15, {_}:
+ and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45)
+ [45, 44, 43] by and_star_associativity ?43 ?44 ?45
+22850: Id : 16, {_}:
+ and_star ?47 ?48 =?= and_star ?48 ?47
+ [48, 47] by and_star_commutativity ?47 ?48
+22850: Id : 17, {_}: not truth =>= falsehood [] by false_definition
+22850: Goal:
+22850: Id : 1, {_}:
+ and_star (xor (and_star (xor truth x) y) truth) y
+ =?=
+ and_star (xor (and_star (xor truth y) x) truth) x
+ [] by prove_alternative_wajsberg_axiom
+22850: Order:
+22850: kbo
+22850: Leaf order:
+22850: falsehood 1 0 0
+22850: and 9 2 0
+22850: or 10 2 0
+22850: not 12 1 0
+22850: implies 14 2 0
+22850: and_star 11 2 4 0,2
+22850: y 3 0 3 2,1,1,2
+22850: xor 7 2 4 0,1,2
+22850: x 3 0 3 2,1,1,1,2
+22850: truth 8 0 4 1,1,1,1,2
+NO CLASH, using fixed ground order
+22851: Facts:
+22851: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+22851: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+22851: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+22851: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+22851: Id : 6, {_}:
+ or ?14 ?15 =<= implies (not ?14) ?15
+ [15, 14] by or_definition ?14 ?15
+22851: Id : 7, {_}:
+ or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
+ [19, 18, 17] by or_associativity ?17 ?18 ?19
+22851: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
+22851: Id : 9, {_}:
+ and ?24 ?25 =<= not (or (not ?24) (not ?25))
+ [25, 24] by and_definition ?24 ?25
+22851: Id : 10, {_}:
+ and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
+ [29, 28, 27] by and_associativity ?27 ?28 ?29
+22851: Id : 11, {_}:
+ and ?31 ?32 =?= and ?32 ?31
+ [32, 31] by and_commutativity ?31 ?32
+22851: Id : 12, {_}:
+ xor ?34 ?35 =>= or (and ?34 (not ?35)) (and (not ?34) ?35)
+ [35, 34] by xor_definition ?34 ?35
+22851: Id : 13, {_}:
+ xor ?37 ?38 =?= xor ?38 ?37
+ [38, 37] by xor_commutativity ?37 ?38
+22851: Id : 14, {_}:
+ and_star ?40 ?41 =>= not (or (not ?40) (not ?41))
+ [41, 40] by and_star_definition ?40 ?41
+22851: Id : 15, {_}:
+ and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45)
+ [45, 44, 43] by and_star_associativity ?43 ?44 ?45
+22851: Id : 16, {_}:
+ and_star ?47 ?48 =?= and_star ?48 ?47
+ [48, 47] by and_star_commutativity ?47 ?48
+22851: Id : 17, {_}: not truth =>= falsehood [] by false_definition
+22851: Goal:
+22851: Id : 1, {_}:
+ and_star (xor (and_star (xor truth x) y) truth) y
+ =>=
+ and_star (xor (and_star (xor truth y) x) truth) x
+ [] by prove_alternative_wajsberg_axiom
+22851: Order:
+22851: lpo
+22851: Leaf order:
+22851: falsehood 1 0 0
+22851: and 9 2 0
+22851: or 10 2 0
+22851: not 12 1 0
+22851: implies 14 2 0
+22851: and_star 11 2 4 0,2
+22851: y 3 0 3 2,1,1,2
+22851: xor 7 2 4 0,1,2
+22851: x 3 0 3 2,1,1,1,2
+22851: truth 8 0 4 1,1,1,1,2
+% SZS status Timeout for LCL160-1.p
+NO CLASH, using fixed ground order
+22879: Facts:
+22879: Id : 2, {_}: add ?2 additive_identity =>= ?2 [2] by right_identity ?2
+22879: Id : 3, {_}:
+ add ?4 (additive_inverse ?4) =>= additive_identity
+ [4] by right_additive_inverse ?4
+22879: Id : 4, {_}:
+ multiply ?6 (add ?7 ?8) =<= add (multiply ?6 ?7) (multiply ?6 ?8)
+ [8, 7, 6] by distribute1 ?6 ?7 ?8
+22879: Id : 5, {_}:
+ multiply (add ?10 ?11) ?12
+ =<=
+ add (multiply ?10 ?12) (multiply ?11 ?12)
+ [12, 11, 10] by distribute2 ?10 ?11 ?12
+22879: Id : 6, {_}:
+ add (add ?14 ?15) ?16 =?= add ?14 (add ?15 ?16)
+ [16, 15, 14] by associative_addition ?14 ?15 ?16
+22879: Id : 7, {_}:
+ add ?18 ?19 =?= add ?19 ?18
+ [19, 18] by commutative_addition ?18 ?19
+22879: Id : 8, {_}:
+ multiply (multiply ?21 ?22) ?23 =?= multiply ?21 (multiply ?22 ?23)
+ [23, 22, 21] by associative_multiplication ?21 ?22 ?23
+22879: Id : 9, {_}: multiply ?25 (multiply ?25 ?25) =>= ?25 [25] by x_cubed_is_x ?25
+22879: Goal:
+22879: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_commutativity
+22879: Order:
+22879: nrkbo
+22879: Leaf order:
+22879: additive_inverse 1 1 0
+22879: add 12 2 0
+22879: additive_identity 2 0 0
+22879: multiply 14 2 2 0,2
+22879: b 2 0 2 2,2
+22879: a 2 0 2 1,2
+NO CLASH, using fixed ground order
+22880: Facts:
+22880: Id : 2, {_}: add ?2 additive_identity =>= ?2 [2] by right_identity ?2
+22880: Id : 3, {_}:
+ add ?4 (additive_inverse ?4) =>= additive_identity
+ [4] by right_additive_inverse ?4
+22880: Id : 4, {_}:
+ multiply ?6 (add ?7 ?8) =<= add (multiply ?6 ?7) (multiply ?6 ?8)
+ [8, 7, 6] by distribute1 ?6 ?7 ?8
+22880: Id : 5, {_}:
+ multiply (add ?10 ?11) ?12
+ =<=
+ add (multiply ?10 ?12) (multiply ?11 ?12)
+ [12, 11, 10] by distribute2 ?10 ?11 ?12
+22880: Id : 6, {_}:
+ add (add ?14 ?15) ?16 =>= add ?14 (add ?15 ?16)
+ [16, 15, 14] by associative_addition ?14 ?15 ?16
+22880: Id : 7, {_}:
+ add ?18 ?19 =?= add ?19 ?18
+ [19, 18] by commutative_addition ?18 ?19
+22880: Id : 8, {_}:
+ multiply (multiply ?21 ?22) ?23 =>= multiply ?21 (multiply ?22 ?23)
+ [23, 22, 21] by associative_multiplication ?21 ?22 ?23
+22880: Id : 9, {_}: multiply ?25 (multiply ?25 ?25) =>= ?25 [25] by x_cubed_is_x ?25
+22880: Goal:
+22880: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_commutativity
+22880: Order:
+22880: kbo
+22880: Leaf order:
+22880: additive_inverse 1 1 0
+22880: add 12 2 0
+22880: additive_identity 2 0 0
+22880: multiply 14 2 2 0,2
+22880: b 2 0 2 2,2
+22880: a 2 0 2 1,2
+NO CLASH, using fixed ground order
+22881: Facts:
+22881: Id : 2, {_}: add ?2 additive_identity =>= ?2 [2] by right_identity ?2
+22881: Id : 3, {_}:
+ add ?4 (additive_inverse ?4) =>= additive_identity
+ [4] by right_additive_inverse ?4
+22881: Id : 4, {_}:
+ multiply ?6 (add ?7 ?8) =>= add (multiply ?6 ?7) (multiply ?6 ?8)
+ [8, 7, 6] by distribute1 ?6 ?7 ?8
+22881: Id : 5, {_}:
+ multiply (add ?10 ?11) ?12
+ =>=
+ add (multiply ?10 ?12) (multiply ?11 ?12)
+ [12, 11, 10] by distribute2 ?10 ?11 ?12
+22881: Id : 6, {_}:
+ add (add ?14 ?15) ?16 =>= add ?14 (add ?15 ?16)
+ [16, 15, 14] by associative_addition ?14 ?15 ?16
+22881: Id : 7, {_}:
+ add ?18 ?19 =?= add ?19 ?18
+ [19, 18] by commutative_addition ?18 ?19
+22881: Id : 8, {_}:
+ multiply (multiply ?21 ?22) ?23 =>= multiply ?21 (multiply ?22 ?23)
+ [23, 22, 21] by associative_multiplication ?21 ?22 ?23
+22881: Id : 9, {_}: multiply ?25 (multiply ?25 ?25) =>= ?25 [25] by x_cubed_is_x ?25
+22881: Goal:
+22881: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_commutativity
+22881: Order:
+22881: lpo
+22881: Leaf order:
+22881: additive_inverse 1 1 0
+22881: add 12 2 0
+22881: additive_identity 2 0 0
+22881: multiply 14 2 2 0,2
+22881: b 2 0 2 2,2
+22881: a 2 0 2 1,2
+% SZS status Timeout for RNG009-5.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+22919: Facts:
+22919: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+22919: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+22919: Id : 4, {_}:
+ add (additive_inverse ?6) ?6 =>= additive_identity
+ [6] by left_additive_inverse ?6
+22919: Id : 5, {_}:
+ add ?8 (additive_inverse ?8) =>= additive_identity
+ [8] by right_additive_inverse ?8
+22919: Id : 6, {_}:
+ add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
+ [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
+22919: Id : 7, {_}:
+ add ?14 ?15 =?= add ?15 ?14
+ [15, 14] by commutativity_for_addition ?14 ?15
+22919: Id : 8, {_}:
+ multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
+ [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
+22919: Id : 9, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+22919: Id : 10, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+22919: Id : 11, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29
+22919: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
+22919: Goal:
+22919: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
+22919: Order:
+22919: kbo
+22919: Leaf order:
+22919: additive_inverse 2 1 0
+22919: add 14 2 0
+22919: additive_identity 4 0 0
+22919: c 2 0 1 3
+22919: multiply 14 2 1 0,2
+22919: a 2 0 1 2,2
+22919: b 2 0 1 1,2
+22918: Facts:
+22918: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+22918: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+22918: Id : 4, {_}:
+ add (additive_inverse ?6) ?6 =>= additive_identity
+ [6] by left_additive_inverse ?6
+22918: Id : 5, {_}:
+ add ?8 (additive_inverse ?8) =>= additive_identity
+ [8] by right_additive_inverse ?8
+22918: Id : 6, {_}:
+ add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12
+ [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
+22918: Id : 7, {_}:
+ add ?14 ?15 =?= add ?15 ?14
+ [15, 14] by commutativity_for_addition ?14 ?15
+22918: Id : 8, {_}:
+ multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19
+ [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
+22918: Id : 9, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+22918: Id : 10, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+22918: Id : 11, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29
+22918: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
+22918: Goal:
+22918: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
+22918: Order:
+22918: nrkbo
+22918: Leaf order:
+22918: additive_inverse 2 1 0
+22918: add 14 2 0
+22918: additive_identity 4 0 0
+22918: c 2 0 1 3
+22918: multiply 14 2 1 0,2
+22918: a 2 0 1 2,2
+22918: b 2 0 1 1,2
+NO CLASH, using fixed ground order
+22920: Facts:
+22920: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+22920: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+22920: Id : 4, {_}:
+ add (additive_inverse ?6) ?6 =>= additive_identity
+ [6] by left_additive_inverse ?6
+22920: Id : 5, {_}:
+ add ?8 (additive_inverse ?8) =>= additive_identity
+ [8] by right_additive_inverse ?8
+22920: Id : 6, {_}:
+ add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
+ [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
+22920: Id : 7, {_}:
+ add ?14 ?15 =?= add ?15 ?14
+ [15, 14] by commutativity_for_addition ?14 ?15
+22920: Id : 8, {_}:
+ multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
+ [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
+22920: Id : 9, {_}:
+ multiply ?21 (add ?22 ?23)
+ =>=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+22920: Id : 10, {_}:
+ multiply (add ?25 ?26) ?27
+ =>=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+22920: Id : 11, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29
+22920: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
+22920: Goal:
+22920: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
+22920: Order:
+22920: lpo
+22920: Leaf order:
+22920: additive_inverse 2 1 0
+22920: add 14 2 0
+22920: additive_identity 4 0 0
+22920: c 2 0 1 3
+22920: multiply 14 2 1 0,2
+22920: a 2 0 1 2,2
+22920: b 2 0 1 1,2
+% SZS status Timeout for RNG009-7.p
+NO CLASH, using fixed ground order
+22947: Facts:
+22947: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+22947: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+22947: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+22947: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+22947: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+22947: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+22947: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+22947: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+22947: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+22947: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+22947: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+22947: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+22947: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+22947: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+22947: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+22947: Goal:
+22947: Id : 1, {_}:
+ add
+ (add (associator (multiply a b) c d)
+ (associator a b (multiply c d)))
+ (additive_inverse
+ (add
+ (add (associator a (multiply b c) d)
+ (multiply a (associator b c d)))
+ (multiply (associator a b c) d)))
+ =>=
+ additive_identity
+ [] by prove_teichmuller_identity
+22947: Order:
+22947: nrkbo
+22947: Leaf order:
+22947: commutator 1 2 0
+22947: additive_identity 9 0 1 3
+22947: additive_inverse 7 1 1 0,2,2
+22947: add 20 2 4 0,2
+22947: associator 6 3 5 0,1,1,2
+22947: d 5 0 5 3,1,1,2
+22947: c 5 0 5 2,1,1,2
+22947: multiply 27 2 5 0,1,1,1,2
+22947: b 5 0 5 2,1,1,1,2
+22947: a 5 0 5 1,1,1,1,2
+NO CLASH, using fixed ground order
+22948: Facts:
+22948: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+22948: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+22948: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+22948: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+22948: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+22948: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+22948: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+22948: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+22948: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+22948: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+22948: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+22948: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+22948: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+22948: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+22948: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+22948: Goal:
+22948: Id : 1, {_}:
+ add
+ (add (associator (multiply a b) c d)
+ (associator a b (multiply c d)))
+ (additive_inverse
+ (add
+ (add (associator a (multiply b c) d)
+ (multiply a (associator b c d)))
+ (multiply (associator a b c) d)))
+ =>=
+ additive_identity
+ [] by prove_teichmuller_identity
+22948: Order:
+22948: kbo
+22948: Leaf order:
+22948: commutator 1 2 0
+22948: additive_identity 9 0 1 3
+22948: additive_inverse 7 1 1 0,2,2
+22948: add 20 2 4 0,2
+22948: associator 6 3 5 0,1,1,2
+22948: d 5 0 5 3,1,1,2
+22948: c 5 0 5 2,1,1,2
+22948: multiply 27 2 5 0,1,1,1,2
+22948: b 5 0 5 2,1,1,1,2
+22948: a 5 0 5 1,1,1,1,2
+NO CLASH, using fixed ground order
+22949: Facts:
+22949: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+22949: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+22949: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+22949: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+22949: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+22949: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+22949: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+22949: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+22949: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+22949: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+22949: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+22949: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+22949: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+22949: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+22949: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+22949: Goal:
+22949: Id : 1, {_}:
+ add
+ (add (associator (multiply a b) c d)
+ (associator a b (multiply c d)))
+ (additive_inverse
+ (add
+ (add (associator a (multiply b c) d)
+ (multiply a (associator b c d)))
+ (multiply (associator a b c) d)))
+ =>=
+ additive_identity
+ [] by prove_teichmuller_identity
+22949: Order:
+22949: lpo
+22949: Leaf order:
+22949: commutator 1 2 0
+22949: additive_identity 9 0 1 3
+22949: additive_inverse 7 1 1 0,2,2
+22949: add 20 2 4 0,2
+22949: associator 6 3 5 0,1,1,2
+22949: d 5 0 5 3,1,1,2
+22949: c 5 0 5 2,1,1,2
+22949: multiply 27 2 5 0,1,1,1,2
+22949: b 5 0 5 2,1,1,1,2
+22949: a 5 0 5 1,1,1,1,2
+% SZS status Timeout for RNG026-6.p
+NO CLASH, using fixed ground order
+22966: Facts:
+NO CLASH, using fixed ground order
+22967: Facts:
+22967: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+22967: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+22967: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+NO CLASH, using fixed ground order
+22966: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+22966: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+22966: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+22966: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+22966: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+22966: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+22966: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+22965: Facts:
+22966: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+22966: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+22966: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+22965: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+22965: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+22965: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+22965: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+22965: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+22965: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+22965: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+22965: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+22965: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+22965: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+22965: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+22965: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+22965: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+22965: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+22965: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+22965: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+22965: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+22965: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+22965: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+22965: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+22965: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+22965: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+22965: Goal:
+22965: Id : 1, {_}:
+ add
+ (add (associator (multiply a b) c d)
+ (associator a b (multiply c d)))
+ (additive_inverse
+ (add
+ (add (associator a (multiply b c) d)
+ (multiply a (associator b c d)))
+ (multiply (associator a b c) d)))
+ =>=
+ additive_identity
+ [] by prove_teichmuller_identity
+22965: Order:
+22965: nrkbo
+22965: Leaf order:
+22965: commutator 1 2 0
+22965: additive_identity 9 0 1 3
+22965: additive_inverse 23 1 1 0,2,2
+22965: add 28 2 4 0,2
+22965: associator 6 3 5 0,1,1,2
+22965: d 5 0 5 3,1,1,2
+22965: c 5 0 5 2,1,1,2
+22965: multiply 45 2 5 0,1,1,1,2
+22965: b 5 0 5 2,1,1,1,2
+22965: a 5 0 5 1,1,1,1,2
+22967: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+22966: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+22966: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+22966: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+22966: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+22966: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+22966: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+22966: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+22966: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+22966: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+22966: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+22966: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+22966: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+22966: Goal:
+22966: Id : 1, {_}:
+ add
+ (add (associator (multiply a b) c d)
+ (associator a b (multiply c d)))
+ (additive_inverse
+ (add
+ (add (associator a (multiply b c) d)
+ (multiply a (associator b c d)))
+ (multiply (associator a b c) d)))
+ =>=
+ additive_identity
+ [] by prove_teichmuller_identity
+22966: Order:
+22966: kbo
+22966: Leaf order:
+22966: commutator 1 2 0
+22966: additive_identity 9 0 1 3
+22966: additive_inverse 23 1 1 0,2,2
+22966: add 28 2 4 0,2
+22966: associator 6 3 5 0,1,1,2
+22966: d 5 0 5 3,1,1,2
+22966: c 5 0 5 2,1,1,2
+22966: multiply 45 2 5 0,1,1,1,2
+22966: b 5 0 5 2,1,1,1,2
+22966: a 5 0 5 1,1,1,1,2
+22967: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+22967: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+22967: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+22967: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+22967: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+22967: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+22967: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+22967: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+22967: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+22967: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+22967: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+22967: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+22967: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+22967: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+22967: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =>=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+22967: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =>=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+22967: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =>=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+22967: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =>=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+22967: Goal:
+22967: Id : 1, {_}:
+ add
+ (add (associator (multiply a b) c d)
+ (associator a b (multiply c d)))
+ (additive_inverse
+ (add
+ (add (associator a (multiply b c) d)
+ (multiply a (associator b c d)))
+ (multiply (associator a b c) d)))
+ =>=
+ additive_identity
+ [] by prove_teichmuller_identity
+22967: Order:
+22967: lpo
+22967: Leaf order:
+22967: commutator 1 2 0
+22967: additive_identity 9 0 1 3
+22967: additive_inverse 23 1 1 0,2,2
+22967: add 28 2 4 0,2
+22967: associator 6 3 5 0,1,1,2
+22967: d 5 0 5 3,1,1,2
+22967: c 5 0 5 2,1,1,2
+22967: multiply 45 2 5 0,1,1,1,2
+22967: b 5 0 5 2,1,1,1,2
+22967: a 5 0 5 1,1,1,1,2
+% SZS status Timeout for RNG026-7.p
+NO CLASH, using fixed ground order
+22994: Facts:
+22994: Id : 2, {_}:
+ nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by sh_1 ?2 ?3 ?4
+22994: Goal:
+22994: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+22994: Order:
+22994: nrkbo
+22994: Leaf order:
+22994: nand 12 2 6 0,2
+22994: c 2 0 2 2,2,2,2
+22994: b 3 0 3 1,2,2
+22994: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+22995: Facts:
+22995: Id : 2, {_}:
+ nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by sh_1 ?2 ?3 ?4
+22995: Goal:
+22995: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+22995: Order:
+22995: kbo
+22995: Leaf order:
+22995: nand 12 2 6 0,2
+22995: c 2 0 2 2,2,2,2
+22995: b 3 0 3 1,2,2
+22995: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+22996: Facts:
+22996: Id : 2, {_}:
+ nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by sh_1 ?2 ?3 ?4
+22996: Goal:
+22996: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+22996: Order:
+22996: lpo
+22996: Leaf order:
+22996: nand 12 2 6 0,2
+22996: c 2 0 2 2,2,2,2
+22996: b 3 0 3 1,2,2
+22996: a 3 0 3 1,2
+% SZS status Timeout for BOO076-1.p
+CLASH, statistics insufficient
+23012: Facts:
+23012: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+23012: Id : 3, {_}:
+ apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
+ [8, 7] by w_definition ?7 ?8
+23012: Goal:
+23012: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_strong_fixed_point ?1
+23012: Order:
+23012: nrkbo
+23012: Leaf order:
+23012: w 1 0 0
+23012: b 1 0 0
+23012: apply 12 2 3 0,2
+23012: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+23013: Facts:
+23013: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+23013: Id : 3, {_}:
+ apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
+ [8, 7] by w_definition ?7 ?8
+23013: Goal:
+23013: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_strong_fixed_point ?1
+23013: Order:
+23013: kbo
+23013: Leaf order:
+23013: w 1 0 0
+23013: b 1 0 0
+23013: apply 12 2 3 0,2
+23013: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+23014: Facts:
+23014: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+23014: Id : 3, {_}:
+ apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
+ [8, 7] by w_definition ?7 ?8
+23014: Goal:
+23014: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_strong_fixed_point ?1
+23014: Order:
+23014: lpo
+23014: Leaf order:
+23014: w 1 0 0
+23014: b 1 0 0
+23014: apply 12 2 3 0,2
+23014: f 3 1 3 0,2,2
+% SZS status Timeout for COL003-1.p
+CLASH, statistics insufficient
+23460: Facts:
+23460: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+23460: Id : 3, {_}:
+ apply (apply w1 ?7) ?8 =?= apply (apply ?8 ?7) ?7
+ [8, 7] by w1_definition ?7 ?8
+23460: Goal:
+23460: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+23460: Order:
+23460: nrkbo
+23460: Leaf order:
+23460: w1 1 0 0
+23460: b 1 0 0
+23460: apply 12 2 3 0,2
+23460: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+23462: Facts:
+23462: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+23462: Id : 3, {_}:
+ apply (apply w1 ?7) ?8 =?= apply (apply ?8 ?7) ?7
+ [8, 7] by w1_definition ?7 ?8
+23462: Goal:
+23462: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+23462: Order:
+23462: lpo
+23462: Leaf order:
+23462: w1 1 0 0
+23462: b 1 0 0
+23462: apply 12 2 3 0,2
+23462: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+23461: Facts:
+23461: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+23461: Id : 3, {_}:
+ apply (apply w1 ?7) ?8 =?= apply (apply ?8 ?7) ?7
+ [8, 7] by w1_definition ?7 ?8
+23461: Goal:
+23461: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+23461: Order:
+23461: kbo
+23461: Leaf order:
+23461: w1 1 0 0
+23461: b 1 0 0
+23461: apply 12 2 3 0,2
+23461: f 3 1 3 0,2,2
+% SZS status Timeout for COL042-1.p
+NO CLASH, using fixed ground order
+23502: Facts:
+23502: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+23502: Id : 3, {_}:
+ apply (apply (apply h ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?7) ?8) ?7
+ [8, 7, 6] by h_definition ?6 ?7 ?8
+23502: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply h
+ (apply (apply b (apply (apply b h) (apply b b)))
+ (apply h (apply (apply b h) (apply b b))))) h)) b)) b
+ [] by strong_fixed_point
+23502: Goal:
+23502: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+23502: Order:
+23502: nrkbo
+23502: Leaf order:
+23502: h 6 0 0
+23502: b 12 0 0
+23502: apply 29 2 3 0,2
+23502: fixed_pt 3 0 3 2,2
+23502: strong_fixed_point 3 0 2 1,2
+NO CLASH, using fixed ground order
+23503: Facts:
+23503: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+23503: Id : 3, {_}:
+ apply (apply (apply h ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?7) ?8) ?7
+ [8, 7, 6] by h_definition ?6 ?7 ?8
+23503: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply h
+ (apply (apply b (apply (apply b h) (apply b b)))
+ (apply h (apply (apply b h) (apply b b))))) h)) b)) b
+ [] by strong_fixed_point
+23503: Goal:
+23503: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+23503: Order:
+23503: kbo
+23503: Leaf order:
+23503: h 6 0 0
+23503: b 12 0 0
+23503: apply 29 2 3 0,2
+23503: fixed_pt 3 0 3 2,2
+23503: strong_fixed_point 3 0 2 1,2
+NO CLASH, using fixed ground order
+23504: Facts:
+23504: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+23504: Id : 3, {_}:
+ apply (apply (apply h ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?7) ?8) ?7
+ [8, 7, 6] by h_definition ?6 ?7 ?8
+23504: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply h
+ (apply (apply b (apply (apply b h) (apply b b)))
+ (apply h (apply (apply b h) (apply b b))))) h)) b)) b
+ [] by strong_fixed_point
+23504: Goal:
+23504: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+23504: Order:
+23504: lpo
+23504: Leaf order:
+23504: h 6 0 0
+23504: b 12 0 0
+23504: apply 29 2 3 0,2
+23504: fixed_pt 3 0 3 2,2
+23504: strong_fixed_point 3 0 2 1,2
+% SZS status Timeout for COL043-3.p
+NO CLASH, using fixed ground order
+23537: Facts:
+23537: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+23537: Id : 3, {_}:
+ apply (apply (apply n ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?8) ?7) ?8
+ [8, 7, 6] by n_definition ?6 ?7 ?8
+23537: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply n
+ (apply n
+ (apply (apply b (apply b b))
+ (apply n (apply (apply b b) n))))) n)) b)) b
+ [] by strong_fixed_point
+23537: Goal:
+23537: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+23537: Order:
+23537: nrkbo
+23537: Leaf order:
+23537: n 6 0 0
+23537: b 10 0 0
+23537: apply 27 2 3 0,2
+23537: fixed_pt 3 0 3 2,2
+23537: strong_fixed_point 3 0 2 1,2
+NO CLASH, using fixed ground order
+23538: Facts:
+23538: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+23538: Id : 3, {_}:
+ apply (apply (apply n ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?8) ?7) ?8
+ [8, 7, 6] by n_definition ?6 ?7 ?8
+23538: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply n
+ (apply n
+ (apply (apply b (apply b b))
+ (apply n (apply (apply b b) n))))) n)) b)) b
+ [] by strong_fixed_point
+23538: Goal:
+23538: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+23538: Order:
+23538: kbo
+23538: Leaf order:
+23538: n 6 0 0
+23538: b 10 0 0
+23538: apply 27 2 3 0,2
+23538: fixed_pt 3 0 3 2,2
+23538: strong_fixed_point 3 0 2 1,2
+NO CLASH, using fixed ground order
+23539: Facts:
+23539: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+23539: Id : 3, {_}:
+ apply (apply (apply n ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?8) ?7) ?8
+ [8, 7, 6] by n_definition ?6 ?7 ?8
+23539: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply n
+ (apply n
+ (apply (apply b (apply b b))
+ (apply n (apply (apply b b) n))))) n)) b)) b
+ [] by strong_fixed_point
+23539: Goal:
+23539: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+23539: Order:
+23539: lpo
+23539: Leaf order:
+23539: n 6 0 0
+23539: b 10 0 0
+23539: apply 27 2 3 0,2
+23539: fixed_pt 3 0 3 2,2
+23539: strong_fixed_point 3 0 2 1,2
+% SZS status Timeout for COL044-8.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+23557: Facts:
+23557: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+23557: Id : 3, {_}:
+ apply (apply (apply n ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?8) ?7) ?8
+ [8, 7, 6] by n_definition ?6 ?7 ?8
+23557: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply n
+ (apply n
+ (apply (apply b (apply b b))
+ (apply n (apply n (apply b b)))))) n)) b)) b
+ [] by strong_fixed_point
+23557: Goal:
+23557: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+23557: Order:
+23557: kbo
+23557: Leaf order:
+23557: n 6 0 0
+23557: b 10 0 0
+23557: apply 27 2 3 0,2
+23557: fixed_pt 3 0 3 2,2
+23557: strong_fixed_point 3 0 2 1,2
+NO CLASH, using fixed ground order
+23558: Facts:
+23558: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+23558: Id : 3, {_}:
+ apply (apply (apply n ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?8) ?7) ?8
+ [8, 7, 6] by n_definition ?6 ?7 ?8
+23558: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply n
+ (apply n
+ (apply (apply b (apply b b))
+ (apply n (apply n (apply b b)))))) n)) b)) b
+ [] by strong_fixed_point
+23558: Goal:
+23558: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+23558: Order:
+23558: lpo
+23558: Leaf order:
+23558: n 6 0 0
+23558: b 10 0 0
+23558: apply 27 2 3 0,2
+23558: fixed_pt 3 0 3 2,2
+23558: strong_fixed_point 3 0 2 1,2
+23556: Facts:
+23556: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+23556: Id : 3, {_}:
+ apply (apply (apply n ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?8) ?7) ?8
+ [8, 7, 6] by n_definition ?6 ?7 ?8
+23556: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply n
+ (apply n
+ (apply (apply b (apply b b))
+ (apply n (apply n (apply b b)))))) n)) b)) b
+ [] by strong_fixed_point
+23556: Goal:
+23556: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+23556: Order:
+23556: nrkbo
+23556: Leaf order:
+23556: n 6 0 0
+23556: b 10 0 0
+23556: apply 27 2 3 0,2
+23556: fixed_pt 3 0 3 2,2
+23556: strong_fixed_point 3 0 2 1,2
+% SZS status Timeout for COL044-9.p
+NO CLASH, using fixed ground order
+23710: Facts:
+23710: Id : 2, {_}:
+ multiply
+ (inverse
+ (multiply
+ (inverse
+ (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
+ (multiply (inverse (multiply ?4 ?5))
+ (multiply ?4
+ (inverse
+ (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
+ ?7
+ =>=
+ ?6
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+23710: Goal:
+23710: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+23710: Order:
+23710: nrkbo
+23710: Leaf order:
+23710: a2 2 0 2 2,2
+23710: multiply 12 2 2 0,2
+23710: inverse 8 1 1 0,1,1,2
+23710: b2 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+23711: Facts:
+23711: Id : 2, {_}:
+ multiply
+ (inverse
+ (multiply
+ (inverse
+ (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
+ (multiply (inverse (multiply ?4 ?5))
+ (multiply ?4
+ (inverse
+ (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
+ ?7
+ =>=
+ ?6
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+23711: Goal:
+23711: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+23711: Order:
+23711: kbo
+23711: Leaf order:
+23711: a2 2 0 2 2,2
+23711: multiply 12 2 2 0,2
+23711: inverse 8 1 1 0,1,1,2
+23711: b2 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+23712: Facts:
+23712: Id : 2, {_}:
+ multiply
+ (inverse
+ (multiply
+ (inverse
+ (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
+ (multiply (inverse (multiply ?4 ?5))
+ (multiply ?4
+ (inverse
+ (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
+ ?7
+ =>=
+ ?6
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+23712: Goal:
+23712: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+23712: Order:
+23712: lpo
+23712: Leaf order:
+23712: a2 2 0 2 2,2
+23712: multiply 12 2 2 0,2
+23712: inverse 8 1 1 0,1,1,2
+23712: b2 2 0 2 1,1,1,2
+% SZS status Timeout for GRP506-1.p
+NO CLASH, using fixed ground order
+23731: Facts:
+23731: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+23731: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+23731: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+23731: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+23731: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+23731: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+23731: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+23731: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+23731: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+23731: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+23731: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+23731: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+23731: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+23731: Id : 15, {_}:
+ join (meet (complement ?38) (join ?38 ?39))
+ (join (complement ?39) (meet ?38 ?39))
+ =>=
+ n1
+ [39, 38] by megill ?38 ?39
+23731: Goal:
+23731: Id : 1, {_}:
+ meet a (join b (meet a (join (complement a) (meet a b))))
+ =>=
+ meet a (join (complement a) (meet a b))
+ [] by prove_this
+23731: Order:
+23731: nrkbo
+23731: Leaf order:
+23731: n0 1 0 0
+23731: n1 2 0 0
+23731: join 18 2 3 0,2,2
+23731: meet 19 2 5 0,2
+23731: complement 14 1 2 0,1,2,2,2,2
+23731: b 3 0 3 1,2,2
+23731: a 7 0 7 1,2
+NO CLASH, using fixed ground order
+23732: Facts:
+23732: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+23732: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+23732: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+23732: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+23732: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+23732: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+23732: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+23732: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+23732: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+23732: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+23732: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+23732: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+23732: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+23732: Id : 15, {_}:
+ join (meet (complement ?38) (join ?38 ?39))
+ (join (complement ?39) (meet ?38 ?39))
+ =>=
+ n1
+ [39, 38] by megill ?38 ?39
+23732: Goal:
+23732: Id : 1, {_}:
+ meet a (join b (meet a (join (complement a) (meet a b))))
+ =>=
+ meet a (join (complement a) (meet a b))
+ [] by prove_this
+23732: Order:
+23732: kbo
+23732: Leaf order:
+23732: n0 1 0 0
+23732: n1 2 0 0
+23732: join 18 2 3 0,2,2
+23732: meet 19 2 5 0,2
+23732: complement 14 1 2 0,1,2,2,2,2
+23732: b 3 0 3 1,2,2
+23732: a 7 0 7 1,2
+NO CLASH, using fixed ground order
+23733: Facts:
+23733: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+23733: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+23733: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+23733: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+23733: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+23733: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+23733: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+23733: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+23733: Id : 10, {_}:
+ complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+23733: Id : 11, {_}:
+ complement (meet ?29 ?30) =>= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+23733: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+23733: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+23733: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+23733: Id : 15, {_}:
+ join (meet (complement ?38) (join ?38 ?39))
+ (join (complement ?39) (meet ?38 ?39))
+ =>=
+ n1
+ [39, 38] by megill ?38 ?39
+23733: Goal:
+23733: Id : 1, {_}:
+ meet a (join b (meet a (join (complement a) (meet a b))))
+ =>=
+ meet a (join (complement a) (meet a b))
+ [] by prove_this
+23733: Order:
+23733: lpo
+23733: Leaf order:
+23733: n0 1 0 0
+23733: n1 2 0 0
+23733: join 18 2 3 0,2,2
+23733: meet 19 2 5 0,2
+23733: complement 14 1 2 0,1,2,2,2,2
+23733: b 3 0 3 1,2,2
+23733: a 7 0 7 1,2
+% SZS status Timeout for LAT053-1.p
+NO CLASH, using fixed ground order
+23764: Facts:
+NO CLASH, using fixed ground order
+23765: Facts:
+23764: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+23764: Goal:
+23764: Id : 1, {_}: meet a b =>= meet b a [] by prove_normal_axioms_2
+23764: Order:
+23764: nrkbo
+23764: Leaf order:
+23764: join 20 2 0
+23764: meet 20 2 2 0,2
+23764: b 2 0 2 2,2
+23764: a 2 0 2 1,2
+23765: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+23765: Goal:
+23765: Id : 1, {_}: meet a b =>= meet b a [] by prove_normal_axioms_2
+23765: Order:
+23765: kbo
+23765: Leaf order:
+23765: join 20 2 0
+23765: meet 20 2 2 0,2
+23765: b 2 0 2 2,2
+23765: a 2 0 2 1,2
+NO CLASH, using fixed ground order
+23766: Facts:
+23766: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+23766: Goal:
+23766: Id : 1, {_}: meet a b =>= meet b a [] by prove_normal_axioms_2
+23766: Order:
+23766: lpo
+23766: Leaf order:
+23766: join 20 2 0
+23766: meet 20 2 2 0,2
+23766: b 2 0 2 2,2
+23766: a 2 0 2 1,2
+% SZS status Timeout for LAT081-1.p
+NO CLASH, using fixed ground order
+23787: Facts:
+23787: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+23787: Goal:
+23787: Id : 1, {_}: join a b =>= join b a [] by prove_normal_axioms_5
+23787: Order:
+23787: nrkbo
+23787: Leaf order:
+23787: meet 18 2 0
+23787: join 22 2 2 0,2
+23787: b 2 0 2 2,2
+23787: a 2 0 2 1,2
+NO CLASH, using fixed ground order
+23788: Facts:
+23788: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+23788: Goal:
+23788: Id : 1, {_}: join a b =>= join b a [] by prove_normal_axioms_5
+23788: Order:
+23788: kbo
+23788: Leaf order:
+23788: meet 18 2 0
+23788: join 22 2 2 0,2
+23788: b 2 0 2 2,2
+23788: a 2 0 2 1,2
+NO CLASH, using fixed ground order
+23789: Facts:
+23789: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+23789: Goal:
+23789: Id : 1, {_}: join a b =>= join b a [] by prove_normal_axioms_5
+23789: Order:
+23789: lpo
+23789: Leaf order:
+23789: meet 18 2 0
+23789: join 22 2 2 0,2
+23789: b 2 0 2 2,2
+23789: a 2 0 2 1,2
+% SZS status Timeout for LAT084-1.p
+NO CLASH, using fixed ground order
+23816: Facts:
+23816: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+23816: Goal:
+23816: Id : 1, {_}: meet a (join a b) =>= a [] by prove_normal_axioms_7
+23816: Order:
+23816: nrkbo
+23816: Leaf order:
+23816: meet 19 2 1 0,2
+23816: join 21 2 1 0,2,2
+23816: b 1 0 1 2,2,2
+23816: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+23817: Facts:
+23817: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+23817: Goal:
+23817: Id : 1, {_}: meet a (join a b) =>= a [] by prove_normal_axioms_7
+23817: Order:
+23817: kbo
+23817: Leaf order:
+23817: meet 19 2 1 0,2
+23817: join 21 2 1 0,2,2
+23817: b 1 0 1 2,2,2
+23817: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+23818: Facts:
+23818: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+23818: Goal:
+23818: Id : 1, {_}: meet a (join a b) =>= a [] by prove_normal_axioms_7
+23818: Order:
+23818: lpo
+23818: Leaf order:
+23818: meet 19 2 1 0,2
+23818: join 21 2 1 0,2,2
+23818: b 1 0 1 2,2,2
+23818: a 3 0 3 1,2
+% SZS status Timeout for LAT086-1.p
+NO CLASH, using fixed ground order
+23840: Facts:
+23840: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+23840: Goal:
+23840: Id : 1, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8
+23840: Order:
+23840: nrkbo
+23840: Leaf order:
+23840: join 21 2 1 0,2
+23840: meet 19 2 1 0,2,2
+23840: b 1 0 1 2,2,2
+23840: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+23842: Facts:
+23842: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+23842: Goal:
+23842: Id : 1, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8
+23842: Order:
+23842: lpo
+23842: Leaf order:
+23842: join 21 2 1 0,2
+23842: meet 19 2 1 0,2,2
+23842: b 1 0 1 2,2,2
+23842: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+23841: Facts:
+23841: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+23841: Goal:
+23841: Id : 1, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8
+23841: Order:
+23841: kbo
+23841: Leaf order:
+23841: join 21 2 1 0,2
+23841: meet 19 2 1 0,2,2
+23841: b 1 0 1 2,2,2
+23841: a 3 0 3 1,2
+% SZS status Timeout for LAT087-1.p
+NO CLASH, using fixed ground order
+23873: Facts:
+23873: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+23873: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+23873: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+23873: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+23873: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+23873: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+23873: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+23873: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+23873: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?28 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))))
+ [28, 27, 26] by equation_H3 ?26 ?27 ?28
+23873: Goal:
+23873: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+23873: Order:
+23873: nrkbo
+23873: Leaf order:
+23873: join 17 2 4 0,2,2
+23873: meet 21 2 6 0,2
+23873: c 4 0 4 2,2,2,2
+23873: b 4 0 4 1,2,2
+23873: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+23874: Facts:
+23874: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+23874: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+23874: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+23874: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+23874: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+23874: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+23874: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+23874: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+23874: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?28 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))))
+ [28, 27, 26] by equation_H3 ?26 ?27 ?28
+23874: Goal:
+23874: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+23874: Order:
+23874: kbo
+23874: Leaf order:
+23874: join 17 2 4 0,2,2
+23874: meet 21 2 6 0,2
+23874: c 4 0 4 2,2,2,2
+23874: b 4 0 4 1,2,2
+23874: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+23875: Facts:
+23875: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+23875: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+23875: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+23875: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+23875: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+23875: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+23875: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+23875: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+23875: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?28 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))))
+ [28, 27, 26] by equation_H3 ?26 ?27 ?28
+23875: Goal:
+23875: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+23875: Order:
+23875: lpo
+23875: Leaf order:
+23875: join 17 2 4 0,2,2
+23875: meet 21 2 6 0,2
+23875: c 4 0 4 2,2,2,2
+23875: b 4 0 4 1,2,2
+23875: a 4 0 4 1,2
+% SZS status Timeout for LAT099-1.p
+NO CLASH, using fixed ground order
+24259: Facts:
+24259: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24259: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24259: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24259: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24259: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24259: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24259: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24259: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24259: Id : 10, {_}:
+ meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
+24259: Goal:
+24259: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+24259: Order:
+24259: nrkbo
+24259: Leaf order:
+24259: meet 19 2 5 0,2
+24259: join 19 2 5 0,2,2
+24259: d 2 0 2 2,2,2,2,2
+24259: c 3 0 3 1,2,2,2
+24259: b 3 0 3 1,2,2
+24259: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+24260: Facts:
+24260: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24260: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24260: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24260: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24260: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24260: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24260: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24260: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24260: Id : 10, {_}:
+ meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
+24260: Goal:
+24260: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+24260: Order:
+24260: kbo
+24260: Leaf order:
+24260: meet 19 2 5 0,2
+24260: join 19 2 5 0,2,2
+24260: d 2 0 2 2,2,2,2,2
+24260: c 3 0 3 1,2,2,2
+24260: b 3 0 3 1,2,2
+24260: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+24261: Facts:
+24261: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24261: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24261: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24261: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24261: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24261: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24261: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24261: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24261: Id : 10, {_}:
+ meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
+ =?=
+ meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
+24261: Goal:
+24261: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =>=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+24261: Order:
+24261: lpo
+24261: Leaf order:
+24261: meet 19 2 5 0,2
+24261: join 19 2 5 0,2,2
+24261: d 2 0 2 2,2,2,2,2
+24261: c 3 0 3 1,2,2,2
+24261: b 3 0 3 1,2,2
+24261: a 4 0 4 1,2
+% SZS status Timeout for LAT110-1.p
+NO CLASH, using fixed ground order
+24393: Facts:
+24393: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24393: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24393: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24393: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24393: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24393: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24393: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24393: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24393: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join (meet ?26 (join ?27 (meet ?26 ?28))) (meet ?28 ?29))
+ [29, 28, 27, 26] by equation_H79 ?26 ?27 ?28 ?29
+24393: Goal:
+24393: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+24393: Order:
+24393: nrkbo
+24393: Leaf order:
+24393: meet 20 2 5 0,2
+24393: join 17 2 4 0,2,2
+24393: c 3 0 3 2,2,2
+24393: b 3 0 3 1,2,2
+24393: a 5 0 5 1,2
+NO CLASH, using fixed ground order
+24394: Facts:
+24394: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24394: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24394: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24394: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24394: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24394: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24394: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24394: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24394: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join (meet ?26 (join ?27 (meet ?26 ?28))) (meet ?28 ?29))
+ [29, 28, 27, 26] by equation_H79 ?26 ?27 ?28 ?29
+24394: Goal:
+24394: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+24394: Order:
+24394: kbo
+24394: Leaf order:
+24394: meet 20 2 5 0,2
+24394: join 17 2 4 0,2,2
+24394: c 3 0 3 2,2,2
+24394: b 3 0 3 1,2,2
+24394: a 5 0 5 1,2
+NO CLASH, using fixed ground order
+24395: Facts:
+24395: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24395: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24395: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24395: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24395: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24395: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24395: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24395: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24395: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join (meet ?26 (join ?27 (meet ?26 ?28))) (meet ?28 ?29))
+ [29, 28, 27, 26] by equation_H79 ?26 ?27 ?28 ?29
+24395: Goal:
+24395: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+24395: Order:
+24395: lpo
+24395: Leaf order:
+24395: meet 20 2 5 0,2
+24395: join 17 2 4 0,2,2
+24395: c 3 0 3 2,2,2
+24395: b 3 0 3 1,2,2
+24395: a 5 0 5 1,2
+% SZS status Timeout for LAT118-1.p
+NO CLASH, using fixed ground order
+24412: Facts:
+24412: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24412: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24412: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24412: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24412: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24412: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24412: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24412: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24412: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?28 (meet ?26 ?27)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H22 ?26 ?27 ?28
+24412: Goal:
+24412: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+24412: Order:
+24412: nrkbo
+24412: Leaf order:
+24412: join 17 2 4 0,2,2
+24412: meet 21 2 6 0,2
+24412: c 3 0 3 2,2,2,2
+24412: b 3 0 3 1,2,2
+24412: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+24413: Facts:
+24413: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24413: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24413: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24413: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24413: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24413: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24413: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24413: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24413: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?28 (meet ?26 ?27)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H22 ?26 ?27 ?28
+24413: Goal:
+24413: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+24413: Order:
+24413: kbo
+24413: Leaf order:
+24413: join 17 2 4 0,2,2
+24413: meet 21 2 6 0,2
+24413: c 3 0 3 2,2,2,2
+24413: b 3 0 3 1,2,2
+24413: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+24414: Facts:
+24414: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24414: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24414: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24414: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24414: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24414: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24414: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24414: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24414: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?28 (meet ?26 ?27)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H22 ?26 ?27 ?28
+24414: Goal:
+24414: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+24414: Order:
+24414: lpo
+24414: Leaf order:
+24414: join 17 2 4 0,2,2
+24414: meet 21 2 6 0,2
+24414: c 3 0 3 2,2,2,2
+24414: b 3 0 3 1,2,2
+24414: a 6 0 6 1,2
+% SZS status Timeout for LAT142-1.p
+NO CLASH, using fixed ground order
+24444: Facts:
+24444: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24444: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24444: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24444: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24444: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24444: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24444: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24444: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24444: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 ?29))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
+24444: Goal:
+24444: Id : 1, {_}:
+ meet a (meet b (join c (meet a d)))
+ =<=
+ meet a (meet b (join c (meet d (join a (meet b c)))))
+ [] by prove_H45
+24444: Order:
+24444: nrkbo
+24444: Leaf order:
+24444: join 16 2 3 0,2,2,2
+24444: meet 21 2 7 0,2
+24444: d 2 0 2 2,2,2,2,2
+24444: c 3 0 3 1,2,2,2
+24444: b 3 0 3 1,2,2
+24444: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+24445: Facts:
+24445: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24445: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24445: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24445: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24445: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24445: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24445: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24445: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24445: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 ?29))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
+24445: Goal:
+24445: Id : 1, {_}:
+ meet a (meet b (join c (meet a d)))
+ =<=
+ meet a (meet b (join c (meet d (join a (meet b c)))))
+ [] by prove_H45
+24445: Order:
+24445: kbo
+24445: Leaf order:
+24445: join 16 2 3 0,2,2,2
+24445: meet 21 2 7 0,2
+24445: d 2 0 2 2,2,2,2,2
+24445: c 3 0 3 1,2,2,2
+24445: b 3 0 3 1,2,2
+24445: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+24446: Facts:
+24446: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24446: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24446: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24446: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24446: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24446: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24446: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24446: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24446: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 ?29))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
+24446: Goal:
+24446: Id : 1, {_}:
+ meet a (meet b (join c (meet a d)))
+ =>=
+ meet a (meet b (join c (meet d (join a (meet b c)))))
+ [] by prove_H45
+24446: Order:
+24446: lpo
+24446: Leaf order:
+24446: join 16 2 3 0,2,2,2
+24446: meet 21 2 7 0,2
+24446: d 2 0 2 2,2,2,2,2
+24446: c 3 0 3 1,2,2,2
+24446: b 3 0 3 1,2,2
+24446: a 4 0 4 1,2
+% SZS status Timeout for LAT147-1.p
+NO CLASH, using fixed ground order
+24463: Facts:
+24463: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24463: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24463: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24463: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24463: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24463: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24463: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24463: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24463: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?27 (join ?29 (meet ?26 ?28)))))
+ [29, 28, 27, 26] by equation_H42 ?26 ?27 ?28 ?29
+24463: Goal:
+24463: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+24463: Order:
+24463: kbo
+24463: Leaf order:
+24463: join 18 2 4 0,2,2
+24463: meet 20 2 6 0,2
+24463: c 3 0 3 2,2,2,2
+24463: b 3 0 3 1,2,2
+24463: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+24464: Facts:
+24464: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24464: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24464: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24464: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24464: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24464: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24464: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24464: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24464: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join ?27 (join ?29 (meet ?26 ?28)))))
+ [29, 28, 27, 26] by equation_H42 ?26 ?27 ?28 ?29
+24464: Goal:
+24464: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+24464: Order:
+24464: lpo
+24464: Leaf order:
+24464: join 18 2 4 0,2,2
+24464: meet 20 2 6 0,2
+24464: c 3 0 3 2,2,2,2
+24464: b 3 0 3 1,2,2
+24464: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+24462: Facts:
+24462: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24462: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24462: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24462: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24462: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24462: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24462: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24462: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24462: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?27 (join ?29 (meet ?26 ?28)))))
+ [29, 28, 27, 26] by equation_H42 ?26 ?27 ?28 ?29
+24462: Goal:
+24462: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+24462: Order:
+24462: nrkbo
+24462: Leaf order:
+24462: join 18 2 4 0,2,2
+24462: meet 20 2 6 0,2
+24462: c 3 0 3 2,2,2,2
+24462: b 3 0 3 1,2,2
+24462: a 6 0 6 1,2
+% SZS status Timeout for LAT154-1.p
+NO CLASH, using fixed ground order
+24500: Facts:
+24500: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24500: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24500: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24500: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24500: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24500: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24500: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24500: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24500: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
+ [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
+24500: Goal:
+24500: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+24500: Order:
+24500: nrkbo
+24500: Leaf order:
+24500: join 18 2 4 0,2,2
+24500: meet 20 2 6 0,2
+24500: c 4 0 4 2,2,2,2
+24500: b 4 0 4 1,2,2
+24500: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+24501: Facts:
+24501: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24501: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24501: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24501: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24501: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24501: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24501: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24501: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24501: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
+ [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
+24501: Goal:
+24501: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+24501: Order:
+24501: kbo
+24501: Leaf order:
+24501: join 18 2 4 0,2,2
+24501: meet 20 2 6 0,2
+24501: c 4 0 4 2,2,2,2
+24501: b 4 0 4 1,2,2
+24501: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+24502: Facts:
+24502: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24502: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24502: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24502: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24502: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24502: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24502: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24502: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24502: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =?=
+ meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
+ [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
+24502: Goal:
+24502: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+24502: Order:
+24502: lpo
+24502: Leaf order:
+24502: join 18 2 4 0,2,2
+24502: meet 20 2 6 0,2
+24502: c 4 0 4 2,2,2,2
+24502: b 4 0 4 1,2,2
+24502: a 4 0 4 1,2
+% SZS status Timeout for LAT155-1.p
+NO CLASH, using fixed ground order
+24518: Facts:
+24518: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24518: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24518: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24518: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24518: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24518: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24518: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24518: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24518: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29))))
+ [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29
+24518: Goal:
+24518: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H58
+24518: Order:
+24518: nrkbo
+24518: Leaf order:
+24518: meet 18 2 4 0,2
+24518: join 18 2 4 0,2,2
+24518: c 2 0 2 2,2,2
+24518: b 4 0 4 1,2,2
+24518: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+24519: Facts:
+24519: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24519: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24519: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24519: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24519: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24519: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24519: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24519: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24519: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29))))
+ [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29
+24519: Goal:
+24519: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H58
+24519: Order:
+24519: kbo
+24519: Leaf order:
+24519: meet 18 2 4 0,2
+24519: join 18 2 4 0,2,2
+24519: c 2 0 2 2,2,2
+24519: b 4 0 4 1,2,2
+24519: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+24520: Facts:
+24520: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24520: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24520: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24520: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24520: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24520: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24520: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24520: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24520: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =?=
+ join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29))))
+ [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29
+24520: Goal:
+24520: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H58
+24520: Order:
+24520: lpo
+24520: Leaf order:
+24520: meet 18 2 4 0,2
+24520: join 18 2 4 0,2,2
+24520: c 2 0 2 2,2,2
+24520: b 4 0 4 1,2,2
+24520: a 4 0 4 1,2
+% SZS status Timeout for LAT170-1.p
+NO CLASH, using fixed ground order
+24547: Facts:
+24547: Id : 2, {_}:
+ add ?2 ?3 =?= add ?3 ?2
+ [3, 2] by commutativity_for_addition ?2 ?3
+24547: Id : 3, {_}:
+ add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7
+ [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
+24547: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
+24547: Id : 5, {_}:
+ add ?11 additive_identity =>= ?11
+ [11] by right_additive_identity ?11
+24547: Id : 6, {_}:
+ multiply additive_identity ?13 =>= additive_identity
+ [13] by left_multiplicative_zero ?13
+24547: Id : 7, {_}:
+ multiply ?15 additive_identity =>= additive_identity
+ [15] by right_multiplicative_zero ?15
+24547: Id : 8, {_}:
+ add (additive_inverse ?17) ?17 =>= additive_identity
+ [17] by left_additive_inverse ?17
+24547: Id : 9, {_}:
+ add ?19 (additive_inverse ?19) =>= additive_identity
+ [19] by right_additive_inverse ?19
+24547: Id : 10, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+24547: Id : 11, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+24547: Id : 12, {_}:
+ additive_inverse (additive_inverse ?29) =>= ?29
+ [29] by additive_inverse_additive_inverse ?29
+24547: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+24547: Id : 14, {_}:
+ associator ?34 ?35 ?36
+ =<=
+ add (multiply (multiply ?34 ?35) ?36)
+ (additive_inverse (multiply ?34 (multiply ?35 ?36)))
+ [36, 35, 34] by associator ?34 ?35 ?36
+24547: Id : 15, {_}:
+ commutator ?38 ?39
+ =<=
+ add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
+ [39, 38] by commutator ?38 ?39
+24547: Goal:
+24547: Id : 1, {_}:
+ multiply
+ (multiply (multiply (associator x x y) (associator x x y)) x)
+ (multiply (associator x x y) (associator x x y))
+ =>=
+ additive_identity
+ [] by prove_conjecture_2
+24547: Order:
+24547: nrkbo
+24547: Leaf order:
+24547: commutator 1 2 0
+24547: additive_inverse 6 1 0
+24547: add 16 2 0
+24547: additive_identity 9 0 1 3
+24547: multiply 22 2 4 0,2
+24547: associator 5 3 4 0,1,1,1,2
+24547: y 4 0 4 3,1,1,1,2
+24547: x 9 0 9 1,1,1,1,2
+NO CLASH, using fixed ground order
+24548: Facts:
+24548: Id : 2, {_}:
+ add ?2 ?3 =?= add ?3 ?2
+ [3, 2] by commutativity_for_addition ?2 ?3
+24548: Id : 3, {_}:
+ add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
+ [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
+24548: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
+24548: Id : 5, {_}:
+ add ?11 additive_identity =>= ?11
+ [11] by right_additive_identity ?11
+24548: Id : 6, {_}:
+ multiply additive_identity ?13 =>= additive_identity
+ [13] by left_multiplicative_zero ?13
+24548: Id : 7, {_}:
+ multiply ?15 additive_identity =>= additive_identity
+ [15] by right_multiplicative_zero ?15
+24548: Id : 8, {_}:
+ add (additive_inverse ?17) ?17 =>= additive_identity
+ [17] by left_additive_inverse ?17
+24548: Id : 9, {_}:
+ add ?19 (additive_inverse ?19) =>= additive_identity
+ [19] by right_additive_inverse ?19
+24548: Id : 10, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+24548: Id : 11, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+24548: Id : 12, {_}:
+ additive_inverse (additive_inverse ?29) =>= ?29
+ [29] by additive_inverse_additive_inverse ?29
+24548: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+24548: Id : 14, {_}:
+ associator ?34 ?35 ?36
+ =<=
+ add (multiply (multiply ?34 ?35) ?36)
+ (additive_inverse (multiply ?34 (multiply ?35 ?36)))
+ [36, 35, 34] by associator ?34 ?35 ?36
+24548: Id : 15, {_}:
+ commutator ?38 ?39
+ =<=
+ add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
+ [39, 38] by commutator ?38 ?39
+24548: Goal:
+24548: Id : 1, {_}:
+ multiply
+ (multiply (multiply (associator x x y) (associator x x y)) x)
+ (multiply (associator x x y) (associator x x y))
+ =>=
+ additive_identity
+ [] by prove_conjecture_2
+24548: Order:
+24548: kbo
+24548: Leaf order:
+24548: commutator 1 2 0
+24548: additive_inverse 6 1 0
+24548: add 16 2 0
+24548: additive_identity 9 0 1 3
+24548: multiply 22 2 4 0,2
+24548: associator 5 3 4 0,1,1,1,2
+24548: y 4 0 4 3,1,1,1,2
+24548: x 9 0 9 1,1,1,1,2
+NO CLASH, using fixed ground order
+24549: Facts:
+24549: Id : 2, {_}:
+ add ?2 ?3 =?= add ?3 ?2
+ [3, 2] by commutativity_for_addition ?2 ?3
+24549: Id : 3, {_}:
+ add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
+ [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
+24549: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
+24549: Id : 5, {_}:
+ add ?11 additive_identity =>= ?11
+ [11] by right_additive_identity ?11
+24549: Id : 6, {_}:
+ multiply additive_identity ?13 =>= additive_identity
+ [13] by left_multiplicative_zero ?13
+24549: Id : 7, {_}:
+ multiply ?15 additive_identity =>= additive_identity
+ [15] by right_multiplicative_zero ?15
+24549: Id : 8, {_}:
+ add (additive_inverse ?17) ?17 =>= additive_identity
+ [17] by left_additive_inverse ?17
+24549: Id : 9, {_}:
+ add ?19 (additive_inverse ?19) =>= additive_identity
+ [19] by right_additive_inverse ?19
+24549: Id : 10, {_}:
+ multiply ?21 (add ?22 ?23)
+ =>=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+24549: Id : 11, {_}:
+ multiply (add ?25 ?26) ?27
+ =>=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+24549: Id : 12, {_}:
+ additive_inverse (additive_inverse ?29) =>= ?29
+ [29] by additive_inverse_additive_inverse ?29
+24549: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+24549: Id : 14, {_}:
+ associator ?34 ?35 ?36
+ =>=
+ add (multiply (multiply ?34 ?35) ?36)
+ (additive_inverse (multiply ?34 (multiply ?35 ?36)))
+ [36, 35, 34] by associator ?34 ?35 ?36
+24549: Id : 15, {_}:
+ commutator ?38 ?39
+ =<=
+ add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
+ [39, 38] by commutator ?38 ?39
+24549: Goal:
+24549: Id : 1, {_}:
+ multiply
+ (multiply (multiply (associator x x y) (associator x x y)) x)
+ (multiply (associator x x y) (associator x x y))
+ =>=
+ additive_identity
+ [] by prove_conjecture_2
+24549: Order:
+24549: lpo
+24549: Leaf order:
+24549: commutator 1 2 0
+24549: additive_inverse 6 1 0
+24549: add 16 2 0
+24549: additive_identity 9 0 1 3
+24549: multiply 22 2 4 0,2
+24549: associator 5 3 4 0,1,1,1,2
+24549: y 4 0 4 3,1,1,1,2
+24549: x 9 0 9 1,1,1,1,2
+% SZS status Timeout for RNG031-6.p
+NO CLASH, using fixed ground order
+24576: Facts:
+24576: Id : 2, {_}:
+ multiply (additive_inverse ?2) (additive_inverse ?3)
+ =>=
+ multiply ?2 ?3
+ [3, 2] by product_of_inverses ?2 ?3
+24576: Id : 3, {_}:
+ multiply (additive_inverse ?5) ?6
+ =>=
+ additive_inverse (multiply ?5 ?6)
+ [6, 5] by inverse_product1 ?5 ?6
+24576: Id : 4, {_}:
+ multiply ?8 (additive_inverse ?9)
+ =>=
+ additive_inverse (multiply ?8 ?9)
+ [9, 8] by inverse_product2 ?8 ?9
+24576: Id : 5, {_}:
+ multiply ?11 (add ?12 (additive_inverse ?13))
+ =<=
+ add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
+ [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
+24576: Id : 6, {_}:
+ multiply (add ?15 (additive_inverse ?16)) ?17
+ =<=
+ add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
+ [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
+24576: Id : 7, {_}:
+ multiply (additive_inverse ?19) (add ?20 ?21)
+ =<=
+ add (additive_inverse (multiply ?19 ?20))
+ (additive_inverse (multiply ?19 ?21))
+ [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
+24576: Id : 8, {_}:
+ multiply (add ?23 ?24) (additive_inverse ?25)
+ =<=
+ add (additive_inverse (multiply ?23 ?25))
+ (additive_inverse (multiply ?24 ?25))
+ [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
+24576: Id : 9, {_}:
+ add ?27 ?28 =?= add ?28 ?27
+ [28, 27] by commutativity_for_addition ?27 ?28
+24576: Id : 10, {_}:
+ add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32
+ [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
+24576: Id : 11, {_}:
+ add additive_identity ?34 =>= ?34
+ [34] by left_additive_identity ?34
+24576: Id : 12, {_}:
+ add ?36 additive_identity =>= ?36
+ [36] by right_additive_identity ?36
+24576: Id : 13, {_}:
+ multiply additive_identity ?38 =>= additive_identity
+ [38] by left_multiplicative_zero ?38
+24576: Id : 14, {_}:
+ multiply ?40 additive_identity =>= additive_identity
+ [40] by right_multiplicative_zero ?40
+24576: Id : 15, {_}:
+ add (additive_inverse ?42) ?42 =>= additive_identity
+ [42] by left_additive_inverse ?42
+24576: Id : 16, {_}:
+ add ?44 (additive_inverse ?44) =>= additive_identity
+ [44] by right_additive_inverse ?44
+24576: Id : 17, {_}:
+ multiply ?46 (add ?47 ?48)
+ =<=
+ add (multiply ?46 ?47) (multiply ?46 ?48)
+ [48, 47, 46] by distribute1 ?46 ?47 ?48
+24576: Id : 18, {_}:
+ multiply (add ?50 ?51) ?52
+ =<=
+ add (multiply ?50 ?52) (multiply ?51 ?52)
+ [52, 51, 50] by distribute2 ?50 ?51 ?52
+24576: Id : 19, {_}:
+ additive_inverse (additive_inverse ?54) =>= ?54
+ [54] by additive_inverse_additive_inverse ?54
+24576: Id : 20, {_}:
+ multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57)
+ [57, 56] by right_alternative ?56 ?57
+24576: Id : 21, {_}:
+ associator ?59 ?60 ?61
+ =<=
+ add (multiply (multiply ?59 ?60) ?61)
+ (additive_inverse (multiply ?59 (multiply ?60 ?61)))
+ [61, 60, 59] by associator ?59 ?60 ?61
+24576: Id : 22, {_}:
+ commutator ?63 ?64
+ =<=
+ add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
+ [64, 63] by commutator ?63 ?64
+24576: Goal:
+24576: Id : 1, {_}:
+ multiply
+ (multiply (multiply (associator x x y) (associator x x y)) x)
+ (multiply (associator x x y) (associator x x y))
+ =>=
+ additive_identity
+ [] by prove_conjecture_2
+24576: Order:
+24576: nrkbo
+24576: Leaf order:
+24576: commutator 1 2 0
+24576: add 24 2 0
+24576: additive_inverse 22 1 0
+24576: additive_identity 9 0 1 3
+24576: multiply 40 2 4 0,2add
+24576: associator 5 3 4 0,1,1,1,2
+24576: y 4 0 4 3,1,1,1,2
+24576: x 9 0 9 1,1,1,1,2
+NO CLASH, using fixed ground order
+24577: Facts:
+24577: Id : 2, {_}:
+ multiply (additive_inverse ?2) (additive_inverse ?3)
+ =>=
+ multiply ?2 ?3
+ [3, 2] by product_of_inverses ?2 ?3
+NO CLASH, using fixed ground order
+24578: Facts:
+24578: Id : 2, {_}:
+ multiply (additive_inverse ?2) (additive_inverse ?3)
+ =>=
+ multiply ?2 ?3
+ [3, 2] by product_of_inverses ?2 ?3
+24578: Id : 3, {_}:
+ multiply (additive_inverse ?5) ?6
+ =>=
+ additive_inverse (multiply ?5 ?6)
+ [6, 5] by inverse_product1 ?5 ?6
+24578: Id : 4, {_}:
+ multiply ?8 (additive_inverse ?9)
+ =>=
+ additive_inverse (multiply ?8 ?9)
+ [9, 8] by inverse_product2 ?8 ?9
+24578: Id : 5, {_}:
+ multiply ?11 (add ?12 (additive_inverse ?13))
+ =>=
+ add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
+ [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
+24578: Id : 6, {_}:
+ multiply (add ?15 (additive_inverse ?16)) ?17
+ =>=
+ add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
+ [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
+24578: Id : 7, {_}:
+ multiply (additive_inverse ?19) (add ?20 ?21)
+ =>=
+ add (additive_inverse (multiply ?19 ?20))
+ (additive_inverse (multiply ?19 ?21))
+ [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
+24578: Id : 8, {_}:
+ multiply (add ?23 ?24) (additive_inverse ?25)
+ =>=
+ add (additive_inverse (multiply ?23 ?25))
+ (additive_inverse (multiply ?24 ?25))
+ [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
+24578: Id : 9, {_}:
+ add ?27 ?28 =?= add ?28 ?27
+ [28, 27] by commutativity_for_addition ?27 ?28
+24578: Id : 10, {_}:
+ add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
+ [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
+24578: Id : 11, {_}:
+ add additive_identity ?34 =>= ?34
+ [34] by left_additive_identity ?34
+24578: Id : 12, {_}:
+ add ?36 additive_identity =>= ?36
+ [36] by right_additive_identity ?36
+24578: Id : 13, {_}:
+ multiply additive_identity ?38 =>= additive_identity
+ [38] by left_multiplicative_zero ?38
+24578: Id : 14, {_}:
+ multiply ?40 additive_identity =>= additive_identity
+ [40] by right_multiplicative_zero ?40
+24578: Id : 15, {_}:
+ add (additive_inverse ?42) ?42 =>= additive_identity
+ [42] by left_additive_inverse ?42
+24578: Id : 16, {_}:
+ add ?44 (additive_inverse ?44) =>= additive_identity
+ [44] by right_additive_inverse ?44
+24578: Id : 17, {_}:
+ multiply ?46 (add ?47 ?48)
+ =>=
+ add (multiply ?46 ?47) (multiply ?46 ?48)
+ [48, 47, 46] by distribute1 ?46 ?47 ?48
+24578: Id : 18, {_}:
+ multiply (add ?50 ?51) ?52
+ =>=
+ add (multiply ?50 ?52) (multiply ?51 ?52)
+ [52, 51, 50] by distribute2 ?50 ?51 ?52
+24578: Id : 19, {_}:
+ additive_inverse (additive_inverse ?54) =>= ?54
+ [54] by additive_inverse_additive_inverse ?54
+24578: Id : 20, {_}:
+ multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
+ [57, 56] by right_alternative ?56 ?57
+24578: Id : 21, {_}:
+ associator ?59 ?60 ?61
+ =>=
+ add (multiply (multiply ?59 ?60) ?61)
+ (additive_inverse (multiply ?59 (multiply ?60 ?61)))
+ [61, 60, 59] by associator ?59 ?60 ?61
+24578: Id : 22, {_}:
+ commutator ?63 ?64
+ =<=
+ add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
+ [64, 63] by commutator ?63 ?64
+24578: Goal:
+24578: Id : 1, {_}:
+ multiply
+ (multiply (multiply (associator x x y) (associator x x y)) x)
+ (multiply (associator x x y) (associator x x y))
+ =>=
+ additive_identity
+ [] by prove_conjecture_2
+24578: Order:
+24578: lpo
+24578: Leaf order:
+24578: commutator 1 2 0
+24578: add 24 2 0
+24578: additive_inverse 22 1 0
+24578: additive_identity 9 0 1 3
+24578: multiply 40 2 4 0,2add
+24578: associator 5 3 4 0,1,1,1,2
+24578: y 4 0 4 3,1,1,1,2
+24578: x 9 0 9 1,1,1,1,2
+24577: Id : 3, {_}:
+ multiply (additive_inverse ?5) ?6
+ =>=
+ additive_inverse (multiply ?5 ?6)
+ [6, 5] by inverse_product1 ?5 ?6
+24577: Id : 4, {_}:
+ multiply ?8 (additive_inverse ?9)
+ =>=
+ additive_inverse (multiply ?8 ?9)
+ [9, 8] by inverse_product2 ?8 ?9
+24577: Id : 5, {_}:
+ multiply ?11 (add ?12 (additive_inverse ?13))
+ =<=
+ add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
+ [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
+24577: Id : 6, {_}:
+ multiply (add ?15 (additive_inverse ?16)) ?17
+ =<=
+ add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
+ [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
+24577: Id : 7, {_}:
+ multiply (additive_inverse ?19) (add ?20 ?21)
+ =<=
+ add (additive_inverse (multiply ?19 ?20))
+ (additive_inverse (multiply ?19 ?21))
+ [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
+24577: Id : 8, {_}:
+ multiply (add ?23 ?24) (additive_inverse ?25)
+ =<=
+ add (additive_inverse (multiply ?23 ?25))
+ (additive_inverse (multiply ?24 ?25))
+ [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
+24577: Id : 9, {_}:
+ add ?27 ?28 =?= add ?28 ?27
+ [28, 27] by commutativity_for_addition ?27 ?28
+24577: Id : 10, {_}:
+ add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
+ [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
+24577: Id : 11, {_}:
+ add additive_identity ?34 =>= ?34
+ [34] by left_additive_identity ?34
+24577: Id : 12, {_}:
+ add ?36 additive_identity =>= ?36
+ [36] by right_additive_identity ?36
+24577: Id : 13, {_}:
+ multiply additive_identity ?38 =>= additive_identity
+ [38] by left_multiplicative_zero ?38
+24577: Id : 14, {_}:
+ multiply ?40 additive_identity =>= additive_identity
+ [40] by right_multiplicative_zero ?40
+24577: Id : 15, {_}:
+ add (additive_inverse ?42) ?42 =>= additive_identity
+ [42] by left_additive_inverse ?42
+24577: Id : 16, {_}:
+ add ?44 (additive_inverse ?44) =>= additive_identity
+ [44] by right_additive_inverse ?44
+24577: Id : 17, {_}:
+ multiply ?46 (add ?47 ?48)
+ =<=
+ add (multiply ?46 ?47) (multiply ?46 ?48)
+ [48, 47, 46] by distribute1 ?46 ?47 ?48
+24577: Id : 18, {_}:
+ multiply (add ?50 ?51) ?52
+ =<=
+ add (multiply ?50 ?52) (multiply ?51 ?52)
+ [52, 51, 50] by distribute2 ?50 ?51 ?52
+24577: Id : 19, {_}:
+ additive_inverse (additive_inverse ?54) =>= ?54
+ [54] by additive_inverse_additive_inverse ?54
+24577: Id : 20, {_}:
+ multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
+ [57, 56] by right_alternative ?56 ?57
+24577: Id : 21, {_}:
+ associator ?59 ?60 ?61
+ =<=
+ add (multiply (multiply ?59 ?60) ?61)
+ (additive_inverse (multiply ?59 (multiply ?60 ?61)))
+ [61, 60, 59] by associator ?59 ?60 ?61
+24577: Id : 22, {_}:
+ commutator ?63 ?64
+ =<=
+ add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
+ [64, 63] by commutator ?63 ?64
+24577: Goal:
+24577: Id : 1, {_}:
+ multiply
+ (multiply (multiply (associator x x y) (associator x x y)) x)
+ (multiply (associator x x y) (associator x x y))
+ =>=
+ additive_identity
+ [] by prove_conjecture_2
+24577: Order:
+24577: kbo
+24577: Leaf order:
+24577: commutator 1 2 0
+24577: add 24 2 0
+24577: additive_inverse 22 1 0
+24577: additive_identity 9 0 1 3
+24577: multiply 40 2 4 0,2add
+24577: associator 5 3 4 0,1,1,1,2
+24577: y 4 0 4 3,1,1,1,2
+24577: x 9 0 9 1,1,1,1,2
+% SZS status Timeout for RNG031-7.p
+NO CLASH, using fixed ground order
+24609: Facts:
+24609: Id : 2, {_}: f (g1 ?3) =>= ?3 [3] by clause1 ?3
+24609: Id : 3, {_}: f (g2 ?5) =>= ?5 [5] by clause2 ?5
+24609: Goal:
+24609: Id : 1, {_}: g1 ?1 =>= g2 ?1 [1] by clause3 ?1
+24609: Order:
+24609: nrkbo
+24609: Leaf order:
+24609: f 2 1 0
+24609: g2 2 1 1 0,3
+24609: g1 2 1 1 0,2
+NO CLASH, using fixed ground order
+24610: Facts:
+24610: Id : 2, {_}: f (g1 ?3) =>= ?3 [3] by clause1 ?3
+24610: Id : 3, {_}: f (g2 ?5) =>= ?5 [5] by clause2 ?5
+24610: Goal:
+24610: Id : 1, {_}: g1 ?1 =>= g2 ?1 [1] by clause3 ?1
+24610: Order:
+24610: kbo
+24610: Leaf order:
+24610: f 2 1 0
+24610: g2 2 1 1 0,3
+24610: g1 2 1 1 0,2
+NO CLASH, using fixed ground order
+24611: Facts:
+24611: Id : 2, {_}: f (g1 ?3) =>= ?3 [3] by clause1 ?3
+24611: Id : 3, {_}: f (g2 ?5) =>= ?5 [5] by clause2 ?5
+24611: Goal:
+24611: Id : 1, {_}: g1 ?1 =>= g2 ?1 [1] by clause3 ?1
+24611: Order:
+24611: lpo
+24611: Leaf order:
+24611: f 2 1 0
+24611: g2 2 1 1 0,3
+24611: g1 2 1 1 0,2
+24609: status GaveUp for SYN305-1.p
+24610: status GaveUp for SYN305-1.p
+24611: status GaveUp for SYN305-1.p
+% SZS status Timeout for SYN305-1.p
+CLASH, statistics insufficient
+24616: Facts:
+24616: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+24616: Id : 3, {_}:
+ apply (apply (apply h ?7) ?8) ?9
+ =?=
+ apply (apply (apply ?7 ?8) ?9) ?8
+ [9, 8, 7] by h_definition ?7 ?8 ?9
+24616: Goal:
+24616: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+24616: Order:
+24616: nrkbo
+24616: Leaf order:
+24616: h 1 0 0
+24616: b 1 0 0
+24616: apply 14 2 3 0,2
+24616: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+24617: Facts:
+24617: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+24617: Id : 3, {_}:
+ apply (apply (apply h ?7) ?8) ?9
+ =?=
+ apply (apply (apply ?7 ?8) ?9) ?8
+ [9, 8, 7] by h_definition ?7 ?8 ?9
+24617: Goal:
+24617: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+24617: Order:
+24617: kbo
+24617: Leaf order:
+24617: h 1 0 0
+24617: b 1 0 0
+24617: apply 14 2 3 0,2
+24617: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+24618: Facts:
+24618: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+24618: Id : 3, {_}:
+ apply (apply (apply h ?7) ?8) ?9
+ =?=
+ apply (apply (apply ?7 ?8) ?9) ?8
+ [9, 8, 7] by h_definition ?7 ?8 ?9
+24618: Goal:
+24618: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+24618: Order:
+24618: lpo
+24618: Leaf order:
+24618: h 1 0 0
+24618: b 1 0 0
+24618: apply 14 2 3 0,2
+24618: f 3 1 3 0,2,2
+% SZS status Timeout for COL043-1.p
+CLASH, statistics insufficient
+24654: Facts:
+CLASH, statistics insufficient
+24655: Facts:
+24655: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+24655: Id : 3, {_}:
+ apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
+ [9, 8, 7] by q_definition ?7 ?8 ?9
+24655: Id : 4, {_}:
+ apply (apply w ?11) ?12 =?= apply (apply ?11 ?12) ?12
+ [12, 11] by w_definition ?11 ?12
+24655: Goal:
+24655: Id : 1, {_}:
+ apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (g ?1)) (h ?1)
+ =<=
+ apply (apply (f ?1) (g ?1)) (apply (apply (f ?1) (g ?1)) (h ?1))
+ [1] by prove_p_combinator ?1
+24655: Order:
+24655: kbo
+24655: Leaf order:
+24655: w 1 0 0
+24655: q 1 0 0
+24655: b 1 0 0
+24655: h 2 1 2 0,2,2
+24655: g 4 1 4 0,2,1,1,2
+24655: apply 22 2 8 0,2
+24655: f 3 1 3 0,2,1,1,1,2
+CLASH, statistics insufficient
+24656: Facts:
+24656: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+24656: Id : 3, {_}:
+ apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
+ [9, 8, 7] by q_definition ?7 ?8 ?9
+24656: Id : 4, {_}:
+ apply (apply w ?11) ?12 =?= apply (apply ?11 ?12) ?12
+ [12, 11] by w_definition ?11 ?12
+24656: Goal:
+24656: Id : 1, {_}:
+ apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (apply (f ?1) (g ?1)) (apply (apply (f ?1) (g ?1)) (h ?1))
+ [1] by prove_p_combinator ?1
+24656: Order:
+24656: lpo
+24656: Leaf order:
+24656: w 1 0 0
+24656: q 1 0 0
+24656: b 1 0 0
+24656: h 2 1 2 0,2,2
+24656: g 4 1 4 0,2,1,1,2
+24656: apply 22 2 8 0,2
+24656: f 3 1 3 0,2,1,1,1,2
+24654: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+24654: Id : 3, {_}:
+ apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
+ [9, 8, 7] by q_definition ?7 ?8 ?9
+24654: Id : 4, {_}:
+ apply (apply w ?11) ?12 =?= apply (apply ?11 ?12) ?12
+ [12, 11] by w_definition ?11 ?12
+24654: Goal:
+24654: Id : 1, {_}:
+ apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (g ?1)) (h ?1)
+ =<=
+ apply (apply (f ?1) (g ?1)) (apply (apply (f ?1) (g ?1)) (h ?1))
+ [1] by prove_p_combinator ?1
+24654: Order:
+24654: nrkbo
+24654: Leaf order:
+24654: w 1 0 0
+24654: q 1 0 0
+24654: b 1 0 0
+24654: h 2 1 2 0,2,2
+24654: g 4 1 4 0,2,1,1,2
+24654: apply 22 2 8 0,2
+24654: f 3 1 3 0,2,1,1,1,2
+% SZS status Timeout for COL066-1.p
+NO CLASH, using fixed ground order
+24759: Facts:
+24759: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
+24759: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
+24759: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
+24759: Id : 5, {_}:
+ meet ?9 ?10 =?= meet ?10 ?9
+ [10, 9] by commutativity_of_meet ?9 ?10
+24759: Id : 6, {_}:
+ join ?12 ?13 =?= join ?13 ?12
+ [13, 12] by commutativity_of_join ?12 ?13
+24759: Id : 7, {_}:
+ meet (meet ?15 ?16) ?17 =?= meet ?15 (meet ?16 ?17)
+ [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
+24759: Id : 8, {_}:
+ join (join ?19 ?20) ?21 =?= join ?19 (join ?20 ?21)
+ [21, 20, 19] by associativity_of_join ?19 ?20 ?21
+24759: Id : 9, {_}:
+ complement (complement ?23) =>= ?23
+ [23] by complement_involution ?23
+24759: Id : 10, {_}:
+ join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
+ [26, 25] by join_complement ?25 ?26
+24759: Id : 11, {_}:
+ meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
+ [29, 28] by meet_complement ?28 ?29
+24759: Goal:
+24759: Id : 1, {_}:
+ join
+ (complement
+ (join
+ (join (meet (complement a) b)
+ (meet (complement a) (complement b)))
+ (meet a (join (complement a) b)))) (join (complement a) b)
+ =>=
+ n1
+ [] by prove_e3
+24759: Order:
+24759: nrkbo
+24759: Leaf order:
+24759: n0 1 0 0
+24759: n1 2 0 1 3
+24759: join 17 2 5 0,2
+24759: meet 12 2 3 0,1,1,1,1,2
+24759: b 4 0 4 2,1,1,1,1,2
+24759: complement 15 1 6 0,1,2
+24759: a 5 0 5 1,1,1,1,1,1,2
+NO CLASH, using fixed ground order
+24760: Facts:
+24760: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
+24760: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
+24760: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
+24760: Id : 5, {_}:
+ meet ?9 ?10 =?= meet ?10 ?9
+ [10, 9] by commutativity_of_meet ?9 ?10
+24760: Id : 6, {_}:
+ join ?12 ?13 =?= join ?13 ?12
+ [13, 12] by commutativity_of_join ?12 ?13
+24760: Id : 7, {_}:
+ meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
+ [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
+24760: Id : 8, {_}:
+ join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
+ [21, 20, 19] by associativity_of_join ?19 ?20 ?21
+24760: Id : 9, {_}:
+ complement (complement ?23) =>= ?23
+ [23] by complement_involution ?23
+24760: Id : 10, {_}:
+ join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
+ [26, 25] by join_complement ?25 ?26
+24760: Id : 11, {_}:
+ meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
+ [29, 28] by meet_complement ?28 ?29
+24760: Goal:
+24760: Id : 1, {_}:
+ join
+ (complement
+ (join
+ (join (meet (complement a) b)
+ (meet (complement a) (complement b)))
+ (meet a (join (complement a) b)))) (join (complement a) b)
+ =>=
+ n1
+ [] by prove_e3
+24760: Order:
+24760: kbo
+24760: Leaf order:
+24760: n0 1 0 0
+24760: n1 2 0 1 3
+24760: join 17 2 5 0,2
+24760: meet 12 2 3 0,1,1,1,1,2
+24760: b 4 0 4 2,1,1,1,1,2
+24760: complement 15 1 6 0,1,2
+24760: a 5 0 5 1,1,1,1,1,1,2
+NO CLASH, using fixed ground order
+24761: Facts:
+24761: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
+24761: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
+24761: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
+24761: Id : 5, {_}:
+ meet ?9 ?10 =?= meet ?10 ?9
+ [10, 9] by commutativity_of_meet ?9 ?10
+24761: Id : 6, {_}:
+ join ?12 ?13 =?= join ?13 ?12
+ [13, 12] by commutativity_of_join ?12 ?13
+24761: Id : 7, {_}:
+ meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
+ [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
+24761: Id : 8, {_}:
+ join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
+ [21, 20, 19] by associativity_of_join ?19 ?20 ?21
+24761: Id : 9, {_}:
+ complement (complement ?23) =>= ?23
+ [23] by complement_involution ?23
+24761: Id : 10, {_}:
+ join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
+ [26, 25] by join_complement ?25 ?26
+24761: Id : 11, {_}:
+ meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
+ [29, 28] by meet_complement ?28 ?29
+24761: Goal:
+24761: Id : 1, {_}:
+ join
+ (complement
+ (join
+ (join (meet (complement a) b)
+ (meet (complement a) (complement b)))
+ (meet a (join (complement a) b)))) (join (complement a) b)
+ =>=
+ n1
+ [] by prove_e3
+24761: Order:
+24761: lpo
+24761: Leaf order:
+24761: n0 1 0 0
+24761: n1 2 0 1 3
+24761: join 17 2 5 0,2
+24761: meet 12 2 3 0,1,1,1,1,2
+24761: b 4 0 4 2,1,1,1,1,2
+24761: complement 15 1 6 0,1,2
+24761: a 5 0 5 1,1,1,1,1,1,2
+% SZS status Timeout for LAT018-1.p
+NO CLASH, using fixed ground order
+24778: Facts:
+24778: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+24778: Goal:
+24778: Id : 1, {_}:
+ meet (meet a b) c =>= meet a (meet b c)
+ [] by prove_normal_axioms_3
+24778: Order:
+24778: nrkbo
+24778: Leaf order:
+24778: join 20 2 0
+24778: c 2 0 2 2,2
+24778: meet 22 2 4 0,2
+24778: b 2 0 2 2,1,2
+24778: a 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+24779: Facts:
+24779: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+24779: Goal:
+24779: Id : 1, {_}:
+ meet (meet a b) c =>= meet a (meet b c)
+ [] by prove_normal_axioms_3
+24779: Order:
+24779: kbo
+24779: Leaf order:
+24779: join 20 2 0
+24779: c 2 0 2 2,2
+24779: meet 22 2 4 0,2
+24779: b 2 0 2 2,1,2
+24779: a 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+24780: Facts:
+24780: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+24780: Goal:
+24780: Id : 1, {_}:
+ meet (meet a b) c =>= meet a (meet b c)
+ [] by prove_normal_axioms_3
+24780: Order:
+24780: lpo
+24780: Leaf order:
+24780: join 20 2 0
+24780: c 2 0 2 2,2
+24780: meet 22 2 4 0,2
+24780: b 2 0 2 2,1,2
+24780: a 2 0 2 1,1,2
+% SZS status Timeout for LAT082-1.p
+NO CLASH, using fixed ground order
+24809: Facts:
+24809: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+24809: Goal:
+24809: Id : 1, {_}:
+ join (join a b) c =>= join a (join b c)
+ [] by prove_normal_axioms_6
+24809: Order:
+24809: kbo
+24809: Leaf order:
+24809: meet 18 2 0
+24809: c 2 0 2 2,2
+24809: join 24 2 4 0,2
+24809: b 2 0 2 2,1,2
+24809: a 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+24810: Facts:
+24810: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+24810: Goal:
+24810: Id : 1, {_}:
+ join (join a b) c =>= join a (join b c)
+ [] by prove_normal_axioms_6
+24810: Order:
+24810: lpo
+24810: Leaf order:
+24810: meet 18 2 0
+24810: c 2 0 2 2,2
+24810: join 24 2 4 0,2
+24810: b 2 0 2 2,1,2
+24810: a 2 0 2 1,1,2
+NO CLASH, using fixed ground order
+24808: Facts:
+24808: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+24808: Goal:
+24808: Id : 1, {_}:
+ join (join a b) c =>= join a (join b c)
+ [] by prove_normal_axioms_6
+24808: Order:
+24808: nrkbo
+24808: Leaf order:
+24808: meet 18 2 0
+24808: c 2 0 2 2,2
+24808: join 24 2 4 0,2
+24808: b 2 0 2 2,1,2
+24808: a 2 0 2 1,1,2
+% SZS status Timeout for LAT085-1.p
+NO CLASH, using fixed ground order
+24831: Facts:
+24831: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24831: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24831: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24831: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24831: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24831: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24831: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24831: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24831: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
+ [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
+24831: Goal:
+24831: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+24831: Order:
+24831: nrkbo
+24831: Leaf order:
+24831: join 16 2 4 0,2,2
+24831: meet 22 2 6 0,2
+24831: c 4 0 4 2,2,2,2
+24831: b 4 0 4 1,2,2
+24831: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+24832: Facts:
+24832: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24832: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24832: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24832: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24832: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24832: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24832: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24832: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24832: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
+ [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
+24832: Goal:
+24832: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+24832: Order:
+24832: kbo
+24832: Leaf order:
+24832: join 16 2 4 0,2,2
+24832: meet 22 2 6 0,2
+24832: c 4 0 4 2,2,2,2
+24832: b 4 0 4 1,2,2
+24832: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+24833: Facts:
+24833: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24833: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24833: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24833: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24833: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24833: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24833: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24833: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24833: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
+ [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
+24833: Goal:
+24833: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+24833: Order:
+24833: lpo
+24833: Leaf order:
+24833: join 16 2 4 0,2,2
+24833: meet 22 2 6 0,2
+24833: c 4 0 4 2,2,2,2
+24833: b 4 0 4 1,2,2
+24833: a 4 0 4 1,2
+% SZS status Timeout for LAT144-1.p
+NO CLASH, using fixed ground order
+24860: Facts:
+24860: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24860: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24860: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24860: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24860: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24860: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24860: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24860: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24860: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
+ [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
+24860: Goal:
+24860: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+24860: Order:
+24860: nrkbo
+24860: Leaf order:
+24860: meet 19 2 5 0,2
+24860: join 18 2 5 0,2,2
+24860: d 2 0 2 2,2,2,2,2
+24860: c 3 0 3 1,2,2,2
+24860: b 3 0 3 1,2,2
+24860: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+24861: Facts:
+24861: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24861: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24861: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24861: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24861: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24861: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24861: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24861: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24861: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
+ [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
+24861: Goal:
+24861: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+24861: Order:
+24861: kbo
+24861: Leaf order:
+24861: meet 19 2 5 0,2
+24861: join 18 2 5 0,2,2
+24861: d 2 0 2 2,2,2,2,2
+24861: c 3 0 3 1,2,2,2
+24861: b 3 0 3 1,2,2
+24861: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+24862: Facts:
+24862: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24862: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24862: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24862: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24862: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24862: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24862: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24862: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24862: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
+ [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
+24862: Goal:
+24862: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+24862: Order:
+24862: lpo
+24862: Leaf order:
+24862: meet 19 2 5 0,2
+24862: join 18 2 5 0,2,2
+24862: d 2 0 2 2,2,2,2,2
+24862: c 3 0 3 1,2,2,2
+24862: b 3 0 3 1,2,2
+24862: a 4 0 4 1,2
+% SZS status Timeout for LAT150-1.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+24889: Facts:
+24889: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24889: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24889: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24889: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24889: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24889: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24889: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24889: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24889: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
+ [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
+24889: Goal:
+24889: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+24889: Order:
+24889: kbo
+24889: Leaf order:
+24889: meet 19 2 5 0,2
+24889: join 18 2 5 0,2,2
+24889: d 2 0 2 2,2,2,2,2
+24889: c 3 0 3 1,2,2,2
+24889: b 3 0 3 1,2,2
+24889: a 4 0 4 1,2
+24888: Facts:
+24888: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24888: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24888: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24888: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24888: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24888: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24888: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24888: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24888: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
+ [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
+24888: Goal:
+24888: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+24888: Order:
+24888: nrkbo
+24888: Leaf order:
+24888: meet 19 2 5 0,2
+24888: join 18 2 5 0,2,2
+24888: d 2 0 2 2,2,2,2,2
+24888: c 3 0 3 1,2,2,2
+24888: b 3 0 3 1,2,2
+24888: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+24890: Facts:
+24890: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24890: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24890: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24890: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24890: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24890: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24890: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24890: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24890: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
+ [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
+24890: Goal:
+24890: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =>=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+24890: Order:
+24890: lpo
+24890: Leaf order:
+24890: meet 19 2 5 0,2
+24890: join 18 2 5 0,2,2
+24890: d 2 0 2 2,2,2,2,2
+24890: c 3 0 3 1,2,2,2
+24890: b 3 0 3 1,2,2
+24890: a 4 0 4 1,2
+% SZS status Timeout for LAT151-1.p
+NO CLASH, using fixed ground order
+24921: Facts:
+24921: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24921: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24921: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24921: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24921: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24921: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24921: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24921: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24921: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
+ [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
+24921: Goal:
+24921: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+24921: Order:
+24921: nrkbo
+24921: Leaf order:
+24921: join 18 2 4 0,2,2
+24921: meet 20 2 6 0,2
+24921: c 3 0 3 2,2,2,2
+24921: b 3 0 3 1,2,2
+24921: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+24922: Facts:
+24922: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24922: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24922: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24922: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24922: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24922: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24922: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24922: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24922: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
+ [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
+24922: Goal:
+24922: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+24922: Order:
+24922: kbo
+24922: Leaf order:
+24922: join 18 2 4 0,2,2
+24922: meet 20 2 6 0,2
+24922: c 3 0 3 2,2,2,2
+24922: b 3 0 3 1,2,2
+24922: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+24923: Facts:
+24923: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24923: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24923: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24923: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24923: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24923: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24923: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24923: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24923: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
+ [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
+24923: Goal:
+24923: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+24923: Order:
+24923: lpo
+24923: Leaf order:
+24923: join 18 2 4 0,2,2
+24923: meet 20 2 6 0,2
+24923: c 3 0 3 2,2,2,2
+24923: b 3 0 3 1,2,2
+24923: a 6 0 6 1,2
+% SZS status Timeout for LAT152-1.p
+NO CLASH, using fixed ground order
+24939: Facts:
+24939: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24939: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24939: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24939: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24939: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24939: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24939: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24939: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24939: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
+ [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
+24939: Goal:
+24939: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
+ [] by prove_H7
+24939: Order:
+24939: nrkbo
+24939: Leaf order:
+24939: join 18 2 4 0,2,2
+24939: meet 20 2 6 0,2
+24939: c 2 0 2 2,2,2,2
+24939: b 4 0 4 1,2,2
+24939: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+24940: Facts:
+24940: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24940: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24940: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24940: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24940: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24940: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24940: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24940: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24940: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
+ [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
+24940: Goal:
+24940: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
+ [] by prove_H7
+24940: Order:
+24940: kbo
+24940: Leaf order:
+24940: join 18 2 4 0,2,2
+24940: meet 20 2 6 0,2
+24940: c 2 0 2 2,2,2,2
+24940: b 4 0 4 1,2,2
+24940: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+24941: Facts:
+24941: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24941: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24941: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24941: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24941: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24941: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24941: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24941: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24941: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
+ [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
+24941: Goal:
+24941: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
+ [] by prove_H7
+24941: Order:
+24941: lpo
+24941: Leaf order:
+24941: join 18 2 4 0,2,2
+24941: meet 20 2 6 0,2
+24941: c 2 0 2 2,2,2,2
+24941: b 4 0 4 1,2,2
+24941: a 6 0 6 1,2
+% SZS status Timeout for LAT159-1.p
+NO CLASH, using fixed ground order
+24972: Facts:
+24972: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24972: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24972: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+NO CLASH, using fixed ground order
+24972: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24972: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24972: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24972: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24972: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24972: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
+ [28, 27, 26] by equation_H68 ?26 ?27 ?28
+24972: Goal:
+24972: Id : 1, {_}:
+ meet a (meet b (join c d))
+ =<=
+ meet a (meet b (join c (meet a (join d (meet b c)))))
+ [] by prove_H73
+24972: Order:
+24972: nrkbo
+24972: Leaf order:
+24972: meet 19 2 6 0,2
+24972: join 15 2 3 0,2,2,2
+24972: d 2 0 2 2,2,2,2
+24972: c 3 0 3 1,2,2,2
+24972: b 3 0 3 1,2,2
+24972: a 3 0 3 1,2
+24973: Facts:
+24973: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24973: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24973: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24973: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24973: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24973: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24973: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24973: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24973: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
+ [28, 27, 26] by equation_H68 ?26 ?27 ?28
+24973: Goal:
+24973: Id : 1, {_}:
+ meet a (meet b (join c d))
+ =<=
+ meet a (meet b (join c (meet a (join d (meet b c)))))
+ [] by prove_H73
+24973: Order:
+24973: kbo
+24973: Leaf order:
+24973: meet 19 2 6 0,2
+24973: join 15 2 3 0,2,2,2
+24973: d 2 0 2 2,2,2,2
+24973: c 3 0 3 1,2,2,2
+24973: b 3 0 3 1,2,2
+24973: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+24974: Facts:
+24974: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24974: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24974: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24974: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24974: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24974: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24974: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24974: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24974: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
+ [28, 27, 26] by equation_H68 ?26 ?27 ?28
+24974: Goal:
+24974: Id : 1, {_}:
+ meet a (meet b (join c d))
+ =<=
+ meet a (meet b (join c (meet a (join d (meet b c)))))
+ [] by prove_H73
+24974: Order:
+24974: lpo
+24974: Leaf order:
+24974: meet 19 2 6 0,2
+24974: join 15 2 3 0,2,2,2
+24974: d 2 0 2 2,2,2,2
+24974: c 3 0 3 1,2,2,2
+24974: b 3 0 3 1,2,2
+24974: a 3 0 3 1,2
+% SZS status Timeout for LAT162-1.p
+NO CLASH, using fixed ground order
+24990: Facts:
+24990: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24990: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24990: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24990: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24990: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24990: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24990: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24990: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24990: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
+24990: Goal:
+24990: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+24990: Order:
+24990: nrkbo
+24990: Leaf order:
+24990: join 17 2 4 0,2,2
+24990: meet 20 2 6 0,2
+24990: c 3 0 3 2,2,2,2
+24990: b 3 0 3 1,2,2
+24990: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+24991: Facts:
+24991: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24991: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24991: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24991: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24991: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24991: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24991: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24991: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24991: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
+24991: Goal:
+24991: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+24991: Order:
+24991: kbo
+24991: Leaf order:
+24991: join 17 2 4 0,2,2
+24991: meet 20 2 6 0,2
+24991: c 3 0 3 2,2,2,2
+24991: b 3 0 3 1,2,2
+24991: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+24992: Facts:
+24992: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24992: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24992: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24992: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24992: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24992: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24992: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24992: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24992: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
+24992: Goal:
+24992: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+24992: Order:
+24992: lpo
+24992: Leaf order:
+24992: join 17 2 4 0,2,2
+24992: meet 20 2 6 0,2
+24992: c 3 0 3 2,2,2,2
+24992: b 3 0 3 1,2,2
+24992: a 6 0 6 1,2
+% SZS status Timeout for LAT164-1.p
+NO CLASH, using fixed ground order
+25019: Facts:
+NO CLASH, using fixed ground order
+25020: Facts:
+25020: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25020: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25020: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25020: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25020: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25020: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25020: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25020: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25020: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?27 (meet ?26 (join ?27 ?28)))
+ (join ?28 (meet ?26 ?27)))
+ [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
+25020: Goal:
+25020: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H58
+25020: Order:
+25020: kbo
+25020: Leaf order:
+25020: meet 17 2 4 0,2
+25020: join 19 2 4 0,2,2
+25020: c 2 0 2 2,2,2
+25020: b 4 0 4 1,2,2
+25020: a 4 0 4 1,2
+25019: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25019: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25019: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25019: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25019: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25019: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25019: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+NO CLASH, using fixed ground order
+25019: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25019: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?27 (meet ?26 (join ?27 ?28)))
+ (join ?28 (meet ?26 ?27)))
+ [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
+25019: Goal:
+25019: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H58
+25019: Order:
+25019: nrkbo
+25019: Leaf order:
+25019: meet 17 2 4 0,2
+25019: join 19 2 4 0,2,2
+25019: c 2 0 2 2,2,2
+25019: b 4 0 4 1,2,2
+25019: a 4 0 4 1,2
+25021: Facts:
+25021: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25021: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25021: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25021: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25021: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25021: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25021: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25021: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25021: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?27 (meet ?26 (join ?27 ?28)))
+ (join ?28 (meet ?26 ?27)))
+ [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
+25021: Goal:
+25021: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H58
+25021: Order:
+25021: lpo
+25021: Leaf order:
+25021: meet 17 2 4 0,2
+25021: join 19 2 4 0,2,2
+25021: c 2 0 2 2,2,2
+25021: b 4 0 4 1,2,2
+25021: a 4 0 4 1,2
+% SZS status Timeout for LAT169-1.p
+NO CLASH, using fixed ground order
+25071: Facts:
+25071: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25071: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25071: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25071: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25071: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25071: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25071: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25071: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25071: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
+25071: Goal:
+25071: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+25071: Order:
+25071: nrkbo
+25071: Leaf order:
+25071: join 18 2 4 0,2,2
+25071: meet 19 2 6 0,2
+25071: c 3 0 3 2,2,2,2
+25071: b 3 0 3 1,2,2
+25071: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+25072: Facts:
+25072: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25072: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25072: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25072: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25072: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25072: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25072: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25072: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25072: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
+25072: Goal:
+25072: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+25072: Order:
+25072: kbo
+25072: Leaf order:
+25072: join 18 2 4 0,2,2
+25072: meet 19 2 6 0,2
+25072: c 3 0 3 2,2,2,2
+25072: b 3 0 3 1,2,2
+25072: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+25073: Facts:
+25073: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25073: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25073: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25073: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25073: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25073: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25073: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25073: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25073: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
+ =?=
+ join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
+25073: Goal:
+25073: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+25073: Order:
+25073: lpo
+25073: Leaf order:
+25073: join 18 2 4 0,2,2
+25073: meet 19 2 6 0,2
+25073: c 3 0 3 2,2,2,2
+25073: b 3 0 3 1,2,2
+25073: a 6 0 6 1,2
+% SZS status Timeout for LAT174-1.p
+NO CLASH, using fixed ground order
+25101: Facts:
+25101: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25101: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25101: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25101: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25101: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25101: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25101: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25101: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25101: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25101: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25101: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25101: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25101: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25101: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25101: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25101: Goal:
+25101: Id : 1, {_}:
+ multiply cz (multiply cx (multiply cy cx))
+ =<=
+ multiply (multiply (multiply cz cx) cy) cx
+ [] by prove_right_moufang
+25101: Order:
+25101: nrkbo
+25101: Leaf order:
+25101: commutator 1 2 0
+25101: associator 1 3 0
+25101: additive_inverse 6 1 0
+25101: add 16 2 0
+25101: additive_identity 8 0 0
+25101: multiply 28 2 6 0,2
+25101: cy 2 0 2 1,2,2,2
+25101: cx 4 0 4 1,2,2
+25101: cz 2 0 2 1,2
+NO CLASH, using fixed ground order
+25102: Facts:
+25102: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25102: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25102: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25102: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25102: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25102: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25102: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25102: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25102: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25102: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+NO CLASH, using fixed ground order
+25103: Facts:
+25103: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25103: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25103: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25103: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25103: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25103: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25103: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25103: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25103: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25102: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25102: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25102: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25102: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25102: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25102: Goal:
+25102: Id : 1, {_}:
+ multiply cz (multiply cx (multiply cy cx))
+ =<=
+ multiply (multiply (multiply cz cx) cy) cx
+ [] by prove_right_moufang
+25102: Order:
+25102: kbo
+25102: Leaf order:
+25102: commutator 1 2 0
+25102: associator 1 3 0
+25102: additive_inverse 6 1 0
+25102: add 16 2 0
+25102: additive_identity 8 0 0
+25102: multiply 28 2 6 0,2
+25102: cy 2 0 2 1,2,2,2
+25102: cx 4 0 4 1,2,2
+25102: cz 2 0 2 1,2
+25103: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25103: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25103: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25103: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25103: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25103: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25103: Goal:
+25103: Id : 1, {_}:
+ multiply cz (multiply cx (multiply cy cx))
+ =<=
+ multiply (multiply (multiply cz cx) cy) cx
+ [] by prove_right_moufang
+25103: Order:
+25103: lpo
+25103: Leaf order:
+25103: commutator 1 2 0
+25103: associator 1 3 0
+25103: additive_inverse 6 1 0
+25103: add 16 2 0
+25103: additive_identity 8 0 0
+25103: multiply 28 2 6 0,2
+25103: cy 2 0 2 1,2,2,2
+25103: cx 4 0 4 1,2,2
+25103: cz 2 0 2 1,2
+% SZS status Timeout for RNG027-5.p
+NO CLASH, using fixed ground order
+25119: Facts:
+25119: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25119: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25119: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25119: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25119: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25119: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25119: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25119: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25119: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25119: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25119: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25119: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25119: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25119: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25119: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25119: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+25119: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+25119: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+25119: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+25119: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+25119: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+25119: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+25119: Goal:
+25119: Id : 1, {_}:
+ multiply cz (multiply cx (multiply cy cx))
+ =<=
+ multiply (multiply (multiply cz cx) cy) cx
+ [] by prove_right_moufang
+25119: Order:
+25119: nrkbo
+25119: Leaf order:
+25119: commutator 1 2 0
+25119: associator 1 3 0
+25119: additive_inverse 22 1 0
+25119: add 24 2 0
+25119: additive_identity 8 0 0
+25119: multiply 46 2 6 0,2
+25119: cy 2 0 2 1,2,2,2
+25119: cx 4 0 4 1,2,2
+25119: cz 2 0 2 1,2
+NO CLASH, using fixed ground order
+25120: Facts:
+25120: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25120: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25120: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25120: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25120: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25120: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25120: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25120: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25120: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25120: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25120: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25120: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25120: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25120: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25120: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25120: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+25120: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+25120: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+25120: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+25120: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+25120: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+25120: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+25120: Goal:
+25120: Id : 1, {_}:
+ multiply cz (multiply cx (multiply cy cx))
+ =<=
+ multiply (multiply (multiply cz cx) cy) cx
+ [] by prove_right_moufang
+25120: Order:
+25120: kbo
+25120: Leaf order:
+25120: commutator 1 2 0
+25120: associator 1 3 0
+25120: additive_inverse 22 1 0
+25120: add 24 2 0
+25120: additive_identity 8 0 0
+25120: multiply 46 2 6 0,2
+25120: cy 2 0 2 1,2,2,2
+25120: cx 4 0 4 1,2,2
+25120: cz 2 0 2 1,2
+NO CLASH, using fixed ground order
+25121: Facts:
+25121: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25121: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25121: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25121: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25121: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25121: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25121: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25121: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25121: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25121: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25121: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25121: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25121: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25121: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25121: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25121: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+25121: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+25121: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+25121: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =>=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+25121: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =>=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+25121: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =>=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+25121: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =>=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+25121: Goal:
+25121: Id : 1, {_}:
+ multiply cz (multiply cx (multiply cy cx))
+ =<=
+ multiply (multiply (multiply cz cx) cy) cx
+ [] by prove_right_moufang
+25121: Order:
+25121: lpo
+25121: Leaf order:
+25121: commutator 1 2 0
+25121: associator 1 3 0
+25121: additive_inverse 22 1 0
+25121: add 24 2 0
+25121: additive_identity 8 0 0
+25121: multiply 46 2 6 0,2
+25121: cy 2 0 2 1,2,2,2
+25121: cx 4 0 4 1,2,2
+25121: cz 2 0 2 1,2
+% SZS status Timeout for RNG027-7.p
+NO CLASH, using fixed ground order
+25148: Facts:
+25148: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25148: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25148: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25148: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25148: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25148: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25148: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25148: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25148: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25148: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25148: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25148: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25148: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25148: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25148: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25148: Goal:
+25148: Id : 1, {_}:
+ associator x (multiply x y) z =<= multiply (associator x y z) x
+ [] by prove_right_moufang
+25148: Order:
+25148: nrkbo
+25148: Leaf order:
+25148: commutator 1 2 0
+25148: additive_inverse 6 1 0
+25148: add 16 2 0
+25148: additive_identity 8 0 0
+25148: associator 3 3 2 0,2
+25148: z 2 0 2 3,2
+25148: multiply 24 2 2 0,2,2
+25148: y 2 0 2 2,2,2
+25148: x 4 0 4 1,2
+NO CLASH, using fixed ground order
+25149: Facts:
+25149: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25149: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25149: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25149: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25149: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25149: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25149: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25149: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25149: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25149: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25149: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25149: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25149: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25149: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25149: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25149: Goal:
+25149: Id : 1, {_}:
+ associator x (multiply x y) z =<= multiply (associator x y z) x
+ [] by prove_right_moufang
+25149: Order:
+25149: kbo
+25149: Leaf order:
+25149: commutator 1 2 0
+25149: additive_inverse 6 1 0
+25149: add 16 2 0
+25149: additive_identity 8 0 0
+25149: associator 3 3 2 0,2
+25149: z 2 0 2 3,2
+25149: multiply 24 2 2 0,2,2
+25149: y 2 0 2 2,2,2
+25149: x 4 0 4 1,2
+NO CLASH, using fixed ground order
+25150: Facts:
+25150: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25150: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25150: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25150: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25150: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25150: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25150: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25150: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25150: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25150: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25150: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25150: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25150: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25150: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25150: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25150: Goal:
+25150: Id : 1, {_}:
+ associator x (multiply x y) z =<= multiply (associator x y z) x
+ [] by prove_right_moufang
+25150: Order:
+25150: lpo
+25150: Leaf order:
+25150: commutator 1 2 0
+25150: additive_inverse 6 1 0
+25150: add 16 2 0
+25150: additive_identity 8 0 0
+25150: associator 3 3 2 0,2
+25150: z 2 0 2 3,2
+25150: multiply 24 2 2 0,2,2
+25150: y 2 0 2 2,2,2
+25150: x 4 0 4 1,2
+% SZS status Timeout for RNG027-8.p
+NO CLASH, using fixed ground order
+25166: Facts:
+25166: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25166: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25166: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25166: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25166: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25166: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25166: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25166: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25166: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25166: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25166: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25166: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25166: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25166: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25166: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25166: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+25166: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+25166: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+25166: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+25166: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+25166: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+25166: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+25166: Goal:
+25166: Id : 1, {_}:
+ associator x (multiply x y) z =<= multiply (associator x y z) x
+ [] by prove_right_moufang
+25166: Order:
+25166: nrkbo
+25166: Leaf order:
+25166: commutator 1 2 0
+25166: additive_inverse 22 1 0
+25166: add 24 2 0
+25166: additive_identity 8 0 0
+25166: associator 3 3 2 0,2
+25166: z 2 0 2 3,2
+25166: multiply 42 2 2 0,2,2
+25166: y 2 0 2 2,2,2
+25166: x 4 0 4 1,2
+NO CLASH, using fixed ground order
+25168: Facts:
+25168: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25168: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25168: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25168: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25168: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25168: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25168: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25168: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25168: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25168: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25168: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25168: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25168: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25168: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25168: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25168: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+25168: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+25168: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+25168: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =>=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+25168: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =>=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+25168: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =>=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+25168: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =>=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+25168: Goal:
+25168: Id : 1, {_}:
+ associator x (multiply x y) z =<= multiply (associator x y z) x
+ [] by prove_right_moufang
+25168: Order:
+25168: lpo
+25168: Leaf order:
+25168: commutator 1 2 0
+25168: additive_inverse 22 1 0
+25168: add 24 2 0
+25168: additive_identity 8 0 0
+25168: associator 3 3 2 0,2
+25168: z 2 0 2 3,2
+25168: multiply 42 2 2 0,2,2
+25168: y 2 0 2 2,2,2
+25168: x 4 0 4 1,2
+NO CLASH, using fixed ground order
+25167: Facts:
+25167: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25167: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25167: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25167: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25167: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25167: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25167: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25167: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25167: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25167: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25167: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25167: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25167: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25167: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25167: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25167: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+25167: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+25167: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+25167: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+25167: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+25167: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+25167: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+25167: Goal:
+25167: Id : 1, {_}:
+ associator x (multiply x y) z =<= multiply (associator x y z) x
+ [] by prove_right_moufang
+25167: Order:
+25167: kbo
+25167: Leaf order:
+25167: commutator 1 2 0
+25167: additive_inverse 22 1 0
+25167: add 24 2 0
+25167: additive_identity 8 0 0
+25167: associator 3 3 2 0,2
+25167: z 2 0 2 3,2
+25167: multiply 42 2 2 0,2,2
+25167: y 2 0 2 2,2,2
+25167: x 4 0 4 1,2
+% SZS status Timeout for RNG027-9.p
+NO CLASH, using fixed ground order
+25195: Facts:
+25195: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25195: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25195: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25195: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25195: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25195: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25195: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25195: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25195: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25195: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25195: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25195: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25195: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25195: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25195: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25195: Goal:
+25195: Id : 1, {_}:
+ multiply (multiply cx (multiply cy cx)) cz
+ =>=
+ multiply cx (multiply cy (multiply cx cz))
+ [] by prove_left_moufang
+25195: Order:
+25195: nrkbo
+25195: Leaf order:
+25195: commutator 1 2 0
+25195: associator 1 3 0
+25195: additive_inverse 6 1 0
+25195: add 16 2 0
+25195: additive_identity 8 0 0
+25195: cz 2 0 2 2,2
+25195: multiply 28 2 6 0,2
+25195: cy 2 0 2 1,2,1,2
+25195: cx 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+25196: Facts:
+25196: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25196: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25196: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25196: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25196: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25196: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25196: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25196: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25196: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25196: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25196: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25196: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25196: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25196: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25196: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25196: Goal:
+25196: Id : 1, {_}:
+ multiply (multiply cx (multiply cy cx)) cz
+ =>=
+ multiply cx (multiply cy (multiply cx cz))
+ [] by prove_left_moufang
+25196: Order:
+25196: kbo
+25196: Leaf order:
+25196: commutator 1 2 0
+25196: associator 1 3 0
+25196: additive_inverse 6 1 0
+25196: add 16 2 0
+25196: additive_identity 8 0 0
+25196: cz 2 0 2 2,2
+25196: multiply 28 2 6 0,2
+25196: cy 2 0 2 1,2,1,2
+25196: cx 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+25197: Facts:
+25197: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25197: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25197: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25197: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25197: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25197: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25197: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25197: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25197: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25197: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25197: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25197: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25197: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25197: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25197: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25197: Goal:
+25197: Id : 1, {_}:
+ multiply (multiply cx (multiply cy cx)) cz
+ =>=
+ multiply cx (multiply cy (multiply cx cz))
+ [] by prove_left_moufang
+25197: Order:
+25197: lpo
+25197: Leaf order:
+25197: commutator 1 2 0
+25197: associator 1 3 0
+25197: additive_inverse 6 1 0
+25197: add 16 2 0
+25197: additive_identity 8 0 0
+25197: cz 2 0 2 2,2
+25197: multiply 28 2 6 0,2
+25197: cy 2 0 2 1,2,1,2
+25197: cx 4 0 4 1,1,2
+% SZS status Timeout for RNG028-5.p
+NO CLASH, using fixed ground order
+25213: Facts:
+25213: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25213: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25213: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25213: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25213: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25213: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25213: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25213: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25213: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25213: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25213: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25213: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25213: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25213: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25213: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25213: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+25213: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+25213: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+25213: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+25213: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+25213: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+25213: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+25213: Goal:
+25213: Id : 1, {_}:
+ multiply (multiply cx (multiply cy cx)) cz
+ =>=
+ multiply cx (multiply cy (multiply cx cz))
+ [] by prove_left_moufang
+25213: Order:
+25213: nrkbo
+25213: Leaf order:
+25213: commutator 1 2 0
+25213: associator 1 3 0
+25213: additive_inverse 22 1 0
+25213: add 24 2 0
+25213: additive_identity 8 0 0
+25213: cz 2 0 2 2,2
+25213: multiply 46 2 6 0,2
+25213: cy 2 0 2 1,2,1,2
+25213: cx 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+25214: Facts:
+25214: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25214: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25214: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25214: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25214: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25214: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25214: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25214: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25214: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25214: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25214: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25214: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25214: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25214: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25214: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25214: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+25214: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+25214: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+25214: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+25214: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+25214: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+25214: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+25214: Goal:
+25214: Id : 1, {_}:
+ multiply (multiply cx (multiply cy cx)) cz
+ =>=
+ multiply cx (multiply cy (multiply cx cz))
+ [] by prove_left_moufang
+25214: Order:
+25214: kbo
+25214: Leaf order:
+25214: commutator 1 2 0
+25214: associator 1 3 0
+25214: additive_inverse 22 1 0
+25214: add 24 2 0
+25214: additive_identity 8 0 0
+25214: cz 2 0 2 2,2
+25214: multiply 46 2 6 0,2
+25214: cy 2 0 2 1,2,1,2
+25214: cx 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+25215: Facts:
+25215: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25215: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25215: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25215: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25215: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25215: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25215: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25215: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25215: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25215: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25215: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25215: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25215: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25215: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25215: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25215: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+25215: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+25215: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+25215: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =>=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+25215: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =>=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+25215: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =>=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+25215: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =>=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+25215: Goal:
+25215: Id : 1, {_}:
+ multiply (multiply cx (multiply cy cx)) cz
+ =>=
+ multiply cx (multiply cy (multiply cx cz))
+ [] by prove_left_moufang
+25215: Order:
+25215: lpo
+25215: Leaf order:
+25215: commutator 1 2 0
+25215: associator 1 3 0
+25215: additive_inverse 22 1 0
+25215: add 24 2 0
+25215: additive_identity 8 0 0
+25215: cz 2 0 2 2,2
+25215: multiply 46 2 6 0,2
+25215: cy 2 0 2 1,2,1,2
+25215: cx 4 0 4 1,1,2
+% SZS status Timeout for RNG028-7.p
+NO CLASH, using fixed ground order
+25251: Facts:
+25251: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25251: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25251: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25251: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25251: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25251: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25251: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25251: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25251: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25251: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25251: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25251: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25251: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25251: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25251: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25251: Goal:
+25251: Id : 1, {_}:
+ associator x (multiply y x) z =<= multiply x (associator x y z)
+ [] by prove_left_moufang
+25251: Order:
+25251: nrkbo
+25251: Leaf order:
+25251: commutator 1 2 0
+25251: additive_inverse 6 1 0
+25251: add 16 2 0
+25251: additive_identity 8 0 0
+25251: associator 3 3 2 0,2
+25251: z 2 0 2 3,2
+25251: multiply 24 2 2 0,2,2
+25251: y 2 0 2 1,2,2
+25251: x 4 0 4 1,2
+NO CLASH, using fixed ground order
+25252: Facts:
+25252: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25252: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25252: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25252: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25252: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25252: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25252: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25252: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25252: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25252: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25252: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25252: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25252: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25252: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25252: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25252: Goal:
+25252: Id : 1, {_}:
+ associator x (multiply y x) z =<= multiply x (associator x y z)
+ [] by prove_left_moufang
+25252: Order:
+25252: kbo
+25252: Leaf order:
+25252: commutator 1 2 0
+25252: additive_inverse 6 1 0
+25252: add 16 2 0
+25252: additive_identity 8 0 0
+25252: associator 3 3 2 0,2
+25252: z 2 0 2 3,2
+25252: multiply 24 2 2 0,2,2
+25252: y 2 0 2 1,2,2
+25252: x 4 0 4 1,2
+NO CLASH, using fixed ground order
+25253: Facts:
+25253: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25253: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25253: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25253: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25253: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25253: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25253: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25253: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25253: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25253: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25253: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25253: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25253: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25253: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25253: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25253: Goal:
+25253: Id : 1, {_}:
+ associator x (multiply y x) z =<= multiply x (associator x y z)
+ [] by prove_left_moufang
+25253: Order:
+25253: lpo
+25253: Leaf order:
+25253: commutator 1 2 0
+25253: additive_inverse 6 1 0
+25253: add 16 2 0
+25253: additive_identity 8 0 0
+25253: associator 3 3 2 0,2
+25253: z 2 0 2 3,2
+25253: multiply 24 2 2 0,2,2
+25253: y 2 0 2 1,2,2
+25253: x 4 0 4 1,2
+% SZS status Timeout for RNG028-8.p
+NO CLASH, using fixed ground order
+25289: Facts:
+25289: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25289: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25289: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25289: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25289: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25289: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25289: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25289: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25289: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25289: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25289: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25289: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25289: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25289: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25289: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25289: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+25289: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+25289: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+25289: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+25289: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+25289: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+25289: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+25289: Goal:
+25289: Id : 1, {_}:
+ associator x (multiply y x) z =<= multiply x (associator x y z)
+ [] by prove_left_moufang
+25289: Order:
+25289: nrkbo
+25289: Leaf order:
+25289: commutator 1 2 0
+25289: additive_inverse 22 1 0
+25289: add 24 2 0
+25289: additive_identity 8 0 0
+25289: associator 3 3 2 0,2
+25289: z 2 0 2 3,2
+25289: multiply 42 2 2 0,2,2
+25289: y 2 0 2 1,2,2
+25289: x 4 0 4 1,2
+NO CLASH, using fixed ground order
+25290: Facts:
+25290: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25290: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25290: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25290: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25290: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25290: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25290: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25290: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25290: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25290: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25290: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25290: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25290: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25290: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25290: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25290: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+25290: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+25290: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+25290: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+25290: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+25290: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+25290: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+25290: Goal:
+25290: Id : 1, {_}:
+ associator x (multiply y x) z =<= multiply x (associator x y z)
+ [] by prove_left_moufang
+25290: Order:
+25290: kbo
+25290: Leaf order:
+25290: commutator 1 2 0
+25290: additive_inverse 22 1 0
+25290: add 24 2 0
+25290: additive_identity 8 0 0
+25290: associator 3 3 2 0,2
+25290: z 2 0 2 3,2
+25290: multiply 42 2 2 0,2,2
+25290: y 2 0 2 1,2,2
+25290: x 4 0 4 1,2
+NO CLASH, using fixed ground order
+25291: Facts:
+25291: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25291: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25291: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25291: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25291: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25291: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25291: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25291: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25291: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25291: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25291: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25291: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25291: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25291: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25291: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25291: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+25291: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+25291: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+25291: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =>=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+25291: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =>=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+25291: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =>=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+25291: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =>=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+25291: Goal:
+25291: Id : 1, {_}:
+ associator x (multiply y x) z =<= multiply x (associator x y z)
+ [] by prove_left_moufang
+25291: Order:
+25291: lpo
+25291: Leaf order:
+25291: commutator 1 2 0
+25291: additive_inverse 22 1 0
+25291: add 24 2 0
+25291: additive_identity 8 0 0
+25291: associator 3 3 2 0,2
+25291: z 2 0 2 3,2
+25291: multiply 42 2 2 0,2,2
+25291: y 2 0 2 1,2,2
+25291: x 4 0 4 1,2
+% SZS status Timeout for RNG028-9.p
+NO CLASH, using fixed ground order
+25318: Facts:
+25318: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25318: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25318: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25318: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25318: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25318: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25318: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25318: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25318: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25318: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25318: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25318: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25318: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25318: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25318: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25318: Goal:
+25318: Id : 1, {_}:
+ multiply (multiply cx cy) (multiply cz cx)
+ =>=
+ multiply cx (multiply (multiply cy cz) cx)
+ [] by prove_middle_law
+25318: Order:
+25318: nrkbo
+25318: Leaf order:
+25318: commutator 1 2 0
+25318: associator 1 3 0
+25318: additive_inverse 6 1 0
+25318: add 16 2 0
+25318: additive_identity 8 0 0
+25318: cz 2 0 2 1,2,2
+25318: multiply 28 2 6 0,2
+25318: cy 2 0 2 2,1,2
+25318: cx 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+25320: Facts:
+25320: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25320: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25320: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25320: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25320: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25320: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25320: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25320: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25320: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25320: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25320: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25320: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25320: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25320: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25320: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25320: Goal:
+25320: Id : 1, {_}:
+ multiply (multiply cx cy) (multiply cz cx)
+ =>=
+ multiply cx (multiply (multiply cy cz) cx)
+ [] by prove_middle_law
+25320: Order:
+25320: lpo
+25320: Leaf order:
+25320: commutator 1 2 0
+25320: associator 1 3 0
+25320: additive_inverse 6 1 0
+25320: add 16 2 0
+25320: additive_identity 8 0 0
+25320: cz 2 0 2 1,2,2
+25320: multiply 28 2 6 0,2
+25320: cy 2 0 2 2,1,2
+25320: cx 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+25319: Facts:
+25319: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25319: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25319: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25319: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25319: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25319: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25319: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25319: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25319: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25319: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25319: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25319: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25319: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25319: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25319: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25319: Goal:
+25319: Id : 1, {_}:
+ multiply (multiply cx cy) (multiply cz cx)
+ =>=
+ multiply cx (multiply (multiply cy cz) cx)
+ [] by prove_middle_law
+25319: Order:
+25319: kbo
+25319: Leaf order:
+25319: commutator 1 2 0
+25319: associator 1 3 0
+25319: additive_inverse 6 1 0
+25319: add 16 2 0
+25319: additive_identity 8 0 0
+25319: cz 2 0 2 1,2,2
+25319: multiply 28 2 6 0,2
+25319: cy 2 0 2 2,1,2
+25319: cx 4 0 4 1,1,2
+% SZS status Timeout for RNG029-5.p
+NO CLASH, using fixed ground order
+25337: Facts:
+25337: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25337: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25337: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25337: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25337: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25337: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25337: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25337: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25337: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25337: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25337: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25337: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25337: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25337: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25337: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25337: Goal:
+25337: Id : 1, {_}:
+ multiply (multiply x y) (multiply z x)
+ =<=
+ multiply (multiply x (multiply y z)) x
+ [] by prove_middle_moufang
+25337: Order:
+25337: nrkbo
+25337: Leaf order:
+25337: commutator 1 2 0
+25337: associator 1 3 0
+25337: additive_inverse 6 1 0
+25337: add 16 2 0
+25337: additive_identity 8 0 0
+25337: z 2 0 2 1,2,2
+25337: multiply 28 2 6 0,2
+25337: y 2 0 2 2,1,2
+25337: x 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+25338: Facts:
+25338: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25338: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25338: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25338: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25338: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25338: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25338: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25338: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25338: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25338: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25338: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25338: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25338: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25338: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25338: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25338: Goal:
+25338: Id : 1, {_}:
+ multiply (multiply x y) (multiply z x)
+ =<=
+ multiply (multiply x (multiply y z)) x
+ [] by prove_middle_moufang
+25338: Order:
+25338: kbo
+25338: Leaf order:
+25338: commutator 1 2 0
+25338: associator 1 3 0
+25338: additive_inverse 6 1 0
+25338: add 16 2 0
+25338: additive_identity 8 0 0
+25338: z 2 0 2 1,2,2
+25338: multiply 28 2 6 0,2
+25338: y 2 0 2 2,1,2
+25338: x 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+25339: Facts:
+25339: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25339: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25339: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25339: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25339: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25339: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25339: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25339: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25339: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25339: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25339: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25339: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25339: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25339: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25339: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25339: Goal:
+25339: Id : 1, {_}:
+ multiply (multiply x y) (multiply z x)
+ =<=
+ multiply (multiply x (multiply y z)) x
+ [] by prove_middle_moufang
+25339: Order:
+25339: lpo
+25339: Leaf order:
+25339: commutator 1 2 0
+25339: associator 1 3 0
+25339: additive_inverse 6 1 0
+25339: add 16 2 0
+25339: additive_identity 8 0 0
+25339: z 2 0 2 1,2,2
+25339: multiply 28 2 6 0,2
+25339: y 2 0 2 2,1,2
+25339: x 4 0 4 1,1,2
+% SZS status Timeout for RNG029-6.p
+NO CLASH, using fixed ground order
+25367: Facts:
+25367: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25367: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25367: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25367: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25367: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25367: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25367: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25367: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25367: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25367: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25367: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25367: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25367: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25367: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25367: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25367: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+25367: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+25367: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+25367: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+25367: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+25367: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+25367: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+25367: Goal:
+25367: Id : 1, {_}:
+ multiply (multiply x y) (multiply z x)
+ =<=
+ multiply (multiply x (multiply y z)) x
+ [] by prove_middle_moufang
+25367: Order:
+25367: nrkbo
+25367: Leaf order:
+25367: commutator 1 2 0
+25367: associator 1 3 0
+25367: additive_inverse 22 1 0
+25367: add 24 2 0
+25367: additive_identity 8 0 0
+25367: z 2 0 2 1,2,2
+25367: multiply 46 2 6 0,2
+25367: y 2 0 2 2,1,2
+25367: x 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+25368: Facts:
+25368: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25368: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25368: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+NO CLASH, using fixed ground order
+25369: Facts:
+25369: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25369: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25369: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25369: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25369: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25369: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25369: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25369: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25369: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25369: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25369: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25369: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25369: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25369: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25369: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25369: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+25369: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+25369: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+25369: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =>=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+25369: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =>=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+25369: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =>=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+25369: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =>=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+25369: Goal:
+25369: Id : 1, {_}:
+ multiply (multiply x y) (multiply z x)
+ =<=
+ multiply (multiply x (multiply y z)) x
+ [] by prove_middle_moufang
+25369: Order:
+25369: lpo
+25369: Leaf order:
+25369: commutator 1 2 0
+25369: associator 1 3 0
+25369: additive_inverse 22 1 0
+25369: add 24 2 0
+25369: additive_identity 8 0 0
+25369: z 2 0 2 1,2,2
+25369: multiply 46 2 6 0,2
+25369: y 2 0 2 2,1,2
+25369: x 4 0 4 1,1,2
+25368: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25368: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25368: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25368: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25368: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25368: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25368: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25368: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25368: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25368: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25368: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25368: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25368: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+25368: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+25368: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+25368: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+25368: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+25368: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+25368: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+25368: Goal:
+25368: Id : 1, {_}:
+ multiply (multiply x y) (multiply z x)
+ =<=
+ multiply (multiply x (multiply y z)) x
+ [] by prove_middle_moufang
+25368: Order:
+25368: kbo
+25368: Leaf order:
+25368: commutator 1 2 0
+25368: associator 1 3 0
+25368: additive_inverse 22 1 0
+25368: add 24 2 0
+25368: additive_identity 8 0 0
+25368: z 2 0 2 1,2,2
+25368: multiply 46 2 6 0,2
+25368: y 2 0 2 2,1,2
+25368: x 4 0 4 1,1,2
+% SZS status Timeout for RNG029-7.p
+NO CLASH, using fixed ground order
+25651: Facts:
+25651: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+25651: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+25651: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+25651: Id : 5, {_}: add c d =>= d [] by absorbtion
+25651: Goal:
+NO CLASH, using fixed ground order
+25652: Facts:
+25652: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+25652: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+25652: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+25652: Id : 5, {_}: add c d =>= d [] by absorbtion
+25652: Goal:
+25652: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+25652: Order:
+25652: kbo
+25652: Leaf order:
+25652: d 2 0 0
+25652: c 1 0 0
+25652: add 13 2 3 0,2
+25652: negate 9 1 5 0,1,2
+25652: b 3 0 3 1,2,1,1,2
+25652: a 2 0 2 1,1,1,2
+25651: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+25651: Order:
+25651: nrkbo
+25651: Leaf order:
+25651: d 2 0 0
+25651: c 1 0 0
+25651: add 13 2 3 0,2
+25651: negate 9 1 5 0,1,2
+25651: b 3 0 3 1,2,1,1,2
+25651: a 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+25653: Facts:
+25653: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+25653: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+25653: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+25653: Id : 5, {_}: add c d =>= d [] by absorbtion
+25653: Goal:
+25653: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+25653: Order:
+25653: lpo
+25653: Leaf order:
+25653: d 2 0 0
+25653: c 1 0 0
+25653: add 13 2 3 0,2
+25653: negate 9 1 5 0,1,2
+25653: b 3 0 3 1,2,1,1,2
+25653: a 2 0 2 1,1,1,2
+% SZS status Timeout for ROB006-1.p
+NO CLASH, using fixed ground order
+25684: Facts:
+25684: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
+25684: Id : 3, {_}:
+ add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8)
+ [8, 7, 6] by associativity_of_add ?6 ?7 ?8
+25684: Id : 4, {_}:
+ negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
+ =>=
+ ?10
+ [11, 10] by robbins_axiom ?10 ?11
+25684: Id : 5, {_}: add c d =>= d [] by absorbtion
+25684: Goal:
+25684: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
+25684: Order:
+25684: nrkbo
+25684: Leaf order:
+25684: d 2 0 0
+25684: c 1 0 0
+25684: negate 4 1 0
+25684: add 11 2 1 0,2
+NO CLASH, using fixed ground order
+25685: Facts:
+25685: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
+25685: Id : 3, {_}:
+ add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
+ [8, 7, 6] by associativity_of_add ?6 ?7 ?8
+25685: Id : 4, {_}:
+ negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
+ =>=
+ ?10
+ [11, 10] by robbins_axiom ?10 ?11
+25685: Id : 5, {_}: add c d =>= d [] by absorbtion
+25685: Goal:
+25685: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
+25685: Order:
+25685: kbo
+25685: Leaf order:
+25685: d 2 0 0
+25685: c 1 0 0
+25685: negate 4 1 0
+25685: add 11 2 1 0,2
+NO CLASH, using fixed ground order
+25686: Facts:
+25686: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
+25686: Id : 3, {_}:
+ add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
+ [8, 7, 6] by associativity_of_add ?6 ?7 ?8
+25686: Id : 4, {_}:
+ negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
+ =>=
+ ?10
+ [11, 10] by robbins_axiom ?10 ?11
+25686: Id : 5, {_}: add c d =>= d [] by absorbtion
+25686: Goal:
+25686: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
+25686: Order:
+25686: lpo
+25686: Leaf order:
+25686: d 2 0 0
+25686: c 1 0 0
+25686: negate 4 1 0
+25686: add 11 2 1 0,2
+% SZS status Timeout for ROB006-2.p
+NO CLASH, using fixed ground order
+25702: Facts:
+25702: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+25702: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+25702: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+25702: Id : 5, {_}: add c d =>= c [] by identity_constant
+25702: Goal:
+25702: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+25702: Order:
+25702: nrkbo
+25702: Leaf order:
+25702: d 1 0 0
+25702: c 2 0 0
+25702: add 13 2 3 0,2
+25702: negate 9 1 5 0,1,2
+25702: b 3 0 3 1,2,1,1,2
+25702: a 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+25704: Facts:
+25704: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+25704: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+25704: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+25704: Id : 5, {_}: add c d =>= c [] by identity_constant
+25704: Goal:
+25704: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+25704: Order:
+25704: lpo
+25704: Leaf order:
+25704: d 1 0 0
+25704: c 2 0 0
+25704: add 13 2 3 0,2
+25704: negate 9 1 5 0,1,2
+25704: b 3 0 3 1,2,1,1,2
+25704: a 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+25703: Facts:
+25703: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+25703: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+25703: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+25703: Id : 5, {_}: add c d =>= c [] by identity_constant
+25703: Goal:
+25703: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+25703: Order:
+25703: kbo
+25703: Leaf order:
+25703: d 1 0 0
+25703: c 2 0 0
+25703: add 13 2 3 0,2
+25703: negate 9 1 5 0,1,2
+25703: b 3 0 3 1,2,1,1,2
+25703: a 2 0 2 1,1,1,2
+% SZS status Timeout for ROB026-1.p
+NO CLASH, using fixed ground order
+25731: Facts:
+25731: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25731: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25731: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25731: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25731: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25731: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25731: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25731: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25731: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25731: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25731: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25731: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25731: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25731: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25731: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25731: Goal:
+25731: Id : 1, {_}:
+ least_upper_bound a (greatest_lower_bound b c)
+ =<=
+ greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c)
+ [] by prove_distrnu
+25731: Order:
+25731: nrkbo
+25731: Leaf order:
+25731: inverse 1 1 0
+25731: multiply 18 2 0
+25731: identity 2 0 0
+25731: least_upper_bound 16 2 3 0,2
+25731: greatest_lower_bound 15 2 2 0,2,2
+25731: c 2 0 2 2,2,2
+25731: b 2 0 2 1,2,2
+25731: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+25732: Facts:
+25732: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25732: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25732: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25732: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25732: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25732: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25732: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25732: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25732: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25732: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25732: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25732: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25732: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25732: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25732: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25732: Goal:
+25732: Id : 1, {_}:
+ least_upper_bound a (greatest_lower_bound b c)
+ =<=
+ greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c)
+ [] by prove_distrnu
+25732: Order:
+25732: kbo
+25732: Leaf order:
+25732: inverse 1 1 0
+25732: multiply 18 2 0
+25732: identity 2 0 0
+25732: least_upper_bound 16 2 3 0,2
+25732: greatest_lower_bound 15 2 2 0,2,2
+25732: c 2 0 2 2,2,2
+25732: b 2 0 2 1,2,2
+25732: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+25733: Facts:
+25733: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25733: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25733: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25733: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25733: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25733: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25733: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25733: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25733: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25733: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25733: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25733: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25733: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25733: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25733: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25733: Goal:
+25733: Id : 1, {_}:
+ least_upper_bound a (greatest_lower_bound b c)
+ =<=
+ greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c)
+ [] by prove_distrnu
+25733: Order:
+25733: lpo
+25733: Leaf order:
+25733: inverse 1 1 0
+25733: multiply 18 2 0
+25733: identity 2 0 0
+25733: least_upper_bound 16 2 3 0,2
+25733: greatest_lower_bound 15 2 2 0,2,2
+25733: c 2 0 2 2,2,2
+25733: b 2 0 2 1,2,2
+25733: a 3 0 3 1,2
+% SZS status Timeout for GRP164-1.p
+NO CLASH, using fixed ground order
+25749: Facts:
+25749: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25749: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25749: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25749: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25749: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25749: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25749: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25749: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25749: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25749: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25749: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25749: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25749: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25749: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25749: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25749: Goal:
+25749: Id : 1, {_}:
+ greatest_lower_bound a (least_upper_bound b c)
+ =<=
+ least_upper_bound (greatest_lower_bound a b)
+ (greatest_lower_bound a c)
+ [] by prove_distrun
+25749: Order:
+25749: nrkbo
+25749: Leaf order:
+25749: inverse 1 1 0
+25749: multiply 18 2 0
+25749: identity 2 0 0
+25749: greatest_lower_bound 16 2 3 0,2
+25749: least_upper_bound 15 2 2 0,2,2
+25749: c 2 0 2 2,2,2
+25749: b 2 0 2 1,2,2
+25749: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+25750: Facts:
+25750: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25750: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25750: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25750: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25750: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25750: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25750: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25750: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25750: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25750: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25750: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+NO CLASH, using fixed ground order
+25751: Facts:
+25751: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25751: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25751: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25751: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25751: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25751: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25751: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25751: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25751: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25751: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25751: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25751: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25751: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25751: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25751: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25751: Goal:
+25751: Id : 1, {_}:
+ greatest_lower_bound a (least_upper_bound b c)
+ =<=
+ least_upper_bound (greatest_lower_bound a b)
+ (greatest_lower_bound a c)
+ [] by prove_distrun
+25751: Order:
+25751: lpo
+25751: Leaf order:
+25751: inverse 1 1 0
+25751: multiply 18 2 0
+25751: identity 2 0 0
+25751: greatest_lower_bound 16 2 3 0,2
+25751: least_upper_bound 15 2 2 0,2,2
+25751: c 2 0 2 2,2,2
+25751: b 2 0 2 1,2,2
+25751: a 3 0 3 1,2
+25750: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25750: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25750: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25750: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25750: Goal:
+25750: Id : 1, {_}:
+ greatest_lower_bound a (least_upper_bound b c)
+ =<=
+ least_upper_bound (greatest_lower_bound a b)
+ (greatest_lower_bound a c)
+ [] by prove_distrun
+25750: Order:
+25750: kbo
+25750: Leaf order:
+25750: inverse 1 1 0
+25750: multiply 18 2 0
+25750: identity 2 0 0
+25750: greatest_lower_bound 16 2 3 0,2
+25750: least_upper_bound 15 2 2 0,2,2
+25750: c 2 0 2 2,2,2
+25750: b 2 0 2 1,2,2
+25750: a 3 0 3 1,2
+% SZS status Timeout for GRP164-2.p
+NO CLASH, using fixed ground order
+25782: Facts:
+25782: Id : 2, {_}:
+ multiply (multiply ?2 ?3) ?4 =?= multiply ?2 (multiply ?3 ?4)
+ [4, 3, 2] by associativity_of_multiply ?2 ?3 ?4
+25782: Id : 3, {_}:
+ multiply ?6 (multiply ?7 (multiply ?7 ?7))
+ =?=
+ multiply ?7 (multiply ?7 (multiply ?7 ?6))
+ [7, 6] by condition ?6 ?7
+25782: Goal:
+25782: Id : 1, {_}:
+ multiply a
+ (multiply b
+ (multiply a
+ (multiply b
+ (multiply a
+ (multiply b
+ (multiply a
+ (multiply b
+ (multiply a
+ (multiply b
+ (multiply a
+ (multiply b
+ (multiply a
+ (multiply b
+ (multiply a (multiply b (multiply a b))))))))))))))))
+ =<=
+ multiply a
+ (multiply a
+ (multiply a
+ (multiply a
+ (multiply a
+ (multiply a
+ (multiply a
+ (multiply a
+ (multiply a
+ (multiply b
+ (multiply b
+ (multiply b
+ (multiply b
+ (multiply b
+ (multiply b (multiply b (multiply b b))))))))))))))))
+ [] by prove_this
+25782: Order:
+25782: nrkbo
+25782: Leaf order:
+25782: multiply 44 2 34 0,2
+25782: b 18 0 18 1,2,2
+25782: a 18 0 18 1,2
+NO CLASH, using fixed ground order
+25783: Facts:
+25783: Id : 2, {_}:
+ multiply (multiply ?2 ?3) ?4 =>= multiply ?2 (multiply ?3 ?4)
+ [4, 3, 2] by associativity_of_multiply ?2 ?3 ?4
+25783: Id : 3, {_}:
+ multiply ?6 (multiply ?7 (multiply ?7 ?7))
+ =?=
+ multiply ?7 (multiply ?7 (multiply ?7 ?6))
+ [7, 6] by condition ?6 ?7
+25783: Goal:
+25783: Id : 1, {_}:
+ multiply a
+ (multiply b
+ (multiply a
+ (multiply b
+ (multiply a
+ (multiply b
+ (multiply a
+ (multiply b
+ (multiply a
+ (multiply b
+ (multiply a
+ (multiply b
+ (multiply a
+ (multiply b
+ (multiply a (multiply b (multiply a b))))))))))))))))
+ =?=
+ multiply a
+ (multiply a
+ (multiply a
+ (multiply a
+ (multiply a
+ (multiply a
+ (multiply a
+ (multiply a
+ (multiply a
+ (multiply b
+ (multiply b
+ (multiply b
+ (multiply b
+ (multiply b
+ (multiply b (multiply b (multiply b b))))))))))))))))
+ [] by prove_this
+25783: Order:
+25783: kbo
+25783: Leaf order:
+25783: multiply 44 2 34 0,2
+25783: b 18 0 18 1,2,2
+25783: a 18 0 18 1,2
+NO CLASH, using fixed ground order
+% SZS status Timeout for GRP196-1.p
+NO CLASH, using fixed ground order
+25809: Facts:
+25809: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
+ (f ?3 (f (f ?3 (f (f ?2 ?2) ?2)) ?4))
+ =>=
+ ?3
+ [5, 4, 3, 2] by ol_23A ?2 ?3 ?4 ?5
+25809: Goal:
+25809: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
+ [] by associativity
+25809: Order:
+25809: nrkbo
+25809: Leaf order:
+25809: f 18 2 8 0,2
+25809: c 3 0 3 2,1,2,2
+25809: b 4 0 4 1,1,2,2
+25809: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+25810: Facts:
+25810: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
+ (f ?3 (f (f ?3 (f (f ?2 ?2) ?2)) ?4))
+ =>=
+ ?3
+ [5, 4, 3, 2] by ol_23A ?2 ?3 ?4 ?5
+25810: Goal:
+25810: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
+ [] by associativity
+25810: Order:
+25810: kbo
+25810: Leaf order:
+25810: f 18 2 8 0,2
+25810: c 3 0 3 2,1,2,2
+25810: b 4 0 4 1,1,2,2
+25810: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+25811: Facts:
+25811: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
+ (f ?3 (f (f ?3 (f (f ?2 ?2) ?2)) ?4))
+ =>=
+ ?3
+ [5, 4, 3, 2] by ol_23A ?2 ?3 ?4 ?5
+25811: Goal:
+25811: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
+ [] by associativity
+25811: Order:
+25811: lpo
+25811: Leaf order:
+25811: f 18 2 8 0,2
+25811: c 3 0 3 2,1,2,2
+25811: b 4 0 4 1,1,2,2
+25811: a 3 0 3 1,2
+% SZS status Timeout for LAT070-1.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+25843: Facts:
+25843: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25843: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25843: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25843: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25843: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25843: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25843: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25843: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25843: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
+ [28, 27, 26] by equation_H7 ?26 ?27 ?28
+25843: Goal:
+25843: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+25843: Order:
+25843: kbo
+25843: Leaf order:
+25843: join 17 2 4 0,2,2
+25843: meet 21 2 6 0,2
+25843: c 3 0 3 2,2,2,2
+25843: b 3 0 3 1,2,2
+25843: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+25844: Facts:
+25844: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25844: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25844: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25844: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25844: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25844: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25844: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25844: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25844: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
+ [28, 27, 26] by equation_H7 ?26 ?27 ?28
+25844: Goal:
+25844: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+25844: Order:
+25844: lpo
+25844: Leaf order:
+25844: join 17 2 4 0,2,2
+25844: meet 21 2 6 0,2
+25844: c 3 0 3 2,2,2,2
+25844: b 3 0 3 1,2,2
+25844: a 6 0 6 1,2
+25842: Facts:
+25842: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25842: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25842: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25842: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25842: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25842: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25842: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25842: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25842: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
+ [28, 27, 26] by equation_H7 ?26 ?27 ?28
+25842: Goal:
+25842: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+25842: Order:
+25842: nrkbo
+25842: Leaf order:
+25842: join 17 2 4 0,2,2
+25842: meet 21 2 6 0,2
+25842: c 3 0 3 2,2,2,2
+25842: b 3 0 3 1,2,2
+25842: a 6 0 6 1,2
+% SZS status Timeout for LAT138-1.p
+NO CLASH, using fixed ground order
+25866: Facts:
+25866: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25866: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25866: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25866: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25866: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25866: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25866: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25866: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25866: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?26 (meet ?27 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H21 ?26 ?27 ?28
+25866: Goal:
+25866: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+25866: Order:
+25866: nrkbo
+25866: Leaf order:
+25866: join 17 2 4 0,2,2
+25866: meet 21 2 6 0,2
+25866: c 4 0 4 2,2,2,2
+25866: b 4 0 4 1,2,2
+25866: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+25867: Facts:
+25867: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25867: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25867: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25867: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25867: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25867: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25867: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25867: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25867: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?26 (meet ?27 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H21 ?26 ?27 ?28
+25867: Goal:
+25867: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+25867: Order:
+25867: kbo
+25867: Leaf order:
+25867: join 17 2 4 0,2,2
+25867: meet 21 2 6 0,2
+25867: c 4 0 4 2,2,2,2
+25867: b 4 0 4 1,2,2
+25867: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+25868: Facts:
+25868: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25868: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25868: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25868: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25868: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25868: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25868: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25868: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25868: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?26 (meet ?27 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H21 ?26 ?27 ?28
+25868: Goal:
+25868: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+25868: Order:
+25868: lpo
+25868: Leaf order:
+25868: join 17 2 4 0,2,2
+25868: meet 21 2 6 0,2
+25868: c 4 0 4 2,2,2,2
+25868: b 4 0 4 1,2,2
+25868: a 4 0 4 1,2
+% SZS status Timeout for LAT140-1.p
+NO CLASH, using fixed ground order
+25928: Facts:
+25928: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25928: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25928: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25928: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25928: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25928: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25928: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25928: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25928: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
+ [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
+25928: Goal:
+NO CLASH, using fixed ground order
+25929: Facts:
+25929: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25929: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25929: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25929: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25929: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25929: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25929: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25929: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25929: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
+ [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
+25929: Goal:
+25929: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+25929: Order:
+25929: kbo
+25929: Leaf order:
+25929: join 16 2 4 0,2,2
+25929: meet 22 2 6 0,2
+25929: c 3 0 3 2,2,2,2
+25929: b 3 0 3 1,2,2
+25929: a 6 0 6 1,2
+25928: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+25928: Order:
+25928: nrkbo
+25928: Leaf order:
+25928: join 16 2 4 0,2,2
+25928: meet 22 2 6 0,2
+25928: c 3 0 3 2,2,2,2
+25928: b 3 0 3 1,2,2
+25928: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+25930: Facts:
+25930: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25930: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25930: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25930: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25930: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25930: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25930: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25930: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25930: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
+ [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
+25930: Goal:
+25930: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+25930: Order:
+25930: lpo
+25930: Leaf order:
+25930: join 16 2 4 0,2,2
+25930: meet 22 2 6 0,2
+25930: c 3 0 3 2,2,2,2
+25930: b 3 0 3 1,2,2
+25930: a 6 0 6 1,2
+% SZS status Timeout for LAT145-1.p
+NO CLASH, using fixed ground order
+25948: Facts:
+25948: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25948: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25948: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25948: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25948: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25948: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25948: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25948: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25948: Id : 10, {_}:
+ meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
+25948: Goal:
+25948: Id : 1, {_}:
+ meet a (join b (meet c (join b d)))
+ =<=
+ meet a (join b (meet c (join d (meet a (join b d)))))
+ [] by prove_H43
+25948: Order:
+25948: nrkbo
+25948: Leaf order:
+25948: meet 19 2 5 0,2
+25948: join 19 2 5 0,2,2
+25948: d 3 0 3 2,2,2,2,2
+25948: c 2 0 2 1,2,2,2
+25948: b 4 0 4 1,2,2
+25948: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+25949: Facts:
+25949: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25949: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25949: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25949: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25949: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25949: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25949: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25949: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25949: Id : 10, {_}:
+ meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
+25949: Goal:
+25949: Id : 1, {_}:
+ meet a (join b (meet c (join b d)))
+ =<=
+ meet a (join b (meet c (join d (meet a (join b d)))))
+ [] by prove_H43
+25949: Order:
+25949: kbo
+25949: Leaf order:
+25949: meet 19 2 5 0,2
+25949: join 19 2 5 0,2,2
+25949: d 3 0 3 2,2,2,2,2
+25949: c 2 0 2 1,2,2,2
+25949: b 4 0 4 1,2,2
+25949: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+25950: Facts:
+25950: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25950: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25950: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25950: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25950: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25950: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25950: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25950: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25950: Id : 10, {_}:
+ meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
+ =?=
+ meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
+25950: Goal:
+25950: Id : 1, {_}:
+ meet a (join b (meet c (join b d)))
+ =<=
+ meet a (join b (meet c (join d (meet a (join b d)))))
+ [] by prove_H43
+25950: Order:
+25950: lpo
+25950: Leaf order:
+25950: meet 19 2 5 0,2
+25950: join 19 2 5 0,2,2
+25950: d 3 0 3 2,2,2,2,2
+25950: c 2 0 2 1,2,2,2
+25950: b 4 0 4 1,2,2
+25950: a 3 0 3 1,2
+% SZS status Timeout for LAT149-1.p
+NO CLASH, using fixed ground order
+26495: Facts:
+26495: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26495: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26495: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26495: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26495: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26495: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26495: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26495: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26495: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
+ [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
+26495: Goal:
+26495: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
+ [] by prove_H7
+26495: Order:
+26495: nrkbo
+26495: Leaf order:
+26495: join 18 2 4 0,2,2
+26495: meet 20 2 6 0,2
+26495: c 2 0 2 2,2,2,2
+26495: b 4 0 4 1,2,2
+26495: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+26496: Facts:
+26496: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26496: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26496: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26496: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26496: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26496: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26496: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26496: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26496: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
+ [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
+26496: Goal:
+26496: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
+ [] by prove_H7
+26496: Order:
+26496: kbo
+26496: Leaf order:
+26496: join 18 2 4 0,2,2
+26496: meet 20 2 6 0,2
+26496: c 2 0 2 2,2,2,2
+26496: b 4 0 4 1,2,2
+26496: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+26497: Facts:
+26497: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26497: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26497: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26497: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26497: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26497: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26497: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26497: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26497: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
+ [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
+26497: Goal:
+26497: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
+ [] by prove_H7
+26497: Order:
+26497: lpo
+26497: Leaf order:
+26497: join 18 2 4 0,2,2
+26497: meet 20 2 6 0,2
+26497: c 2 0 2 2,2,2,2
+26497: b 4 0 4 1,2,2
+26497: a 6 0 6 1,2
+% SZS status Timeout for LAT153-1.p
+NO CLASH, using fixed ground order
+26513: Facts:
+26513: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26513: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26513: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26513: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26513: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26513: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26513: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26513: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26513: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
+ [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
+26513: Goal:
+26513: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+26513: Order:
+26513: nrkbo
+26513: Leaf order:
+26513: join 18 2 4 0,2,2
+26513: meet 20 2 6 0,2
+26513: c 4 0 4 2,2,2,2
+26513: b 4 0 4 1,2,2
+26513: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+26514: Facts:
+26514: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26514: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26514: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26514: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26514: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26514: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26514: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26514: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26514: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
+ [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
+26514: Goal:
+26514: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+26514: Order:
+26514: kbo
+26514: Leaf order:
+26514: join 18 2 4 0,2,2
+26514: meet 20 2 6 0,2
+26514: c 4 0 4 2,2,2,2
+26514: b 4 0 4 1,2,2
+26514: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+26515: Facts:
+26515: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26515: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26515: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26515: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26515: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26515: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26515: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26515: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26515: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
+ [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
+26515: Goal:
+26515: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+26515: Order:
+26515: lpo
+26515: Leaf order:
+26515: join 18 2 4 0,2,2
+26515: meet 20 2 6 0,2
+26515: c 4 0 4 2,2,2,2
+26515: b 4 0 4 1,2,2
+26515: a 4 0 4 1,2
+% SZS status Timeout for LAT157-1.p
+NO CLASH, using fixed ground order
+26542: Facts:
+26542: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26542: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26542: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26542: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26542: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26542: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26542: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26542: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26542: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
+ [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
+26542: Goal:
+26542: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (join (meet a c) (meet c (join b d))))
+ [] by prove_H49
+26542: Order:
+26542: nrkbo
+26542: Leaf order:
+26542: meet 19 2 5 0,2
+26542: join 19 2 5 0,2,2
+26542: d 2 0 2 2,2,2,2,2
+26542: c 3 0 3 1,2,2,2
+26542: b 3 0 3 1,2,2
+26542: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+26543: Facts:
+26543: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26543: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26543: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26543: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26543: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26543: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26543: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26543: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26543: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
+ [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
+26543: Goal:
+26543: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (join (meet a c) (meet c (join b d))))
+ [] by prove_H49
+26543: Order:
+26543: kbo
+26543: Leaf order:
+26543: meet 19 2 5 0,2
+26543: join 19 2 5 0,2,2
+26543: d 2 0 2 2,2,2,2,2
+26543: c 3 0 3 1,2,2,2
+26543: b 3 0 3 1,2,2
+26543: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+26544: Facts:
+26544: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26544: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26544: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26544: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26544: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26544: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26544: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26544: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26544: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
+ [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
+26544: Goal:
+26544: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (join (meet a c) (meet c (join b d))))
+ [] by prove_H49
+26544: Order:
+26544: lpo
+26544: Leaf order:
+26544: meet 19 2 5 0,2
+26544: join 19 2 5 0,2,2
+26544: d 2 0 2 2,2,2,2,2
+26544: c 3 0 3 1,2,2,2
+26544: b 3 0 3 1,2,2
+26544: a 4 0 4 1,2
+% SZS status Timeout for LAT158-1.p
+NO CLASH, using fixed ground order
+26561: Facts:
+26561: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26561: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26561: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26561: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26561: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26561: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26561: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26561: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26561: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
+26561: Goal:
+26561: Id : 1, {_}:
+ meet a (join b (meet a (meet c d)))
+ =<=
+ meet a (join b (meet c (join (meet a d) (meet b d))))
+ [] by prove_H32
+26561: Order:
+26561: nrkbo
+26561: Leaf order:
+26561: join 16 2 3 0,2,2
+26561: meet 21 2 7 0,2
+26561: d 3 0 3 2,2,2,2,2
+26561: c 2 0 2 1,2,2,2,2
+26561: b 3 0 3 1,2,2
+26561: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+26562: Facts:
+26562: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26562: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26562: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26562: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26562: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26562: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26562: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26562: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26562: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
+26562: Goal:
+26562: Id : 1, {_}:
+ meet a (join b (meet a (meet c d)))
+ =<=
+ meet a (join b (meet c (join (meet a d) (meet b d))))
+ [] by prove_H32
+26562: Order:
+26562: kbo
+26562: Leaf order:
+26562: join 16 2 3 0,2,2
+26562: meet 21 2 7 0,2
+26562: d 3 0 3 2,2,2,2,2
+26562: c 2 0 2 1,2,2,2,2
+26562: b 3 0 3 1,2,2
+26562: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+26563: Facts:
+26563: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26563: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26563: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26563: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26563: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26563: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26563: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26563: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26563: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
+26563: Goal:
+26563: Id : 1, {_}:
+ meet a (join b (meet a (meet c d)))
+ =>=
+ meet a (join b (meet c (join (meet a d) (meet b d))))
+ [] by prove_H32
+26563: Order:
+26563: lpo
+26563: Leaf order:
+26563: join 16 2 3 0,2,2
+26563: meet 21 2 7 0,2
+26563: d 3 0 3 2,2,2,2,2
+26563: c 2 0 2 1,2,2,2,2
+26563: b 3 0 3 1,2,2
+26563: a 4 0 4 1,2
+% SZS status Timeout for LAT163-1.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+26595: Facts:
+26595: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26595: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26595: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26595: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26595: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26595: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26595: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26595: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26595: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
+26595: Goal:
+26595: Id : 1, {_}:
+ meet a (join b (meet c (join b d)))
+ =<=
+ meet a (join b (meet c (join d (meet a (meet b c)))))
+ [] by prove_H77
+26595: Order:
+26595: kbo
+26595: Leaf order:
+26595: meet 20 2 6 0,2
+26595: join 17 2 4 0,2,2
+26595: d 2 0 2 2,2,2,2,2
+26595: c 3 0 3 1,2,2,2
+26595: b 4 0 4 1,2,2
+26595: a 3 0 3 1,2
+26594: Facts:
+26594: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26594: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26594: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26594: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26594: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26594: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26594: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26594: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26594: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
+26594: Goal:
+26594: Id : 1, {_}:
+ meet a (join b (meet c (join b d)))
+ =<=
+ meet a (join b (meet c (join d (meet a (meet b c)))))
+ [] by prove_H77
+26594: Order:
+26594: nrkbo
+26594: Leaf order:
+26594: meet 20 2 6 0,2
+26594: join 17 2 4 0,2,2
+26594: d 2 0 2 2,2,2,2,2
+26594: c 3 0 3 1,2,2,2
+26594: b 4 0 4 1,2,2
+26594: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+26596: Facts:
+26596: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26596: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26596: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26596: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26596: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26596: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26596: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26596: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26596: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
+26596: Goal:
+26596: Id : 1, {_}:
+ meet a (join b (meet c (join b d)))
+ =>=
+ meet a (join b (meet c (join d (meet a (meet b c)))))
+ [] by prove_H77
+26596: Order:
+26596: lpo
+26596: Leaf order:
+26596: meet 20 2 6 0,2
+26596: join 17 2 4 0,2,2
+26596: d 2 0 2 2,2,2,2,2
+26596: c 3 0 3 1,2,2,2
+26596: b 4 0 4 1,2,2
+26596: a 3 0 3 1,2
+% SZS status Timeout for LAT165-1.p
+NO CLASH, using fixed ground order
+26645: Facts:
+26645: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26645: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26645: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26645: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26645: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26645: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26645: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26645: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26645: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29
+26645: Goal:
+26645: Id : 1, {_}:
+ meet a (join b (meet c (join b d)))
+ =<=
+ meet a (join b (meet c (join d (meet b (join a d)))))
+ [] by prove_H78
+26645: Order:
+26645: nrkbo
+26645: Leaf order:
+26645: meet 20 2 5 0,2
+26645: join 18 2 5 0,2,2
+26645: d 3 0 3 2,2,2,2,2
+26645: c 2 0 2 1,2,2,2
+26645: b 4 0 4 1,2,2
+26645: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+26646: Facts:
+26646: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26646: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26646: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26646: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26646: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26646: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26646: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26646: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26646: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29
+26646: Goal:
+26646: Id : 1, {_}:
+ meet a (join b (meet c (join b d)))
+ =<=
+ meet a (join b (meet c (join d (meet b (join a d)))))
+ [] by prove_H78
+26646: Order:
+26646: kbo
+26646: Leaf order:
+26646: meet 20 2 5 0,2
+26646: join 18 2 5 0,2,2
+26646: d 3 0 3 2,2,2,2,2
+26646: c 2 0 2 1,2,2,2
+26646: b 4 0 4 1,2,2
+26646: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+26647: Facts:
+26647: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26647: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26647: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26647: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26647: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26647: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26647: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26647: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26647: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29
+26647: Goal:
+26647: Id : 1, {_}:
+ meet a (join b (meet c (join b d)))
+ =<=
+ meet a (join b (meet c (join d (meet b (join a d)))))
+ [] by prove_H78
+26647: Order:
+26647: lpo
+26647: Leaf order:
+26647: meet 20 2 5 0,2
+26647: join 18 2 5 0,2,2
+26647: d 3 0 3 2,2,2,2,2
+26647: c 2 0 2 1,2,2,2
+26647: b 4 0 4 1,2,2
+26647: a 3 0 3 1,2
+% SZS status Timeout for LAT166-1.p
+NO CLASH, using fixed ground order
+26677: Facts:
+26677: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26677: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26677: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26677: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26677: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26677: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26677: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26677: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26677: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?27 (join ?26 ?29)))))
+ [29, 28, 27, 26] by equation_H78 ?26 ?27 ?28 ?29
+26677: Goal:
+26677: Id : 1, {_}:
+ meet a (join b (meet c (join b d)))
+ =<=
+ meet a (join b (meet c (join d (meet a (meet b c)))))
+ [] by prove_H77
+26677: Order:
+26677: kbo
+26677: Leaf order:
+26677: meet 20 2 6 0,2
+26677: join 18 2 4 0,2,2
+26677: d 2 0 2 2,2,2,2,2
+26677: c 3 0 3 1,2,2,2
+26677: b 4 0 4 1,2,2
+26677: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+26676: Facts:
+26676: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26676: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26676: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26676: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26676: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26676: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26676: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26676: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26676: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?27 (join ?26 ?29)))))
+ [29, 28, 27, 26] by equation_H78 ?26 ?27 ?28 ?29
+26676: Goal:
+26676: Id : 1, {_}:
+ meet a (join b (meet c (join b d)))
+ =<=
+ meet a (join b (meet c (join d (meet a (meet b c)))))
+ [] by prove_H77
+26676: Order:
+26676: nrkbo
+26676: Leaf order:
+26676: meet 20 2 6 0,2
+26676: join 18 2 4 0,2,2
+26676: d 2 0 2 2,2,2,2,2
+26676: c 3 0 3 1,2,2,2
+26676: b 4 0 4 1,2,2
+26676: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+26678: Facts:
+26678: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26678: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26678: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26678: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26678: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26678: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26678: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26678: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26678: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?27 (join ?26 ?29)))))
+ [29, 28, 27, 26] by equation_H78 ?26 ?27 ?28 ?29
+26678: Goal:
+26678: Id : 1, {_}:
+ meet a (join b (meet c (join b d)))
+ =>=
+ meet a (join b (meet c (join d (meet a (meet b c)))))
+ [] by prove_H77
+26678: Order:
+26678: lpo
+26678: Leaf order:
+26678: meet 20 2 6 0,2
+26678: join 18 2 4 0,2,2
+26678: d 2 0 2 2,2,2,2,2
+26678: c 3 0 3 1,2,2,2
+26678: b 4 0 4 1,2,2
+26678: a 3 0 3 1,2
+% SZS status Timeout for LAT167-1.p
+NO CLASH, using fixed ground order
+26697: Facts:
+26697: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26697: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26697: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26697: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26697: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26697: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26697: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26697: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26697: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
+26697: Goal:
+26697: Id : 1, {_}:
+ meet a (join b (meet a (meet c d)))
+ =<=
+ meet a (join b (meet c (join (meet a d) (meet b d))))
+ [] by prove_H32
+26697: Order:
+26697: nrkbo
+26697: Leaf order:
+26697: join 17 2 3 0,2,2
+26697: meet 20 2 7 0,2
+26697: d 3 0 3 2,2,2,2,2
+26697: c 2 0 2 1,2,2,2,2
+26697: b 3 0 3 1,2,2
+26697: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+26698: Facts:
+26698: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26698: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26698: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26698: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26698: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26698: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26698: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26698: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26698: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
+26698: Goal:
+26698: Id : 1, {_}:
+ meet a (join b (meet a (meet c d)))
+ =<=
+ meet a (join b (meet c (join (meet a d) (meet b d))))
+ [] by prove_H32
+26698: Order:
+26698: kbo
+26698: Leaf order:
+26698: join 17 2 3 0,2,2
+26698: meet 20 2 7 0,2
+26698: d 3 0 3 2,2,2,2,2
+26698: c 2 0 2 1,2,2,2,2
+26698: b 3 0 3 1,2,2
+26698: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+26699: Facts:
+26699: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26699: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26699: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26699: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26699: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26699: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26699: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26699: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26699: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
+ =?=
+ join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
+26699: Goal:
+26699: Id : 1, {_}:
+ meet a (join b (meet a (meet c d)))
+ =>=
+ meet a (join b (meet c (join (meet a d) (meet b d))))
+ [] by prove_H32
+26699: Order:
+26699: lpo
+26699: Leaf order:
+26699: join 17 2 3 0,2,2
+26699: meet 20 2 7 0,2
+26699: d 3 0 3 2,2,2,2,2
+26699: c 2 0 2 1,2,2,2,2
+26699: b 3 0 3 1,2,2
+26699: a 4 0 4 1,2
+% SZS status Timeout for LAT172-1.p
+NO CLASH, using fixed ground order
+26727: Facts:
+26727: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26727: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26727: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26727: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26727: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26727: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26727: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26727: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26727: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
+26727: Goal:
+26727: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+26727: Order:
+26727: nrkbo
+26727: Leaf order:
+26727: meet 18 2 5 0,2
+26727: join 19 2 5 0,2,2
+26727: d 2 0 2 2,2,2,2,2
+26727: c 3 0 3 1,2,2,2
+26727: b 3 0 3 1,2,2
+26727: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+26728: Facts:
+26728: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26728: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26728: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26728: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26728: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26728: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26728: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26728: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26728: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
+26728: Goal:
+26728: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+26728: Order:
+26728: kbo
+26728: Leaf order:
+26728: meet 18 2 5 0,2
+26728: join 19 2 5 0,2,2
+26728: d 2 0 2 2,2,2,2,2
+26728: c 3 0 3 1,2,2,2
+26728: b 3 0 3 1,2,2
+26728: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+26729: Facts:
+26729: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26729: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26729: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26729: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26729: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26729: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26729: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26729: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26729: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
+ =?=
+ join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
+26729: Goal:
+26729: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+26729: Order:
+26729: lpo
+26729: Leaf order:
+26729: meet 18 2 5 0,2
+26729: join 19 2 5 0,2,2
+26729: d 2 0 2 2,2,2,2,2
+26729: c 3 0 3 1,2,2,2
+26729: b 3 0 3 1,2,2
+26729: a 4 0 4 1,2
+% SZS status Timeout for LAT173-1.p
+NO CLASH, using fixed ground order
+26747: Facts:
+26747: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26747: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26747: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26747: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26747: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26747: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26747: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26747: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26747: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
+ [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
+26747: Goal:
+26747: Id : 1, {_}:
+ meet a (join b (meet a (meet c d)))
+ =<=
+ meet a (join b (meet c (join (meet a d) (meet b d))))
+ [] by prove_H32
+26747: Order:
+26747: kbo
+26747: Leaf order:
+26747: join 18 2 3 0,2,2
+26747: meet 20 2 7 0,2
+26747: d 3 0 3 2,2,2,2,2
+26747: c 2 0 2 1,2,2,2,2
+26747: b 3 0 3 1,2,2
+26747: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+26746: Facts:
+26746: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26746: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26746: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26746: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26746: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26746: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26746: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26746: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26746: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
+ [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
+26746: Goal:
+26746: Id : 1, {_}:
+ meet a (join b (meet a (meet c d)))
+ =<=
+ meet a (join b (meet c (join (meet a d) (meet b d))))
+ [] by prove_H32
+26746: Order:
+26746: nrkbo
+26746: Leaf order:
+26746: join 18 2 3 0,2,2
+26746: meet 20 2 7 0,2
+26746: d 3 0 3 2,2,2,2,2
+26746: c 2 0 2 1,2,2,2,2
+26746: b 3 0 3 1,2,2
+26746: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+26748: Facts:
+26748: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26748: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26748: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26748: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26748: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26748: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26748: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26748: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26748: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
+ [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
+26748: Goal:
+26748: Id : 1, {_}:
+ meet a (join b (meet a (meet c d)))
+ =>=
+ meet a (join b (meet c (join (meet a d) (meet b d))))
+ [] by prove_H32
+26748: Order:
+26748: lpo
+26748: Leaf order:
+26748: join 18 2 3 0,2,2
+26748: meet 20 2 7 0,2
+26748: d 3 0 3 2,2,2,2,2
+26748: c 2 0 2 1,2,2,2,2
+26748: b 3 0 3 1,2,2
+26748: a 4 0 4 1,2
+% SZS status Timeout for LAT175-1.p
+NO CLASH, using fixed ground order
+26789: Facts:
+26789: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26789: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26789: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26789: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26789: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26789: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26789: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26789: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26789: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
+ [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
+26789: Goal:
+26789: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+26789: Order:
+26789: nrkbo
+26789: Leaf order:
+26789: meet 18 2 5 0,2
+26789: join 20 2 5 0,2,2
+26789: d 2 0 2 2,2,2,2,2
+26789: c 3 0 3 1,2,2,2
+26789: b 3 0 3 1,2,2
+26789: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+26790: Facts:
+26790: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26790: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26790: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26790: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26790: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26790: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26790: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26790: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26790: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
+ [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
+26790: Goal:
+26790: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+26790: Order:
+26790: kbo
+26790: Leaf order:
+26790: meet 18 2 5 0,2
+26790: join 20 2 5 0,2,2
+26790: d 2 0 2 2,2,2,2,2
+26790: c 3 0 3 1,2,2,2
+26790: b 3 0 3 1,2,2
+26790: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+26791: Facts:
+26791: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26791: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26791: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26791: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26791: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26791: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26791: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26791: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26791: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =?=
+ join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
+ [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
+26791: Goal:
+26791: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =>=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+26791: Order:
+26791: lpo
+26791: Leaf order:
+26791: meet 18 2 5 0,2
+26791: join 20 2 5 0,2,2
+26791: d 2 0 2 2,2,2,2,2
+26791: c 3 0 3 1,2,2,2
+26791: b 3 0 3 1,2,2
+26791: a 4 0 4 1,2
+% SZS status Timeout for LAT176-1.p
+NO CLASH, using fixed ground order
+27075: Facts:
+27075: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+27075: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+27075: Id : 4, {_}:
+ add (additive_inverse ?6) ?6 =>= additive_identity
+ [6] by left_additive_inverse ?6
+27075: Id : 5, {_}:
+ add ?8 (additive_inverse ?8) =>= additive_identity
+ [8] by right_additive_inverse ?8
+27075: Id : 6, {_}:
+ add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12
+ [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
+27075: Id : 7, {_}:
+ add ?14 ?15 =?= add ?15 ?14
+ [15, 14] by commutativity_for_addition ?14 ?15
+27075: Id : 8, {_}:
+ multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19
+ [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
+27075: Id : 9, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+27075: Id : 10, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+27075: Id : 11, {_}:
+ multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29
+ [29] by x_fourthed_is_x ?29
+27075: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
+27075: Goal:
+27075: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
+27075: Order:
+27075: nrkbo
+27075: Leaf order:
+27075: additive_inverse 2 1 0
+27075: add 14 2 0
+27075: additive_identity 4 0 0
+27075: c 2 0 1 3
+27075: multiply 15 2 1 0,2
+27075: a 2 0 1 2,2
+27075: b 2 0 1 1,2
+NO CLASH, using fixed ground order
+27077: Facts:
+27077: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+27077: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+27077: Id : 4, {_}:
+ add (additive_inverse ?6) ?6 =>= additive_identity
+ [6] by left_additive_inverse ?6
+27077: Id : 5, {_}:
+ add ?8 (additive_inverse ?8) =>= additive_identity
+ [8] by right_additive_inverse ?8
+27077: Id : 6, {_}:
+ add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
+ [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
+27077: Id : 7, {_}:
+ add ?14 ?15 =?= add ?15 ?14
+ [15, 14] by commutativity_for_addition ?14 ?15
+27077: Id : 8, {_}:
+ multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
+ [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
+27077: Id : 9, {_}:
+ multiply ?21 (add ?22 ?23)
+ =>=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+27077: Id : 10, {_}:
+ multiply (add ?25 ?26) ?27
+ =>=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+27077: Id : 11, {_}:
+ multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29
+ [29] by x_fourthed_is_x ?29
+27077: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
+27077: Goal:
+27077: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
+27077: Order:
+27077: lpo
+27077: Leaf order:
+27077: additive_inverse 2 1 0
+27077: add 14 2 0
+27077: additive_identity 4 0 0
+27077: c 2 0 1 3
+27077: multiply 15 2 1 0,2
+27077: a 2 0 1 2,2
+27077: b 2 0 1 1,2
+NO CLASH, using fixed ground order
+27076: Facts:
+27076: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+27076: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+27076: Id : 4, {_}:
+ add (additive_inverse ?6) ?6 =>= additive_identity
+ [6] by left_additive_inverse ?6
+27076: Id : 5, {_}:
+ add ?8 (additive_inverse ?8) =>= additive_identity
+ [8] by right_additive_inverse ?8
+27076: Id : 6, {_}:
+ add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
+ [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
+27076: Id : 7, {_}:
+ add ?14 ?15 =?= add ?15 ?14
+ [15, 14] by commutativity_for_addition ?14 ?15
+27076: Id : 8, {_}:
+ multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
+ [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
+27076: Id : 9, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+27076: Id : 10, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+27076: Id : 11, {_}:
+ multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29
+ [29] by x_fourthed_is_x ?29
+27076: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
+27076: Goal:
+27076: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
+27076: Order:
+27076: kbo
+27076: Leaf order:
+27076: additive_inverse 2 1 0
+27076: add 14 2 0
+27076: additive_identity 4 0 0
+27076: c 2 0 1 3
+27076: multiply 15 2 1 0,2
+27076: a 2 0 1 2,2
+27076: b 2 0 1 1,2
+% SZS status Timeout for RNG035-7.p
+NO CLASH, using fixed ground order
+27109: Facts:
+27109: Id : 2, {_}:
+ nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c1 ?2 ?3 ?4
+27109: Goal:
+27109: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27109: Order:
+27109: nrkbo
+27109: Leaf order:
+27109: b 1 0 1 1,2,2
+27109: nand 9 2 3 0,2
+27109: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27110: Facts:
+27110: Id : 2, {_}:
+ nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c1 ?2 ?3 ?4
+27110: Goal:
+27110: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27110: Order:
+27110: kbo
+27110: Leaf order:
+27110: b 1 0 1 1,2,2
+27110: nand 9 2 3 0,2
+27110: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27111: Facts:
+27111: Id : 2, {_}:
+ nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c1 ?2 ?3 ?4
+27111: Goal:
+27111: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27111: Order:
+27111: lpo
+27111: Leaf order:
+27111: b 1 0 1 1,2,2
+27111: nand 9 2 3 0,2
+27111: a 4 0 4 1,1,2
+% SZS status Timeout for BOO077-1.p
+NO CLASH, using fixed ground order
+27127: Facts:
+27127: Id : 2, {_}:
+ nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c1 ?2 ?3 ?4
+27127: Goal:
+27127: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27127: Order:
+27127: nrkbo
+27127: Leaf order:
+27127: nand 12 2 6 0,2
+27127: c 2 0 2 2,2,2,2
+27127: b 3 0 3 1,2,2
+27127: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27128: Facts:
+27128: Id : 2, {_}:
+ nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c1 ?2 ?3 ?4
+27128: Goal:
+27128: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27128: Order:
+27128: kbo
+27128: Leaf order:
+27128: nand 12 2 6 0,2
+27128: c 2 0 2 2,2,2,2
+27128: b 3 0 3 1,2,2
+27128: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27129: Facts:
+27129: Id : 2, {_}:
+ nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c1 ?2 ?3 ?4
+27129: Goal:
+27129: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27129: Order:
+27129: lpo
+27129: Leaf order:
+27129: nand 12 2 6 0,2
+27129: c 2 0 2 2,2,2,2
+27129: b 3 0 3 1,2,2
+27129: a 3 0 3 1,2
+% SZS status Timeout for BOO078-1.p
+NO CLASH, using fixed ground order
+27161: Facts:
+27161: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c2 ?2 ?3 ?4
+27161: Goal:
+27161: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27161: Order:
+27161: kbo
+27161: Leaf order:
+27161: b 1 0 1 1,2,2
+27161: nand 9 2 3 0,2
+27161: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27162: Facts:
+27162: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c2 ?2 ?3 ?4
+27162: Goal:
+27162: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27162: Order:
+27162: lpo
+27162: Leaf order:
+27162: b 1 0 1 1,2,2
+27162: nand 9 2 3 0,2
+27162: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27160: Facts:
+27160: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c2 ?2 ?3 ?4
+27160: Goal:
+27160: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27160: Order:
+27160: nrkbo
+27160: Leaf order:
+27160: b 1 0 1 1,2,2
+27160: nand 9 2 3 0,2
+27160: a 4 0 4 1,1,2
+% SZS status Timeout for BOO079-1.p
+NO CLASH, using fixed ground order
+27178: Facts:
+27178: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c2 ?2 ?3 ?4
+27178: Goal:
+27178: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27178: Order:
+27178: nrkbo
+27178: Leaf order:
+27178: nand 12 2 6 0,2
+27178: c 2 0 2 2,2,2,2
+27178: b 3 0 3 1,2,2
+27178: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27179: Facts:
+27179: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c2 ?2 ?3 ?4
+27179: Goal:
+27179: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27179: Order:
+27179: kbo
+27179: Leaf order:
+27179: nand 12 2 6 0,2
+27179: c 2 0 2 2,2,2,2
+27179: b 3 0 3 1,2,2
+27179: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27180: Facts:
+27180: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c2 ?2 ?3 ?4
+27180: Goal:
+27180: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27180: Order:
+27180: lpo
+27180: Leaf order:
+27180: nand 12 2 6 0,2
+27180: c 2 0 2 2,2,2,2
+27180: b 3 0 3 1,2,2
+27180: a 3 0 3 1,2
+% SZS status Timeout for BOO080-1.p
+NO CLASH, using fixed ground order
+27207: Facts:
+27207: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c3 ?2 ?3 ?4
+27207: Goal:
+27207: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27207: Order:
+27207: nrkbo
+27207: Leaf order:
+27207: b 1 0 1 1,2,2
+27207: nand 9 2 3 0,2
+27207: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27208: Facts:
+27208: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c3 ?2 ?3 ?4
+27208: Goal:
+27208: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27208: Order:
+27208: kbo
+27208: Leaf order:
+27208: b 1 0 1 1,2,2
+27208: nand 9 2 3 0,2
+27208: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27209: Facts:
+27209: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c3 ?2 ?3 ?4
+27209: Goal:
+27209: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27209: Order:
+27209: lpo
+27209: Leaf order:
+27209: b 1 0 1 1,2,2
+27209: nand 9 2 3 0,2
+27209: a 4 0 4 1,1,2
+% SZS status Timeout for BOO081-1.p
+NO CLASH, using fixed ground order
+27227: Facts:
+27227: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c3 ?2 ?3 ?4
+27227: Goal:
+27227: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27227: Order:
+27227: nrkbo
+27227: Leaf order:
+27227: nand 12 2 6 0,2
+27227: c 2 0 2 2,2,2,2
+27227: b 3 0 3 1,2,2
+27227: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27228: Facts:
+27228: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c3 ?2 ?3 ?4
+27228: Goal:
+27228: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27228: Order:
+27228: kbo
+27228: Leaf order:
+27228: nand 12 2 6 0,2
+27228: c 2 0 2 2,2,2,2
+27228: b 3 0 3 1,2,2
+27228: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27229: Facts:
+27229: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c3 ?2 ?3 ?4
+27229: Goal:
+27229: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27229: Order:
+27229: lpo
+27229: Leaf order:
+27229: nand 12 2 6 0,2
+27229: c 2 0 2 2,2,2,2
+27229: b 3 0 3 1,2,2
+27229: a 3 0 3 1,2
+% SZS status Timeout for BOO082-1.p
+NO CLASH, using fixed ground order
+27257: Facts:
+27257: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c4 ?2 ?3 ?4
+27257: Goal:
+27257: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27257: Order:
+27257: nrkbo
+27257: Leaf order:
+27257: b 1 0 1 1,2,2
+27257: nand 9 2 3 0,2
+27257: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27258: Facts:
+27258: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c4 ?2 ?3 ?4
+27258: Goal:
+27258: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27258: Order:
+27258: kbo
+27258: Leaf order:
+27258: b 1 0 1 1,2,2
+27258: nand 9 2 3 0,2
+27258: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27259: Facts:
+27259: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c4 ?2 ?3 ?4
+27259: Goal:
+27259: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27259: Order:
+27259: lpo
+27259: Leaf order:
+27259: b 1 0 1 1,2,2
+27259: nand 9 2 3 0,2
+27259: a 4 0 4 1,1,2
+% SZS status Timeout for BOO083-1.p
+NO CLASH, using fixed ground order
+27275: Facts:
+27275: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c4 ?2 ?3 ?4
+27275: Goal:
+27275: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27275: Order:
+27275: nrkbo
+27275: Leaf order:
+27275: nand 12 2 6 0,2
+27275: c 2 0 2 2,2,2,2
+27275: b 3 0 3 1,2,2
+27275: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27276: Facts:
+27276: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c4 ?2 ?3 ?4
+27276: Goal:
+27276: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27276: Order:
+27276: kbo
+27276: Leaf order:
+27276: nand 12 2 6 0,2
+27276: c 2 0 2 2,2,2,2
+27276: b 3 0 3 1,2,2
+27276: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27277: Facts:
+27277: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c4 ?2 ?3 ?4
+27277: Goal:
+27277: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27277: Order:
+27277: lpo
+27277: Leaf order:
+27277: nand 12 2 6 0,2
+27277: c 2 0 2 2,2,2,2
+27277: b 3 0 3 1,2,2
+27277: a 3 0 3 1,2
+% SZS status Timeout for BOO084-1.p
+NO CLASH, using fixed ground order
+27304: Facts:
+27304: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c5 ?2 ?3 ?4
+27304: Goal:
+27304: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27304: Order:
+27304: nrkbo
+27304: Leaf order:
+27304: b 1 0 1 1,2,2
+27304: nand 9 2 3 0,2
+27304: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27305: Facts:
+27305: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c5 ?2 ?3 ?4
+27305: Goal:
+27305: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27305: Order:
+27305: kbo
+27305: Leaf order:
+27305: b 1 0 1 1,2,2
+27305: nand 9 2 3 0,2
+27305: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27306: Facts:
+27306: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c5 ?2 ?3 ?4
+27306: Goal:
+27306: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27306: Order:
+27306: lpo
+27306: Leaf order:
+27306: b 1 0 1 1,2,2
+27306: nand 9 2 3 0,2
+27306: a 4 0 4 1,1,2
+% SZS status Timeout for BOO085-1.p
+NO CLASH, using fixed ground order
+27328: Facts:
+27328: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c5 ?2 ?3 ?4
+27328: Goal:
+27328: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27328: Order:
+27328: nrkbo
+27328: Leaf order:
+27328: nand 12 2 6 0,2
+27328: c 2 0 2 2,2,2,2
+27328: b 3 0 3 1,2,2
+27328: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27331: Facts:
+27331: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c5 ?2 ?3 ?4
+27331: Goal:
+27331: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27331: Order:
+27331: lpo
+27331: Leaf order:
+27331: nand 12 2 6 0,2
+27331: c 2 0 2 2,2,2,2
+27331: b 3 0 3 1,2,2
+27331: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27329: Facts:
+27329: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c5 ?2 ?3 ?4
+27329: Goal:
+27329: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27329: Order:
+27329: kbo
+27329: Leaf order:
+27329: nand 12 2 6 0,2
+27329: c 2 0 2 2,2,2,2
+27329: b 3 0 3 1,2,2
+27329: a 3 0 3 1,2
+% SZS status Timeout for BOO086-1.p
+NO CLASH, using fixed ground order
+27408: Facts:
+27408: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
+ [4, 3, 2] by c6 ?2 ?3 ?4
+27408: Goal:
+27408: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27408: Order:
+27408: kbo
+27408: Leaf order:
+27408: b 1 0 1 1,2,2
+27408: nand 9 2 3 0,2
+27408: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27407: Facts:
+27407: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
+ [4, 3, 2] by c6 ?2 ?3 ?4
+27407: Goal:
+27407: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27407: Order:
+27407: nrkbo
+27407: Leaf order:
+27407: b 1 0 1 1,2,2
+27407: nand 9 2 3 0,2
+27407: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27409: Facts:
+27409: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
+ [4, 3, 2] by c6 ?2 ?3 ?4
+27409: Goal:
+27409: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27409: Order:
+27409: lpo
+27409: Leaf order:
+27409: b 1 0 1 1,2,2
+27409: nand 9 2 3 0,2
+27409: a 4 0 4 1,1,2
+% SZS status Timeout for BOO087-1.p
+NO CLASH, using fixed ground order
+27425: Facts:
+27425: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
+ [4, 3, 2] by c6 ?2 ?3 ?4
+27425: Goal:
+27425: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27425: Order:
+27425: nrkbo
+27425: Leaf order:
+27425: nand 12 2 6 0,2
+27425: c 2 0 2 2,2,2,2
+27425: b 3 0 3 1,2,2
+27425: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27426: Facts:
+27426: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
+ [4, 3, 2] by c6 ?2 ?3 ?4
+27426: Goal:
+27426: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27426: Order:
+27426: kbo
+27426: Leaf order:
+27426: nand 12 2 6 0,2
+27426: c 2 0 2 2,2,2,2
+27426: b 3 0 3 1,2,2
+27426: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27427: Facts:
+27427: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
+ [4, 3, 2] by c6 ?2 ?3 ?4
+27427: Goal:
+27427: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27427: Order:
+27427: lpo
+27427: Leaf order:
+27427: nand 12 2 6 0,2
+27427: c 2 0 2 2,2,2,2
+27427: b 3 0 3 1,2,2
+27427: a 3 0 3 1,2
+% SZS status Timeout for BOO088-1.p
+NO CLASH, using fixed ground order
+27458: Facts:
+27458: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c7 ?2 ?3 ?4
+27458: Goal:
+27458: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27458: Order:
+27458: nrkbo
+27458: Leaf order:
+27458: b 1 0 1 1,2,2
+27458: nand 9 2 3 0,2
+27458: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27459: Facts:
+27459: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c7 ?2 ?3 ?4
+27459: Goal:
+27459: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27459: Order:
+27459: kbo
+27459: Leaf order:
+27459: b 1 0 1 1,2,2
+27459: nand 9 2 3 0,2
+27459: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27460: Facts:
+27460: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c7 ?2 ?3 ?4
+27460: Goal:
+27460: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27460: Order:
+27460: lpo
+27460: Leaf order:
+27460: b 1 0 1 1,2,2
+27460: nand 9 2 3 0,2
+27460: a 4 0 4 1,1,2
+% SZS status Timeout for BOO089-1.p
+NO CLASH, using fixed ground order
+27496: Facts:
+27496: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c7 ?2 ?3 ?4
+27496: Goal:
+27496: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27496: Order:
+27496: nrkbo
+27496: Leaf order:
+27496: nand 12 2 6 0,2
+27496: c 2 0 2 2,2,2,2
+27496: b 3 0 3 1,2,2
+27496: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27497: Facts:
+27497: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c7 ?2 ?3 ?4
+27497: Goal:
+27497: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27497: Order:
+27497: kbo
+27497: Leaf order:
+27497: nand 12 2 6 0,2
+27497: c 2 0 2 2,2,2,2
+27497: b 3 0 3 1,2,2
+27497: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27498: Facts:
+27498: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c7 ?2 ?3 ?4
+27498: Goal:
+27498: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27498: Order:
+27498: lpo
+27498: Leaf order:
+27498: nand 12 2 6 0,2
+27498: c 2 0 2 2,2,2,2
+27498: b 3 0 3 1,2,2
+27498: a 3 0 3 1,2
+% SZS status Timeout for BOO090-1.p
+NO CLASH, using fixed ground order
+27534: Facts:
+27534: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c8 ?2 ?3 ?4
+27534: Goal:
+27534: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27534: Order:
+27534: nrkbo
+27534: Leaf order:
+27534: b 1 0 1 1,2,2
+27534: nand 9 2 3 0,2
+27534: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27535: Facts:
+27535: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c8 ?2 ?3 ?4
+27535: Goal:
+27535: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27535: Order:
+27535: kbo
+27535: Leaf order:
+27535: b 1 0 1 1,2,2
+27535: nand 9 2 3 0,2
+27535: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27536: Facts:
+27536: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c8 ?2 ?3 ?4
+27536: Goal:
+27536: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27536: Order:
+27536: lpo
+27536: Leaf order:
+27536: b 1 0 1 1,2,2
+27536: nand 9 2 3 0,2
+27536: a 4 0 4 1,1,2
+% SZS status Timeout for BOO091-1.p
+NO CLASH, using fixed ground order
+27553: Facts:
+27553: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c8 ?2 ?3 ?4
+27553: Goal:
+27553: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27553: Order:
+27553: nrkbo
+27553: Leaf order:
+27553: nand 12 2 6 0,2
+27553: c 2 0 2 2,2,2,2
+27553: b 3 0 3 1,2,2
+27553: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27554: Facts:
+27554: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c8 ?2 ?3 ?4
+27554: Goal:
+27554: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27554: Order:
+27554: kbo
+27554: Leaf order:
+27554: nand 12 2 6 0,2
+27554: c 2 0 2 2,2,2,2
+27554: b 3 0 3 1,2,2
+27554: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27555: Facts:
+27555: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c8 ?2 ?3 ?4
+27555: Goal:
+27555: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27555: Order:
+27555: lpo
+27555: Leaf order:
+27555: nand 12 2 6 0,2
+27555: c 2 0 2 2,2,2,2
+27555: b 3 0 3 1,2,2
+27555: a 3 0 3 1,2
+% SZS status Timeout for BOO092-1.p
+NO CLASH, using fixed ground order
+27585: Facts:
+27585: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c9 ?2 ?3 ?4
+27585: Goal:
+27585: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27585: Order:
+27585: kbo
+27585: Leaf order:
+27585: b 1 0 1 1,2,2
+27585: nand 9 2 3 0,2
+27585: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27584: Facts:
+27584: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c9 ?2 ?3 ?4
+27584: Goal:
+27584: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27584: Order:
+27584: nrkbo
+27584: Leaf order:
+27584: b 1 0 1 1,2,2
+27584: nand 9 2 3 0,2
+27584: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27586: Facts:
+27586: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c9 ?2 ?3 ?4
+27586: Goal:
+27586: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27586: Order:
+27586: lpo
+27586: Leaf order:
+27586: b 1 0 1 1,2,2
+27586: nand 9 2 3 0,2
+27586: a 4 0 4 1,1,2
+% SZS status Timeout for BOO093-1.p
+NO CLASH, using fixed ground order
+27602: Facts:
+27602: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c9 ?2 ?3 ?4
+27602: Goal:
+27602: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27602: Order:
+27602: nrkbo
+27602: Leaf order:
+27602: nand 12 2 6 0,2
+27602: c 2 0 2 2,2,2,2
+27602: b 3 0 3 1,2,2
+27602: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27603: Facts:
+27603: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c9 ?2 ?3 ?4
+27603: Goal:
+27603: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27603: Order:
+27603: kbo
+27603: Leaf order:
+27603: nand 12 2 6 0,2
+27603: c 2 0 2 2,2,2,2
+27603: b 3 0 3 1,2,2
+27603: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27604: Facts:
+27604: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c9 ?2 ?3 ?4
+27604: Goal:
+27604: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27604: Order:
+27604: lpo
+27604: Leaf order:
+27604: nand 12 2 6 0,2
+27604: c 2 0 2 2,2,2,2
+27604: b 3 0 3 1,2,2
+27604: a 3 0 3 1,2
+% SZS status Timeout for BOO094-1.p
+NO CLASH, using fixed ground order
+27635: Facts:
+27635: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c10 ?2 ?3 ?4
+27635: Goal:
+27635: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27635: Order:
+27635: nrkbo
+27635: Leaf order:
+27635: b 1 0 1 1,2,2
+27635: nand 9 2 3 0,2
+27635: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27636: Facts:
+27636: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c10 ?2 ?3 ?4
+27636: Goal:
+27636: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27636: Order:
+27636: kbo
+27636: Leaf order:
+27636: b 1 0 1 1,2,2
+27636: nand 9 2 3 0,2
+27636: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27637: Facts:
+27637: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c10 ?2 ?3 ?4
+27637: Goal:
+27637: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27637: Order:
+27637: lpo
+27637: Leaf order:
+27637: b 1 0 1 1,2,2
+27637: nand 9 2 3 0,2
+27637: a 4 0 4 1,1,2
+% SZS status Timeout for BOO095-1.p
+NO CLASH, using fixed ground order
+27662: Facts:
+27662: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c10 ?2 ?3 ?4
+27662: Goal:
+27662: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27662: Order:
+27662: nrkbo
+27662: Leaf order:
+27662: nand 12 2 6 0,2
+27662: c 2 0 2 2,2,2,2
+27662: b 3 0 3 1,2,2
+27662: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27663: Facts:
+27663: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c10 ?2 ?3 ?4
+27663: Goal:
+27663: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27663: Order:
+27663: kbo
+27663: Leaf order:
+27663: nand 12 2 6 0,2
+27663: c 2 0 2 2,2,2,2
+27663: b 3 0 3 1,2,2
+27663: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27664: Facts:
+27664: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c10 ?2 ?3 ?4
+27664: Goal:
+27664: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27664: Order:
+27664: lpo
+27664: Leaf order:
+27664: nand 12 2 6 0,2
+27664: c 2 0 2 2,2,2,2
+27664: b 3 0 3 1,2,2
+27664: a 3 0 3 1,2
+% SZS status Timeout for BOO096-1.p
+NO CLASH, using fixed ground order
+27691: Facts:
+27691: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
+ [4, 3, 2] by c11 ?2 ?3 ?4
+27691: Goal:
+27691: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27691: Order:
+27691: nrkbo
+27691: Leaf order:
+27691: b 1 0 1 1,2,2
+27691: nand 9 2 3 0,2
+27691: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27692: Facts:
+27692: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
+ [4, 3, 2] by c11 ?2 ?3 ?4
+27692: Goal:
+27692: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27692: Order:
+27692: kbo
+27692: Leaf order:
+27692: b 1 0 1 1,2,2
+27692: nand 9 2 3 0,2
+27692: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27693: Facts:
+27693: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
+ [4, 3, 2] by c11 ?2 ?3 ?4
+27693: Goal:
+27693: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27693: Order:
+27693: lpo
+27693: Leaf order:
+27693: b 1 0 1 1,2,2
+27693: nand 9 2 3 0,2
+27693: a 4 0 4 1,1,2
+% SZS status Timeout for BOO097-1.p
+NO CLASH, using fixed ground order
+27766: Facts:
+27766: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
+ [4, 3, 2] by c11 ?2 ?3 ?4
+27766: Goal:
+27766: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27766: Order:
+27766: nrkbo
+27766: Leaf order:
+27766: nand 12 2 6 0,2
+27766: c 2 0 2 2,2,2,2
+27766: b 3 0 3 1,2,2
+27766: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27767: Facts:
+27767: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
+ [4, 3, 2] by c11 ?2 ?3 ?4
+27767: Goal:
+27767: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27767: Order:
+27767: kbo
+27767: Leaf order:
+27767: nand 12 2 6 0,2
+27767: c 2 0 2 2,2,2,2
+27767: b 3 0 3 1,2,2
+27767: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27768: Facts:
+27768: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
+ [4, 3, 2] by c11 ?2 ?3 ?4
+27768: Goal:
+27768: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27768: Order:
+27768: lpo
+27768: Leaf order:
+27768: nand 12 2 6 0,2
+27768: c 2 0 2 2,2,2,2
+27768: b 3 0 3 1,2,2
+27768: a 3 0 3 1,2
+% SZS status Timeout for BOO098-1.p
+NO CLASH, using fixed ground order
+27800: Facts:
+27800: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c12 ?2 ?3 ?4
+27800: Goal:
+27800: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27800: Order:
+27800: nrkbo
+27800: Leaf order:
+27800: b 1 0 1 1,2,2
+27800: nand 9 2 3 0,2
+27800: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27801: Facts:
+27801: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c12 ?2 ?3 ?4
+27801: Goal:
+27801: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27801: Order:
+27801: kbo
+27801: Leaf order:
+27801: b 1 0 1 1,2,2
+27801: nand 9 2 3 0,2
+27801: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27802: Facts:
+27802: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c12 ?2 ?3 ?4
+27802: Goal:
+27802: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27802: Order:
+27802: lpo
+27802: Leaf order:
+27802: b 1 0 1 1,2,2
+27802: nand 9 2 3 0,2
+27802: a 4 0 4 1,1,2
+% SZS status Timeout for BOO099-1.p
+NO CLASH, using fixed ground order
+27864: Facts:
+27864: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c12 ?2 ?3 ?4
+27864: Goal:
+27864: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27864: Order:
+27864: nrkbo
+27864: Leaf order:
+27864: nand 12 2 6 0,2
+27864: c 2 0 2 2,2,2,2
+27864: b 3 0 3 1,2,2
+27864: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27865: Facts:
+27865: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c12 ?2 ?3 ?4
+27865: Goal:
+27865: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27865: Order:
+27865: kbo
+27865: Leaf order:
+27865: nand 12 2 6 0,2
+27865: c 2 0 2 2,2,2,2
+27865: b 3 0 3 1,2,2
+27865: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27866: Facts:
+27866: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c12 ?2 ?3 ?4
+27866: Goal:
+27866: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27866: Order:
+27866: lpo
+27866: Leaf order:
+27866: nand 12 2 6 0,2
+27866: c 2 0 2 2,2,2,2
+27866: b 3 0 3 1,2,2
+27866: a 3 0 3 1,2
+% SZS status Timeout for BOO100-1.p
+NO CLASH, using fixed ground order
+27893: Facts:
+27893: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c13 ?2 ?3 ?4
+27893: Goal:
+27893: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27893: Order:
+27893: nrkbo
+27893: Leaf order:
+27893: b 1 0 1 1,2,2
+27893: nand 9 2 3 0,2
+27893: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27894: Facts:
+27894: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c13 ?2 ?3 ?4
+27894: Goal:
+27894: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27894: Order:
+27894: kbo
+27894: Leaf order:
+27894: b 1 0 1 1,2,2
+27894: nand 9 2 3 0,2
+27894: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27895: Facts:
+27895: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c13 ?2 ?3 ?4
+27895: Goal:
+27895: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27895: Order:
+27895: lpo
+27895: Leaf order:
+27895: b 1 0 1 1,2,2
+27895: nand 9 2 3 0,2
+27895: a 4 0 4 1,1,2
+% SZS status Timeout for BOO101-1.p
+NO CLASH, using fixed ground order
+27912: Facts:
+27912: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c13 ?2 ?3 ?4
+27912: Goal:
+27912: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27912: Order:
+27912: nrkbo
+27912: Leaf order:
+27912: nand 12 2 6 0,2
+27912: c 2 0 2 2,2,2,2
+27912: b 3 0 3 1,2,2
+27912: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27913: Facts:
+27913: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c13 ?2 ?3 ?4
+27913: Goal:
+27913: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27913: Order:
+27913: kbo
+27913: Leaf order:
+27913: nand 12 2 6 0,2
+27913: c 2 0 2 2,2,2,2
+27913: b 3 0 3 1,2,2
+27913: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27914: Facts:
+27914: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c13 ?2 ?3 ?4
+27914: Goal:
+27914: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27914: Order:
+27914: lpo
+27914: Leaf order:
+27914: nand 12 2 6 0,2
+27914: c 2 0 2 2,2,2,2
+27914: b 3 0 3 1,2,2
+27914: a 3 0 3 1,2
+% SZS status Timeout for BOO102-1.p
+NO CLASH, using fixed ground order
+27942: Facts:
+27942: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c14 ?2 ?3 ?4
+27942: Goal:
+27942: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27942: Order:
+27942: nrkbo
+27942: Leaf order:
+27942: b 1 0 1 1,2,2
+27942: nand 9 2 3 0,2
+27942: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27943: Facts:
+27943: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c14 ?2 ?3 ?4
+27943: Goal:
+27943: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27943: Order:
+27943: kbo
+27943: Leaf order:
+27943: b 1 0 1 1,2,2
+27943: nand 9 2 3 0,2
+27943: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27944: Facts:
+27944: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c14 ?2 ?3 ?4
+27944: Goal:
+27944: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27944: Order:
+27944: lpo
+27944: Leaf order:
+27944: b 1 0 1 1,2,2
+27944: nand 9 2 3 0,2
+27944: a 4 0 4 1,1,2
+% SZS status Timeout for BOO103-1.p
+NO CLASH, using fixed ground order
+27963: Facts:
+27963: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c14 ?2 ?3 ?4
+27963: Goal:
+27963: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27963: Order:
+27963: nrkbo
+27963: Leaf order:
+27963: nand 12 2 6 0,2
+27963: c 2 0 2 2,2,2,2
+27963: b 3 0 3 1,2,2
+27963: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27964: Facts:
+27964: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c14 ?2 ?3 ?4
+27964: Goal:
+27964: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27964: Order:
+27964: kbo
+27964: Leaf order:
+27964: nand 12 2 6 0,2
+27964: c 2 0 2 2,2,2,2
+27964: b 3 0 3 1,2,2
+27964: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+27965: Facts:
+27965: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c14 ?2 ?3 ?4
+27965: Goal:
+27965: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+27965: Order:
+27965: lpo
+27965: Leaf order:
+27965: nand 12 2 6 0,2
+27965: c 2 0 2 2,2,2,2
+27965: b 3 0 3 1,2,2
+27965: a 3 0 3 1,2
+% SZS status Timeout for BOO104-1.p
+NO CLASH, using fixed ground order
+27992: Facts:
+27992: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c15 ?2 ?3 ?4
+27992: Goal:
+27992: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27992: Order:
+27992: nrkbo
+27992: Leaf order:
+27992: b 1 0 1 1,2,2
+27992: nand 9 2 3 0,2
+27992: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27993: Facts:
+27993: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c15 ?2 ?3 ?4
+27993: Goal:
+27993: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27993: Order:
+27993: kbo
+27993: Leaf order:
+27993: b 1 0 1 1,2,2
+27993: nand 9 2 3 0,2
+27993: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+27994: Facts:
+27994: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c15 ?2 ?3 ?4
+27994: Goal:
+27994: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+27994: Order:
+27994: lpo
+27994: Leaf order:
+27994: b 1 0 1 1,2,2
+27994: nand 9 2 3 0,2
+27994: a 4 0 4 1,1,2
+% SZS status Timeout for BOO105-1.p
+NO CLASH, using fixed ground order
+28010: Facts:
+28010: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c15 ?2 ?3 ?4
+28010: Goal:
+28010: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+28010: Order:
+28010: nrkbo
+28010: Leaf order:
+28010: nand 12 2 6 0,2
+28010: c 2 0 2 2,2,2,2
+28010: b 3 0 3 1,2,2
+28010: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+28011: Facts:
+28011: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c15 ?2 ?3 ?4
+28011: Goal:
+28011: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+28011: Order:
+28011: kbo
+28011: Leaf order:
+28011: nand 12 2 6 0,2
+28011: c 2 0 2 2,2,2,2
+28011: b 3 0 3 1,2,2
+28011: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+28012: Facts:
+28012: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c15 ?2 ?3 ?4
+28012: Goal:
+28012: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+28012: Order:
+28012: lpo
+28012: Leaf order:
+28012: nand 12 2 6 0,2
+28012: c 2 0 2 2,2,2,2
+28012: b 3 0 3 1,2,2
+28012: a 3 0 3 1,2
+% SZS status Timeout for BOO106-1.p
+NO CLASH, using fixed ground order
+28046: Facts:
+28046: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c16 ?2 ?3 ?4
+28046: Goal:
+28046: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+28046: Order:
+28046: nrkbo
+28046: Leaf order:
+28046: b 1 0 1 1,2,2
+28046: nand 9 2 3 0,2
+28046: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+28047: Facts:
+28047: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c16 ?2 ?3 ?4
+28047: Goal:
+28047: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+28047: Order:
+28047: kbo
+28047: Leaf order:
+28047: b 1 0 1 1,2,2
+28047: nand 9 2 3 0,2
+28047: a 4 0 4 1,1,2
+NO CLASH, using fixed ground order
+28048: Facts:
+28048: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c16 ?2 ?3 ?4
+28048: Goal:
+28048: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+28048: Order:
+28048: lpo
+28048: Leaf order:
+28048: b 1 0 1 1,2,2
+28048: nand 9 2 3 0,2
+28048: a 4 0 4 1,1,2
+% SZS status Timeout for BOO107-1.p
+NO CLASH, using fixed ground order
+28069: Facts:
+28069: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c16 ?2 ?3 ?4
+28069: Goal:
+28069: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+28069: Order:
+28069: nrkbo
+28069: Leaf order:
+28069: nand 12 2 6 0,2
+28069: c 2 0 2 2,2,2,2
+28069: b 3 0 3 1,2,2
+28069: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+28070: Facts:
+28070: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c16 ?2 ?3 ?4
+28070: Goal:
+28070: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+28070: Order:
+28070: kbo
+28070: Leaf order:
+28070: nand 12 2 6 0,2
+28070: c 2 0 2 2,2,2,2
+28070: b 3 0 3 1,2,2
+28070: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+28071: Facts:
+28071: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c16 ?2 ?3 ?4
+28071: Goal:
+28071: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+28071: Order:
+28071: lpo
+28071: Leaf order:
+28071: nand 12 2 6 0,2
+28071: c 2 0 2 2,2,2,2
+28071: b 3 0 3 1,2,2
+28071: a 3 0 3 1,2
+% SZS status Timeout for BOO108-1.p
+CLASH, statistics insufficient
+28456: Facts:
+28456: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+28456: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+28456: Goal:
+28456: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+28456: Order:
+28456: nrkbo
+28456: Leaf order:
+28456: b 1 0 0
+28456: s 1 0 0
+28456: apply 14 2 3 0,2
+28456: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+28457: Facts:
+28457: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+28457: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+28457: Goal:
+28457: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+28457: Order:
+28457: kbo
+28457: Leaf order:
+28457: b 1 0 0
+28457: s 1 0 0
+28457: apply 14 2 3 0,2
+28457: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+28458: Facts:
+28458: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+28458: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+28458: Goal:
+28458: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+28458: Order:
+28458: lpo
+28458: Leaf order:
+28458: b 1 0 0
+28458: s 1 0 0
+28458: apply 14 2 3 0,2
+28458: f 3 1 3 0,2,2
+% SZS status Timeout for COL067-1.p
+CLASH, statistics insufficient
+28873: Facts:
+28873: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+28873: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+28873: Goal:
+28873: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
+28873: Order:
+28873: nrkbo
+28873: Leaf order:
+28873: b 1 0 0
+28873: s 1 0 0
+28873: apply 12 2 1 0,3
+28873: combinator 1 0 1 1,3
+CLASH, statistics insufficient
+28874: Facts:
+28874: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+28874: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+28874: Goal:
+28874: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
+28874: Order:
+28874: kbo
+28874: Leaf order:
+28874: b 1 0 0
+28874: s 1 0 0
+28874: apply 12 2 1 0,3
+28874: combinator 1 0 1 1,3
+CLASH, statistics insufficient
+28875: Facts:
+28875: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+28875: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+28875: Goal:
+28875: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
+28875: Order:
+28875: lpo
+28875: Leaf order:
+28875: b 1 0 0
+28875: s 1 0 0
+28875: apply 12 2 1 0,3
+28875: combinator 1 0 1 1,3
+% SZS status Timeout for COL068-1.p
+CLASH, statistics insufficient
+28902: Facts:
+28902: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+28902: Id : 3, {_}:
+ apply (apply l ?7) ?8 =?= apply ?7 (apply ?8 ?8)
+ [8, 7] by l_definition ?7 ?8
+28902: Goal:
+28902: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+28902: Order:
+28902: nrkbo
+28902: Leaf order:
+28902: l 1 0 0
+28902: b 1 0 0
+28902: apply 12 2 3 0,2
+28902: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+28903: Facts:
+28903: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+28903: Id : 3, {_}:
+ apply (apply l ?7) ?8 =?= apply ?7 (apply ?8 ?8)
+ [8, 7] by l_definition ?7 ?8
+28903: Goal:
+28903: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+28903: Order:
+28903: kbo
+28903: Leaf order:
+28903: l 1 0 0
+28903: b 1 0 0
+28903: apply 12 2 3 0,2
+28903: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+28904: Facts:
+28904: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+28904: Id : 3, {_}:
+ apply (apply l ?7) ?8 =?= apply ?7 (apply ?8 ?8)
+ [8, 7] by l_definition ?7 ?8
+28904: Goal:
+28904: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+28904: Order:
+28904: lpo
+28904: Leaf order:
+28904: l 1 0 0
+28904: b 1 0 0
+28904: apply 12 2 3 0,2
+28904: f 3 1 3 0,2,2
+% SZS status Timeout for COL069-1.p
+CLASH, statistics insufficient
+28921: Facts:
+28921: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by definition_B ?3 ?4 ?5
+28921: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by definition_M ?7
+28921: Goal:
+28921: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by strong_fixpoint ?1
+28921: Order:
+28921: nrkbo
+28921: Leaf order:
+28921: m 1 0 0
+28921: b 1 0 0
+28921: apply 10 2 3 0,2
+28921: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+28922: Facts:
+28922: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by definition_B ?3 ?4 ?5
+28922: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by definition_M ?7
+28922: Goal:
+28922: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by strong_fixpoint ?1
+28922: Order:
+28922: kbo
+28922: Leaf order:
+28922: m 1 0 0
+28922: b 1 0 0
+28922: apply 10 2 3 0,2
+28922: f 3 1 3 0,2,2
+CLASH, statistics insufficient
+28923: Facts:
+28923: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by definition_B ?3 ?4 ?5
+28923: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by definition_M ?7
+28923: Goal:
+28923: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by strong_fixpoint ?1
+28923: Order:
+28923: lpo
+28923: Leaf order:
+28923: m 1 0 0
+28923: b 1 0 0
+28923: apply 10 2 3 0,2
+28923: f 3 1 3 0,2,2
+% SZS status Timeout for COL087-1.p
+NO CLASH, using fixed ground order
+28951: Facts:
+28951: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+28951: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+28951: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+28951: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+28951: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+28951: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+28951: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+28951: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+28951: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+28951: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+28951: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+28951: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+28951: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+28951: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+28951: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+28951: Id : 17, {_}: least_upper_bound identity a =>= a [] by p08a_1
+28951: Id : 18, {_}: least_upper_bound identity b =>= b [] by p08a_2
+28951: Id : 19, {_}: least_upper_bound identity c =>= c [] by p08a_3
+28951: Goal:
+28951: Id : 1, {_}:
+ least_upper_bound (greatest_lower_bound a (multiply b c))
+ (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
+ =>=
+ multiply (greatest_lower_bound a b) (greatest_lower_bound a c)
+ [] by prove_p08a
+28951: Order:
+28951: nrkbo
+28951: Leaf order:
+28951: inverse 1 1 0
+28951: identity 5 0 0
+28951: least_upper_bound 17 2 1 0,2
+28951: greatest_lower_bound 18 2 5 0,1,2
+28951: multiply 21 2 3 0,2,1,2
+28951: c 5 0 3 2,2,1,2
+28951: b 5 0 3 1,2,1,2
+28951: a 7 0 5 1,1,2
+NO CLASH, using fixed ground order
+28952: Facts:
+28952: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+28952: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+28952: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+28952: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+28952: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+28952: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+28952: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+28952: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+28952: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+28952: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+28952: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+28952: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+28952: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+28952: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+28952: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+28952: Id : 17, {_}: least_upper_bound identity a =>= a [] by p08a_1
+28952: Id : 18, {_}: least_upper_bound identity b =>= b [] by p08a_2
+28952: Id : 19, {_}: least_upper_bound identity c =>= c [] by p08a_3
+28952: Goal:
+28952: Id : 1, {_}:
+ least_upper_bound (greatest_lower_bound a (multiply b c))
+ (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
+ =>=
+ multiply (greatest_lower_bound a b) (greatest_lower_bound a c)
+ [] by prove_p08a
+28952: Order:
+28952: kbo
+28952: Leaf order:
+28952: inverse 1 1 0
+28952: identity 5 0 0
+28952: least_upper_bound 17 2 1 0,2
+28952: greatest_lower_bound 18 2 5 0,1,2
+28952: multiply 21 2 3 0,2,1,2
+28952: c 5 0 3 2,2,1,2
+28952: b 5 0 3 1,2,1,2
+28952: a 7 0 5 1,1,2
+NO CLASH, using fixed ground order
+28953: Facts:
+28953: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+28953: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+28953: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+28953: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+28953: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+28953: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+28953: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+28953: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+28953: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+28953: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+28953: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+28953: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+28953: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+28953: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+28953: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+28953: Id : 17, {_}: least_upper_bound identity a =>= a [] by p08a_1
+28953: Id : 18, {_}: least_upper_bound identity b =>= b [] by p08a_2
+28953: Id : 19, {_}: least_upper_bound identity c =>= c [] by p08a_3
+28953: Goal:
+28953: Id : 1, {_}:
+ least_upper_bound (greatest_lower_bound a (multiply b c))
+ (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
+ =>=
+ multiply (greatest_lower_bound a b) (greatest_lower_bound a c)
+ [] by prove_p08a
+28953: Order:
+28953: lpo
+28953: Leaf order:
+28953: inverse 1 1 0
+28953: identity 5 0 0
+28953: least_upper_bound 17 2 1 0,2
+28953: greatest_lower_bound 18 2 5 0,1,2
+28953: multiply 21 2 3 0,2,1,2
+28953: c 5 0 3 2,2,1,2
+28953: b 5 0 3 1,2,1,2
+28953: a 7 0 5 1,1,2
+% SZS status Timeout for GRP177-1.p
+NO CLASH, using fixed ground order
+28970: Facts:
+28970: Id : 2, {_}:
+ f (f ?2 ?3) (f (f (f (f ?2 ?3) ?3) (f ?4 ?3)) (f (f ?3 ?3) ?5))
+ =>=
+ ?3
+ [5, 4, 3, 2] by oml_21C ?2 ?3 ?4 ?5
+28970: Goal:
+28970: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
+ [] by associativity
+28970: Order:
+28970: nrkbo
+28970: Leaf order:
+28970: f 17 2 8 0,2
+28970: c 3 0 3 2,1,2,2
+28970: b 4 0 4 1,1,2,2
+28970: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+28971: Facts:
+28971: Id : 2, {_}:
+ f (f ?2 ?3) (f (f (f (f ?2 ?3) ?3) (f ?4 ?3)) (f (f ?3 ?3) ?5))
+ =>=
+ ?3
+ [5, 4, 3, 2] by oml_21C ?2 ?3 ?4 ?5
+28971: Goal:
+28971: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
+ [] by associativity
+28971: Order:
+28971: kbo
+28971: Leaf order:
+28971: f 17 2 8 0,2
+28971: c 3 0 3 2,1,2,2
+28971: b 4 0 4 1,1,2,2
+28971: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+28972: Facts:
+28972: Id : 2, {_}:
+ f (f ?2 ?3) (f (f (f (f ?2 ?3) ?3) (f ?4 ?3)) (f (f ?3 ?3) ?5))
+ =>=
+ ?3
+ [5, 4, 3, 2] by oml_21C ?2 ?3 ?4 ?5
+28972: Goal:
+28972: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
+ [] by associativity
+28972: Order:
+28972: lpo
+28972: Leaf order:
+28972: f 17 2 8 0,2
+28972: c 3 0 3 2,1,2,2
+28972: b 4 0 4 1,1,2,2
+28972: a 3 0 3 1,2
+% SZS status Timeout for LAT071-1.p
+NO CLASH, using fixed ground order
+29000: Facts:
+29000: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
+ (f ?3 (f (f ?4 (f (f ?3 ?3) ?4)) ?4))
+ =>=
+ ?3
+ [5, 4, 3, 2] by oml_23A ?2 ?3 ?4 ?5
+29000: Goal:
+29000: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
+ [] by associativity
+29000: Order:
+29000: nrkbo
+29000: Leaf order:
+29000: f 18 2 8 0,2
+29000: c 3 0 3 2,1,2,2
+29000: b 4 0 4 1,1,2,2
+29000: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+29001: Facts:
+29001: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
+ (f ?3 (f (f ?4 (f (f ?3 ?3) ?4)) ?4))
+ =>=
+ ?3
+ [5, 4, 3, 2] by oml_23A ?2 ?3 ?4 ?5
+29001: Goal:
+29001: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
+ [] by associativity
+29001: Order:
+29001: kbo
+29001: Leaf order:
+29001: f 18 2 8 0,2
+29001: c 3 0 3 2,1,2,2
+29001: b 4 0 4 1,1,2,2
+29001: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+29002: Facts:
+29002: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
+ (f ?3 (f (f ?4 (f (f ?3 ?3) ?4)) ?4))
+ =>=
+ ?3
+ [5, 4, 3, 2] by oml_23A ?2 ?3 ?4 ?5
+29002: Goal:
+29002: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
+ [] by associativity
+29002: Order:
+29002: lpo
+29002: Leaf order:
+29002: f 18 2 8 0,2
+29002: c 3 0 3 2,1,2,2
+29002: b 4 0 4 1,1,2,2
+29002: a 3 0 3 1,2
+% SZS status Timeout for LAT072-1.p
+NO CLASH, using fixed ground order
+29018: Facts:
+29018: Id : 2, {_}:
+ f (f (f ?2 (f ?3 ?2)) ?2)
+ (f ?3 (f ?4 (f (f ?3 ?2) (f (f ?4 ?4) ?5))))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_23C ?2 ?3 ?4 ?5
+29018: Goal:
+29018: Id : 1, {_}:
+ f a (f b (f a (f c c))) =>= f a (f c (f a (f b b)))
+ [] by modularity
+29018: Order:
+29018: nrkbo
+29018: Leaf order:
+29018: f 18 2 8 0,2
+29018: c 3 0 3 1,2,2,2,2
+29018: b 3 0 3 1,2,2
+29018: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+29019: Facts:
+29019: Id : 2, {_}:
+ f (f (f ?2 (f ?3 ?2)) ?2)
+ (f ?3 (f ?4 (f (f ?3 ?2) (f (f ?4 ?4) ?5))))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_23C ?2 ?3 ?4 ?5
+29019: Goal:
+29019: Id : 1, {_}:
+ f a (f b (f a (f c c))) =?= f a (f c (f a (f b b)))
+ [] by modularity
+29019: Order:
+29019: kbo
+29019: Leaf order:
+29019: f 18 2 8 0,2
+29019: c 3 0 3 1,2,2,2,2
+29019: b 3 0 3 1,2,2
+29019: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+29020: Facts:
+29020: Id : 2, {_}:
+ f (f (f ?2 (f ?3 ?2)) ?2)
+ (f ?3 (f ?4 (f (f ?3 ?2) (f (f ?4 ?4) ?5))))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_23C ?2 ?3 ?4 ?5
+29020: Goal:
+29020: Id : 1, {_}:
+ f a (f b (f a (f c c))) =<= f a (f c (f a (f b b)))
+ [] by modularity
+29020: Order:
+29020: lpo
+29020: Leaf order:
+29020: f 18 2 8 0,2
+29020: c 3 0 3 1,2,2,2,2
+29020: b 3 0 3 1,2,2
+29020: a 4 0 4 1,2
+% SZS status Timeout for LAT073-1.p
+NO CLASH, using fixed ground order
+29047: Facts:
+29047: Id : 2, {_}:
+ f (f ?2 ?3)
+ (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
+29047: Goal:
+29047: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
+ [] by associativity
+29047: Order:
+29047: nrkbo
+29047: Leaf order:
+29047: f 19 2 8 0,2
+29047: c 3 0 3 2,1,2,2
+29047: b 4 0 4 1,1,2,2
+29047: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+29048: Facts:
+29048: Id : 2, {_}:
+ f (f ?2 ?3)
+ (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
+29048: Goal:
+29048: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
+ [] by associativity
+29048: Order:
+29048: kbo
+29048: Leaf order:
+29048: f 19 2 8 0,2
+29048: c 3 0 3 2,1,2,2
+29048: b 4 0 4 1,1,2,2
+29048: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+29049: Facts:
+29049: Id : 2, {_}:
+ f (f ?2 ?3)
+ (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
+29049: Goal:
+29049: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
+ [] by associativity
+29049: Order:
+29049: lpo
+29049: Leaf order:
+29049: f 19 2 8 0,2
+29049: c 3 0 3 2,1,2,2
+29049: b 4 0 4 1,1,2,2
+29049: a 3 0 3 1,2
+% SZS status Timeout for LAT074-1.p
+NO CLASH, using fixed ground order
+29065: Facts:
+29065: Id : 2, {_}:
+ f (f ?2 ?3)
+ (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
+29065: Goal:
+29065: Id : 1, {_}:
+ f a (f b (f a (f c c))) =>= f a (f c (f a (f b b)))
+ [] by modularity
+29065: Order:
+29065: nrkbo
+29065: Leaf order:
+29065: f 19 2 8 0,2
+29065: c 3 0 3 1,2,2,2,2
+29065: b 3 0 3 1,2,2
+29065: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+29066: Facts:
+29066: Id : 2, {_}:
+ f (f ?2 ?3)
+ (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
+29066: Goal:
+29066: Id : 1, {_}:
+ f a (f b (f a (f c c))) =?= f a (f c (f a (f b b)))
+ [] by modularity
+29066: Order:
+29066: kbo
+29066: Leaf order:
+29066: f 19 2 8 0,2
+29066: c 3 0 3 1,2,2,2,2
+29066: b 3 0 3 1,2,2
+29066: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+29067: Facts:
+29067: Id : 2, {_}:
+ f (f ?2 ?3)
+ (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
+29067: Goal:
+29067: Id : 1, {_}:
+ f a (f b (f a (f c c))) =<= f a (f c (f a (f b b)))
+ [] by modularity
+29067: Order:
+29067: lpo
+29067: Leaf order:
+29067: f 19 2 8 0,2
+29067: c 3 0 3 1,2,2,2,2
+29067: b 3 0 3 1,2,2
+29067: a 4 0 4 1,2
+% SZS status Timeout for LAT075-1.p
+NO CLASH, using fixed ground order
+29098: Facts:
+29098: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
+ (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
+29098: Goal:
+29098: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
+ [] by associativity
+29098: Order:
+29098: nrkbo
+29098: Leaf order:
+29098: f 20 2 8 0,2
+29098: c 3 0 3 2,1,2,2
+29098: b 4 0 4 1,1,2,2
+29098: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+29099: Facts:
+29099: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
+ (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
+29099: Goal:
+29099: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
+ [] by associativity
+29099: Order:
+29099: kbo
+29099: Leaf order:
+29099: f 20 2 8 0,2
+29099: c 3 0 3 2,1,2,2
+29099: b 4 0 4 1,1,2,2
+29099: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+29100: Facts:
+29100: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
+ (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
+29100: Goal:
+29100: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
+ [] by associativity
+29100: Order:
+29100: lpo
+29100: Leaf order:
+29100: f 20 2 8 0,2
+29100: c 3 0 3 2,1,2,2
+29100: b 4 0 4 1,1,2,2
+29100: a 3 0 3 1,2
+% SZS status Timeout for LAT076-1.p
+NO CLASH, using fixed ground order
+29161: Facts:
+NO CLASH, using fixed ground order
+29162: Facts:
+29162: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
+ (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
+29162: Goal:
+29162: Id : 1, {_}:
+ f a (f b (f a (f c c))) =?= f a (f c (f a (f b b)))
+ [] by modularity
+29162: Order:
+29162: kbo
+29162: Leaf order:
+29162: f 20 2 8 0,2
+29162: c 3 0 3 1,2,2,2,2
+29162: b 3 0 3 1,2,2
+29162: a 4 0 4 1,2
+29161: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
+ (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
+29161: Goal:
+29161: Id : 1, {_}:
+ f a (f b (f a (f c c))) =>= f a (f c (f a (f b b)))
+ [] by modularity
+29161: Order:
+29161: nrkbo
+29161: Leaf order:
+29161: f 20 2 8 0,2
+29161: c 3 0 3 1,2,2,2,2
+29161: b 3 0 3 1,2,2
+29161: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+29163: Facts:
+29163: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
+ (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
+29163: Goal:
+29163: Id : 1, {_}:
+ f a (f b (f a (f c c))) =<= f a (f c (f a (f b b)))
+ [] by modularity
+29163: Order:
+29163: lpo
+29163: Leaf order:
+29163: f 20 2 8 0,2
+29163: c 3 0 3 1,2,2,2,2
+29163: b 3 0 3 1,2,2
+29163: a 4 0 4 1,2
+% SZS status Timeout for LAT077-1.p
+NO CLASH, using fixed ground order
+29191: Facts:
+29191: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
+ (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
+29191: Goal:
+29191: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
+ [] by associativity
+29191: Order:
+29191: nrkbo
+29191: Leaf order:
+29191: f 20 2 8 0,2
+29191: c 3 0 3 2,1,2,2
+29191: b 4 0 4 1,1,2,2
+29191: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+29192: Facts:
+29192: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
+ (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
+29192: Goal:
+29192: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
+ [] by associativity
+29192: Order:
+29192: kbo
+29192: Leaf order:
+29192: f 20 2 8 0,2
+29192: c 3 0 3 2,1,2,2
+29192: b 4 0 4 1,1,2,2
+29192: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+29193: Facts:
+29193: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
+ (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
+29193: Goal:
+29193: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
+ [] by associativity
+29193: Order:
+29193: lpo
+29193: Leaf order:
+29193: f 20 2 8 0,2
+29193: c 3 0 3 2,1,2,2
+29193: b 4 0 4 1,1,2,2
+29193: a 3 0 3 1,2
+% SZS status Timeout for LAT078-1.p
+NO CLASH, using fixed ground order
+29210: Facts:
+29210: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
+ (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
+29210: Goal:
+29210: Id : 1, {_}:
+ f a (f b (f a (f c c))) =>= f a (f c (f a (f b b)))
+ [] by modularity
+29210: Order:
+29210: nrkbo
+29210: Leaf order:
+29210: f 20 2 8 0,2
+29210: c 3 0 3 1,2,2,2,2
+29210: b 3 0 3 1,2,2
+29210: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+29211: Facts:
+29211: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
+ (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
+29211: Goal:
+29211: Id : 1, {_}:
+ f a (f b (f a (f c c))) =?= f a (f c (f a (f b b)))
+ [] by modularity
+29211: Order:
+29211: kbo
+29211: Leaf order:
+29211: f 20 2 8 0,2
+29211: c 3 0 3 1,2,2,2,2
+29211: b 3 0 3 1,2,2
+29211: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+29212: Facts:
+29212: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
+ (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
+29212: Goal:
+29212: Id : 1, {_}:
+ f a (f b (f a (f c c))) =<= f a (f c (f a (f b b)))
+ [] by modularity
+29212: Order:
+29212: lpo
+29212: Leaf order:
+29212: f 20 2 8 0,2
+29212: c 3 0 3 1,2,2,2,2
+29212: b 3 0 3 1,2,2
+29212: a 4 0 4 1,2
+% SZS status Timeout for LAT079-1.p
+NO CLASH, using fixed ground order
+29240: Facts:
+29240: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29240: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29240: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29240: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29240: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29240: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29240: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29240: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29240: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?28 (join ?26 (meet ?27 (join ?28 (meet ?26 ?27))))))
+ [28, 27, 26] by equation_H11 ?26 ?27 ?28
+29240: Goal:
+29240: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join a (meet b c))))
+ [] by prove_H10
+29240: Order:
+29240: nrkbo
+29240: Leaf order:
+29240: join 16 2 3 0,2,2
+29240: meet 20 2 5 0,2
+29240: c 3 0 3 2,2,2,2
+29240: b 3 0 3 1,2,2
+29240: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+29241: Facts:
+29241: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29241: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29241: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29241: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29241: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29241: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29241: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29241: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29241: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?28 (join ?26 (meet ?27 (join ?28 (meet ?26 ?27))))))
+ [28, 27, 26] by equation_H11 ?26 ?27 ?28
+29241: Goal:
+29241: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join a (meet b c))))
+ [] by prove_H10
+29241: Order:
+29241: kbo
+29241: Leaf order:
+29241: join 16 2 3 0,2,2
+29241: meet 20 2 5 0,2
+29241: c 3 0 3 2,2,2,2
+29241: b 3 0 3 1,2,2
+29241: a 4 0 4 1,2
+NO CLASH, using fixed ground order
+29242: Facts:
+29242: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29242: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29242: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29242: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29242: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29242: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29242: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29242: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29242: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =?=
+ meet ?26
+ (join ?27
+ (meet ?28 (join ?26 (meet ?27 (join ?28 (meet ?26 ?27))))))
+ [28, 27, 26] by equation_H11 ?26 ?27 ?28
+29242: Goal:
+29242: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =>=
+ meet a (join b (meet c (join a (meet b c))))
+ [] by prove_H10
+29242: Order:
+29242: lpo
+29242: Leaf order:
+29242: join 16 2 3 0,2,2
+29242: meet 20 2 5 0,2
+29242: c 3 0 3 2,2,2,2
+29242: b 3 0 3 1,2,2
+29242: a 4 0 4 1,2
+% SZS status Timeout for LAT139-1.p
+NO CLASH, using fixed ground order
+29258: Facts:
+29258: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29258: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29258: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29258: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29258: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29258: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29258: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29258: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29258: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?26 (meet ?27 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H21 ?26 ?27 ?28
+29258: Goal:
+29258: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+29258: Order:
+29258: nrkbo
+29258: Leaf order:
+29258: join 17 2 4 0,2,2
+29258: meet 21 2 6 0,2
+29258: c 3 0 3 2,2,2,2
+29258: b 3 0 3 1,2,2
+29258: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+29259: Facts:
+29259: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29259: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29259: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29259: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29259: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29259: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29259: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29259: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29259: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?26 (meet ?27 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H21 ?26 ?27 ?28
+29259: Goal:
+29259: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+29259: Order:
+29259: kbo
+29259: Leaf order:
+29259: join 17 2 4 0,2,2
+29259: meet 21 2 6 0,2
+29259: c 3 0 3 2,2,2,2
+NO CLASH, using fixed ground order
+29260: Facts:
+29260: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29260: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29260: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29260: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29260: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29260: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29260: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29260: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29260: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?26 (meet ?27 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H21 ?26 ?27 ?28
+29260: Goal:
+29260: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+29260: Order:
+29260: lpo
+29260: Leaf order:
+29260: join 17 2 4 0,2,2
+29260: meet 21 2 6 0,2
+29260: c 3 0 3 2,2,2,2
+29260: b 3 0 3 1,2,2
+29260: a 6 0 6 1,2
+29259: b 3 0 3 1,2,2
+29259: a 6 0 6 1,2
+% SZS status Timeout for LAT141-1.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+29297: Facts:
+29297: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29297: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29297: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29297: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29297: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29297: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29297: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29297: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29297: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ meet ?26 (join ?27 (meet (join ?26 ?27) (join ?28 (meet ?26 ?27))))
+ [28, 27, 26] by equation_H58 ?26 ?27 ?28
+29297: Goal:
+29297: Id : 1, {_}:
+ meet a (meet (join b c) (join b d))
+ =<=
+ meet a (join b (meet (join b d) (join c (meet a b))))
+ [] by prove_H59
+29297: Order:
+29297: kbo
+29297: Leaf order:
+29297: meet 18 2 5 0,2
+29297: d 2 0 2 2,2,2,2
+29297: join 18 2 5 0,1,2,2
+29297: c 2 0 2 2,1,2,2
+29297: b 5 0 5 1,1,2,2
+29297: a 3 0 3 1,2
+29296: Facts:
+29296: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29296: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29296: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29296: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29296: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29296: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29296: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29296: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29296: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ meet ?26 (join ?27 (meet (join ?26 ?27) (join ?28 (meet ?26 ?27))))
+ [28, 27, 26] by equation_H58 ?26 ?27 ?28
+29296: Goal:
+29296: Id : 1, {_}:
+ meet a (meet (join b c) (join b d))
+ =<=
+ meet a (join b (meet (join b d) (join c (meet a b))))
+ [] by prove_H59
+29296: Order:
+29296: nrkbo
+29296: Leaf order:
+29296: meet 18 2 5 0,2
+29296: d 2 0 2 2,2,2,2
+29296: join 18 2 5 0,1,2,2
+29296: c 2 0 2 2,1,2,2
+29296: b 5 0 5 1,1,2,2
+29296: a 3 0 3 1,2
+NO CLASH, using fixed ground order
+29298: Facts:
+29298: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29298: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29298: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29298: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29298: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29298: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29298: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29298: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29298: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ meet ?26 (join ?27 (meet (join ?26 ?27) (join ?28 (meet ?26 ?27))))
+ [28, 27, 26] by equation_H58 ?26 ?27 ?28
+29298: Goal:
+29298: Id : 1, {_}:
+ meet a (meet (join b c) (join b d))
+ =<=
+ meet a (join b (meet (join b d) (join c (meet a b))))
+ [] by prove_H59
+29298: Order:
+29298: lpo
+29298: Leaf order:
+29298: meet 18 2 5 0,2
+29298: d 2 0 2 2,2,2,2
+29298: join 18 2 5 0,1,2,2
+29298: c 2 0 2 2,1,2,2
+29298: b 5 0 5 1,1,2,2
+29298: a 3 0 3 1,2
+% SZS status Timeout for LAT161-1.p
+NO CLASH, using fixed ground order
+29316: Facts:
+29316: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29316: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29316: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29316: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29316: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29316: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29316: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29316: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29316: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
+ [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
+29316: Goal:
+29316: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+29316: Order:
+29316: nrkbo
+29316: Leaf order:
+29316: join 19 2 4 0,2,2
+29316: meet 19 2 6 0,2
+29316: c 3 0 3 2,2,2,2
+29316: b 3 0 3 1,2,2
+29316: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+29317: Facts:
+29317: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29317: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29317: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29317: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29317: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29317: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29317: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29317: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29317: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
+ [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
+29317: Goal:
+29317: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+29317: Order:
+29317: kbo
+29317: Leaf order:
+29317: join 19 2 4 0,2,2
+29317: meet 19 2 6 0,2
+29317: c 3 0 3 2,2,2,2
+29317: b 3 0 3 1,2,2
+29317: a 6 0 6 1,2
+NO CLASH, using fixed ground order
+29318: Facts:
+29318: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29318: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29318: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29318: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29318: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29318: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29318: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29318: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29318: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
+ [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
+29318: Goal:
+29318: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+29318: Order:
+29318: lpo
+29318: Leaf order:
+29318: join 19 2 4 0,2,2
+29318: meet 19 2 6 0,2
+29318: c 3 0 3 2,2,2,2
+29318: b 3 0 3 1,2,2
+29318: a 6 0 6 1,2
+% SZS status Timeout for LAT177-1.p
+NO CLASH, using fixed ground order
+29346: Facts:
+29346: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutative_addition ?2 ?3
+29346: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associative_addition ?5 ?6 ?7
+NO CLASH, using fixed ground order
+29347: Facts:
+29347: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutative_addition ?2 ?3
+29347: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associative_addition ?5 ?6 ?7
+29347: Id : 4, {_}: add ?9 additive_identity =>= ?9 [9] by right_identity ?9
+29347: Id : 5, {_}: add additive_identity ?11 =>= ?11 [11] by left_identity ?11
+29347: Id : 6, {_}:
+ add ?13 (additive_inverse ?13) =>= additive_identity
+ [13] by right_additive_inverse ?13
+29347: Id : 7, {_}:
+ add (additive_inverse ?15) ?15 =>= additive_identity
+ [15] by left_additive_inverse ?15
+29347: Id : 8, {_}:
+ additive_inverse additive_identity =>= additive_identity
+ [] by additive_inverse_identity
+29347: Id : 9, {_}:
+ add ?18 (add (additive_inverse ?18) ?19) =>= ?19
+ [19, 18] by property_of_inverse_and_add ?18 ?19
+29347: Id : 10, {_}:
+ additive_inverse (add ?21 ?22)
+ =>=
+ add (additive_inverse ?21) (additive_inverse ?22)
+ [22, 21] by distribute_additive_inverse ?21 ?22
+29347: Id : 11, {_}:
+ additive_inverse (additive_inverse ?24) =>= ?24
+ [24] by additive_inverse_additive_inverse ?24
+29347: Id : 12, {_}:
+ multiply ?26 additive_identity =>= additive_identity
+ [26] by multiply_additive_id1 ?26
+29347: Id : 13, {_}:
+ multiply additive_identity ?28 =>= additive_identity
+ [28] by multiply_additive_id2 ?28
+29347: Id : 14, {_}:
+ multiply (additive_inverse ?30) (additive_inverse ?31)
+ =>=
+ multiply ?30 ?31
+ [31, 30] by product_of_inverse ?30 ?31
+NO CLASH, using fixed ground order
+29346: Id : 4, {_}: add ?9 additive_identity =>= ?9 [9] by right_identity ?9
+29346: Id : 5, {_}: add additive_identity ?11 =>= ?11 [11] by left_identity ?11
+29346: Id : 6, {_}:
+ add ?13 (additive_inverse ?13) =>= additive_identity
+ [13] by right_additive_inverse ?13
+29346: Id : 7, {_}:
+ add (additive_inverse ?15) ?15 =>= additive_identity
+ [15] by left_additive_inverse ?15
+29346: Id : 8, {_}:
+ additive_inverse additive_identity =>= additive_identity
+ [] by additive_inverse_identity
+29345: Facts:
+29346: Id : 9, {_}:
+ add ?18 (add (additive_inverse ?18) ?19) =>= ?19
+ [19, 18] by property_of_inverse_and_add ?18 ?19
+29346: Id : 10, {_}:
+ additive_inverse (add ?21 ?22)
+ =<=
+ add (additive_inverse ?21) (additive_inverse ?22)
+ [22, 21] by distribute_additive_inverse ?21 ?22
+29345: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutative_addition ?2 ?3
+29345: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associative_addition ?5 ?6 ?7
+29346: Id : 11, {_}:
+ additive_inverse (additive_inverse ?24) =>= ?24
+ [24] by additive_inverse_additive_inverse ?24
+29345: Id : 4, {_}: add ?9 additive_identity =>= ?9 [9] by right_identity ?9
+29346: Id : 12, {_}:
+ multiply ?26 additive_identity =>= additive_identity
+ [26] by multiply_additive_id1 ?26
+29345: Id : 5, {_}: add additive_identity ?11 =>= ?11 [11] by left_identity ?11
+29346: Id : 13, {_}:
+ multiply additive_identity ?28 =>= additive_identity
+ [28] by multiply_additive_id2 ?28
+29346: Id : 14, {_}:
+ multiply (additive_inverse ?30) (additive_inverse ?31)
+ =>=
+ multiply ?30 ?31
+ [31, 30] by product_of_inverse ?30 ?31
+29346: Id : 15, {_}:
+ multiply ?33 (additive_inverse ?34)
+ =<=
+ additive_inverse (multiply ?33 ?34)
+ [34, 33] by multiply_additive_inverse1 ?33 ?34
+29345: Id : 6, {_}:
+ add ?13 (additive_inverse ?13) =>= additive_identity
+ [13] by right_additive_inverse ?13
+29345: Id : 7, {_}:
+ add (additive_inverse ?15) ?15 =>= additive_identity
+ [15] by left_additive_inverse ?15
+29345: Id : 8, {_}:
+ additive_inverse additive_identity =>= additive_identity
+ [] by additive_inverse_identity
+29346: Id : 16, {_}:
+ multiply (additive_inverse ?36) ?37
+ =<=
+ additive_inverse (multiply ?36 ?37)
+ [37, 36] by multiply_additive_inverse2 ?36 ?37
+29345: Id : 9, {_}:
+ add ?18 (add (additive_inverse ?18) ?19) =>= ?19
+ [19, 18] by property_of_inverse_and_add ?18 ?19
+29346: Id : 17, {_}:
+ multiply ?39 (add ?40 ?41)
+ =<=
+ add (multiply ?39 ?40) (multiply ?39 ?41)
+ [41, 40, 39] by distribute1 ?39 ?40 ?41
+29345: Id : 10, {_}:
+ additive_inverse (add ?21 ?22)
+ =<=
+ add (additive_inverse ?21) (additive_inverse ?22)
+ [22, 21] by distribute_additive_inverse ?21 ?22
+29346: Id : 18, {_}:
+ multiply (add ?43 ?44) ?45
+ =<=
+ add (multiply ?43 ?45) (multiply ?44 ?45)
+ [45, 44, 43] by distribute2 ?43 ?44 ?45
+29345: Id : 11, {_}:
+ additive_inverse (additive_inverse ?24) =>= ?24
+ [24] by additive_inverse_additive_inverse ?24
+29345: Id : 12, {_}:
+ multiply ?26 additive_identity =>= additive_identity
+ [26] by multiply_additive_id1 ?26
+29345: Id : 13, {_}:
+ multiply additive_identity ?28 =>= additive_identity
+ [28] by multiply_additive_id2 ?28
+29345: Id : 14, {_}:
+ multiply (additive_inverse ?30) (additive_inverse ?31)
+ =>=
+ multiply ?30 ?31
+ [31, 30] by product_of_inverse ?30 ?31
+29345: Id : 15, {_}:
+ multiply ?33 (additive_inverse ?34)
+ =<=
+ additive_inverse (multiply ?33 ?34)
+ [34, 33] by multiply_additive_inverse1 ?33 ?34
+29345: Id : 16, {_}:
+ multiply (additive_inverse ?36) ?37
+ =<=
+ additive_inverse (multiply ?36 ?37)
+ [37, 36] by multiply_additive_inverse2 ?36 ?37
+29345: Id : 17, {_}:
+ multiply ?39 (add ?40 ?41)
+ =<=
+ add (multiply ?39 ?40) (multiply ?39 ?41)
+ [41, 40, 39] by distribute1 ?39 ?40 ?41
+29345: Id : 18, {_}:
+ multiply (add ?43 ?44) ?45
+ =<=
+ add (multiply ?43 ?45) (multiply ?44 ?45)
+ [45, 44, 43] by distribute2 ?43 ?44 ?45
+29345: Id : 19, {_}:
+ multiply (multiply ?47 ?48) ?48 =?= multiply ?47 (multiply ?48 ?48)
+ [48, 47] by right_alternative ?47 ?48
+29347: Id : 15, {_}:
+ multiply ?33 (additive_inverse ?34)
+ =<=
+ additive_inverse (multiply ?33 ?34)
+ [34, 33] by multiply_additive_inverse1 ?33 ?34
+29345: Id : 20, {_}:
+ associator ?50 ?51 ?52
+ =<=
+ add (multiply (multiply ?50 ?51) ?52)
+ (additive_inverse (multiply ?50 (multiply ?51 ?52)))
+ [52, 51, 50] by associator ?50 ?51 ?52
+29345: Id : 21, {_}:
+ commutator ?54 ?55
+ =<=
+ add (multiply ?55 ?54) (additive_inverse (multiply ?54 ?55))
+ [55, 54] by commutator ?54 ?55
+29347: Id : 16, {_}:
+ multiply (additive_inverse ?36) ?37
+ =<=
+ additive_inverse (multiply ?36 ?37)
+ [37, 36] by multiply_additive_inverse2 ?36 ?37
+29347: Id : 17, {_}:
+ multiply ?39 (add ?40 ?41)
+ =<=
+ add (multiply ?39 ?40) (multiply ?39 ?41)
+ [41, 40, 39] by distribute1 ?39 ?40 ?41
+29347: Id : 18, {_}:
+ multiply (add ?43 ?44) ?45
+ =<=
+ add (multiply ?43 ?45) (multiply ?44 ?45)
+ [45, 44, 43] by distribute2 ?43 ?44 ?45
+29347: Id : 19, {_}:
+ multiply (multiply ?47 ?48) ?48 =>= multiply ?47 (multiply ?48 ?48)
+ [48, 47] by right_alternative ?47 ?48
+29347: Id : 20, {_}:
+ associator ?50 ?51 ?52
+ =<=
+ add (multiply (multiply ?50 ?51) ?52)
+ (additive_inverse (multiply ?50 (multiply ?51 ?52)))
+ [52, 51, 50] by associator ?50 ?51 ?52
+29347: Id : 21, {_}:
+ commutator ?54 ?55
+ =<=
+ add (multiply ?55 ?54) (additive_inverse (multiply ?54 ?55))
+ [55, 54] by commutator ?54 ?55
+29347: Id : 22, {_}:
+ multiply (multiply (associator ?57 ?57 ?58) ?57)
+ (associator ?57 ?57 ?58)
+ =>=
+ additive_identity
+ [58, 57] by middle_associator ?57 ?58
+29347: Id : 23, {_}:
+ multiply (multiply ?60 ?60) ?61 =>= multiply ?60 (multiply ?60 ?61)
+ [61, 60] by left_alternative ?60 ?61
+29347: Id : 24, {_}:
+ s ?63 ?64 ?65 ?66
+ =>=
+ add
+ (add (associator (multiply ?63 ?64) ?65 ?66)
+ (additive_inverse (multiply ?64 (associator ?63 ?65 ?66))))
+ (additive_inverse (multiply (associator ?64 ?65 ?66) ?63))
+ [66, 65, 64, 63] by defines_s ?63 ?64 ?65 ?66
+29347: Id : 25, {_}:
+ multiply ?68 (multiply ?69 (multiply ?70 ?69))
+ =<=
+ multiply (multiply (multiply ?68 ?69) ?70) ?69
+ [70, 69, 68] by right_moufang ?68 ?69 ?70
+29347: Id : 26, {_}:
+ multiply (multiply ?72 (multiply ?73 ?72)) ?74
+ =>=
+ multiply ?72 (multiply ?73 (multiply ?72 ?74))
+ [74, 73, 72] by left_moufang ?72 ?73 ?74
+29347: Id : 27, {_}:
+ multiply (multiply ?76 ?77) (multiply ?78 ?76)
+ =<=
+ multiply (multiply ?76 (multiply ?77 ?78)) ?76
+ [78, 77, 76] by middle_moufang ?76 ?77 ?78
+29347: Goal:
+29347: Id : 1, {_}:
+ s a b c d =>= additive_inverse (s b a c d)
+ [] by prove_skew_symmetry
+29347: Order:
+29347: lpo
+29347: Leaf order:
+29347: commutator 1 2 0
+29347: associator 6 3 0
+29347: multiply 51 2 0
+29347: additive_identity 11 0 0
+29347: add 22 2 0
+29347: additive_inverse 20 1 1 0,3
+29347: s 3 4 2 0,2
+29347: d 2 0 2 4,2
+29347: c 2 0 2 3,2
+29347: b 2 0 2 2,2
+29347: a 2 0 2 1,2
+29346: Id : 19, {_}:
+ multiply (multiply ?47 ?48) ?48 =>= multiply ?47 (multiply ?48 ?48)
+ [48, 47] by right_alternative ?47 ?48
+29345: Id : 22, {_}:
+ multiply (multiply (associator ?57 ?57 ?58) ?57)
+ (associator ?57 ?57 ?58)
+ =>=
+ additive_identity
+ [58, 57] by middle_associator ?57 ?58
+29345: Id : 23, {_}:
+ multiply (multiply ?60 ?60) ?61 =?= multiply ?60 (multiply ?60 ?61)
+ [61, 60] by left_alternative ?60 ?61
+29345: Id : 24, {_}:
+ s ?63 ?64 ?65 ?66
+ =<=
+ add
+ (add (associator (multiply ?63 ?64) ?65 ?66)
+ (additive_inverse (multiply ?64 (associator ?63 ?65 ?66))))
+ (additive_inverse (multiply (associator ?64 ?65 ?66) ?63))
+ [66, 65, 64, 63] by defines_s ?63 ?64 ?65 ?66
+29345: Id : 25, {_}:
+ multiply ?68 (multiply ?69 (multiply ?70 ?69))
+ =?=
+ multiply (multiply (multiply ?68 ?69) ?70) ?69
+ [70, 69, 68] by right_moufang ?68 ?69 ?70
+29345: Id : 26, {_}:
+ multiply (multiply ?72 (multiply ?73 ?72)) ?74
+ =?=
+ multiply ?72 (multiply ?73 (multiply ?72 ?74))
+ [74, 73, 72] by left_moufang ?72 ?73 ?74
+29345: Id : 27, {_}:
+ multiply (multiply ?76 ?77) (multiply ?78 ?76)
+ =?=
+ multiply (multiply ?76 (multiply ?77 ?78)) ?76
+ [78, 77, 76] by middle_moufang ?76 ?77 ?78
+29345: Goal:
+29345: Id : 1, {_}:
+ s a b c d =<= additive_inverse (s b a c d)
+ [] by prove_skew_symmetry
+29345: Order:
+29345: nrkbo
+29345: Leaf order:
+29345: commutator 1 2 0
+29345: associator 6 3 0
+29345: multiply 51 2 0
+29345: additive_identity 11 0 0
+29345: add 22 2 0
+29345: additive_inverse 20 1 1 0,3
+29345: s 3 4 2 0,2
+29345: d 2 0 2 4,2
+29345: c 2 0 2 3,2
+29345: b 2 0 2 2,2
+29345: a 2 0 2 1,2
+29346: Id : 20, {_}:
+ associator ?50 ?51 ?52
+ =<=
+ add (multiply (multiply ?50 ?51) ?52)
+ (additive_inverse (multiply ?50 (multiply ?51 ?52)))
+ [52, 51, 50] by associator ?50 ?51 ?52
+29346: Id : 21, {_}:
+ commutator ?54 ?55
+ =<=
+ add (multiply ?55 ?54) (additive_inverse (multiply ?54 ?55))
+ [55, 54] by commutator ?54 ?55
+29346: Id : 22, {_}:
+ multiply (multiply (associator ?57 ?57 ?58) ?57)
+ (associator ?57 ?57 ?58)
+ =>=
+ additive_identity
+ [58, 57] by middle_associator ?57 ?58
+29346: Id : 23, {_}:
+ multiply (multiply ?60 ?60) ?61 =>= multiply ?60 (multiply ?60 ?61)
+ [61, 60] by left_alternative ?60 ?61
+29346: Id : 24, {_}:
+ s ?63 ?64 ?65 ?66
+ =<=
+ add
+ (add (associator (multiply ?63 ?64) ?65 ?66)
+ (additive_inverse (multiply ?64 (associator ?63 ?65 ?66))))
+ (additive_inverse (multiply (associator ?64 ?65 ?66) ?63))
+ [66, 65, 64, 63] by defines_s ?63 ?64 ?65 ?66
+29346: Id : 25, {_}:
+ multiply ?68 (multiply ?69 (multiply ?70 ?69))
+ =<=
+ multiply (multiply (multiply ?68 ?69) ?70) ?69
+ [70, 69, 68] by right_moufang ?68 ?69 ?70
+29346: Id : 26, {_}:
+ multiply (multiply ?72 (multiply ?73 ?72)) ?74
+ =>=
+ multiply ?72 (multiply ?73 (multiply ?72 ?74))
+ [74, 73, 72] by left_moufang ?72 ?73 ?74
+29346: Id : 27, {_}:
+ multiply (multiply ?76 ?77) (multiply ?78 ?76)
+ =<=
+ multiply (multiply ?76 (multiply ?77 ?78)) ?76
+ [78, 77, 76] by middle_moufang ?76 ?77 ?78
+29346: Goal:
+29346: Id : 1, {_}:
+ s a b c d =<= additive_inverse (s b a c d)
+ [] by prove_skew_symmetry
+29346: Order:
+29346: kbo
+29346: Leaf order:
+29346: commutator 1 2 0
+29346: associator 6 3 0
+29346: multiply 51 2 0
+29346: additive_identity 11 0 0
+29346: add 22 2 0
+29346: additive_inverse 20 1 1 0,3
+29346: s 3 4 2 0,2
+29346: d 2 0 2 4,2
+29346: c 2 0 2 3,2
+29346: b 2 0 2 2,2
+29346: a 2 0 2 1,2
+% SZS status Timeout for RNG010-5.p
+NO CLASH, using fixed ground order
+29364: Facts:
+29364: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29364: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29364: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29364: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29364: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29364: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29364: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29364: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29364: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29364: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29364: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29364: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29364: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29364: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29364: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29364: Id : 17, {_}:
+ s ?44 ?45 ?46 ?47
+ =<=
+ add
+ (add (associator (multiply ?44 ?45) ?46 ?47)
+ (additive_inverse (multiply ?45 (associator ?44 ?46 ?47))))
+ (additive_inverse (multiply (associator ?45 ?46 ?47) ?44))
+ [47, 46, 45, 44] by defines_s ?44 ?45 ?46 ?47
+29364: Id : 18, {_}:
+ multiply ?49 (multiply ?50 (multiply ?51 ?50))
+ =<=
+ multiply (multiply (multiply ?49 ?50) ?51) ?50
+ [51, 50, 49] by right_moufang ?49 ?50 ?51
+29364: Id : 19, {_}:
+ multiply (multiply ?53 (multiply ?54 ?53)) ?55
+ =>=
+ multiply ?53 (multiply ?54 (multiply ?53 ?55))
+ [55, 54, 53] by left_moufang ?53 ?54 ?55
+29364: Id : 20, {_}:
+ multiply (multiply ?57 ?58) (multiply ?59 ?57)
+ =<=
+ multiply (multiply ?57 (multiply ?58 ?59)) ?57
+ [59, 58, 57] by middle_moufang ?57 ?58 ?59
+29364: Goal:
+29364: Id : 1, {_}:
+ s a b c d =<= additive_inverse (s b a c d)
+ [] by prove_skew_symmetry
+29364: Order:
+29364: kbo
+29364: Leaf order:
+29364: commutator 1 2 0
+29364: associator 4 3 0
+29364: multiply 43 2 0
+29364: add 18 2 0
+29364: additive_identity 8 0 0
+29364: additive_inverse 9 1 1 0,3
+29364: s 3 4 2 0,2
+29364: d 2 0 2 4,2
+29364: c 2 0 2 3,2
+29364: b 2 0 2 2,2
+29364: a 2 0 2 1,2
+NO CLASH, using fixed ground order
+29363: Facts:
+29363: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29363: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29363: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29363: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29363: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29363: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29363: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29363: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29363: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29363: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29363: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29363: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29363: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29363: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29363: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29363: Id : 17, {_}:
+ s ?44 ?45 ?46 ?47
+ =<=
+ add
+ (add (associator (multiply ?44 ?45) ?46 ?47)
+ (additive_inverse (multiply ?45 (associator ?44 ?46 ?47))))
+ (additive_inverse (multiply (associator ?45 ?46 ?47) ?44))
+ [47, 46, 45, 44] by defines_s ?44 ?45 ?46 ?47
+29363: Id : 18, {_}:
+ multiply ?49 (multiply ?50 (multiply ?51 ?50))
+ =?=
+ multiply (multiply (multiply ?49 ?50) ?51) ?50
+ [51, 50, 49] by right_moufang ?49 ?50 ?51
+29363: Id : 19, {_}:
+ multiply (multiply ?53 (multiply ?54 ?53)) ?55
+ =?=
+ multiply ?53 (multiply ?54 (multiply ?53 ?55))
+ [55, 54, 53] by left_moufang ?53 ?54 ?55
+29363: Id : 20, {_}:
+ multiply (multiply ?57 ?58) (multiply ?59 ?57)
+ =?=
+ multiply (multiply ?57 (multiply ?58 ?59)) ?57
+ [59, 58, 57] by middle_moufang ?57 ?58 ?59
+29363: Goal:
+29363: Id : 1, {_}:
+ s a b c d =<= additive_inverse (s b a c d)
+ [] by prove_skew_symmetry
+29363: Order:
+29363: nrkbo
+29363: Leaf order:
+29363: commutator 1 2 0
+29363: associator 4 3 0
+29363: multiply 43 2 0
+29363: add 18 2 0
+29363: additive_identity 8 0 0
+29363: additive_inverse 9 1 1 0,3
+29363: s 3 4 2 0,2
+29363: d 2 0 2 4,2
+29363: c 2 0 2 3,2
+29363: b 2 0 2 2,2
+29363: a 2 0 2 1,2
+NO CLASH, using fixed ground order
+29365: Facts:
+29365: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29365: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29365: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29365: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29365: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29365: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29365: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29365: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29365: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29365: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29365: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29365: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29365: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29365: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29365: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29365: Id : 17, {_}:
+ s ?44 ?45 ?46 ?47
+ =>=
+ add
+ (add (associator (multiply ?44 ?45) ?46 ?47)
+ (additive_inverse (multiply ?45 (associator ?44 ?46 ?47))))
+ (additive_inverse (multiply (associator ?45 ?46 ?47) ?44))
+ [47, 46, 45, 44] by defines_s ?44 ?45 ?46 ?47
+29365: Id : 18, {_}:
+ multiply ?49 (multiply ?50 (multiply ?51 ?50))
+ =<=
+ multiply (multiply (multiply ?49 ?50) ?51) ?50
+ [51, 50, 49] by right_moufang ?49 ?50 ?51
+29365: Id : 19, {_}:
+ multiply (multiply ?53 (multiply ?54 ?53)) ?55
+ =>=
+ multiply ?53 (multiply ?54 (multiply ?53 ?55))
+ [55, 54, 53] by left_moufang ?53 ?54 ?55
+29365: Id : 20, {_}:
+ multiply (multiply ?57 ?58) (multiply ?59 ?57)
+ =<=
+ multiply (multiply ?57 (multiply ?58 ?59)) ?57
+ [59, 58, 57] by middle_moufang ?57 ?58 ?59
+29365: Goal:
+29365: Id : 1, {_}:
+ s a b c d =>= additive_inverse (s b a c d)
+ [] by prove_skew_symmetry
+29365: Order:
+29365: lpo
+29365: Leaf order:
+29365: commutator 1 2 0
+29365: associator 4 3 0
+29365: multiply 43 2 0
+29365: add 18 2 0
+29365: additive_identity 8 0 0
+29365: additive_inverse 9 1 1 0,3
+29365: s 3 4 2 0,2
+29365: d 2 0 2 4,2
+29365: c 2 0 2 3,2
+29365: b 2 0 2 2,2
+29365: a 2 0 2 1,2
+% SZS status Timeout for RNG010-6.p
+NO CLASH, using fixed ground order
+29396: Facts:
+29396: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29396: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29396: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29396: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29396: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29396: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29396: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29396: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29396: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29396: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29396: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29396: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29396: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29396: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29396: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29396: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+29396: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =<=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+29396: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =<=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+29396: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+29396: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+29396: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+29396: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+29396: Id : 24, {_}:
+ s ?69 ?70 ?71 ?72
+ =<=
+ add
+ (add (associator (multiply ?69 ?70) ?71 ?72)
+ (additive_inverse (multiply ?70 (associator ?69 ?71 ?72))))
+ (additive_inverse (multiply (associator ?70 ?71 ?72) ?69))
+ [72, 71, 70, 69] by defines_s ?69 ?70 ?71 ?72
+29396: Id : 25, {_}:
+ multiply ?74 (multiply ?75 (multiply ?76 ?75))
+ =?=
+ multiply (multiply (multiply ?74 ?75) ?76) ?75
+ [76, 75, 74] by right_moufang ?74 ?75 ?76
+29396: Id : 26, {_}:
+ multiply (multiply ?78 (multiply ?79 ?78)) ?80
+ =?=
+ multiply ?78 (multiply ?79 (multiply ?78 ?80))
+ [80, 79, 78] by left_moufang ?78 ?79 ?80
+29396: Id : 27, {_}:
+ multiply (multiply ?82 ?83) (multiply ?84 ?82)
+ =?=
+ multiply (multiply ?82 (multiply ?83 ?84)) ?82
+ [84, 83, 82] by middle_moufang ?82 ?83 ?84
+29396: Goal:
+29396: Id : 1, {_}:
+ s a b c d =<= additive_inverse (s b a c d)
+ [] by prove_skew_symmetry
+29396: Order:
+29396: nrkbo
+29396: Leaf order:
+29396: commutator 1 2 0
+29396: associator 4 3 0
+29396: multiply 61 2 0
+29396: add 26 2 0
+29396: additive_identity 8 0 0
+29396: additive_inverse 25 1 1 0,3
+29396: s 3 4 2 0,2
+29396: d 2 0 2 4,2
+29396: c 2 0 2 3,2
+29396: b 2 0 2 2,2
+29396: a 2 0 2 1,2
+NO CLASH, using fixed ground order
+29397: Facts:
+29397: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29397: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29397: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29397: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29397: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29397: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29397: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29397: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29397: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29397: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29397: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29397: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29397: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29397: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29397: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29397: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+29397: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =<=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+29397: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =<=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+29397: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+29397: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+29397: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+29397: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+29397: Id : 24, {_}:
+ s ?69 ?70 ?71 ?72
+ =<=
+ add
+ (add (associator (multiply ?69 ?70) ?71 ?72)
+ (additive_inverse (multiply ?70 (associator ?69 ?71 ?72))))
+ (additive_inverse (multiply (associator ?70 ?71 ?72) ?69))
+ [72, 71, 70, 69] by defines_s ?69 ?70 ?71 ?72
+29397: Id : 25, {_}:
+ multiply ?74 (multiply ?75 (multiply ?76 ?75))
+ =<=
+ multiply (multiply (multiply ?74 ?75) ?76) ?75
+ [76, 75, 74] by right_moufang ?74 ?75 ?76
+29397: Id : 26, {_}:
+ multiply (multiply ?78 (multiply ?79 ?78)) ?80
+ =>=
+ multiply ?78 (multiply ?79 (multiply ?78 ?80))
+ [80, 79, 78] by left_moufang ?78 ?79 ?80
+29397: Id : 27, {_}:
+ multiply (multiply ?82 ?83) (multiply ?84 ?82)
+ =<=
+ multiply (multiply ?82 (multiply ?83 ?84)) ?82
+ [84, 83, 82] by middle_moufang ?82 ?83 ?84
+29397: Goal:
+29397: Id : 1, {_}:
+ s a b c d =<= additive_inverse (s b a c d)
+ [] by prove_skew_symmetry
+29397: Order:
+29397: kbo
+29397: Leaf order:
+29397: commutator 1 2 0
+29397: associator 4 3 0
+29397: multiply 61 2 0
+29397: add 26 2 0
+29397: additive_identity 8 0 0
+29397: additive_inverse 25 1 1 0,3
+29397: s 3 4 2 0,2
+29397: d 2 0 2 4,2
+29397: c 2 0 2 3,2
+29397: b 2 0 2 2,2
+29397: a 2 0 2 1,2
+NO CLASH, using fixed ground order
+29398: Facts:
+29398: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29398: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29398: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29398: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29398: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29398: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29398: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29398: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29398: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29398: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29398: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29398: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29398: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29398: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29398: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29398: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+29398: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =<=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+29398: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =<=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+29398: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+29398: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+29398: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+29398: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+29398: Id : 24, {_}:
+ s ?69 ?70 ?71 ?72
+ =>=
+ add
+ (add (associator (multiply ?69 ?70) ?71 ?72)
+ (additive_inverse (multiply ?70 (associator ?69 ?71 ?72))))
+ (additive_inverse (multiply (associator ?70 ?71 ?72) ?69))
+ [72, 71, 70, 69] by defines_s ?69 ?70 ?71 ?72
+29398: Id : 25, {_}:
+ multiply ?74 (multiply ?75 (multiply ?76 ?75))
+ =<=
+ multiply (multiply (multiply ?74 ?75) ?76) ?75
+ [76, 75, 74] by right_moufang ?74 ?75 ?76
+29398: Id : 26, {_}:
+ multiply (multiply ?78 (multiply ?79 ?78)) ?80
+ =>=
+ multiply ?78 (multiply ?79 (multiply ?78 ?80))
+ [80, 79, 78] by left_moufang ?78 ?79 ?80
+29398: Id : 27, {_}:
+ multiply (multiply ?82 ?83) (multiply ?84 ?82)
+ =<=
+ multiply (multiply ?82 (multiply ?83 ?84)) ?82
+ [84, 83, 82] by middle_moufang ?82 ?83 ?84
+29398: Goal:
+29398: Id : 1, {_}:
+ s a b c d =>= additive_inverse (s b a c d)
+ [] by prove_skew_symmetry
+29398: Order:
+29398: lpo
+29398: Leaf order:
+29398: commutator 1 2 0
+29398: associator 4 3 0
+29398: multiply 61 2 0
+29398: add 26 2 0
+29398: additive_identity 8 0 0
+29398: additive_inverse 25 1 1 0,3
+29398: s 3 4 2 0,2
+29398: d 2 0 2 4,2
+29398: c 2 0 2 3,2
+29398: b 2 0 2 2,2
+29398: a 2 0 2 1,2
+% SZS status Timeout for RNG010-7.p
+NO CLASH, using fixed ground order
+29437: Facts:
+29437: Id : 2, {_}:
+ add ?2 ?3 =?= add ?3 ?2
+ [3, 2] by commutativity_for_addition ?2 ?3
+29437: Id : 3, {_}:
+ add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7
+ [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
+29437: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
+29437: Id : 5, {_}:
+ add ?11 additive_identity =>= ?11
+ [11] by right_additive_identity ?11
+29437: Id : 6, {_}:
+ multiply additive_identity ?13 =>= additive_identity
+ [13] by left_multiplicative_zero ?13
+29437: Id : 7, {_}:
+ multiply ?15 additive_identity =>= additive_identity
+ [15] by right_multiplicative_zero ?15
+29437: Id : 8, {_}:
+ add (additive_inverse ?17) ?17 =>= additive_identity
+ [17] by left_additive_inverse ?17
+29437: Id : 9, {_}:
+ add ?19 (additive_inverse ?19) =>= additive_identity
+ [19] by right_additive_inverse ?19
+29437: Id : 10, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+29437: Id : 11, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+29437: Id : 12, {_}:
+ additive_inverse (additive_inverse ?29) =>= ?29
+ [29] by additive_inverse_additive_inverse ?29
+29437: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29437: Id : 14, {_}:
+ associator ?34 ?35 ?36
+ =<=
+ add (multiply (multiply ?34 ?35) ?36)
+ (additive_inverse (multiply ?34 (multiply ?35 ?36)))
+ [36, 35, 34] by associator ?34 ?35 ?36
+29437: Id : 15, {_}:
+ commutator ?38 ?39
+ =<=
+ add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
+ [39, 38] by commutator ?38 ?39
+29437: Goal:
+29437: Id : 1, {_}:
+ add
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ =>=
+ additive_identity
+ [] by prove_conjecture_1
+29437: Order:
+29437: nrkbo
+29437: Leaf order:
+29437: commutator 1 2 0
+29437: additive_inverse 6 1 0
+29437: additive_identity 9 0 1 3
+29437: add 17 2 1 0,2
+29437: multiply 22 2 4 0,1,2
+29437: associator 7 3 6 0,1,1,2
+29437: y 6 0 6 3,1,1,2
+29437: x 12 0 12 1,1,1,2
+NO CLASH, using fixed ground order
+29438: Facts:
+29438: Id : 2, {_}:
+ add ?2 ?3 =?= add ?3 ?2
+ [3, 2] by commutativity_for_addition ?2 ?3
+29438: Id : 3, {_}:
+ add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
+ [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
+29438: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
+29438: Id : 5, {_}:
+ add ?11 additive_identity =>= ?11
+ [11] by right_additive_identity ?11
+29438: Id : 6, {_}:
+ multiply additive_identity ?13 =>= additive_identity
+ [13] by left_multiplicative_zero ?13
+29438: Id : 7, {_}:
+ multiply ?15 additive_identity =>= additive_identity
+ [15] by right_multiplicative_zero ?15
+29438: Id : 8, {_}:
+ add (additive_inverse ?17) ?17 =>= additive_identity
+ [17] by left_additive_inverse ?17
+29438: Id : 9, {_}:
+ add ?19 (additive_inverse ?19) =>= additive_identity
+ [19] by right_additive_inverse ?19
+29438: Id : 10, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+29438: Id : 11, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+29438: Id : 12, {_}:
+ additive_inverse (additive_inverse ?29) =>= ?29
+ [29] by additive_inverse_additive_inverse ?29
+29438: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29438: Id : 14, {_}:
+ associator ?34 ?35 ?36
+ =<=
+ add (multiply (multiply ?34 ?35) ?36)
+ (additive_inverse (multiply ?34 (multiply ?35 ?36)))
+ [36, 35, 34] by associator ?34 ?35 ?36
+29438: Id : 15, {_}:
+ commutator ?38 ?39
+ =<=
+ add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
+ [39, 38] by commutator ?38 ?39
+29438: Goal:
+29438: Id : 1, {_}:
+ add
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ =>=
+ additive_identity
+ [] by prove_conjecture_1
+29438: Order:
+29438: kbo
+29438: Leaf order:
+29438: commutator 1 2 0
+29438: additive_inverse 6 1 0
+29438: additive_identity 9 0 1 3
+29438: add 17 2 1 0,2
+29438: multiply 22 2 4 0,1,2
+29438: associator 7 3 6 0,1,1,2
+29438: y 6 0 6 3,1,1,2
+29438: x 12 0 12 1,1,1,2
+NO CLASH, using fixed ground order
+29439: Facts:
+29439: Id : 2, {_}:
+ add ?2 ?3 =?= add ?3 ?2
+ [3, 2] by commutativity_for_addition ?2 ?3
+29439: Id : 3, {_}:
+ add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
+ [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
+29439: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
+29439: Id : 5, {_}:
+ add ?11 additive_identity =>= ?11
+ [11] by right_additive_identity ?11
+29439: Id : 6, {_}:
+ multiply additive_identity ?13 =>= additive_identity
+ [13] by left_multiplicative_zero ?13
+29439: Id : 7, {_}:
+ multiply ?15 additive_identity =>= additive_identity
+ [15] by right_multiplicative_zero ?15
+29439: Id : 8, {_}:
+ add (additive_inverse ?17) ?17 =>= additive_identity
+ [17] by left_additive_inverse ?17
+29439: Id : 9, {_}:
+ add ?19 (additive_inverse ?19) =>= additive_identity
+ [19] by right_additive_inverse ?19
+29439: Id : 10, {_}:
+ multiply ?21 (add ?22 ?23)
+ =>=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+29439: Id : 11, {_}:
+ multiply (add ?25 ?26) ?27
+ =>=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+29439: Id : 12, {_}:
+ additive_inverse (additive_inverse ?29) =>= ?29
+ [29] by additive_inverse_additive_inverse ?29
+29439: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29439: Id : 14, {_}:
+ associator ?34 ?35 ?36
+ =>=
+ add (multiply (multiply ?34 ?35) ?36)
+ (additive_inverse (multiply ?34 (multiply ?35 ?36)))
+ [36, 35, 34] by associator ?34 ?35 ?36
+29439: Id : 15, {_}:
+ commutator ?38 ?39
+ =<=
+ add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
+ [39, 38] by commutator ?38 ?39
+29439: Goal:
+29439: Id : 1, {_}:
+ add
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ =>=
+ additive_identity
+ [] by prove_conjecture_1
+29439: Order:
+29439: lpo
+29439: Leaf order:
+29439: commutator 1 2 0
+29439: additive_inverse 6 1 0
+29439: additive_identity 9 0 1 3
+29439: add 17 2 1 0,2
+29439: multiply 22 2 4 0,1,2
+29439: associator 7 3 6 0,1,1,2
+29439: y 6 0 6 3,1,1,2
+29439: x 12 0 12 1,1,1,2
+% SZS status Timeout for RNG030-6.p
+NO CLASH, using fixed ground order
+29722: Facts:
+29722: Id : 2, {_}:
+ multiply (additive_inverse ?2) (additive_inverse ?3)
+ =>=
+ multiply ?2 ?3
+ [3, 2] by product_of_inverses ?2 ?3
+29722: Id : 3, {_}:
+ multiply (additive_inverse ?5) ?6
+ =>=
+ additive_inverse (multiply ?5 ?6)
+ [6, 5] by inverse_product1 ?5 ?6
+29722: Id : 4, {_}:
+ multiply ?8 (additive_inverse ?9)
+ =>=
+ additive_inverse (multiply ?8 ?9)
+ [9, 8] by inverse_product2 ?8 ?9
+29722: Id : 5, {_}:
+ multiply ?11 (add ?12 (additive_inverse ?13))
+ =<=
+ add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
+ [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
+29722: Id : 6, {_}:
+ multiply (add ?15 (additive_inverse ?16)) ?17
+ =<=
+ add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
+ [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
+29722: Id : 7, {_}:
+ multiply (additive_inverse ?19) (add ?20 ?21)
+ =<=
+ add (additive_inverse (multiply ?19 ?20))
+ (additive_inverse (multiply ?19 ?21))
+ [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
+29722: Id : 8, {_}:
+ multiply (add ?23 ?24) (additive_inverse ?25)
+ =<=
+ add (additive_inverse (multiply ?23 ?25))
+ (additive_inverse (multiply ?24 ?25))
+ [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
+29722: Id : 9, {_}:
+ add ?27 ?28 =?= add ?28 ?27
+ [28, 27] by commutativity_for_addition ?27 ?28
+29722: Id : 10, {_}:
+ add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32
+ [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
+29722: Id : 11, {_}:
+ add additive_identity ?34 =>= ?34
+ [34] by left_additive_identity ?34
+29722: Id : 12, {_}:
+ add ?36 additive_identity =>= ?36
+ [36] by right_additive_identity ?36
+29722: Id : 13, {_}:
+ multiply additive_identity ?38 =>= additive_identity
+ [38] by left_multiplicative_zero ?38
+29722: Id : 14, {_}:
+ multiply ?40 additive_identity =>= additive_identity
+ [40] by right_multiplicative_zero ?40
+29722: Id : 15, {_}:
+ add (additive_inverse ?42) ?42 =>= additive_identity
+ [42] by left_additive_inverse ?42
+29722: Id : 16, {_}:
+ add ?44 (additive_inverse ?44) =>= additive_identity
+ [44] by right_additive_inverse ?44
+29722: Id : 17, {_}:
+ multiply ?46 (add ?47 ?48)
+ =<=
+ add (multiply ?46 ?47) (multiply ?46 ?48)
+ [48, 47, 46] by distribute1 ?46 ?47 ?48
+29722: Id : 18, {_}:
+ multiply (add ?50 ?51) ?52
+ =<=
+ add (multiply ?50 ?52) (multiply ?51 ?52)
+ [52, 51, 50] by distribute2 ?50 ?51 ?52
+29722: Id : 19, {_}:
+ additive_inverse (additive_inverse ?54) =>= ?54
+ [54] by additive_inverse_additive_inverse ?54
+29722: Id : 20, {_}:
+ multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57)
+ [57, 56] by right_alternative ?56 ?57
+29722: Id : 21, {_}:
+ associator ?59 ?60 ?61
+ =<=
+ add (multiply (multiply ?59 ?60) ?61)
+ (additive_inverse (multiply ?59 (multiply ?60 ?61)))
+ [61, 60, 59] by associator ?59 ?60 ?61
+29722: Id : 22, {_}:
+ commutator ?63 ?64
+ =<=
+ add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
+ [64, 63] by commutator ?63 ?64
+29722: Goal:
+29722: Id : 1, {_}:
+ add
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ =>=
+ additive_identity
+ [] by prove_conjecture_1
+29722: Order:
+29722: nrkbo
+29722: Leaf order:
+29722: commutator 1 2 0
+29722: additive_inverse 22 1 0
+29722: additive_identity 9 0 1 3
+29722: add 25 2 1 0,2
+29722: multiply 40 2 4 0,1,2add
+29722: associator 7 3 6 0,1,1,2
+29722: y 6 0 6 3,1,1,2
+29722: x 12 0 12 1,1,1,2
+NO CLASH, using fixed ground order
+29723: Facts:
+29723: Id : 2, {_}:
+ multiply (additive_inverse ?2) (additive_inverse ?3)
+ =>=
+ multiply ?2 ?3
+ [3, 2] by product_of_inverses ?2 ?3
+29723: Id : 3, {_}:
+ multiply (additive_inverse ?5) ?6
+ =>=
+ additive_inverse (multiply ?5 ?6)
+ [6, 5] by inverse_product1 ?5 ?6
+29723: Id : 4, {_}:
+ multiply ?8 (additive_inverse ?9)
+ =>=
+ additive_inverse (multiply ?8 ?9)
+ [9, 8] by inverse_product2 ?8 ?9
+29723: Id : 5, {_}:
+ multiply ?11 (add ?12 (additive_inverse ?13))
+ =<=
+ add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
+ [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
+29723: Id : 6, {_}:
+ multiply (add ?15 (additive_inverse ?16)) ?17
+ =<=
+ add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
+ [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
+29723: Id : 7, {_}:
+ multiply (additive_inverse ?19) (add ?20 ?21)
+ =<=
+ add (additive_inverse (multiply ?19 ?20))
+ (additive_inverse (multiply ?19 ?21))
+ [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
+29723: Id : 8, {_}:
+ multiply (add ?23 ?24) (additive_inverse ?25)
+ =<=
+ add (additive_inverse (multiply ?23 ?25))
+ (additive_inverse (multiply ?24 ?25))
+ [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
+29723: Id : 9, {_}:
+ add ?27 ?28 =?= add ?28 ?27
+ [28, 27] by commutativity_for_addition ?27 ?28
+29723: Id : 10, {_}:
+ add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
+ [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
+29723: Id : 11, {_}:
+ add additive_identity ?34 =>= ?34
+ [34] by left_additive_identity ?34
+29723: Id : 12, {_}:
+ add ?36 additive_identity =>= ?36
+ [36] by right_additive_identity ?36
+29723: Id : 13, {_}:
+ multiply additive_identity ?38 =>= additive_identity
+ [38] by left_multiplicative_zero ?38
+29723: Id : 14, {_}:
+ multiply ?40 additive_identity =>= additive_identity
+ [40] by right_multiplicative_zero ?40
+29723: Id : 15, {_}:
+ add (additive_inverse ?42) ?42 =>= additive_identity
+ [42] by left_additive_inverse ?42
+29723: Id : 16, {_}:
+ add ?44 (additive_inverse ?44) =>= additive_identity
+ [44] by right_additive_inverse ?44
+29723: Id : 17, {_}:
+ multiply ?46 (add ?47 ?48)
+ =<=
+ add (multiply ?46 ?47) (multiply ?46 ?48)
+ [48, 47, 46] by distribute1 ?46 ?47 ?48
+29723: Id : 18, {_}:
+ multiply (add ?50 ?51) ?52
+ =<=
+ add (multiply ?50 ?52) (multiply ?51 ?52)
+ [52, 51, 50] by distribute2 ?50 ?51 ?52
+29723: Id : 19, {_}:
+ additive_inverse (additive_inverse ?54) =>= ?54
+ [54] by additive_inverse_additive_inverse ?54
+29723: Id : 20, {_}:
+ multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
+ [57, 56] by right_alternative ?56 ?57
+29723: Id : 21, {_}:
+ associator ?59 ?60 ?61
+ =<=
+ add (multiply (multiply ?59 ?60) ?61)
+ (additive_inverse (multiply ?59 (multiply ?60 ?61)))
+ [61, 60, 59] by associator ?59 ?60 ?61
+29723: Id : 22, {_}:
+ commutator ?63 ?64
+ =<=
+ add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
+ [64, 63] by commutator ?63 ?64
+29723: Goal:
+29723: Id : 1, {_}:
+ add
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ =>=
+ additive_identity
+ [] by prove_conjecture_1
+29723: Order:
+29723: kbo
+29723: Leaf order:
+29723: commutator 1 2 0
+29723: additive_inverse 22 1 0
+29723: additive_identity 9 0 1 3
+29723: add 25 2 1 0,2
+29723: multiply 40 2 4 0,1,2add
+29723: associator 7 3 6 0,1,1,2
+29723: y 6 0 6 3,1,1,2
+29723: x 12 0 12 1,1,1,2
+NO CLASH, using fixed ground order
+29724: Facts:
+29724: Id : 2, {_}:
+ multiply (additive_inverse ?2) (additive_inverse ?3)
+ =>=
+ multiply ?2 ?3
+ [3, 2] by product_of_inverses ?2 ?3
+29724: Id : 3, {_}:
+ multiply (additive_inverse ?5) ?6
+ =>=
+ additive_inverse (multiply ?5 ?6)
+ [6, 5] by inverse_product1 ?5 ?6
+29724: Id : 4, {_}:
+ multiply ?8 (additive_inverse ?9)
+ =>=
+ additive_inverse (multiply ?8 ?9)
+ [9, 8] by inverse_product2 ?8 ?9
+29724: Id : 5, {_}:
+ multiply ?11 (add ?12 (additive_inverse ?13))
+ =>=
+ add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
+ [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
+29724: Id : 6, {_}:
+ multiply (add ?15 (additive_inverse ?16)) ?17
+ =>=
+ add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
+ [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
+29724: Id : 7, {_}:
+ multiply (additive_inverse ?19) (add ?20 ?21)
+ =>=
+ add (additive_inverse (multiply ?19 ?20))
+ (additive_inverse (multiply ?19 ?21))
+ [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
+29724: Id : 8, {_}:
+ multiply (add ?23 ?24) (additive_inverse ?25)
+ =>=
+ add (additive_inverse (multiply ?23 ?25))
+ (additive_inverse (multiply ?24 ?25))
+ [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
+29724: Id : 9, {_}:
+ add ?27 ?28 =?= add ?28 ?27
+ [28, 27] by commutativity_for_addition ?27 ?28
+29724: Id : 10, {_}:
+ add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
+ [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
+29724: Id : 11, {_}:
+ add additive_identity ?34 =>= ?34
+ [34] by left_additive_identity ?34
+29724: Id : 12, {_}:
+ add ?36 additive_identity =>= ?36
+ [36] by right_additive_identity ?36
+29724: Id : 13, {_}:
+ multiply additive_identity ?38 =>= additive_identity
+ [38] by left_multiplicative_zero ?38
+29724: Id : 14, {_}:
+ multiply ?40 additive_identity =>= additive_identity
+ [40] by right_multiplicative_zero ?40
+29724: Id : 15, {_}:
+ add (additive_inverse ?42) ?42 =>= additive_identity
+ [42] by left_additive_inverse ?42
+29724: Id : 16, {_}:
+ add ?44 (additive_inverse ?44) =>= additive_identity
+ [44] by right_additive_inverse ?44
+29724: Id : 17, {_}:
+ multiply ?46 (add ?47 ?48)
+ =>=
+ add (multiply ?46 ?47) (multiply ?46 ?48)
+ [48, 47, 46] by distribute1 ?46 ?47 ?48
+29724: Id : 18, {_}:
+ multiply (add ?50 ?51) ?52
+ =>=
+ add (multiply ?50 ?52) (multiply ?51 ?52)
+ [52, 51, 50] by distribute2 ?50 ?51 ?52
+29724: Id : 19, {_}:
+ additive_inverse (additive_inverse ?54) =>= ?54
+ [54] by additive_inverse_additive_inverse ?54
+29724: Id : 20, {_}:
+ multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
+ [57, 56] by right_alternative ?56 ?57
+29724: Id : 21, {_}:
+ associator ?59 ?60 ?61
+ =>=
+ add (multiply (multiply ?59 ?60) ?61)
+ (additive_inverse (multiply ?59 (multiply ?60 ?61)))
+ [61, 60, 59] by associator ?59 ?60 ?61
+29724: Id : 22, {_}:
+ commutator ?63 ?64
+ =<=
+ add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
+ [64, 63] by commutator ?63 ?64
+29724: Goal:
+29724: Id : 1, {_}:
+ add
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ =>=
+ additive_identity
+ [] by prove_conjecture_1
+29724: Order:
+29724: lpo
+29724: Leaf order:
+29724: commutator 1 2 0
+29724: additive_inverse 22 1 0
+29724: additive_identity 9 0 1 3
+29724: add 25 2 1 0,2
+29724: multiply 40 2 4 0,1,2add
+29724: associator 7 3 6 0,1,1,2
+29724: y 6 0 6 3,1,1,2
+29724: x 12 0 12 1,1,1,2
+% SZS status Timeout for RNG030-7.p
+NO CLASH, using fixed ground order
+29762: Facts:
+29762: Id : 2, {_}:
+ add ?2 ?3 =?= add ?3 ?2
+ [3, 2] by commutativity_for_addition ?2 ?3
+29762: Id : 3, {_}:
+ add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7
+ [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
+29762: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
+29762: Id : 5, {_}:
+ add ?11 additive_identity =>= ?11
+ [11] by right_additive_identity ?11
+29762: Id : 6, {_}:
+ multiply additive_identity ?13 =>= additive_identity
+ [13] by left_multiplicative_zero ?13
+29762: Id : 7, {_}:
+ multiply ?15 additive_identity =>= additive_identity
+ [15] by right_multiplicative_zero ?15
+29762: Id : 8, {_}:
+ add (additive_inverse ?17) ?17 =>= additive_identity
+ [17] by left_additive_inverse ?17
+29762: Id : 9, {_}:
+ add ?19 (additive_inverse ?19) =>= additive_identity
+ [19] by right_additive_inverse ?19
+29762: Id : 10, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+29762: Id : 11, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+29762: Id : 12, {_}:
+ additive_inverse (additive_inverse ?29) =>= ?29
+ [29] by additive_inverse_additive_inverse ?29
+29762: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29762: Id : 14, {_}:
+ associator ?34 ?35 ?36
+ =<=
+ add (multiply (multiply ?34 ?35) ?36)
+ (additive_inverse (multiply ?34 (multiply ?35 ?36)))
+ [36, 35, 34] by associator ?34 ?35 ?36
+29762: Id : 15, {_}:
+ commutator ?38 ?39
+ =<=
+ add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
+ [39, 38] by commutator ?38 ?39
+29762: Goal:
+29762: Id : 1, {_}:
+ add
+ (add
+ (add
+ (add
+ (add
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ =>=
+ additive_identity
+ [] by prove_conjecture_3
+29762: Order:
+29762: nrkbo
+29762: Leaf order:
+29762: commutator 1 2 0
+29762: additive_inverse 6 1 0
+29762: additive_identity 9 0 1 3
+29762: add 21 2 5 0,2
+29762: multiply 30 2 12 0,1,1,1,1,1,2
+29762: associator 19 3 18 0,1,1,1,1,1,1,2
+29762: y 18 0 18 3,1,1,1,1,1,1,2
+29762: x 36 0 36 1,1,1,1,1,1,1,2
+NO CLASH, using fixed ground order
+29763: Facts:
+29763: Id : 2, {_}:
+ add ?2 ?3 =?= add ?3 ?2
+ [3, 2] by commutativity_for_addition ?2 ?3
+29763: Id : 3, {_}:
+ add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
+ [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
+29763: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
+29763: Id : 5, {_}:
+ add ?11 additive_identity =>= ?11
+ [11] by right_additive_identity ?11
+29763: Id : 6, {_}:
+ multiply additive_identity ?13 =>= additive_identity
+ [13] by left_multiplicative_zero ?13
+29763: Id : 7, {_}:
+ multiply ?15 additive_identity =>= additive_identity
+ [15] by right_multiplicative_zero ?15
+29763: Id : 8, {_}:
+ add (additive_inverse ?17) ?17 =>= additive_identity
+ [17] by left_additive_inverse ?17
+NO CLASH, using fixed ground order
+29764: Facts:
+29764: Id : 2, {_}:
+ add ?2 ?3 =?= add ?3 ?2
+ [3, 2] by commutativity_for_addition ?2 ?3
+29764: Id : 3, {_}:
+ add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
+ [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
+29764: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
+29764: Id : 5, {_}:
+ add ?11 additive_identity =>= ?11
+ [11] by right_additive_identity ?11
+29764: Id : 6, {_}:
+ multiply additive_identity ?13 =>= additive_identity
+ [13] by left_multiplicative_zero ?13
+29764: Id : 7, {_}:
+ multiply ?15 additive_identity =>= additive_identity
+ [15] by right_multiplicative_zero ?15
+29764: Id : 8, {_}:
+ add (additive_inverse ?17) ?17 =>= additive_identity
+ [17] by left_additive_inverse ?17
+29764: Id : 9, {_}:
+ add ?19 (additive_inverse ?19) =>= additive_identity
+ [19] by right_additive_inverse ?19
+29764: Id : 10, {_}:
+ multiply ?21 (add ?22 ?23)
+ =>=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+29764: Id : 11, {_}:
+ multiply (add ?25 ?26) ?27
+ =>=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+29764: Id : 12, {_}:
+ additive_inverse (additive_inverse ?29) =>= ?29
+ [29] by additive_inverse_additive_inverse ?29
+29764: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29764: Id : 14, {_}:
+ associator ?34 ?35 ?36
+ =>=
+ add (multiply (multiply ?34 ?35) ?36)
+ (additive_inverse (multiply ?34 (multiply ?35 ?36)))
+ [36, 35, 34] by associator ?34 ?35 ?36
+29764: Id : 15, {_}:
+ commutator ?38 ?39
+ =<=
+ add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
+ [39, 38] by commutator ?38 ?39
+29764: Goal:
+29764: Id : 1, {_}:
+ add
+ (add
+ (add
+ (add
+ (add
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ =>=
+ additive_identity
+ [] by prove_conjecture_3
+29764: Order:
+29764: lpo
+29764: Leaf order:
+29764: commutator 1 2 0
+29764: additive_inverse 6 1 0
+29764: additive_identity 9 0 1 3
+29764: add 21 2 5 0,2
+29764: multiply 30 2 12 0,1,1,1,1,1,2
+29764: associator 19 3 18 0,1,1,1,1,1,1,2
+29764: y 18 0 18 3,1,1,1,1,1,1,2
+29764: x 36 0 36 1,1,1,1,1,1,1,2
+29763: Id : 9, {_}:
+ add ?19 (additive_inverse ?19) =>= additive_identity
+ [19] by right_additive_inverse ?19
+29763: Id : 10, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+29763: Id : 11, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+29763: Id : 12, {_}:
+ additive_inverse (additive_inverse ?29) =>= ?29
+ [29] by additive_inverse_additive_inverse ?29
+29763: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29763: Id : 14, {_}:
+ associator ?34 ?35 ?36
+ =<=
+ add (multiply (multiply ?34 ?35) ?36)
+ (additive_inverse (multiply ?34 (multiply ?35 ?36)))
+ [36, 35, 34] by associator ?34 ?35 ?36
+29763: Id : 15, {_}:
+ commutator ?38 ?39
+ =<=
+ add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
+ [39, 38] by commutator ?38 ?39
+29763: Goal:
+29763: Id : 1, {_}:
+ add
+ (add
+ (add
+ (add
+ (add
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ =>=
+ additive_identity
+ [] by prove_conjecture_3
+29763: Order:
+29763: kbo
+29763: Leaf order:
+29763: commutator 1 2 0
+29763: additive_inverse 6 1 0
+29763: additive_identity 9 0 1 3
+29763: add 21 2 5 0,2
+29763: multiply 30 2 12 0,1,1,1,1,1,2
+29763: associator 19 3 18 0,1,1,1,1,1,1,2
+29763: y 18 0 18 3,1,1,1,1,1,1,2
+29763: x 36 0 36 1,1,1,1,1,1,1,2
+% SZS status Timeout for RNG032-6.p
+NO CLASH, using fixed ground order
+29792: Facts:
+29792: Id : 2, {_}:
+ multiply (additive_inverse ?2) (additive_inverse ?3)
+ =>=
+ multiply ?2 ?3
+ [3, 2] by product_of_inverses ?2 ?3
+29792: Id : 3, {_}:
+ multiply (additive_inverse ?5) ?6
+ =>=
+ additive_inverse (multiply ?5 ?6)
+ [6, 5] by inverse_product1 ?5 ?6
+29792: Id : 4, {_}:
+ multiply ?8 (additive_inverse ?9)
+ =>=
+ additive_inverse (multiply ?8 ?9)
+ [9, 8] by inverse_product2 ?8 ?9
+29792: Id : 5, {_}:
+ multiply ?11 (add ?12 (additive_inverse ?13))
+ =<=
+ add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
+ [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
+29792: Id : 6, {_}:
+ multiply (add ?15 (additive_inverse ?16)) ?17
+ =<=
+ add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
+ [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
+29792: Id : 7, {_}:
+ multiply (additive_inverse ?19) (add ?20 ?21)
+ =<=
+ add (additive_inverse (multiply ?19 ?20))
+ (additive_inverse (multiply ?19 ?21))
+ [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
+29792: Id : 8, {_}:
+ multiply (add ?23 ?24) (additive_inverse ?25)
+ =<=
+ add (additive_inverse (multiply ?23 ?25))
+ (additive_inverse (multiply ?24 ?25))
+ [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
+29792: Id : 9, {_}:
+ add ?27 ?28 =?= add ?28 ?27
+ [28, 27] by commutativity_for_addition ?27 ?28
+29792: Id : 10, {_}:
+ add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32
+ [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
+29792: Id : 11, {_}:
+ add additive_identity ?34 =>= ?34
+ [34] by left_additive_identity ?34
+29792: Id : 12, {_}:
+ add ?36 additive_identity =>= ?36
+ [36] by right_additive_identity ?36
+29792: Id : 13, {_}:
+ multiply additive_identity ?38 =>= additive_identity
+ [38] by left_multiplicative_zero ?38
+29792: Id : 14, {_}:
+ multiply ?40 additive_identity =>= additive_identity
+ [40] by right_multiplicative_zero ?40
+29792: Id : 15, {_}:
+ add (additive_inverse ?42) ?42 =>= additive_identity
+ [42] by left_additive_inverse ?42
+29792: Id : 16, {_}:
+ add ?44 (additive_inverse ?44) =>= additive_identity
+ [44] by right_additive_inverse ?44
+29792: Id : 17, {_}:
+ multiply ?46 (add ?47 ?48)
+ =<=
+ add (multiply ?46 ?47) (multiply ?46 ?48)
+ [48, 47, 46] by distribute1 ?46 ?47 ?48
+29792: Id : 18, {_}:
+ multiply (add ?50 ?51) ?52
+ =<=
+ add (multiply ?50 ?52) (multiply ?51 ?52)
+ [52, 51, 50] by distribute2 ?50 ?51 ?52
+29792: Id : 19, {_}:
+ additive_inverse (additive_inverse ?54) =>= ?54
+ [54] by additive_inverse_additive_inverse ?54
+29792: Id : 20, {_}:
+ multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57)
+ [57, 56] by right_alternative ?56 ?57
+29792: Id : 21, {_}:
+ associator ?59 ?60 ?61
+ =<=
+ add (multiply (multiply ?59 ?60) ?61)
+ (additive_inverse (multiply ?59 (multiply ?60 ?61)))
+ [61, 60, 59] by associator ?59 ?60 ?61
+29792: Id : 22, {_}:
+ commutator ?63 ?64
+ =<=
+ add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
+ [64, 63] by commutator ?63 ?64
+29792: Goal:
+29792: Id : 1, {_}:
+ add
+ (add
+ (add
+ (add
+ (add
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ =>=
+ additive_identity
+ [] by prove_conjecture_3
+29792: Order:
+29792: nrkbo
+29792: Leaf order:
+29792: commutator 1 2 0
+29792: additive_inverse 22 1 0
+29792: additive_identity 9 0 1 3
+29792: add 29 2 5 0,2
+29792: multiply 48 2 12 0,1,1,1,1,1,2add
+29792: associator 19 3 18 0,1,1,1,1,1,1,2
+29792: y 18 0 18 3,1,1,1,1,1,1,2
+29792: x 36 0 36 1,1,1,1,1,1,1,2
+NO CLASH, using fixed ground order
+29793: Facts:
+29793: Id : 2, {_}:
+ multiply (additive_inverse ?2) (additive_inverse ?3)
+ =>=
+ multiply ?2 ?3
+ [3, 2] by product_of_inverses ?2 ?3
+29793: Id : 3, {_}:
+ multiply (additive_inverse ?5) ?6
+ =>=
+ additive_inverse (multiply ?5 ?6)
+ [6, 5] by inverse_product1 ?5 ?6
+29793: Id : 4, {_}:
+ multiply ?8 (additive_inverse ?9)
+ =>=
+ additive_inverse (multiply ?8 ?9)
+ [9, 8] by inverse_product2 ?8 ?9
+29793: Id : 5, {_}:
+ multiply ?11 (add ?12 (additive_inverse ?13))
+ =<=
+ add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
+ [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
+29793: Id : 6, {_}:
+ multiply (add ?15 (additive_inverse ?16)) ?17
+ =<=
+ add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
+ [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
+29793: Id : 7, {_}:
+ multiply (additive_inverse ?19) (add ?20 ?21)
+ =<=
+ add (additive_inverse (multiply ?19 ?20))
+ (additive_inverse (multiply ?19 ?21))
+ [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
+29793: Id : 8, {_}:
+ multiply (add ?23 ?24) (additive_inverse ?25)
+ =<=
+ add (additive_inverse (multiply ?23 ?25))
+ (additive_inverse (multiply ?24 ?25))
+ [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
+29793: Id : 9, {_}:
+ add ?27 ?28 =?= add ?28 ?27
+ [28, 27] by commutativity_for_addition ?27 ?28
+29793: Id : 10, {_}:
+ add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
+ [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
+29793: Id : 11, {_}:
+ add additive_identity ?34 =>= ?34
+ [34] by left_additive_identity ?34
+29793: Id : 12, {_}:
+ add ?36 additive_identity =>= ?36
+ [36] by right_additive_identity ?36
+29793: Id : 13, {_}:
+ multiply additive_identity ?38 =>= additive_identity
+ [38] by left_multiplicative_zero ?38
+29793: Id : 14, {_}:
+ multiply ?40 additive_identity =>= additive_identity
+ [40] by right_multiplicative_zero ?40
+29793: Id : 15, {_}:
+ add (additive_inverse ?42) ?42 =>= additive_identity
+ [42] by left_additive_inverse ?42
+29793: Id : 16, {_}:
+ add ?44 (additive_inverse ?44) =>= additive_identity
+ [44] by right_additive_inverse ?44
+29793: Id : 17, {_}:
+ multiply ?46 (add ?47 ?48)
+ =<=
+ add (multiply ?46 ?47) (multiply ?46 ?48)
+ [48, 47, 46] by distribute1 ?46 ?47 ?48
+29793: Id : 18, {_}:
+ multiply (add ?50 ?51) ?52
+ =<=
+ add (multiply ?50 ?52) (multiply ?51 ?52)
+ [52, 51, 50] by distribute2 ?50 ?51 ?52
+29793: Id : 19, {_}:
+ additive_inverse (additive_inverse ?54) =>= ?54
+ [54] by additive_inverse_additive_inverse ?54
+29793: Id : 20, {_}:
+ multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
+ [57, 56] by right_alternative ?56 ?57
+29793: Id : 21, {_}:
+ associator ?59 ?60 ?61
+ =<=
+ add (multiply (multiply ?59 ?60) ?61)
+ (additive_inverse (multiply ?59 (multiply ?60 ?61)))
+ [61, 60, 59] by associator ?59 ?60 ?61
+29793: Id : 22, {_}:
+ commutator ?63 ?64
+ =<=
+ add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
+ [64, 63] by commutator ?63 ?64
+29793: Goal:
+29793: Id : 1, {_}:
+ add
+ (add
+ (add
+ (add
+ (add
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ =>=
+ additive_identity
+ [] by prove_conjecture_3
+29793: Order:
+29793: kbo
+29793: Leaf order:
+29793: commutator 1 2 0
+29793: additive_inverse 22 1 0
+29793: additive_identity 9 0 1 3
+29793: add 29 2 5 0,2
+29793: multiply 48 2 12 0,1,1,1,1,1,2add
+29793: associator 19 3 18 0,1,1,1,1,1,1,2
+29793: y 18 0 18 3,1,1,1,1,1,1,2
+29793: x 36 0 36 1,1,1,1,1,1,1,2
+NO CLASH, using fixed ground order
+29794: Facts:
+29794: Id : 2, {_}:
+ multiply (additive_inverse ?2) (additive_inverse ?3)
+ =>=
+ multiply ?2 ?3
+ [3, 2] by product_of_inverses ?2 ?3
+29794: Id : 3, {_}:
+ multiply (additive_inverse ?5) ?6
+ =>=
+ additive_inverse (multiply ?5 ?6)
+ [6, 5] by inverse_product1 ?5 ?6
+29794: Id : 4, {_}:
+ multiply ?8 (additive_inverse ?9)
+ =>=
+ additive_inverse (multiply ?8 ?9)
+ [9, 8] by inverse_product2 ?8 ?9
+29794: Id : 5, {_}:
+ multiply ?11 (add ?12 (additive_inverse ?13))
+ =>=
+ add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
+ [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
+29794: Id : 6, {_}:
+ multiply (add ?15 (additive_inverse ?16)) ?17
+ =>=
+ add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
+ [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
+29794: Id : 7, {_}:
+ multiply (additive_inverse ?19) (add ?20 ?21)
+ =>=
+ add (additive_inverse (multiply ?19 ?20))
+ (additive_inverse (multiply ?19 ?21))
+ [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
+29794: Id : 8, {_}:
+ multiply (add ?23 ?24) (additive_inverse ?25)
+ =>=
+ add (additive_inverse (multiply ?23 ?25))
+ (additive_inverse (multiply ?24 ?25))
+ [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
+29794: Id : 9, {_}:
+ add ?27 ?28 =?= add ?28 ?27
+ [28, 27] by commutativity_for_addition ?27 ?28
+29794: Id : 10, {_}:
+ add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
+ [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
+29794: Id : 11, {_}:
+ add additive_identity ?34 =>= ?34
+ [34] by left_additive_identity ?34
+29794: Id : 12, {_}:
+ add ?36 additive_identity =>= ?36
+ [36] by right_additive_identity ?36
+29794: Id : 13, {_}:
+ multiply additive_identity ?38 =>= additive_identity
+ [38] by left_multiplicative_zero ?38
+29794: Id : 14, {_}:
+ multiply ?40 additive_identity =>= additive_identity
+ [40] by right_multiplicative_zero ?40
+29794: Id : 15, {_}:
+ add (additive_inverse ?42) ?42 =>= additive_identity
+ [42] by left_additive_inverse ?42
+29794: Id : 16, {_}:
+ add ?44 (additive_inverse ?44) =>= additive_identity
+ [44] by right_additive_inverse ?44
+29794: Id : 17, {_}:
+ multiply ?46 (add ?47 ?48)
+ =>=
+ add (multiply ?46 ?47) (multiply ?46 ?48)
+ [48, 47, 46] by distribute1 ?46 ?47 ?48
+29794: Id : 18, {_}:
+ multiply (add ?50 ?51) ?52
+ =>=
+ add (multiply ?50 ?52) (multiply ?51 ?52)
+ [52, 51, 50] by distribute2 ?50 ?51 ?52
+29794: Id : 19, {_}:
+ additive_inverse (additive_inverse ?54) =>= ?54
+ [54] by additive_inverse_additive_inverse ?54
+29794: Id : 20, {_}:
+ multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
+ [57, 56] by right_alternative ?56 ?57
+29794: Id : 21, {_}:
+ associator ?59 ?60 ?61
+ =>=
+ add (multiply (multiply ?59 ?60) ?61)
+ (additive_inverse (multiply ?59 (multiply ?60 ?61)))
+ [61, 60, 59] by associator ?59 ?60 ?61
+29794: Id : 22, {_}:
+ commutator ?63 ?64
+ =<=
+ add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
+ [64, 63] by commutator ?63 ?64
+29794: Goal:
+29794: Id : 1, {_}:
+ add
+ (add
+ (add
+ (add
+ (add
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ =>=
+ additive_identity
+ [] by prove_conjecture_3
+29794: Order:
+29794: lpo
+29794: Leaf order:
+29794: commutator 1 2 0
+29794: additive_inverse 22 1 0
+29794: additive_identity 9 0 1 3
+29794: add 29 2 5 0,2
+29794: multiply 48 2 12 0,1,1,1,1,1,2add
+29794: associator 19 3 18 0,1,1,1,1,1,1,2
+29794: y 18 0 18 3,1,1,1,1,1,1,2
+29794: x 36 0 36 1,1,1,1,1,1,1,2
+% SZS status Timeout for RNG032-7.p
+NO CLASH, using fixed ground order
+29810: Facts:
+29810: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29810: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29810: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29810: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29810: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29810: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29810: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29810: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29810: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29810: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29810: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29810: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29810: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29810: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29810: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29810: Goal:
+29810: Id : 1, {_}:
+ add (associator (multiply x y) z w) (associator x y (commutator z w))
+ =<=
+ add (multiply x (associator y z w)) (multiply (associator x z w) y)
+ [] by prove_challenge
+29810: Order:
+29810: nrkbo
+29810: Leaf order:
+29810: additive_inverse 6 1 0
+29810: additive_identity 8 0 0
+29810: add 18 2 2 0,2
+29810: commutator 2 2 1 0,3,2,2
+29810: associator 5 3 4 0,1,2
+29810: w 4 0 4 3,1,2
+29810: z 4 0 4 2,1,2
+29810: multiply 25 2 3 0,1,1,2
+29810: y 4 0 4 2,1,1,2
+29810: x 4 0 4 1,1,1,2
+NO CLASH, using fixed ground order
+29811: Facts:
+29811: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29811: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29811: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29811: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29811: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29811: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29811: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29811: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29811: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29811: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29811: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29811: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29811: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29811: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29811: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29811: Goal:
+29811: Id : 1, {_}:
+ add (associator (multiply x y) z w) (associator x y (commutator z w))
+ =<=
+ add (multiply x (associator y z w)) (multiply (associator x z w) y)
+ [] by prove_challenge
+29811: Order:
+29811: kbo
+29811: Leaf order:
+29811: additive_inverse 6 1 0
+29811: additive_identity 8 0 0
+29811: add 18 2 2 0,2
+29811: commutator 2 2 1 0,3,2,2
+29811: associator 5 3 4 0,1,2
+29811: w 4 0 4 3,1,2
+29811: z 4 0 4 2,1,2
+29811: multiply 25 2 3 0,1,1,2
+29811: y 4 0 4 2,1,1,2
+29811: x 4 0 4 1,1,1,2
+NO CLASH, using fixed ground order
+29812: Facts:
+29812: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29812: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29812: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29812: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29812: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29812: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29812: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29812: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29812: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29812: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29812: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29812: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29812: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29812: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29812: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29812: Goal:
+29812: Id : 1, {_}:
+ add (associator (multiply x y) z w) (associator x y (commutator z w))
+ =<=
+ add (multiply x (associator y z w)) (multiply (associator x z w) y)
+ [] by prove_challenge
+29812: Order:
+29812: lpo
+29812: Leaf order:
+29812: additive_inverse 6 1 0
+29812: additive_identity 8 0 0
+29812: add 18 2 2 0,2
+29812: commutator 2 2 1 0,3,2,2
+29812: associator 5 3 4 0,1,2
+29812: w 4 0 4 3,1,2
+29812: z 4 0 4 2,1,2
+29812: multiply 25 2 3 0,1,1,2
+29812: y 4 0 4 2,1,1,2
+29812: x 4 0 4 1,1,1,2
+% SZS status Timeout for RNG033-6.p
+NO CLASH, using fixed ground order
+29844: Facts:
+29844: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29844: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29844: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29844: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29844: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29844: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29844: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29844: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29844: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29844: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29844: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29844: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29844: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29844: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29844: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29844: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+29844: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+29844: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+29844: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+29844: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+29844: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+29844: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+29844: Goal:
+29844: Id : 1, {_}:
+ add (associator (multiply x y) z w) (associator x y (commutator z w))
+ =<=
+ add (multiply x (associator y z w)) (multiply (associator x z w) y)
+ [] by prove_challenge
+29844: Order:
+29844: nrkbo
+29844: Leaf order:
+29844: additive_inverse 22 1 0
+29844: additive_identity 8 0 0
+29844: add 26 2 2 0,2
+29844: commutator 2 2 1 0,3,2,2
+29844: associator 5 3 4 0,1,2
+29844: w 4 0 4 3,1,2
+29844: z 4 0 4 2,1,2
+29844: multiply 43 2 3 0,1,1,2
+29844: y 4 0 4 2,1,1,2
+29844: x 4 0 4 1,1,1,2
+NO CLASH, using fixed ground order
+29846: Facts:
+29846: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29846: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29846: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29846: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29846: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29846: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29846: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29846: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29846: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29846: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29846: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29846: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29846: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29846: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29846: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29846: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+29846: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+29846: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+29846: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =>=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+29846: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =>=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+29846: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =>=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+29846: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =>=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+29846: Goal:
+29846: Id : 1, {_}:
+ add (associator (multiply x y) z w) (associator x y (commutator z w))
+ =<=
+ add (multiply x (associator y z w)) (multiply (associator x z w) y)
+ [] by prove_challenge
+29846: Order:
+29846: lpo
+29846: Leaf order:
+29846: additive_inverse 22 1 0
+29846: additive_identity 8 0 0
+29846: add 26 2 2 0,2
+29846: commutator 2 2 1 0,3,2,2
+29846: associator 5 3 4 0,1,2
+29846: w 4 0 4 3,1,2
+29846: z 4 0 4 2,1,2
+29846: multiply 43 2 3 0,1,1,2
+29846: y 4 0 4 2,1,1,2
+29846: x 4 0 4 1,1,1,2
+NO CLASH, using fixed ground order
+29845: Facts:
+29845: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29845: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29845: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29845: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29845: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29845: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29845: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29845: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29845: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29845: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29845: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29845: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29845: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29845: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29845: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29845: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+29845: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+29845: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+29845: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+29845: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+29845: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+29845: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+29845: Goal:
+29845: Id : 1, {_}:
+ add (associator (multiply x y) z w) (associator x y (commutator z w))
+ =<=
+ add (multiply x (associator y z w)) (multiply (associator x z w) y)
+ [] by prove_challenge
+29845: Order:
+29845: kbo
+29845: Leaf order:
+29845: additive_inverse 22 1 0
+29845: additive_identity 8 0 0
+29845: add 26 2 2 0,2
+29845: commutator 2 2 1 0,3,2,2
+29845: associator 5 3 4 0,1,2
+29845: w 4 0 4 3,1,2
+29845: z 4 0 4 2,1,2
+29845: multiply 43 2 3 0,1,1,2
+29845: y 4 0 4 2,1,1,2
+29845: x 4 0 4 1,1,1,2
+% SZS status Timeout for RNG033-7.p
+NO CLASH, using fixed ground order
+29862: Facts:
+29862: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29862: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29862: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29862: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29862: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29862: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29862: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29862: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29862: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29862: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29862: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29862: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29862: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29862: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29862: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29862: Id : 17, {_}:
+ multiply ?44 (multiply ?45 (multiply ?46 ?45))
+ =?=
+ multiply (multiply (multiply ?44 ?45) ?46) ?45
+ [46, 45, 44] by right_moufang ?44 ?45 ?46
+29862: Goal:
+29862: Id : 1, {_}:
+ add (associator (multiply x y) z w) (associator x y (commutator z w))
+ =<=
+ add (multiply x (associator y z w)) (multiply (associator x z w) y)
+ [] by prove_challenge
+29862: Order:
+29862: nrkbo
+29862: Leaf order:
+29862: additive_inverse 6 1 0
+29862: additive_identity 8 0 0
+29862: add 18 2 2 0,2
+29862: commutator 2 2 1 0,3,2,2
+29862: associator 5 3 4 0,1,2
+29862: w 4 0 4 3,1,2
+29862: z 4 0 4 2,1,2
+29862: multiply 31 2 3 0,1,1,2
+29862: y 4 0 4 2,1,1,2
+29862: x 4 0 4 1,1,1,2
+NO CLASH, using fixed ground order
+29863: Facts:
+29863: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29863: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29863: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29863: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29863: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29863: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29863: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29863: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29863: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29863: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29863: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29863: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29863: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29863: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29863: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29863: Id : 17, {_}:
+ multiply ?44 (multiply ?45 (multiply ?46 ?45))
+ =<=
+ multiply (multiply (multiply ?44 ?45) ?46) ?45
+ [46, 45, 44] by right_moufang ?44 ?45 ?46
+29863: Goal:
+29863: Id : 1, {_}:
+ add (associator (multiply x y) z w) (associator x y (commutator z w))
+ =<=
+ add (multiply x (associator y z w)) (multiply (associator x z w) y)
+ [] by prove_challenge
+29863: Order:
+29863: kbo
+29863: Leaf order:
+29863: additive_inverse 6 1 0
+29863: additive_identity 8 0 0
+29863: add 18 2 2 0,2
+29863: commutator 2 2 1 0,3,2,2
+29863: associator 5 3 4 0,1,2
+29863: w 4 0 4 3,1,2
+29863: z 4 0 4 2,1,2
+29863: multiply 31 2 3 0,1,1,2
+29863: y 4 0 4 2,1,1,2
+29863: x 4 0 4 1,1,1,2
+NO CLASH, using fixed ground order
+29864: Facts:
+29864: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29864: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29864: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29864: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29864: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29864: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29864: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29864: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29864: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29864: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29864: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29864: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29864: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29864: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29864: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29864: Id : 17, {_}:
+ multiply ?44 (multiply ?45 (multiply ?46 ?45))
+ =<=
+ multiply (multiply (multiply ?44 ?45) ?46) ?45
+ [46, 45, 44] by right_moufang ?44 ?45 ?46
+29864: Goal:
+29864: Id : 1, {_}:
+ add (associator (multiply x y) z w) (associator x y (commutator z w))
+ =<=
+ add (multiply x (associator y z w)) (multiply (associator x z w) y)
+ [] by prove_challenge
+29864: Order:
+29864: lpo
+29864: Leaf order:
+29864: additive_inverse 6 1 0
+29864: additive_identity 8 0 0
+29864: add 18 2 2 0,2
+29864: commutator 2 2 1 0,3,2,2
+29864: associator 5 3 4 0,1,2
+29864: w 4 0 4 3,1,2
+29864: z 4 0 4 2,1,2
+29864: multiply 31 2 3 0,1,1,2
+29864: y 4 0 4 2,1,1,2
+29864: x 4 0 4 1,1,1,2
+% SZS status Timeout for RNG033-8.p
+NO CLASH, using fixed ground order
+29900: Facts:
+29900: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29900: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29900: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29900: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29900: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29900: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29900: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29900: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29900: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29900: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29900: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29900: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29900: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29900: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29900: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29900: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+29900: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+29900: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+29900: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+29900: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+29900: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+29900: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+29900: Id : 24, {_}:
+ multiply ?69 (multiply ?70 (multiply ?71 ?70))
+ =?=
+ multiply (multiply (multiply ?69 ?70) ?71) ?70
+ [71, 70, 69] by right_moufang ?69 ?70 ?71
+29900: Goal:
+29900: Id : 1, {_}:
+ add (associator (multiply x y) z w) (associator x y (commutator z w))
+ =<=
+ add (multiply x (associator y z w)) (multiply (associator x z w) y)
+ [] by prove_challenge
+29900: Order:
+29900: nrkbo
+29900: Leaf order:
+29900: additive_inverse 22 1 0
+29900: additive_identity 8 0 0
+29900: add 26 2 2 0,2
+29900: commutator 2 2 1 0,3,2,2
+29900: associator 5 3 4 0,1,2
+29900: w 4 0 4 3,1,2
+29900: z 4 0 4 2,1,2
+29900: multiply 49 2 3 0,1,1,2
+29900: y 4 0 4 2,1,1,2
+29900: x 4 0 4 1,1,1,2
+NO CLASH, using fixed ground order
+29901: Facts:
+29901: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29901: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29901: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29901: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29901: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29901: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29901: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29901: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29901: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29901: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29901: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29901: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29901: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29901: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29901: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29901: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+29901: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+29901: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+29901: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+29901: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+29901: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+29901: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+29901: Id : 24, {_}:
+ multiply ?69 (multiply ?70 (multiply ?71 ?70))
+ =<=
+ multiply (multiply (multiply ?69 ?70) ?71) ?70
+ [71, 70, 69] by right_moufang ?69 ?70 ?71
+29901: Goal:
+29901: Id : 1, {_}:
+ add (associator (multiply x y) z w) (associator x y (commutator z w))
+ =<=
+ add (multiply x (associator y z w)) (multiply (associator x z w) y)
+ [] by prove_challenge
+29901: Order:
+29901: kbo
+29901: Leaf order:
+29901: additive_inverse 22 1 0
+29901: additive_identity 8 0 0
+29901: add 26 2 2 0,2
+29901: commutator 2 2 1 0,3,2,2
+29901: associator 5 3 4 0,1,2
+29901: w 4 0 4 3,1,2
+29901: z 4 0 4 2,1,2
+29901: multiply 49 2 3 0,1,1,2
+29901: y 4 0 4 2,1,1,2
+29901: x 4 0 4 1,1,1,2
+NO CLASH, using fixed ground order
+29902: Facts:
+29902: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29902: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29902: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29902: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29902: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29902: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29902: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29902: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29902: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29902: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29902: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29902: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29902: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29902: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29902: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29902: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+29902: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+29902: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+29902: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =>=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+29902: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =>=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+29902: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =>=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+29902: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =>=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+29902: Id : 24, {_}:
+ multiply ?69 (multiply ?70 (multiply ?71 ?70))
+ =<=
+ multiply (multiply (multiply ?69 ?70) ?71) ?70
+ [71, 70, 69] by right_moufang ?69 ?70 ?71
+29902: Goal:
+29902: Id : 1, {_}:
+ add (associator (multiply x y) z w) (associator x y (commutator z w))
+ =<=
+ add (multiply x (associator y z w)) (multiply (associator x z w) y)
+ [] by prove_challenge
+29902: Order:
+29902: lpo
+29902: Leaf order:
+29902: additive_inverse 22 1 0
+29902: additive_identity 8 0 0
+29902: add 26 2 2 0,2
+29902: commutator 2 2 1 0,3,2,2
+29902: associator 5 3 4 0,1,2
+29902: w 4 0 4 3,1,2
+29902: z 4 0 4 2,1,2
+29902: multiply 49 2 3 0,1,1,2
+29902: y 4 0 4 2,1,1,2
+29902: x 4 0 4 1,1,1,2
+% SZS status Timeout for RNG033-9.p
+NO CLASH, using fixed ground order
+29918: Facts:
+29918: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29918: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29918: Id : 4, {_}:
+ add (additive_inverse ?6) ?6 =>= additive_identity
+ [6] by left_additive_inverse ?6
+29918: Id : 5, {_}:
+ add ?8 (additive_inverse ?8) =>= additive_identity
+ [8] by right_additive_inverse ?8
+29918: Id : 6, {_}:
+ add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12
+ [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
+29918: Id : 7, {_}:
+ add ?14 ?15 =?= add ?15 ?14
+ [15, 14] by commutativity_for_addition ?14 ?15
+29918: Id : 8, {_}:
+ multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19
+ [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
+29918: Id : 9, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+29918: Id : 10, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+29918: Id : 11, {_}:
+ multiply ?29 (multiply ?29 (multiply ?29 (multiply ?29 ?29))) =>= ?29
+ [29] by x_fifthed_is_x ?29
+29918: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
+29918: Goal:
+29918: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
+29918: Order:
+29918: nrkbo
+29918: Leaf order:
+29918: additive_inverse 2 1 0
+29918: add 14 2 0
+29918: additive_identity 4 0 0
+29918: c 2 0 1 3
+29918: multiply 16 2 1 0,2
+29918: a 2 0 1 2,2
+29918: b 2 0 1 1,2
+NO CLASH, using fixed ground order
+29919: Facts:
+29919: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29919: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29919: Id : 4, {_}:
+ add (additive_inverse ?6) ?6 =>= additive_identity
+ [6] by left_additive_inverse ?6
+29919: Id : 5, {_}:
+ add ?8 (additive_inverse ?8) =>= additive_identity
+ [8] by right_additive_inverse ?8
+29919: Id : 6, {_}:
+ add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
+ [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
+29919: Id : 7, {_}:
+ add ?14 ?15 =?= add ?15 ?14
+ [15, 14] by commutativity_for_addition ?14 ?15
+29919: Id : 8, {_}:
+ multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
+ [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
+29919: Id : 9, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+29919: Id : 10, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+29919: Id : 11, {_}:
+ multiply ?29 (multiply ?29 (multiply ?29 (multiply ?29 ?29))) =>= ?29
+ [29] by x_fifthed_is_x ?29
+29919: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
+29919: Goal:
+29919: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
+29919: Order:
+29919: kbo
+29919: Leaf order:
+29919: additive_inverse 2 1 0
+29919: add 14 2 0
+29919: additive_identity 4 0 0
+NO CLASH, using fixed ground order
+29920: Facts:
+29920: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29920: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29920: Id : 4, {_}:
+ add (additive_inverse ?6) ?6 =>= additive_identity
+ [6] by left_additive_inverse ?6
+29920: Id : 5, {_}:
+ add ?8 (additive_inverse ?8) =>= additive_identity
+ [8] by right_additive_inverse ?8
+29920: Id : 6, {_}:
+ add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
+ [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
+29920: Id : 7, {_}:
+ add ?14 ?15 =?= add ?15 ?14
+ [15, 14] by commutativity_for_addition ?14 ?15
+29920: Id : 8, {_}:
+ multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
+ [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
+29920: Id : 9, {_}:
+ multiply ?21 (add ?22 ?23)
+ =>=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+29920: Id : 10, {_}:
+ multiply (add ?25 ?26) ?27
+ =>=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+29920: Id : 11, {_}:
+ multiply ?29 (multiply ?29 (multiply ?29 (multiply ?29 ?29))) =>= ?29
+ [29] by x_fifthed_is_x ?29
+29920: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
+29920: Goal:
+29920: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
+29920: Order:
+29920: lpo
+29920: Leaf order:
+29920: additive_inverse 2 1 0
+29920: add 14 2 0
+29920: additive_identity 4 0 0
+29920: c 2 0 1 3
+29920: multiply 16 2 1 0,2
+29920: a 2 0 1 2,2
+29920: b 2 0 1 1,2
+29919: c 2 0 1 3
+29919: multiply 16 2 1 0,2
+29919: a 2 0 1 2,2
+29919: b 2 0 1 1,2
+% SZS status Timeout for RNG036-7.p
+NO CLASH, using fixed ground order
+29951: Facts:
+29951: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+29951: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+29951: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+29951: Goal:
+29951: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+29951: Order:
+29951: nrkbo
+29951: Leaf order:
+29951: add 12 2 3 0,2
+29951: negate 9 1 5 0,1,2
+29951: b 3 0 3 1,2,1,1,2
+29951: a 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+29952: Facts:
+29952: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+29952: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+29952: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+29952: Goal:
+29952: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+29952: Order:
+29952: kbo
+29952: Leaf order:
+29952: add 12 2 3 0,2
+29952: negate 9 1 5 0,1,2
+29952: b 3 0 3 1,2,1,1,2
+29952: a 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+29953: Facts:
+29953: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+29953: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+29953: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+29953: Goal:
+29953: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+29953: Order:
+29953: lpo
+29953: Leaf order:
+29953: add 12 2 3 0,2
+29953: negate 9 1 5 0,1,2
+29953: b 3 0 3 1,2,1,1,2
+29953: a 2 0 2 1,1,1,2
+% SZS status Timeout for ROB001-1.p
+NO CLASH, using fixed ground order
+29969: Facts:
+29969: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+29969: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+29969: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+29969: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
+29969: Goal:
+29969: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+29969: Order:
+29969: nrkbo
+29969: Leaf order:
+29969: add 13 2 3 0,2
+29969: negate 11 1 5 0,1,2
+29969: b 5 0 3 1,2,1,1,2
+29969: a 3 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+29970: Facts:
+29970: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+29970: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+29970: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+29970: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
+29970: Goal:
+29970: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+29970: Order:
+29970: kbo
+29970: Leaf order:
+29970: add 13 2 3 0,2
+29970: negate 11 1 5 0,1,2
+29970: b 5 0 3 1,2,1,1,2
+29970: a 3 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+29971: Facts:
+29971: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+29971: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+29971: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+29971: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
+29971: Goal:
+29971: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+29971: Order:
+29971: lpo
+29971: Leaf order:
+29971: add 13 2 3 0,2
+29971: negate 11 1 5 0,1,2
+29971: b 5 0 3 1,2,1,1,2
+29971: a 3 0 2 1,1,1,2
+% SZS status Timeout for ROB007-1.p
+NO CLASH, using fixed ground order
+29998: Facts:
+29998: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
+29998: Id : 3, {_}:
+ add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8)
+ [8, 7, 6] by associativity_of_add ?6 ?7 ?8
+29998: Id : 4, {_}:
+ negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
+ =>=
+ ?10
+ [11, 10] by robbins_axiom ?10 ?11
+29998: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
+29998: Goal:
+29998: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
+29998: Order:
+29998: nrkbo
+29998: Leaf order:
+29998: b 2 0 0
+29998: a 1 0 0
+29998: negate 6 1 0
+29998: add 11 2 1 0,2
+NO CLASH, using fixed ground order
+29999: Facts:
+29999: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
+29999: Id : 3, {_}:
+ add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
+ [8, 7, 6] by associativity_of_add ?6 ?7 ?8
+29999: Id : 4, {_}:
+ negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
+ =>=
+ ?10
+ [11, 10] by robbins_axiom ?10 ?11
+29999: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
+29999: Goal:
+29999: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
+29999: Order:
+29999: kbo
+29999: Leaf order:
+29999: b 2 0 0
+29999: a 1 0 0
+29999: negate 6 1 0
+29999: add 11 2 1 0,2
+NO CLASH, using fixed ground order
+30000: Facts:
+30000: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
+30000: Id : 3, {_}:
+ add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
+ [8, 7, 6] by associativity_of_add ?6 ?7 ?8
+30000: Id : 4, {_}:
+ negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
+ =>=
+ ?10
+ [11, 10] by robbins_axiom ?10 ?11
+30000: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
+30000: Goal:
+30000: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
+30000: Order:
+30000: lpo
+30000: Leaf order:
+30000: b 2 0 0
+30000: a 1 0 0
+30000: negate 6 1 0
+30000: add 11 2 1 0,2
+% SZS status Timeout for ROB007-2.p
+NO CLASH, using fixed ground order
+30074: Facts:
+30074: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+NO CLASH, using fixed ground order
+30075: Facts:
+30075: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+30075: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+30075: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+30075: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
+30075: Goal:
+30075: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+30075: Order:
+30075: kbo
+30075: Leaf order:
+30075: add 13 2 3 0,2
+30075: negate 11 1 5 0,1,2
+30075: b 5 0 3 1,2,1,1,2
+30075: a 3 0 2 1,1,1,2
+30074: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+30074: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+30074: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
+30074: Goal:
+30074: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+30074: Order:
+30074: nrkbo
+30074: Leaf order:
+30074: add 13 2 3 0,2
+30074: negate 11 1 5 0,1,2
+30074: b 5 0 3 1,2,1,1,2
+30074: a 3 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+30076: Facts:
+30076: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+30076: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+30076: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+30076: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
+30076: Goal:
+30076: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+30076: Order:
+30076: lpo
+30076: Leaf order:
+30076: add 13 2 3 0,2
+30076: negate 11 1 5 0,1,2
+30076: b 5 0 3 1,2,1,1,2
+30076: a 3 0 2 1,1,1,2
+% SZS status Timeout for ROB020-1.p
+NO CLASH, using fixed ground order
+30104: Facts:
+30104: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
+30104: Id : 3, {_}:
+ add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8)
+ [8, 7, 6] by associativity_of_add ?6 ?7 ?8
+30104: Id : 4, {_}:
+ negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
+ =>=
+ ?10
+ [11, 10] by robbins_axiom ?10 ?11
+30104: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
+30104: Goal:
+30104: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
+30104: Order:
+30104: nrkbo
+30104: Leaf order:
+30104: b 2 0 0
+30104: a 1 0 0
+30104: negate 6 1 0
+30104: add 11 2 1 0,2
+NO CLASH, using fixed ground order
+30105: Facts:
+30105: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
+30105: Id : 3, {_}:
+ add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
+ [8, 7, 6] by associativity_of_add ?6 ?7 ?8
+30105: Id : 4, {_}:
+ negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
+ =>=
+ ?10
+ [11, 10] by robbins_axiom ?10 ?11
+30105: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
+30105: Goal:
+30105: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
+30105: Order:
+30105: kbo
+30105: Leaf order:
+30105: b 2 0 0
+30105: a 1 0 0
+30105: negate 6 1 0
+30105: add 11 2 1 0,2
+NO CLASH, using fixed ground order
+30106: Facts:
+30106: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
+30106: Id : 3, {_}:
+ add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
+ [8, 7, 6] by associativity_of_add ?6 ?7 ?8
+30106: Id : 4, {_}:
+ negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
+ =>=
+ ?10
+ [11, 10] by robbins_axiom ?10 ?11
+30106: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
+30106: Goal:
+30106: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
+30106: Order:
+30106: lpo
+30106: Leaf order:
+30106: b 2 0 0
+30106: a 1 0 0
+30106: negate 6 1 0
+30106: add 11 2 1 0,2
+% SZS status Timeout for ROB020-2.p
+NO CLASH, using fixed ground order
+30123: Facts:
+30123: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+30123: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+30123: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+30123: Id : 5, {_}:
+ negate (add (negate (add a (add a b))) (negate (add a (negate b))))
+ =>=
+ a
+ [] by the_condition
+30123: Goal:
+30123: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+30123: Order:
+30123: nrkbo
+30123: Leaf order:
+30123: add 16 2 3 0,2
+30123: negate 13 1 5 0,1,2
+30123: b 5 0 3 1,2,1,1,2
+30123: a 6 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+30124: Facts:
+30124: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+30124: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+30124: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+30124: Id : 5, {_}:
+ negate (add (negate (add a (add a b))) (negate (add a (negate b))))
+ =>=
+ a
+ [] by the_condition
+30124: Goal:
+30124: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+30124: Order:
+30124: kbo
+30124: Leaf order:
+30124: add 16 2 3 0,2
+30124: negate 13 1 5 0,1,2
+30124: b 5 0 3 1,2,1,1,2
+30124: a 6 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+30125: Facts:
+30125: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+30125: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+30125: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+30125: Id : 5, {_}:
+ negate (add (negate (add a (add a b))) (negate (add a (negate b))))
+ =>=
+ a
+ [] by the_condition
+30125: Goal:
+30125: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+30125: Order:
+30125: lpo
+30125: Leaf order:
+30125: add 16 2 3 0,2
+30125: negate 13 1 5 0,1,2
+30125: b 5 0 3 1,2,1,1,2
+30125: a 6 0 2 1,1,1,2
+% SZS status Timeout for ROB024-1.p
+NO CLASH, using fixed ground order
+30152: Facts:
+30152: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+30152: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+30152: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+30152: Id : 5, {_}: negate (negate c) =>= c [] by double_negation
+30152: Goal:
+30152: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+30152: Order:
+30152: nrkbo
+30152: Leaf order:
+30152: c 2 0 0
+30152: add 12 2 3 0,2
+30152: negate 11 1 5 0,1,2
+30152: b 3 0 3 1,2,1,1,2
+30152: a 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+30153: Facts:
+30153: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+30153: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+30153: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+30153: Id : 5, {_}: negate (negate c) =>= c [] by double_negation
+30153: Goal:
+30153: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+30153: Order:
+30153: kbo
+30153: Leaf order:
+30153: c 2 0 0
+30153: add 12 2 3 0,2
+30153: negate 11 1 5 0,1,2
+30153: b 3 0 3 1,2,1,1,2
+30153: a 2 0 2 1,1,1,2
+NO CLASH, using fixed ground order
+30154: Facts:
+30154: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+30154: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+30154: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+30154: Id : 5, {_}: negate (negate c) =>= c [] by double_negation
+30154: Goal:
+30154: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+30154: Order:
+30154: lpo
+30154: Leaf order:
+30154: c 2 0 0
+30154: add 12 2 3 0,2
+30154: negate 11 1 5 0,1,2
+30154: b 3 0 3 1,2,1,1,2
+30154: a 2 0 2 1,1,1,2
+% SZS status Timeout for ROB027-1.p
+NO CLASH, using fixed ground order
+30170: Facts:
+30170: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
+30170: Id : 3, {_}:
+ add (add ?7 ?8) ?9 =?= add ?7 (add ?8 ?9)
+ [9, 8, 7] by associativity_of_add ?7 ?8 ?9
+30170: Id : 4, {_}:
+ negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
+ =>=
+ ?11
+ [12, 11] by robbins_axiom ?11 ?12
+30170: Goal:
+30170: Id : 1, {_}:
+ negate (add ?1 ?2) =>= negate ?2
+ [2, 1] by prove_absorption_within_negation ?1 ?2
+30170: Order:
+30170: nrkbo
+30170: Leaf order:
+30170: negate 6 1 2 0,2
+30170: add 10 2 1 0,1,2
+NO CLASH, using fixed ground order
+30171: Facts:
+30171: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
+30171: Id : 3, {_}:
+ add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9)
+ [9, 8, 7] by associativity_of_add ?7 ?8 ?9
+30171: Id : 4, {_}:
+ negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
+ =>=
+ ?11
+ [12, 11] by robbins_axiom ?11 ?12
+30171: Goal:
+30171: Id : 1, {_}:
+ negate (add ?1 ?2) =>= negate ?2
+ [2, 1] by prove_absorption_within_negation ?1 ?2
+30171: Order:
+30171: kbo
+30171: Leaf order:
+30171: negate 6 1 2 0,2
+30171: add 10 2 1 0,1,2
+NO CLASH, using fixed ground order
+30172: Facts:
+30172: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
+30172: Id : 3, {_}:
+ add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9)
+ [9, 8, 7] by associativity_of_add ?7 ?8 ?9
+30172: Id : 4, {_}:
+ negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
+ =>=
+ ?11
+ [12, 11] by robbins_axiom ?11 ?12
+30172: Goal:
+30172: Id : 1, {_}:
+ negate (add ?1 ?2) =>= negate ?2
+ [2, 1] by prove_absorption_within_negation ?1 ?2
+30172: Order:
+30172: lpo
+30172: Leaf order:
+30172: negate 6 1 2 0,2
+30172: add 10 2 1 0,1,2
+% SZS status Timeout for ROB031-1.p
+NO CLASH, using fixed ground order
+30204: Facts:
+30204: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
+NO CLASH, using fixed ground order
+30205: Facts:
+30205: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
+30205: Id : 3, {_}:
+ add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9)
+ [9, 8, 7] by associativity_of_add ?7 ?8 ?9
+30205: Id : 4, {_}:
+ negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
+ =>=
+ ?11
+ [12, 11] by robbins_axiom ?11 ?12
+30205: Goal:
+30205: Id : 1, {_}: add ?1 ?2 =>= ?2 [2, 1] by prove_absorbtion ?1 ?2
+30205: Order:
+30205: kbo
+30205: Leaf order:
+30205: negate 4 1 0
+30205: add 10 2 1 0,2
+30204: Id : 3, {_}:
+ add (add ?7 ?8) ?9 =?= add ?7 (add ?8 ?9)
+ [9, 8, 7] by associativity_of_add ?7 ?8 ?9
+30204: Id : 4, {_}:
+ negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
+ =>=
+ ?11
+ [12, 11] by robbins_axiom ?11 ?12
+30204: Goal:
+30204: Id : 1, {_}: add ?1 ?2 =>= ?2 [2, 1] by prove_absorbtion ?1 ?2
+30204: Order:
+30204: nrkbo
+30204: Leaf order:
+30204: negate 4 1 0
+30204: add 10 2 1 0,2
+NO CLASH, using fixed ground order
+30206: Facts:
+30206: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
+30206: Id : 3, {_}:
+ add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9)
+ [9, 8, 7] by associativity_of_add ?7 ?8 ?9
+30206: Id : 4, {_}:
+ negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
+ =>=
+ ?11
+ [12, 11] by robbins_axiom ?11 ?12
+30206: Goal:
+30206: Id : 1, {_}: add ?1 ?2 =>= ?2 [2, 1] by prove_absorbtion ?1 ?2
+30206: Order:
+30206: lpo
+30206: Leaf order:
+30206: negate 4 1 0
+30206: add 10 2 1 0,2
+% SZS status Timeout for ROB032-1.p
--- /dev/null
+CLASH, statistics insufficient
+CLASH, statistics insufficient
+22279: Facts:
+22279: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+22279: Id : 3, {_}:
+ multiply ?5 ?6 =?= multiply ?6 ?5
+ [6, 5] by commutativity_of_multiply ?5 ?6
+22279: Id : 4, {_}:
+ add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10)
+ [10, 9, 8] by distributivity1 ?8 ?9 ?10
+22279: Id : 5, {_}:
+ add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14)
+ [14, 13, 12] by distributivity2 ?12 ?13 ?14
+22279: Id : 6, {_}:
+ multiply (add ?16 ?17) ?18
+ =<=
+ add (multiply ?16 ?18) (multiply ?17 ?18)
+ [18, 17, 16] by distributivity3 ?16 ?17 ?18
+22279: Id : 7, {_}:
+ multiply ?20 (add ?21 ?22)
+ =<=
+ add (multiply ?20 ?21) (multiply ?20 ?22)
+ [22, 21, 20] by distributivity4 ?20 ?21 ?22
+22279: Id : 8, {_}:
+ add ?24 (inverse ?24) =>= multiplicative_identity
+ [24] by additive_inverse1 ?24
+22279: Id : 9, {_}:
+ add (inverse ?26) ?26 =>= multiplicative_identity
+ [26] by additive_inverse2 ?26
+22279: Id : 10, {_}:
+ multiply ?28 (inverse ?28) =>= additive_identity
+ [28] by multiplicative_inverse1 ?28
+22279: Id : 11, {_}:
+ multiply (inverse ?30) ?30 =>= additive_identity
+ [30] by multiplicative_inverse2 ?30
+22279: Id : 12, {_}:
+ multiply ?32 multiplicative_identity =>= ?32
+ [32] by multiplicative_id1 ?32
+22279: Id : 13, {_}:
+ multiply multiplicative_identity ?34 =>= ?34
+ [34] by multiplicative_id2 ?34
+22279: Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
+22279: Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
+22279: Goal:
+22279: Id : 1, {_}:
+ multiply a (multiply b c) =<= multiply (multiply a b) c
+ [] by prove_associativity
+22279: Order:
+22279: kbo
+22279: Leaf order:
+22279: a 2 0 2 1,2
+22279: b 2 0 2 1,2,2
+22279: c 2 0 2 2,2,2
+22279: multiplicative_identity 4 0 0
+22279: additive_identity 4 0 0
+22279: inverse 4 1 0
+22279: add 16 2 0 multiply
+22279: multiply 20 2 4 0,2add
+CLASH, statistics insufficient
+22280: Facts:
+22280: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+22280: Id : 3, {_}:
+ multiply ?5 ?6 =?= multiply ?6 ?5
+ [6, 5] by commutativity_of_multiply ?5 ?6
+22280: Id : 4, {_}:
+ add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10)
+ [10, 9, 8] by distributivity1 ?8 ?9 ?10
+22280: Id : 5, {_}:
+ add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14)
+ [14, 13, 12] by distributivity2 ?12 ?13 ?14
+22280: Id : 6, {_}:
+ multiply (add ?16 ?17) ?18
+ =>=
+ add (multiply ?16 ?18) (multiply ?17 ?18)
+ [18, 17, 16] by distributivity3 ?16 ?17 ?18
+22280: Id : 7, {_}:
+ multiply ?20 (add ?21 ?22)
+ =>=
+ add (multiply ?20 ?21) (multiply ?20 ?22)
+ [22, 21, 20] by distributivity4 ?20 ?21 ?22
+22280: Id : 8, {_}:
+ add ?24 (inverse ?24) =>= multiplicative_identity
+ [24] by additive_inverse1 ?24
+22280: Id : 9, {_}:
+ add (inverse ?26) ?26 =>= multiplicative_identity
+ [26] by additive_inverse2 ?26
+22280: Id : 10, {_}:
+ multiply ?28 (inverse ?28) =>= additive_identity
+ [28] by multiplicative_inverse1 ?28
+22280: Id : 11, {_}:
+ multiply (inverse ?30) ?30 =>= additive_identity
+ [30] by multiplicative_inverse2 ?30
+22280: Id : 12, {_}:
+ multiply ?32 multiplicative_identity =>= ?32
+ [32] by multiplicative_id1 ?32
+22280: Id : 13, {_}:
+ multiply multiplicative_identity ?34 =>= ?34
+ [34] by multiplicative_id2 ?34
+22280: Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
+22280: Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
+22280: Goal:
+22280: Id : 1, {_}:
+ multiply a (multiply b c) =<= multiply (multiply a b) c
+ [] by prove_associativity
+22280: Order:
+22280: lpo
+22280: Leaf order:
+22280: a 2 0 2 1,2
+22280: b 2 0 2 1,2,2
+22280: c 2 0 2 2,2,2
+22280: multiplicative_identity 4 0 0
+22280: additive_identity 4 0 0
+22280: inverse 4 1 0
+22280: add 16 2 0 multiply
+22280: multiply 20 2 4 0,2add
+22278: Facts:
+22278: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+22278: Id : 3, {_}:
+ multiply ?5 ?6 =?= multiply ?6 ?5
+ [6, 5] by commutativity_of_multiply ?5 ?6
+22278: Id : 4, {_}:
+ add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10)
+ [10, 9, 8] by distributivity1 ?8 ?9 ?10
+22278: Id : 5, {_}:
+ add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14)
+ [14, 13, 12] by distributivity2 ?12 ?13 ?14
+22278: Id : 6, {_}:
+ multiply (add ?16 ?17) ?18
+ =<=
+ add (multiply ?16 ?18) (multiply ?17 ?18)
+ [18, 17, 16] by distributivity3 ?16 ?17 ?18
+22278: Id : 7, {_}:
+ multiply ?20 (add ?21 ?22)
+ =<=
+ add (multiply ?20 ?21) (multiply ?20 ?22)
+ [22, 21, 20] by distributivity4 ?20 ?21 ?22
+22278: Id : 8, {_}:
+ add ?24 (inverse ?24) =>= multiplicative_identity
+ [24] by additive_inverse1 ?24
+22278: Id : 9, {_}:
+ add (inverse ?26) ?26 =>= multiplicative_identity
+ [26] by additive_inverse2 ?26
+22278: Id : 10, {_}:
+ multiply ?28 (inverse ?28) =>= additive_identity
+ [28] by multiplicative_inverse1 ?28
+22278: Id : 11, {_}:
+ multiply (inverse ?30) ?30 =>= additive_identity
+ [30] by multiplicative_inverse2 ?30
+22278: Id : 12, {_}:
+ multiply ?32 multiplicative_identity =>= ?32
+ [32] by multiplicative_id1 ?32
+22278: Id : 13, {_}:
+ multiply multiplicative_identity ?34 =>= ?34
+ [34] by multiplicative_id2 ?34
+22278: Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
+22278: Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
+22278: Goal:
+22278: Id : 1, {_}:
+ multiply a (multiply b c) =<= multiply (multiply a b) c
+ [] by prove_associativity
+22278: Order:
+22278: nrkbo
+22278: Leaf order:
+22278: a 2 0 2 1,2
+22278: b 2 0 2 1,2,2
+22278: c 2 0 2 2,2,2
+22278: multiplicative_identity 4 0 0
+22278: additive_identity 4 0 0
+22278: inverse 4 1 0
+22278: add 16 2 0 multiply
+22278: multiply 20 2 4 0,2add
+Statistics :
+Max weight : 22
+Found proof, 16.771241s
+% SZS status Unsatisfiable for BOO007-2.p
+% SZS output start CNFRefutation for BOO007-2.p
+Id : 12, {_}: multiply ?32 multiplicative_identity =>= ?32 [32] by multiplicative_id1 ?32
+Id : 7, {_}: multiply ?20 (add ?21 ?22) =<= add (multiply ?20 ?21) (multiply ?20 ?22) [22, 21, 20] by distributivity4 ?20 ?21 ?22
+Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
+Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
+Id : 10, {_}: multiply ?28 (inverse ?28) =>= additive_identity [28] by multiplicative_inverse1 ?28
+Id : 13, {_}: multiply multiplicative_identity ?34 =>= ?34 [34] by multiplicative_id2 ?34
+Id : 8, {_}: add ?24 (inverse ?24) =>= multiplicative_identity [24] by additive_inverse1 ?24
+Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+Id : 31, {_}: add (multiply ?78 ?79) ?80 =<= multiply (add ?78 ?80) (add ?79 ?80) [80, 79, 78] by distributivity1 ?78 ?79 ?80
+Id : 5, {_}: add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14) [14, 13, 12] by distributivity2 ?12 ?13 ?14
+Id : 3, {_}: multiply ?5 ?6 =?= multiply ?6 ?5 [6, 5] by commutativity_of_multiply ?5 ?6
+Id : 6, {_}: multiply (add ?16 ?17) ?18 =<= add (multiply ?16 ?18) (multiply ?17 ?18) [18, 17, 16] by distributivity3 ?16 ?17 ?18
+Id : 4, {_}: add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10) [10, 9, 8] by distributivity1 ?8 ?9 ?10
+Id : 65, {_}: add (multiply ?156 (multiply ?157 ?158)) (multiply ?159 ?158) =<= multiply (add ?156 (multiply ?159 ?158)) (multiply (add ?157 ?159) ?158) [159, 158, 157, 156] by Super 4 with 6 at 2,3
+Id : 46, {_}: multiply (add ?110 ?111) (add ?110 ?112) =>= add ?110 (multiply ?112 ?111) [112, 111, 110] by Super 3 with 5 at 3
+Id : 58, {_}: add ?110 (multiply ?111 ?112) =?= add ?110 (multiply ?112 ?111) [112, 111, 110] by Demod 46 with 5 at 2
+Id : 32, {_}: add (multiply ?82 ?83) ?84 =<= multiply (add ?82 ?84) (add ?84 ?83) [84, 83, 82] by Super 31 with 2 at 2,3
+Id : 121, {_}: add ?333 (multiply (inverse ?333) ?334) =>= multiply multiplicative_identity (add ?333 ?334) [334, 333] by Super 5 with 8 at 1,3
+Id : 2169, {_}: add ?2910 (multiply (inverse ?2910) ?2911) =>= add ?2910 ?2911 [2911, 2910] by Demod 121 with 13 at 3
+Id : 2179, {_}: add ?2938 additive_identity =<= add ?2938 (inverse (inverse ?2938)) [2938] by Super 2169 with 10 at 2,2
+Id : 2230, {_}: ?2938 =<= add ?2938 (inverse (inverse ?2938)) [2938] by Demod 2179 with 14 at 2
+Id : 2429, {_}: add (multiply ?3159 (inverse (inverse ?3160))) ?3160 =>= multiply (add ?3159 ?3160) ?3160 [3160, 3159] by Super 32 with 2230 at 2,3
+Id : 2455, {_}: add ?3160 (multiply ?3159 (inverse (inverse ?3160))) =>= multiply (add ?3159 ?3160) ?3160 [3159, 3160] by Demod 2429 with 2 at 2
+Id : 2456, {_}: add ?3160 (multiply ?3159 (inverse (inverse ?3160))) =>= multiply ?3160 (add ?3159 ?3160) [3159, 3160] by Demod 2455 with 3 at 3
+Id : 248, {_}: add (multiply additive_identity ?467) ?468 =<= multiply ?468 (add ?467 ?468) [468, 467] by Super 4 with 15 at 1,3
+Id : 2457, {_}: add ?3160 (multiply ?3159 (inverse (inverse ?3160))) =>= add (multiply additive_identity ?3159) ?3160 [3159, 3160] by Demod 2456 with 248 at 3
+Id : 120, {_}: add ?330 (multiply ?331 (inverse ?330)) =>= multiply (add ?330 ?331) multiplicative_identity [331, 330] by Super 5 with 8 at 2,3
+Id : 124, {_}: add ?330 (multiply ?331 (inverse ?330)) =>= multiply multiplicative_identity (add ?330 ?331) [331, 330] by Demod 120 with 3 at 3
+Id : 3170, {_}: add ?330 (multiply ?331 (inverse ?330)) =>= add ?330 ?331 [331, 330] by Demod 124 with 13 at 3
+Id : 144, {_}: multiply ?347 (add (inverse ?347) ?348) =>= add additive_identity (multiply ?347 ?348) [348, 347] by Super 7 with 10 at 1,3
+Id : 3378, {_}: multiply ?4138 (add (inverse ?4138) ?4139) =>= multiply ?4138 ?4139 [4139, 4138] by Demod 144 with 15 at 3
+Id : 3399, {_}: multiply ?4195 (inverse ?4195) =<= multiply ?4195 (inverse (inverse (inverse ?4195))) [4195] by Super 3378 with 2230 at 2,2
+Id : 3488, {_}: additive_identity =<= multiply ?4195 (inverse (inverse (inverse ?4195))) [4195] by Demod 3399 with 10 at 2
+Id : 3900, {_}: add (inverse (inverse ?4844)) additive_identity =?= add (inverse (inverse ?4844)) ?4844 [4844] by Super 3170 with 3488 at 2,2
+Id : 3924, {_}: add additive_identity (inverse (inverse ?4844)) =<= add (inverse (inverse ?4844)) ?4844 [4844] by Demod 3900 with 2 at 2
+Id : 3925, {_}: add additive_identity (inverse (inverse ?4844)) =?= add ?4844 (inverse (inverse ?4844)) [4844] by Demod 3924 with 2 at 3
+Id : 3926, {_}: inverse (inverse ?4844) =<= add ?4844 (inverse (inverse ?4844)) [4844] by Demod 3925 with 15 at 2
+Id : 3927, {_}: inverse (inverse ?4844) =>= ?4844 [4844] by Demod 3926 with 2230 at 3
+Id : 6845, {_}: add ?3160 (multiply ?3159 ?3160) =?= add (multiply additive_identity ?3159) ?3160 [3159, 3160] by Demod 2457 with 3927 at 2,2,2
+Id : 1130, {_}: add (multiply additive_identity ?1671) ?1672 =<= multiply ?1672 (add ?1671 ?1672) [1672, 1671] by Super 4 with 15 at 1,3
+Id : 1134, {_}: add (multiply additive_identity ?1683) (inverse ?1683) =>= multiply (inverse ?1683) multiplicative_identity [1683] by Super 1130 with 8 at 2,3
+Id : 1186, {_}: add (inverse ?1683) (multiply additive_identity ?1683) =>= multiply (inverse ?1683) multiplicative_identity [1683] by Demod 1134 with 2 at 2
+Id : 1187, {_}: add (inverse ?1683) (multiply additive_identity ?1683) =>= multiply multiplicative_identity (inverse ?1683) [1683] by Demod 1186 with 3 at 3
+Id : 1188, {_}: add (inverse ?1683) (multiply additive_identity ?1683) =>= inverse ?1683 [1683] by Demod 1187 with 13 at 3
+Id : 3360, {_}: multiply ?347 (add (inverse ?347) ?348) =>= multiply ?347 ?348 [348, 347] by Demod 144 with 15 at 3
+Id : 3364, {_}: add (inverse (add (inverse additive_identity) ?4095)) (multiply additive_identity ?4095) =>= inverse (add (inverse additive_identity) ?4095) [4095] by Super 1188 with 3360 at 2,2
+Id : 3442, {_}: add (multiply additive_identity ?4095) (inverse (add (inverse additive_identity) ?4095)) =>= inverse (add (inverse additive_identity) ?4095) [4095] by Demod 3364 with 2 at 2
+Id : 249, {_}: inverse additive_identity =>= multiplicative_identity [] by Super 8 with 15 at 2
+Id : 3443, {_}: add (multiply additive_identity ?4095) (inverse (add (inverse additive_identity) ?4095)) =>= inverse (add multiplicative_identity ?4095) [4095] by Demod 3442 with 249 at 1,1,3
+Id : 3444, {_}: add (multiply additive_identity ?4095) (inverse (add multiplicative_identity ?4095)) =>= inverse (add multiplicative_identity ?4095) [4095] by Demod 3443 with 249 at 1,1,2,2
+Id : 2180, {_}: add ?2940 (inverse ?2940) =>= add ?2940 multiplicative_identity [2940] by Super 2169 with 12 at 2,2
+Id : 2231, {_}: multiplicative_identity =<= add ?2940 multiplicative_identity [2940] by Demod 2180 with 8 at 2
+Id : 2263, {_}: add multiplicative_identity ?3015 =>= multiplicative_identity [3015] by Super 2 with 2231 at 3
+Id : 3445, {_}: add (multiply additive_identity ?4095) (inverse (add multiplicative_identity ?4095)) =>= inverse multiplicative_identity [4095] by Demod 3444 with 2263 at 1,3
+Id : 3446, {_}: add (multiply additive_identity ?4095) (inverse multiplicative_identity) =>= inverse multiplicative_identity [4095] by Demod 3445 with 2263 at 1,2,2
+Id : 191, {_}: inverse multiplicative_identity =>= additive_identity [] by Super 10 with 13 at 2
+Id : 3447, {_}: add (multiply additive_identity ?4095) (inverse multiplicative_identity) =>= additive_identity [4095] by Demod 3446 with 191 at 3
+Id : 3448, {_}: add (inverse multiplicative_identity) (multiply additive_identity ?4095) =>= additive_identity [4095] by Demod 3447 with 2 at 2
+Id : 3449, {_}: add additive_identity (multiply additive_identity ?4095) =>= additive_identity [4095] by Demod 3448 with 191 at 1,2
+Id : 3450, {_}: multiply additive_identity ?4095 =>= additive_identity [4095] by Demod 3449 with 15 at 2
+Id : 6846, {_}: add ?3160 (multiply ?3159 ?3160) =>= add additive_identity ?3160 [3159, 3160] by Demod 6845 with 3450 at 1,3
+Id : 6847, {_}: add ?3160 (multiply ?3159 ?3160) =>= ?3160 [3159, 3160] by Demod 6846 with 15 at 3
+Id : 6852, {_}: add ?8316 (multiply ?8316 ?8317) =>= ?8316 [8317, 8316] by Super 58 with 6847 at 3
+Id : 7003, {_}: add (multiply ?8541 (multiply ?8542 ?8543)) (multiply ?8541 ?8543) =>= multiply ?8541 (multiply (add ?8542 ?8541) ?8543) [8543, 8542, 8541] by Super 65 with 6852 at 1,3
+Id : 7114, {_}: add (multiply ?8541 ?8543) (multiply ?8541 (multiply ?8542 ?8543)) =>= multiply ?8541 (multiply (add ?8542 ?8541) ?8543) [8542, 8543, 8541] by Demod 7003 with 2 at 2
+Id : 7115, {_}: multiply ?8541 (add ?8543 (multiply ?8542 ?8543)) =?= multiply ?8541 (multiply (add ?8542 ?8541) ?8543) [8542, 8543, 8541] by Demod 7114 with 7 at 2
+Id : 21444, {_}: multiply ?30534 ?30535 =<= multiply ?30534 (multiply (add ?30536 ?30534) ?30535) [30536, 30535, 30534] by Demod 7115 with 6847 at 2,2
+Id : 21466, {_}: multiply (multiply ?30625 ?30626) ?30627 =<= multiply (multiply ?30625 ?30626) (multiply ?30626 ?30627) [30627, 30626, 30625] by Super 21444 with 6847 at 1,2,3
+Id : 147, {_}: multiply (add ?355 ?356) (inverse ?355) =>= add additive_identity (multiply ?356 (inverse ?355)) [356, 355] by Super 6 with 10 at 1,3
+Id : 152, {_}: multiply (inverse ?355) (add ?355 ?356) =>= add additive_identity (multiply ?356 (inverse ?355)) [356, 355] by Demod 147 with 3 at 2
+Id : 4375, {_}: multiply (inverse ?355) (add ?355 ?356) =>= multiply ?356 (inverse ?355) [356, 355] by Demod 152 with 15 at 3
+Id : 532, {_}: add (multiply ?866 ?867) ?868 =<= multiply (add ?866 ?868) (add ?868 ?867) [868, 867, 866] by Super 31 with 2 at 2,3
+Id : 547, {_}: add (multiply ?925 ?926) (inverse ?925) =?= multiply multiplicative_identity (add (inverse ?925) ?926) [926, 925] by Super 532 with 8 at 1,3
+Id : 583, {_}: add (inverse ?925) (multiply ?925 ?926) =?= multiply multiplicative_identity (add (inverse ?925) ?926) [926, 925] by Demod 547 with 2 at 2
+Id : 584, {_}: add (inverse ?925) (multiply ?925 ?926) =>= add (inverse ?925) ?926 [926, 925] by Demod 583 with 13 at 3
+Id : 4646, {_}: multiply (inverse (inverse ?5719)) (add (inverse ?5719) ?5720) =>= multiply (multiply ?5719 ?5720) (inverse (inverse ?5719)) [5720, 5719] by Super 4375 with 584 at 2,2
+Id : 4685, {_}: multiply ?5720 (inverse (inverse ?5719)) =<= multiply (multiply ?5719 ?5720) (inverse (inverse ?5719)) [5719, 5720] by Demod 4646 with 4375 at 2
+Id : 4686, {_}: multiply ?5720 (inverse (inverse ?5719)) =<= multiply (inverse (inverse ?5719)) (multiply ?5719 ?5720) [5719, 5720] by Demod 4685 with 3 at 3
+Id : 4687, {_}: multiply ?5720 ?5719 =<= multiply (inverse (inverse ?5719)) (multiply ?5719 ?5720) [5719, 5720] by Demod 4686 with 3927 at 2,2
+Id : 4688, {_}: multiply ?5720 ?5719 =<= multiply ?5719 (multiply ?5719 ?5720) [5719, 5720] by Demod 4687 with 3927 at 1,3
+Id : 21467, {_}: multiply (multiply ?30629 ?30630) ?30631 =<= multiply (multiply ?30629 ?30630) (multiply ?30629 ?30631) [30631, 30630, 30629] by Super 21444 with 6852 at 1,2,3
+Id : 36399, {_}: multiply (multiply ?58815 ?58816) (multiply ?58815 ?58817) =<= multiply (multiply ?58815 ?58817) (multiply (multiply ?58815 ?58817) ?58816) [58817, 58816, 58815] by Super 4688 with 21467 at 2,3
+Id : 36627, {_}: multiply (multiply ?58815 ?58816) ?58817 =<= multiply (multiply ?58815 ?58817) (multiply (multiply ?58815 ?58817) ?58816) [58817, 58816, 58815] by Demod 36399 with 21467 at 2
+Id : 36628, {_}: multiply (multiply ?58815 ?58816) ?58817 =>= multiply ?58816 (multiply ?58815 ?58817) [58817, 58816, 58815] by Demod 36627 with 4688 at 3
+Id : 36893, {_}: multiply ?30626 (multiply ?30625 ?30627) =<= multiply (multiply ?30625 ?30626) (multiply ?30626 ?30627) [30627, 30625, 30626] by Demod 21466 with 36628 at 2
+Id : 36894, {_}: multiply ?30626 (multiply ?30625 ?30627) =<= multiply ?30626 (multiply ?30625 (multiply ?30626 ?30627)) [30627, 30625, 30626] by Demod 36893 with 36628 at 3
+Id : 3522, {_}: add additive_identity ?468 =<= multiply ?468 (add ?467 ?468) [467, 468] by Demod 248 with 3450 at 1,2
+Id : 3543, {_}: ?468 =<= multiply ?468 (add ?467 ?468) [467, 468] by Demod 3522 with 15 at 2
+Id : 7020, {_}: add (multiply ?8599 (multiply ?8600 ?8601)) ?8600 =>= multiply (add ?8599 ?8600) ?8600 [8601, 8600, 8599] by Super 32 with 6852 at 2,3
+Id : 7087, {_}: add ?8600 (multiply ?8599 (multiply ?8600 ?8601)) =>= multiply (add ?8599 ?8600) ?8600 [8601, 8599, 8600] by Demod 7020 with 2 at 2
+Id : 7088, {_}: add ?8600 (multiply ?8599 (multiply ?8600 ?8601)) =>= multiply ?8600 (add ?8599 ?8600) [8601, 8599, 8600] by Demod 7087 with 3 at 3
+Id : 7089, {_}: add ?8600 (multiply ?8599 (multiply ?8600 ?8601)) =>= ?8600 [8601, 8599, 8600] by Demod 7088 with 3543 at 3
+Id : 20142, {_}: multiply ?27776 (multiply ?27777 ?27778) =<= multiply (multiply ?27776 (multiply ?27777 ?27778)) ?27777 [27778, 27777, 27776] by Super 3543 with 7089 at 2,3
+Id : 20329, {_}: multiply ?27776 (multiply ?27777 ?27778) =<= multiply ?27777 (multiply ?27776 (multiply ?27777 ?27778)) [27778, 27777, 27776] by Demod 20142 with 3 at 3
+Id : 36895, {_}: multiply ?30626 (multiply ?30625 ?30627) =?= multiply ?30625 (multiply ?30626 ?30627) [30627, 30625, 30626] by Demod 36894 with 20329 at 3
+Id : 34, {_}: add (multiply ?90 ?91) ?92 =<= multiply (add ?92 ?90) (add ?91 ?92) [92, 91, 90] by Super 31 with 2 at 1,3
+Id : 6868, {_}: add (multiply (multiply ?8366 ?8367) ?8368) ?8367 =>= multiply ?8367 (add ?8368 ?8367) [8368, 8367, 8366] by Super 34 with 6847 at 1,3
+Id : 6940, {_}: add ?8367 (multiply (multiply ?8366 ?8367) ?8368) =>= multiply ?8367 (add ?8368 ?8367) [8368, 8366, 8367] by Demod 6868 with 2 at 2
+Id : 6941, {_}: add ?8367 (multiply (multiply ?8366 ?8367) ?8368) =>= ?8367 [8368, 8366, 8367] by Demod 6940 with 3543 at 3
+Id : 19816, {_}: multiply (multiply ?27180 ?27181) ?27182 =<= multiply (multiply (multiply ?27180 ?27181) ?27182) ?27181 [27182, 27181, 27180] by Super 3543 with 6941 at 2,3
+Id : 19977, {_}: multiply (multiply ?27180 ?27181) ?27182 =<= multiply ?27181 (multiply (multiply ?27180 ?27181) ?27182) [27182, 27181, 27180] by Demod 19816 with 3 at 3
+Id : 36891, {_}: multiply ?27181 (multiply ?27180 ?27182) =<= multiply ?27181 (multiply (multiply ?27180 ?27181) ?27182) [27182, 27180, 27181] by Demod 19977 with 36628 at 2
+Id : 36892, {_}: multiply ?27181 (multiply ?27180 ?27182) =<= multiply ?27181 (multiply ?27181 (multiply ?27180 ?27182)) [27182, 27180, 27181] by Demod 36891 with 36628 at 2,3
+Id : 36900, {_}: multiply ?27181 (multiply ?27180 ?27182) =?= multiply (multiply ?27180 ?27182) ?27181 [27182, 27180, 27181] by Demod 36892 with 4688 at 3
+Id : 36901, {_}: multiply ?27181 (multiply ?27180 ?27182) =?= multiply ?27182 (multiply ?27180 ?27181) [27182, 27180, 27181] by Demod 36900 with 36628 at 3
+Id : 37364, {_}: multiply c (multiply b a) =?= multiply c (multiply b a) [] by Demod 37363 with 3 at 2,2
+Id : 37363, {_}: multiply c (multiply a b) =?= multiply c (multiply b a) [] by Demod 37362 with 3 at 2,3
+Id : 37362, {_}: multiply c (multiply a b) =?= multiply c (multiply a b) [] by Demod 37361 with 36901 at 2
+Id : 37361, {_}: multiply b (multiply a c) =>= multiply c (multiply a b) [] by Demod 37360 with 3 at 3
+Id : 37360, {_}: multiply b (multiply a c) =<= multiply (multiply a b) c [] by Demod 1 with 36895 at 2
+Id : 1, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
+% SZS output end CNFRefutation for BOO007-2.p
+22279: solved BOO007-2.p in 8.384524 using kbo
+22279: status Unsatisfiable for BOO007-2.p
+CLASH, statistics insufficient
+22287: Facts:
+22287: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+22287: Id : 3, {_}:
+ multiply ?5 ?6 =?= multiply ?6 ?5
+ [6, 5] by commutativity_of_multiply ?5 ?6
+22287: Id : 4, {_}:
+ add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10)
+ [10, 9, 8] by distributivity1 ?8 ?9 ?10
+22287: Id : 5, {_}:
+ multiply ?12 (add ?13 ?14)
+ =<=
+ add (multiply ?12 ?13) (multiply ?12 ?14)
+ [14, 13, 12] by distributivity2 ?12 ?13 ?14
+22287: Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
+22287: Id : 7, {_}:
+ multiply ?18 multiplicative_identity =>= ?18
+ [18] by multiplicative_id1 ?18
+22287: Id : 8, {_}:
+ add ?20 (inverse ?20) =>= multiplicative_identity
+ [20] by additive_inverse1 ?20
+22287: Id : 9, {_}:
+ multiply ?22 (inverse ?22) =>= additive_identity
+ [22] by multiplicative_inverse1 ?22
+22287: Goal:
+22287: Id : 1, {_}:
+ multiply a (multiply b c) =<= multiply (multiply a b) c
+ [] by prove_associativity
+22287: Order:
+22287: nrkbo
+22287: Leaf order:
+22287: additive_identity 2 0 0
+22287: multiplicative_identity 2 0 0
+22287: a 2 0 2 1,2
+22287: b 2 0 2 1,2,2
+22287: c 2 0 2 2,2,2
+22287: inverse 2 1 0
+22287: add 9 2 0 multiply
+22287: multiply 13 2 4 0,2add
+CLASH, statistics insufficient
+22288: Facts:
+22288: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+22288: Id : 3, {_}:
+ multiply ?5 ?6 =?= multiply ?6 ?5
+ [6, 5] by commutativity_of_multiply ?5 ?6
+22288: Id : 4, {_}:
+ add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10)
+ [10, 9, 8] by distributivity1 ?8 ?9 ?10
+22288: Id : 5, {_}:
+ multiply ?12 (add ?13 ?14)
+ =<=
+ add (multiply ?12 ?13) (multiply ?12 ?14)
+ [14, 13, 12] by distributivity2 ?12 ?13 ?14
+22288: Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
+22288: Id : 7, {_}:
+ multiply ?18 multiplicative_identity =>= ?18
+ [18] by multiplicative_id1 ?18
+22288: Id : 8, {_}:
+ add ?20 (inverse ?20) =>= multiplicative_identity
+ [20] by additive_inverse1 ?20
+22288: Id : 9, {_}:
+ multiply ?22 (inverse ?22) =>= additive_identity
+ [22] by multiplicative_inverse1 ?22
+22288: Goal:
+22288: Id : 1, {_}:
+ multiply a (multiply b c) =<= multiply (multiply a b) c
+ [] by prove_associativity
+22288: Order:
+22288: kbo
+22288: Leaf order:
+22288: additive_identity 2 0 0
+22288: multiplicative_identity 2 0 0
+22288: a 2 0 2 1,2
+22288: b 2 0 2 1,2,2
+22288: c 2 0 2 2,2,2
+22288: inverse 2 1 0
+22288: add 9 2 0 multiply
+22288: multiply 13 2 4 0,2add
+CLASH, statistics insufficient
+22289: Facts:
+22289: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+22289: Id : 3, {_}:
+ multiply ?5 ?6 =?= multiply ?6 ?5
+ [6, 5] by commutativity_of_multiply ?5 ?6
+22289: Id : 4, {_}:
+ add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10)
+ [10, 9, 8] by distributivity1 ?8 ?9 ?10
+22289: Id : 5, {_}:
+ multiply ?12 (add ?13 ?14)
+ =>=
+ add (multiply ?12 ?13) (multiply ?12 ?14)
+ [14, 13, 12] by distributivity2 ?12 ?13 ?14
+22289: Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
+22289: Id : 7, {_}:
+ multiply ?18 multiplicative_identity =>= ?18
+ [18] by multiplicative_id1 ?18
+22289: Id : 8, {_}:
+ add ?20 (inverse ?20) =>= multiplicative_identity
+ [20] by additive_inverse1 ?20
+22289: Id : 9, {_}:
+ multiply ?22 (inverse ?22) =>= additive_identity
+ [22] by multiplicative_inverse1 ?22
+22289: Goal:
+22289: Id : 1, {_}:
+ multiply a (multiply b c) =<= multiply (multiply a b) c
+ [] by prove_associativity
+22289: Order:
+22289: lpo
+22289: Leaf order:
+22289: additive_identity 2 0 0
+22289: multiplicative_identity 2 0 0
+22289: a 2 0 2 1,2
+22289: b 2 0 2 1,2,2
+22289: c 2 0 2 2,2,2
+22289: inverse 2 1 0
+22289: add 9 2 0 multiply
+22289: multiply 13 2 4 0,2add
+Statistics :
+Max weight : 25
+Found proof, 23.744275s
+% SZS status Unsatisfiable for BOO007-4.p
+% SZS output start CNFRefutation for BOO007-4.p
+Id : 44, {_}: multiply ?112 (add ?113 ?114) =<= add (multiply ?112 ?113) (multiply ?112 ?114) [114, 113, 112] by distributivity2 ?112 ?113 ?114
+Id : 4, {_}: add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10) [10, 9, 8] by distributivity1 ?8 ?9 ?10
+Id : 9, {_}: multiply ?22 (inverse ?22) =>= additive_identity [22] by multiplicative_inverse1 ?22
+Id : 5, {_}: multiply ?12 (add ?13 ?14) =<= add (multiply ?12 ?13) (multiply ?12 ?14) [14, 13, 12] by distributivity2 ?12 ?13 ?14
+Id : 7, {_}: multiply ?18 multiplicative_identity =>= ?18 [18] by multiplicative_id1 ?18
+Id : 3, {_}: multiply ?5 ?6 =?= multiply ?6 ?5 [6, 5] by commutativity_of_multiply ?5 ?6
+Id : 8, {_}: add ?20 (inverse ?20) =>= multiplicative_identity [20] by additive_inverse1 ?20
+Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16
+Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+Id : 25, {_}: add ?62 (multiply ?63 ?64) =<= multiply (add ?62 ?63) (add ?62 ?64) [64, 63, 62] by distributivity1 ?62 ?63 ?64
+Id : 516, {_}: add ?742 (multiply ?743 ?744) =<= multiply (add ?742 ?743) (add ?744 ?742) [744, 743, 742] by Super 25 with 2 at 2,3
+Id : 530, {_}: add ?796 (multiply additive_identity ?797) =<= multiply ?796 (add ?797 ?796) [797, 796] by Super 516 with 6 at 1,3
+Id : 1019, {_}: add ?1448 (multiply additive_identity ?1449) =<= multiply ?1448 (add ?1449 ?1448) [1449, 1448] by Super 516 with 6 at 1,3
+Id : 1024, {_}: add (inverse ?1462) (multiply additive_identity ?1462) =>= multiply (inverse ?1462) multiplicative_identity [1462] by Super 1019 with 8 at 2,3
+Id : 1064, {_}: add (inverse ?1462) (multiply additive_identity ?1462) =>= multiply multiplicative_identity (inverse ?1462) [1462] by Demod 1024 with 3 at 3
+Id : 75, {_}: multiply multiplicative_identity ?178 =>= ?178 [178] by Super 3 with 7 at 3
+Id : 1065, {_}: add (inverse ?1462) (multiply additive_identity ?1462) =>= inverse ?1462 [1462] by Demod 1064 with 75 at 3
+Id : 97, {_}: multiply ?204 (add (inverse ?204) ?205) =>= add additive_identity (multiply ?204 ?205) [205, 204] by Super 5 with 9 at 1,3
+Id : 63, {_}: add additive_identity ?160 =>= ?160 [160] by Super 2 with 6 at 3
+Id : 2714, {_}: multiply ?204 (add (inverse ?204) ?205) =>= multiply ?204 ?205 [205, 204] by Demod 97 with 63 at 3
+Id : 2718, {_}: add (inverse (add (inverse additive_identity) ?3390)) (multiply additive_identity ?3390) =>= inverse (add (inverse additive_identity) ?3390) [3390] by Super 1065 with 2714 at 2,2
+Id : 2791, {_}: add (multiply additive_identity ?3390) (inverse (add (inverse additive_identity) ?3390)) =>= inverse (add (inverse additive_identity) ?3390) [3390] by Demod 2718 with 2 at 2
+Id : 184, {_}: inverse additive_identity =>= multiplicative_identity [] by Super 8 with 63 at 2
+Id : 2792, {_}: add (multiply additive_identity ?3390) (inverse (add (inverse additive_identity) ?3390)) =>= inverse (add multiplicative_identity ?3390) [3390] by Demod 2791 with 184 at 1,1,3
+Id : 2793, {_}: add (multiply additive_identity ?3390) (inverse (add multiplicative_identity ?3390)) =>= inverse (add multiplicative_identity ?3390) [3390] by Demod 2792 with 184 at 1,1,2,2
+Id : 86, {_}: add ?193 (multiply (inverse ?193) ?194) =>= multiply multiplicative_identity (add ?193 ?194) [194, 193] by Super 4 with 8 at 1,3
+Id : 1836, {_}: add ?2310 (multiply (inverse ?2310) ?2311) =>= add ?2310 ?2311 [2311, 2310] by Demod 86 with 75 at 3
+Id : 1846, {_}: add ?2338 (inverse ?2338) =>= add ?2338 multiplicative_identity [2338] by Super 1836 with 7 at 2,2
+Id : 1890, {_}: multiplicative_identity =<= add ?2338 multiplicative_identity [2338] by Demod 1846 with 8 at 2
+Id : 1917, {_}: add multiplicative_identity ?2407 =>= multiplicative_identity [2407] by Super 2 with 1890 at 3
+Id : 2794, {_}: add (multiply additive_identity ?3390) (inverse (add multiplicative_identity ?3390)) =>= inverse multiplicative_identity [3390] by Demod 2793 with 1917 at 1,3
+Id : 2795, {_}: add (multiply additive_identity ?3390) (inverse multiplicative_identity) =>= inverse multiplicative_identity [3390] by Demod 2794 with 1917 at 1,2,2
+Id : 476, {_}: inverse multiplicative_identity =>= additive_identity [] by Super 9 with 75 at 2
+Id : 2796, {_}: add (multiply additive_identity ?3390) (inverse multiplicative_identity) =>= additive_identity [3390] by Demod 2795 with 476 at 3
+Id : 2797, {_}: add (inverse multiplicative_identity) (multiply additive_identity ?3390) =>= additive_identity [3390] by Demod 2796 with 2 at 2
+Id : 2798, {_}: add additive_identity (multiply additive_identity ?3390) =>= additive_identity [3390] by Demod 2797 with 476 at 1,2
+Id : 2799, {_}: multiply additive_identity ?3390 =>= additive_identity [3390] by Demod 2798 with 63 at 2
+Id : 2854, {_}: add ?796 additive_identity =<= multiply ?796 (add ?797 ?796) [797, 796] by Demod 530 with 2799 at 2,2
+Id : 2870, {_}: ?796 =<= multiply ?796 (add ?797 ?796) [797, 796] by Demod 2854 with 6 at 2
+Id : 2113, {_}: add (multiply ?2595 ?2596) (multiply ?2597 (multiply ?2595 ?2598)) =<= multiply (add (multiply ?2595 ?2596) ?2597) (multiply ?2595 (add ?2596 ?2598)) [2598, 2597, 2596, 2595] by Super 4 with 5 at 2,3
+Id : 2126, {_}: add (multiply ?2655 multiplicative_identity) (multiply ?2656 (multiply ?2655 ?2657)) =?= multiply (add (multiply ?2655 multiplicative_identity) ?2656) (multiply ?2655 multiplicative_identity) [2657, 2656, 2655] by Super 2113 with 1917 at 2,2,3
+Id : 2201, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =?= multiply (add (multiply ?2655 multiplicative_identity) ?2656) (multiply ?2655 multiplicative_identity) [2657, 2656, 2655] by Demod 2126 with 7 at 1,2
+Id : 2202, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =?= multiply (multiply ?2655 multiplicative_identity) (add (multiply ?2655 multiplicative_identity) ?2656) [2657, 2656, 2655] by Demod 2201 with 3 at 3
+Id : 62, {_}: add ?157 (multiply additive_identity ?158) =<= multiply ?157 (add ?157 ?158) [158, 157] by Super 4 with 6 at 1,3
+Id : 2203, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =?= add (multiply ?2655 multiplicative_identity) (multiply additive_identity ?2656) [2657, 2656, 2655] by Demod 2202 with 62 at 3
+Id : 2204, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =>= add ?2655 (multiply additive_identity ?2656) [2657, 2656, 2655] by Demod 2203 with 7 at 1,3
+Id : 12654, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =>= add ?2655 additive_identity [2657, 2656, 2655] by Demod 2204 with 2799 at 2,3
+Id : 12655, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =>= ?2655 [2657, 2656, 2655] by Demod 12654 with 6 at 3
+Id : 12666, {_}: multiply ?15534 (multiply ?15535 ?15536) =<= multiply (multiply ?15534 (multiply ?15535 ?15536)) ?15535 [15536, 15535, 15534] by Super 2870 with 12655 at 2,3
+Id : 21339, {_}: multiply ?30912 (multiply ?30913 ?30914) =<= multiply ?30913 (multiply ?30912 (multiply ?30913 ?30914)) [30914, 30913, 30912] by Demod 12666 with 3 at 3
+Id : 21342, {_}: multiply ?30924 (multiply ?30925 ?30926) =<= multiply ?30925 (multiply ?30924 (multiply ?30926 ?30925)) [30926, 30925, 30924] by Super 21339 with 3 at 2,2,3
+Id : 28, {_}: add ?74 (multiply ?75 ?76) =<= multiply (add ?75 ?74) (add ?74 ?76) [76, 75, 74] by Super 25 with 2 at 1,3
+Id : 4808, {_}: multiply ?5796 (add ?5797 ?5798) =<= add (multiply ?5796 ?5797) (multiply ?5798 ?5796) [5798, 5797, 5796] by Super 44 with 3 at 2,3
+Id : 4837, {_}: multiply ?5913 (add multiplicative_identity ?5914) =?= add ?5913 (multiply ?5914 ?5913) [5914, 5913] by Super 4808 with 7 at 1,3
+Id : 4917, {_}: multiply ?5913 multiplicative_identity =<= add ?5913 (multiply ?5914 ?5913) [5914, 5913] by Demod 4837 with 1917 at 2,2
+Id : 4918, {_}: ?5913 =<= add ?5913 (multiply ?5914 ?5913) [5914, 5913] by Demod 4917 with 7 at 2
+Id : 5091, {_}: add ?6286 (multiply ?6287 (multiply ?6288 ?6286)) =>= multiply (add ?6287 ?6286) ?6286 [6288, 6287, 6286] by Super 28 with 4918 at 2,3
+Id : 5151, {_}: add ?6286 (multiply ?6287 (multiply ?6288 ?6286)) =>= multiply ?6286 (add ?6287 ?6286) [6288, 6287, 6286] by Demod 5091 with 3 at 3
+Id : 5152, {_}: add ?6286 (multiply ?6287 (multiply ?6288 ?6286)) =>= ?6286 [6288, 6287, 6286] by Demod 5151 with 2870 at 3
+Id : 19536, {_}: multiply ?27546 (multiply ?27547 ?27548) =<= multiply (multiply ?27546 (multiply ?27547 ?27548)) ?27548 [27548, 27547, 27546] by Super 2870 with 5152 at 2,3
+Id : 19689, {_}: multiply ?27546 (multiply ?27547 ?27548) =<= multiply ?27548 (multiply ?27546 (multiply ?27547 ?27548)) [27548, 27547, 27546] by Demod 19536 with 3 at 3
+Id : 31289, {_}: multiply ?30924 (multiply ?30925 ?30926) =?= multiply ?30924 (multiply ?30926 ?30925) [30926, 30925, 30924] by Demod 21342 with 19689 at 3
+Id : 521, {_}: add (inverse ?761) (multiply ?762 ?761) =?= multiply (add (inverse ?761) ?762) multiplicative_identity [762, 761] by Super 516 with 8 at 2,3
+Id : 550, {_}: add (inverse ?761) (multiply ?762 ?761) =?= multiply multiplicative_identity (add (inverse ?761) ?762) [762, 761] by Demod 521 with 3 at 3
+Id : 551, {_}: add (inverse ?761) (multiply ?762 ?761) =>= add (inverse ?761) ?762 [762, 761] by Demod 550 with 75 at 3
+Id : 3740, {_}: multiply ?4638 (add (inverse ?4638) ?4639) =>= multiply ?4638 (multiply ?4639 ?4638) [4639, 4638] by Super 2714 with 551 at 2,2
+Id : 3782, {_}: multiply ?4638 ?4639 =<= multiply ?4638 (multiply ?4639 ?4638) [4639, 4638] by Demod 3740 with 2714 at 2
+Id : 3863, {_}: multiply ?4768 (add ?4769 (multiply ?4770 ?4768)) =>= add (multiply ?4768 ?4769) (multiply ?4768 ?4770) [4770, 4769, 4768] by Super 5 with 3782 at 2,3
+Id : 15840, {_}: multiply ?20984 (add ?20985 (multiply ?20986 ?20984)) =>= multiply ?20984 (add ?20985 ?20986) [20986, 20985, 20984] by Demod 3863 with 5 at 3
+Id : 15903, {_}: multiply ?21234 (multiply ?21235 (add ?21236 ?21234)) =?= multiply ?21234 (add (multiply ?21235 ?21236) ?21235) [21236, 21235, 21234] by Super 15840 with 5 at 2,2
+Id : 16059, {_}: multiply ?21234 (multiply ?21235 (add ?21236 ?21234)) =?= multiply ?21234 (add ?21235 (multiply ?21235 ?21236)) [21236, 21235, 21234] by Demod 15903 with 2 at 2,3
+Id : 4814, {_}: multiply ?5818 (add ?5819 multiplicative_identity) =?= add (multiply ?5818 ?5819) ?5818 [5819, 5818] by Super 4808 with 75 at 2,3
+Id : 4891, {_}: multiply ?5818 multiplicative_identity =<= add (multiply ?5818 ?5819) ?5818 [5819, 5818] by Demod 4814 with 1890 at 2,2
+Id : 4892, {_}: multiply ?5818 multiplicative_identity =<= add ?5818 (multiply ?5818 ?5819) [5819, 5818] by Demod 4891 with 2 at 3
+Id : 4893, {_}: ?5818 =<= add ?5818 (multiply ?5818 ?5819) [5819, 5818] by Demod 4892 with 7 at 2
+Id : 26804, {_}: multiply ?40743 (multiply ?40744 (add ?40745 ?40743)) =>= multiply ?40743 ?40744 [40745, 40744, 40743] by Demod 16059 with 4893 at 2,3
+Id : 26854, {_}: multiply (multiply ?40962 ?40963) (multiply ?40964 ?40962) =>= multiply (multiply ?40962 ?40963) ?40964 [40964, 40963, 40962] by Super 26804 with 4893 at 2,2,2
+Id : 38294, {_}: multiply (multiply ?63621 ?63622) (multiply ?63621 ?63623) =>= multiply (multiply ?63621 ?63622) ?63623 [63623, 63622, 63621] by Super 31289 with 26854 at 3
+Id : 26855, {_}: multiply (multiply ?40966 ?40967) (multiply ?40968 ?40967) =>= multiply (multiply ?40966 ?40967) ?40968 [40968, 40967, 40966] by Super 26804 with 4918 at 2,2,2
+Id : 38958, {_}: multiply (multiply ?65058 ?65059) (multiply ?65059 ?65060) =>= multiply (multiply ?65058 ?65059) ?65060 [65060, 65059, 65058] by Super 31289 with 26855 at 3
+Id : 38330, {_}: multiply (multiply ?63784 ?63785) (multiply ?63785 ?63786) =>= multiply (multiply ?63785 ?63786) ?63784 [63786, 63785, 63784] by Super 3 with 26854 at 3
+Id : 46713, {_}: multiply (multiply ?65059 ?65060) ?65058 =?= multiply (multiply ?65058 ?65059) ?65060 [65058, 65060, 65059] by Demod 38958 with 38330 at 2
+Id : 46797, {_}: multiply ?81775 (multiply ?81776 ?81777) =<= multiply (multiply ?81775 ?81776) ?81777 [81777, 81776, 81775] by Super 3 with 46713 at 3
+Id : 47389, {_}: multiply ?63621 (multiply ?63622 (multiply ?63621 ?63623)) =>= multiply (multiply ?63621 ?63622) ?63623 [63623, 63622, 63621] by Demod 38294 with 46797 at 2
+Id : 47390, {_}: multiply ?63621 (multiply ?63622 (multiply ?63621 ?63623)) =>= multiply ?63621 (multiply ?63622 ?63623) [63623, 63622, 63621] by Demod 47389 with 46797 at 3
+Id : 12809, {_}: multiply ?15534 (multiply ?15535 ?15536) =<= multiply ?15535 (multiply ?15534 (multiply ?15535 ?15536)) [15536, 15535, 15534] by Demod 12666 with 3 at 3
+Id : 47391, {_}: multiply ?63622 (multiply ?63621 ?63623) =?= multiply ?63621 (multiply ?63622 ?63623) [63623, 63621, 63622] by Demod 47390 with 12809 at 2
+Id : 47371, {_}: multiply ?40962 (multiply ?40963 (multiply ?40964 ?40962)) =>= multiply (multiply ?40962 ?40963) ?40964 [40964, 40963, 40962] by Demod 26854 with 46797 at 2
+Id : 47372, {_}: multiply ?40962 (multiply ?40963 (multiply ?40964 ?40962)) =>= multiply ?40962 (multiply ?40963 ?40964) [40964, 40963, 40962] by Demod 47371 with 46797 at 3
+Id : 47409, {_}: multiply ?40963 (multiply ?40964 ?40962) =?= multiply ?40962 (multiply ?40963 ?40964) [40962, 40964, 40963] by Demod 47372 with 19689 at 2
+Id : 47847, {_}: multiply c (multiply b a) =?= multiply c (multiply b a) [] by Demod 47846 with 3 at 2,3
+Id : 47846, {_}: multiply c (multiply b a) =?= multiply c (multiply a b) [] by Demod 47845 with 47409 at 2
+Id : 47845, {_}: multiply b (multiply a c) =>= multiply c (multiply a b) [] by Demod 47844 with 3 at 3
+Id : 47844, {_}: multiply b (multiply a c) =<= multiply (multiply a b) c [] by Demod 1 with 47391 at 2
+Id : 1, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
+% SZS output end CNFRefutation for BOO007-4.p
+22288: solved BOO007-4.p in 11.836739 using kbo
+22288: status Unsatisfiable for BOO007-4.p
+CLASH, statistics insufficient
+22303: Facts:
+22303: Id : 2, {_}:
+ add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
+ =>=
+ multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
+ [4, 3, 2] by distributivity ?2 ?3 ?4
+22303: Id : 3, {_}:
+ add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
+ [8, 7, 6] by l1 ?6 ?7 ?8
+22303: Id : 4, {_}:
+ add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
+ [12, 11, 10] by l3 ?10 ?11 ?12
+22303: Id : 5, {_}:
+ multiply (add ?14 (inverse ?14)) ?15 =>= ?15
+ [15, 14] by property3 ?14 ?15
+22303: Id : 6, {_}:
+ multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17
+ [19, 18, 17] by l2 ?17 ?18 ?19
+22303: Id : 7, {_}:
+ multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22
+ [23, 22, 21] by l4 ?21 ?22 ?23
+22303: Id : 8, {_}:
+ add (multiply ?25 (inverse ?25)) ?26 =>= ?26
+ [26, 25] by property3_dual ?25 ?26
+22303: Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
+22303: Id : 10, {_}:
+ multiply ?30 (inverse ?30) =>= n0
+ [30] by multiplicative_inverse ?30
+22303: Id : 11, {_}:
+ add (add ?32 ?33) ?34 =?= add ?32 (add ?33 ?34)
+ [34, 33, 32] by associativity_of_add ?32 ?33 ?34
+22303: Id : 12, {_}:
+ multiply (multiply ?36 ?37) ?38 =?= multiply ?36 (multiply ?37 ?38)
+ [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
+22303: Goal:
+22303: Id : 1, {_}:
+ multiply a (add b c) =<= add (multiply b a) (multiply c a)
+ [] by prove_multiply_add_property
+22303: Order:
+22303: nrkbo
+22303: Leaf order:
+22303: n1 1 0 0
+22303: n0 1 0 0
+22303: b 2 0 2 1,2,2
+22303: c 2 0 2 2,2,2
+22303: a 3 0 3 1,2
+22303: inverse 4 1 0
+22303: add 21 2 2 0,2,2multiply
+22303: multiply 22 2 3 0,2add
+CLASH, statistics insufficient
+22304: Facts:
+22304: Id : 2, {_}:
+ add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
+ =>=
+ multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
+ [4, 3, 2] by distributivity ?2 ?3 ?4
+22304: Id : 3, {_}:
+ add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
+ [8, 7, 6] by l1 ?6 ?7 ?8
+22304: Id : 4, {_}:
+ add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
+ [12, 11, 10] by l3 ?10 ?11 ?12
+22304: Id : 5, {_}:
+ multiply (add ?14 (inverse ?14)) ?15 =>= ?15
+ [15, 14] by property3 ?14 ?15
+22304: Id : 6, {_}:
+ multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17
+ [19, 18, 17] by l2 ?17 ?18 ?19
+22304: Id : 7, {_}:
+ multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22
+ [23, 22, 21] by l4 ?21 ?22 ?23
+22304: Id : 8, {_}:
+ add (multiply ?25 (inverse ?25)) ?26 =>= ?26
+ [26, 25] by property3_dual ?25 ?26
+22304: Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
+22304: Id : 10, {_}:
+ multiply ?30 (inverse ?30) =>= n0
+ [30] by multiplicative_inverse ?30
+22304: Id : 11, {_}:
+ add (add ?32 ?33) ?34 =>= add ?32 (add ?33 ?34)
+ [34, 33, 32] by associativity_of_add ?32 ?33 ?34
+22304: Id : 12, {_}:
+ multiply (multiply ?36 ?37) ?38 =>= multiply ?36 (multiply ?37 ?38)
+ [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
+CLASH, statistics insufficient
+22305: Facts:
+22305: Id : 2, {_}:
+ add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
+ =>=
+ multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
+ [4, 3, 2] by distributivity ?2 ?3 ?4
+22305: Id : 3, {_}:
+ add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
+ [8, 7, 6] by l1 ?6 ?7 ?8
+22305: Id : 4, {_}:
+ add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
+ [12, 11, 10] by l3 ?10 ?11 ?12
+22305: Id : 5, {_}:
+ multiply (add ?14 (inverse ?14)) ?15 =>= ?15
+ [15, 14] by property3 ?14 ?15
+22305: Id : 6, {_}:
+ multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17
+ [19, 18, 17] by l2 ?17 ?18 ?19
+22305: Id : 7, {_}:
+ multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22
+ [23, 22, 21] by l4 ?21 ?22 ?23
+22305: Id : 8, {_}:
+ add (multiply ?25 (inverse ?25)) ?26 =>= ?26
+ [26, 25] by property3_dual ?25 ?26
+22305: Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
+22305: Id : 10, {_}:
+ multiply ?30 (inverse ?30) =>= n0
+ [30] by multiplicative_inverse ?30
+22305: Id : 11, {_}:
+ add (add ?32 ?33) ?34 =>= add ?32 (add ?33 ?34)
+ [34, 33, 32] by associativity_of_add ?32 ?33 ?34
+22305: Id : 12, {_}:
+ multiply (multiply ?36 ?37) ?38 =>= multiply ?36 (multiply ?37 ?38)
+ [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
+22305: Goal:
+22305: Id : 1, {_}:
+ multiply a (add b c) =<= add (multiply b a) (multiply c a)
+ [] by prove_multiply_add_property
+22305: Order:
+22305: lpo
+22305: Leaf order:
+22305: n1 1 0 0
+22305: n0 1 0 0
+22305: b 2 0 2 1,2,2
+22305: c 2 0 2 2,2,2
+22305: a 3 0 3 1,2
+22305: inverse 4 1 0
+22305: add 21 2 2 0,2,2multiply
+22305: multiply 22 2 3 0,2add
+22304: Goal:
+22304: Id : 1, {_}:
+ multiply a (add b c) =<= add (multiply b a) (multiply c a)
+ [] by prove_multiply_add_property
+22304: Order:
+22304: kbo
+22304: Leaf order:
+22304: n1 1 0 0
+22304: n0 1 0 0
+22304: b 2 0 2 1,2,2
+22304: c 2 0 2 2,2,2
+22304: a 3 0 3 1,2
+22304: inverse 4 1 0
+22304: add 21 2 2 0,2,2multiply
+22304: multiply 22 2 3 0,2add
+Statistics :
+Max weight : 29
+Found proof, 45.037592s
+% SZS status Unsatisfiable for BOO031-1.p
+% SZS output start CNFRefutation for BOO031-1.p
+Id : 7, {_}: multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22 [23, 22, 21] by l4 ?21 ?22 ?23
+Id : 10, {_}: multiply ?30 (inverse ?30) =>= n0 [30] by multiplicative_inverse ?30
+Id : 8, {_}: add (multiply ?25 (inverse ?25)) ?26 =>= ?26 [26, 25] by property3_dual ?25 ?26
+Id : 12, {_}: multiply (multiply ?36 ?37) ?38 =>= multiply ?36 (multiply ?37 ?38) [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38
+Id : 52, {_}: multiply (multiply (add ?189 ?190) (add ?190 ?191)) ?190 =>= ?190 [191, 190, 189] by l4 ?189 ?190 ?191
+Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28
+Id : 5, {_}: multiply (add ?14 (inverse ?14)) ?15 =>= ?15 [15, 14] by property3 ?14 ?15
+Id : 2, {_}: add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2)) =>= multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2)) [4, 3, 2] by distributivity ?2 ?3 ?4
+Id : 18, {_}: add (add (multiply ?58 ?59) (multiply ?59 ?60)) ?59 =>= ?59 [60, 59, 58] by l3 ?58 ?59 ?60
+Id : 11, {_}: add (add ?32 ?33) ?34 =>= add ?32 (add ?33 ?34) [34, 33, 32] by associativity_of_add ?32 ?33 ?34
+Id : 4, {_}: add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11 [12, 11, 10] by l3 ?10 ?11 ?12
+Id : 37, {_}: multiply ?128 (add ?129 (add ?128 ?130)) =>= ?128 [130, 129, 128] by l2 ?128 ?129 ?130
+Id : 6, {_}: multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17 [19, 18, 17] by l2 ?17 ?18 ?19
+Id : 3, {_}: add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6 [8, 7, 6] by l1 ?6 ?7 ?8
+Id : 35, {_}: add ?121 (multiply ?122 ?121) =>= ?121 [122, 121] by Super 3 with 6 at 2,2,2
+Id : 42, {_}: multiply ?149 (add ?149 ?150) =>= ?149 [150, 149] by Super 37 with 4 at 2,2
+Id : 1579, {_}: add (add ?2436 ?2437) ?2436 =>= add ?2436 ?2437 [2437, 2436] by Super 35 with 42 at 2,2
+Id : 1609, {_}: add ?2436 (add ?2437 ?2436) =>= add ?2436 ?2437 [2437, 2436] by Demod 1579 with 11 at 2
+Id : 19, {_}: add (multiply ?62 ?63) ?63 =>= ?63 [63, 62] by Super 18 with 3 at 1,2
+Id : 39, {_}: multiply ?137 (add ?138 ?137) =>= ?137 [138, 137] by Super 37 with 3 at 2,2,2
+Id : 1363, {_}: add ?2089 (add ?2090 ?2089) =>= add ?2090 ?2089 [2090, 2089] by Super 19 with 39 at 1,2
+Id : 2844, {_}: add ?2437 ?2436 =?= add ?2436 ?2437 [2436, 2437] by Demod 1609 with 1363 at 2
+Id : 32, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add (multiply ?109 ?107) ?107) =<= multiply (add (add ?106 (add ?107 ?108)) ?109) (multiply (add ?109 ?107) (add ?107 (add ?106 (add ?107 ?108)))) [109, 108, 107, 106] by Super 2 with 6 at 2,2,2
+Id : 5786, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add ?107 (multiply ?109 ?107)) =<= multiply (add (add ?106 (add ?107 ?108)) ?109) (multiply (add ?109 ?107) (add ?107 (add ?106 (add ?107 ?108)))) [109, 108, 107, 106] by Demod 32 with 2844 at 2,2
+Id : 5787, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add ?107 (multiply ?109 ?107)) =<= multiply (add ?106 (add (add ?107 ?108) ?109)) (multiply (add ?109 ?107) (add ?107 (add ?106 (add ?107 ?108)))) [109, 108, 107, 106] by Demod 5786 with 11 at 1,3
+Id : 1088, {_}: add (multiply ?1721 ?1722) ?1722 =>= ?1722 [1722, 1721] by Super 18 with 3 at 1,2
+Id : 1091, {_}: add ?1730 (add ?1731 (add ?1730 ?1732)) =>= add ?1731 (add ?1730 ?1732) [1732, 1731, 1730] by Super 1088 with 6 at 1,2
+Id : 5788, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add ?107 (multiply ?109 ?107)) =<= multiply (add ?106 (add (add ?107 ?108) ?109)) (multiply (add ?109 ?107) (add ?106 (add ?107 ?108))) [109, 108, 107, 106] by Demod 5787 with 1091 at 2,2,3
+Id : 5789, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) ?107 =<= multiply (add ?106 (add (add ?107 ?108) ?109)) (multiply (add ?109 ?107) (add ?106 (add ?107 ?108))) [109, 108, 107, 106] by Demod 5788 with 35 at 2,2
+Id : 5790, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) ?107 =<= multiply (add ?106 (add ?107 (add ?108 ?109))) (multiply (add ?109 ?107) (add ?106 (add ?107 ?108))) [109, 108, 107, 106] by Demod 5789 with 11 at 2,1,3
+Id : 5814, {_}: add ?7785 (multiply (add ?7786 (add ?7785 ?7787)) ?7788) =<= multiply (add ?7786 (add ?7785 (add ?7787 ?7788))) (multiply (add ?7788 ?7785) (add ?7786 (add ?7785 ?7787))) [7788, 7787, 7786, 7785] by Demod 5790 with 2844 at 2
+Id : 79, {_}: multiply n1 ?15 =>= ?15 [15] by Demod 5 with 9 at 1,2
+Id : 1095, {_}: add ?1743 ?1743 =>= ?1743 [1743] by Super 1088 with 79 at 1,2
+Id : 5853, {_}: add ?7982 (multiply (add (add ?7982 ?7983) (add ?7982 ?7983)) ?7984) =<= multiply (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) (multiply (add ?7984 ?7982) (add ?7982 ?7983)) [7984, 7983, 7982] by Super 5814 with 1095 at 2,2,3
+Id : 6183, {_}: add ?7982 (multiply (add ?7982 (add ?7983 (add ?7982 ?7983))) ?7984) =<= multiply (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) (multiply (add ?7984 ?7982) (add ?7982 ?7983)) [7984, 7983, 7982] by Demod 5853 with 11 at 1,2,2
+Id : 1663, {_}: multiply (add ?2570 ?2571) ?2571 =>= ?2571 [2571, 2570] by Super 52 with 6 at 1,2
+Id : 1673, {_}: multiply ?2601 (multiply ?2602 ?2601) =>= multiply ?2602 ?2601 [2602, 2601] by Super 1663 with 35 at 1,2
+Id : 1365, {_}: multiply ?2095 (add ?2096 ?2095) =>= ?2095 [2096, 2095] by Super 37 with 3 at 2,2,2
+Id : 22, {_}: add ?71 (multiply ?71 ?72) =>= ?71 [72, 71] by Super 3 with 5 at 2,2
+Id : 1374, {_}: multiply (multiply ?2123 ?2124) ?2123 =>= multiply ?2123 ?2124 [2124, 2123] by Super 1365 with 22 at 2,2
+Id : 1408, {_}: multiply ?2123 (multiply ?2124 ?2123) =>= multiply ?2123 ?2124 [2124, 2123] by Demod 1374 with 12 at 2
+Id : 2987, {_}: multiply ?2601 ?2602 =?= multiply ?2602 ?2601 [2602, 2601] by Demod 1673 with 1408 at 2
+Id : 6184, {_}: add ?7982 (multiply (add ?7982 (add ?7983 (add ?7982 ?7983))) ?7984) =<= multiply (multiply (add ?7984 ?7982) (add ?7982 ?7983)) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) [7984, 7983, 7982] by Demod 6183 with 2987 at 3
+Id : 6185, {_}: add ?7982 (multiply (add ?7983 (add ?7982 ?7983)) ?7984) =<= multiply (multiply (add ?7984 ?7982) (add ?7982 ?7983)) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) [7984, 7983, 7982] by Demod 6184 with 1091 at 1,2,2
+Id : 6186, {_}: add ?7982 (multiply (add ?7983 (add ?7982 ?7983)) ?7984) =<= multiply (add ?7984 ?7982) (multiply (add ?7982 ?7983) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984)))) [7984, 7983, 7982] by Demod 6185 with 12 at 3
+Id : 6187, {_}: add ?7982 (multiply (add ?7982 ?7983) ?7984) =<= multiply (add ?7984 ?7982) (multiply (add ?7982 ?7983) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984)))) [7984, 7983, 7982] by Demod 6186 with 1363 at 1,2,2
+Id : 13074, {_}: add ?18195 (multiply (add ?18195 ?18196) ?18197) =>= multiply (add ?18197 ?18195) (add ?18195 ?18196) [18197, 18196, 18195] by Demod 6187 with 42 at 2,3
+Id : 16401, {_}: add ?22734 (multiply (add ?22735 ?22734) ?22736) =>= multiply (add ?22736 ?22734) (add ?22734 ?22735) [22736, 22735, 22734] by Super 13074 with 2844 at 1,2,2
+Id : 18162, {_}: add ?24925 (multiply ?24926 (add ?24927 ?24925)) =>= multiply (add ?24926 ?24925) (add ?24925 ?24927) [24927, 24926, 24925] by Super 16401 with 2987 at 2,2
+Id : 18171, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =<= multiply (add ?24965 (multiply ?24963 ?24964)) (add (multiply ?24963 ?24964) ?24964) [24965, 24964, 24963] by Super 18162 with 35 at 2,2,2
+Id : 18379, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =<= multiply (add ?24965 (multiply ?24963 ?24964)) (add ?24964 (multiply ?24963 ?24964)) [24965, 24964, 24963] by Demod 18171 with 2844 at 2,3
+Id : 18380, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =>= multiply (add ?24965 (multiply ?24963 ?24964)) ?24964 [24965, 24964, 24963] by Demod 18379 with 35 at 2,3
+Id : 18381, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =>= multiply ?24964 (add ?24965 (multiply ?24963 ?24964)) [24965, 24964, 24963] by Demod 18380 with 2987 at 3
+Id : 1575, {_}: multiply ?2421 ?2422 =<= multiply ?2421 (multiply (add ?2421 ?2423) ?2422) [2423, 2422, 2421] by Super 12 with 42 at 1,2
+Id : 16456, {_}: add ?22968 (multiply ?22969 (add ?22970 ?22968)) =>= multiply (add ?22969 ?22968) (add ?22968 ?22970) [22970, 22969, 22968] by Super 16401 with 2987 at 2,2
+Id : 1247, {_}: add ?1879 ?1880 =<= add ?1879 (add (multiply ?1879 ?1881) ?1880) [1881, 1880, 1879] by Super 11 with 22 at 1,2
+Id : 6619, {_}: multiply (multiply ?8607 ?8608) (add ?8607 ?8609) =>= multiply ?8607 ?8608 [8609, 8608, 8607] by Super 6 with 1247 at 2,2
+Id : 6763, {_}: multiply ?8607 (multiply ?8608 (add ?8607 ?8609)) =>= multiply ?8607 ?8608 [8609, 8608, 8607] by Demod 6619 with 12 at 2
+Id : 65, {_}: add (multiply ?237 ?238) (multiply (inverse ?238) ?237) =<= multiply (add ?237 ?238) (multiply (add ?238 (inverse ?238)) (add (inverse ?238) ?237)) [238, 237] by Super 2 with 8 at 2,2
+Id : 76, {_}: add (multiply ?237 ?238) (multiply (inverse ?238) ?237) =>= multiply (add ?237 ?238) (add (inverse ?238) ?237) [238, 237] by Demod 65 with 5 at 2,3
+Id : 18170, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =<= multiply (add ?24961 (multiply ?24959 ?24960)) (add (multiply ?24959 ?24960) ?24959) [24961, 24960, 24959] by Super 18162 with 22 at 2,2,2
+Id : 18376, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =<= multiply (add ?24961 (multiply ?24959 ?24960)) (add ?24959 (multiply ?24959 ?24960)) [24961, 24960, 24959] by Demod 18170 with 2844 at 2,3
+Id : 18377, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =>= multiply (add ?24961 (multiply ?24959 ?24960)) ?24959 [24961, 24960, 24959] by Demod 18376 with 22 at 2,3
+Id : 18378, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =>= multiply ?24959 (add ?24961 (multiply ?24959 ?24960)) [24961, 24960, 24959] by Demod 18377 with 2987 at 3
+Id : 22657, {_}: multiply ?237 (add (inverse ?238) (multiply ?237 ?238)) =<= multiply (add ?237 ?238) (add (inverse ?238) ?237) [238, 237] by Demod 76 with 18378 at 2
+Id : 22699, {_}: multiply (inverse ?30910) (multiply ?30911 (add (inverse ?30910) (multiply ?30911 ?30910))) =>= multiply (inverse ?30910) (add ?30911 ?30910) [30911, 30910] by Super 6763 with 22657 at 2,2
+Id : 22814, {_}: multiply (inverse ?30910) ?30911 =<= multiply (inverse ?30910) (add ?30911 ?30910) [30911, 30910] by Demod 22699 with 6763 at 2
+Id : 23609, {_}: add ?31619 (multiply (inverse ?31619) ?31620) =<= multiply (add (inverse ?31619) ?31619) (add ?31619 ?31620) [31620, 31619] by Super 16456 with 22814 at 2,2
+Id : 23775, {_}: add ?31619 (multiply (inverse ?31619) ?31620) =<= multiply (add ?31619 (inverse ?31619)) (add ?31619 ?31620) [31620, 31619] by Demod 23609 with 2844 at 1,3
+Id : 23776, {_}: add ?31619 (multiply (inverse ?31619) ?31620) =>= multiply n1 (add ?31619 ?31620) [31620, 31619] by Demod 23775 with 9 at 1,3
+Id : 24286, {_}: add ?32553 (multiply (inverse ?32553) ?32554) =>= add ?32553 ?32554 [32554, 32553] by Demod 23776 with 79 at 3
+Id : 13130, {_}: add ?18432 (multiply ?18433 (add ?18432 ?18434)) =>= multiply (add ?18433 ?18432) (add ?18432 ?18434) [18434, 18433, 18432] by Super 13074 with 2987 at 2,2
+Id : 22705, {_}: multiply ?30931 (add (inverse ?30932) (multiply ?30931 ?30932)) =<= multiply (add ?30931 ?30932) (add (inverse ?30932) ?30931) [30932, 30931] by Demod 76 with 18378 at 2
+Id : 22751, {_}: multiply ?31084 (add (inverse (inverse ?31084)) (multiply ?31084 (inverse ?31084))) =>= multiply n1 (add (inverse (inverse ?31084)) ?31084) [31084] by Super 22705 with 9 at 1,3
+Id : 23065, {_}: multiply ?31084 (add (inverse (inverse ?31084)) n0) =?= multiply n1 (add (inverse (inverse ?31084)) ?31084) [31084] by Demod 22751 with 10 at 2,2,2
+Id : 23066, {_}: multiply ?31084 (add (inverse (inverse ?31084)) n0) =>= add (inverse (inverse ?31084)) ?31084 [31084] by Demod 23065 with 79 at 3
+Id : 130, {_}: multiply (add ?21 ?22) (multiply (add ?22 ?23) ?22) =>= ?22 [23, 22, 21] by Demod 7 with 12 at 2
+Id : 89, {_}: n0 =<= inverse n1 [] by Super 79 with 10 at 2
+Id : 360, {_}: add n1 n0 =>= n1 [] by Super 9 with 89 at 2,2
+Id : 382, {_}: multiply n1 (multiply (add n0 ?765) n0) =>= n0 [765] by Super 130 with 360 at 1,2
+Id : 422, {_}: multiply (add n0 ?765) n0 =>= n0 [765] by Demod 382 with 79 at 2
+Id : 88, {_}: add n0 ?26 =>= ?26 [26] by Demod 8 with 10 at 1,2
+Id : 423, {_}: multiply ?765 n0 =>= n0 [765] by Demod 422 with 88 at 1,2
+Id : 831, {_}: add ?1448 (multiply ?1449 n0) =>= ?1448 [1449, 1448] by Super 3 with 423 at 2,2,2
+Id : 867, {_}: add ?1448 n0 =>= ?1448 [1448] by Demod 831 with 423 at 2,2
+Id : 23067, {_}: multiply ?31084 (inverse (inverse ?31084)) =<= add (inverse (inverse ?31084)) ?31084 [31084] by Demod 23066 with 867 at 2,2
+Id : 23068, {_}: multiply ?31084 (inverse (inverse ?31084)) =<= add ?31084 (inverse (inverse ?31084)) [31084] by Demod 23067 with 2844 at 3
+Id : 23215, {_}: add ?31334 (multiply ?31335 (multiply ?31334 (inverse (inverse ?31334)))) =>= multiply (add ?31335 ?31334) (add ?31334 (inverse (inverse ?31334))) [31335, 31334] by Super 13130 with 23068 at 2,2,2
+Id : 23280, {_}: ?31334 =<= multiply (add ?31335 ?31334) (add ?31334 (inverse (inverse ?31334))) [31335, 31334] by Demod 23215 with 3 at 2
+Id : 23281, {_}: ?31334 =<= multiply (add ?31335 ?31334) (multiply ?31334 (inverse (inverse ?31334))) [31335, 31334] by Demod 23280 with 23068 at 2,3
+Id : 2547, {_}: multiply (multiply ?3698 ?3699) ?3700 =<= multiply ?3698 (multiply (multiply ?3699 ?3698) ?3700) [3700, 3699, 3698] by Super 12 with 1408 at 1,2
+Id : 2578, {_}: multiply ?3698 (multiply ?3699 ?3700) =<= multiply ?3698 (multiply (multiply ?3699 ?3698) ?3700) [3700, 3699, 3698] by Demod 2547 with 12 at 2
+Id : 2579, {_}: multiply ?3698 (multiply ?3699 ?3700) =<= multiply ?3698 (multiply ?3699 (multiply ?3698 ?3700)) [3700, 3699, 3698] by Demod 2578 with 12 at 2,3
+Id : 1667, {_}: multiply ?2583 (multiply ?2584 (multiply ?2583 ?2585)) =>= multiply ?2584 (multiply ?2583 ?2585) [2585, 2584, 2583] by Super 1663 with 3 at 1,2
+Id : 12236, {_}: multiply ?3698 (multiply ?3699 ?3700) =?= multiply ?3699 (multiply ?3698 ?3700) [3700, 3699, 3698] by Demod 2579 with 1667 at 3
+Id : 23282, {_}: ?31334 =<= multiply ?31334 (multiply (add ?31335 ?31334) (inverse (inverse ?31334))) [31335, 31334] by Demod 23281 with 12236 at 3
+Id : 1360, {_}: multiply ?2077 ?2078 =<= multiply ?2077 (multiply (add ?2079 ?2077) ?2078) [2079, 2078, 2077] by Super 12 with 39 at 1,2
+Id : 23283, {_}: ?31334 =<= multiply ?31334 (inverse (inverse ?31334)) [31334] by Demod 23282 with 1360 at 3
+Id : 23386, {_}: add (inverse (inverse ?31435)) ?31435 =>= inverse (inverse ?31435) [31435] by Super 35 with 23283 at 2,2
+Id : 23494, {_}: add ?31435 (inverse (inverse ?31435)) =>= inverse (inverse ?31435) [31435] by Demod 23386 with 2844 at 2
+Id : 23374, {_}: ?31084 =<= add ?31084 (inverse (inverse ?31084)) [31084] by Demod 23068 with 23283 at 2
+Id : 23495, {_}: ?31435 =<= inverse (inverse ?31435) [31435] by Demod 23494 with 23374 at 2
+Id : 24293, {_}: add (inverse ?32572) (multiply ?32572 ?32573) =>= add (inverse ?32572) ?32573 [32573, 32572] by Super 24286 with 23495 at 1,2,2
+Id : 23619, {_}: multiply (multiply (inverse ?31653) ?31654) ?31655 =<= multiply (inverse ?31653) (multiply (add ?31654 ?31653) ?31655) [31655, 31654, 31653] by Super 12 with 22814 at 1,2
+Id : 23754, {_}: multiply (inverse ?31653) (multiply ?31654 ?31655) =<= multiply (inverse ?31653) (multiply (add ?31654 ?31653) ?31655) [31655, 31654, 31653] by Demod 23619 with 12 at 2
+Id : 77768, {_}: add (inverse (inverse ?103133)) (multiply (inverse ?103133) (multiply ?103134 ?103135)) =>= add (inverse (inverse ?103133)) (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Super 24293 with 23754 at 2,2
+Id : 78028, {_}: add (inverse (inverse ?103133)) (multiply ?103134 ?103135) =<= add (inverse (inverse ?103133)) (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Demod 77768 with 24293 at 2
+Id : 78029, {_}: add (inverse (inverse ?103133)) (multiply ?103134 ?103135) =?= add ?103133 (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Demod 78028 with 23495 at 1,3
+Id : 78030, {_}: add ?103133 (multiply ?103134 ?103135) =<= add ?103133 (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Demod 78029 with 23495 at 1,2
+Id : 13094, {_}: add ?18275 (multiply (add ?18276 ?18275) ?18277) =>= multiply (add ?18277 ?18275) (add ?18275 ?18276) [18277, 18276, 18275] by Super 13074 with 2844 at 1,2,2
+Id : 78031, {_}: add ?103133 (multiply ?103134 ?103135) =<= multiply (add ?103135 ?103133) (add ?103133 ?103134) [103135, 103134, 103133] by Demod 78030 with 13094 at 3
+Id : 78812, {_}: multiply ?104288 (add ?104289 ?104290) =<= multiply ?104288 (add ?104289 (multiply ?104290 ?104288)) [104290, 104289, 104288] by Super 1575 with 78031 at 2,3
+Id : 80954, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =>= multiply ?24964 (add ?24965 ?24963) [24965, 24964, 24963] by Demod 18381 with 78812 at 3
+Id : 81595, {_}: multiply a (add c b) =?= multiply a (add c b) [] by Demod 81594 with 2844 at 2,3
+Id : 81594, {_}: multiply a (add c b) =?= multiply a (add b c) [] by Demod 81593 with 80954 at 3
+Id : 81593, {_}: multiply a (add c b) =<= add (multiply c a) (multiply b a) [] by Demod 81592 with 2844 at 3
+Id : 81592, {_}: multiply a (add c b) =<= add (multiply b a) (multiply c a) [] by Demod 1 with 2844 at 2,2
+Id : 1, {_}: multiply a (add b c) =<= add (multiply b a) (multiply c a) [] by prove_multiply_add_property
+% SZS output end CNFRefutation for BOO031-1.p
+22304: solved BOO031-1.p in 22.545408 using kbo
+22304: status Unsatisfiable for BOO031-1.p
+NO CLASH, using fixed ground order
+22316: Facts:
+22316: Id : 2, {_}:
+ inverse
+ (add (inverse (add (inverse (add ?2 ?3)) ?4))
+ (inverse
+ (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
+22316: Goal:
+22316: Id : 1, {_}: add b a =<= add a b [] by huntinton_1
+22316: Order:
+22316: nrkbo
+22316: Leaf order:
+22316: b 2 0 2 1,2
+22316: a 2 0 2 2,2
+22316: inverse 7 1 0
+22316: add 8 2 2 0,2
+NO CLASH, using fixed ground order
+22317: Facts:
+22317: Id : 2, {_}:
+ inverse
+ (add (inverse (add (inverse (add ?2 ?3)) ?4))
+ (inverse
+ (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
+22317: Goal:
+22317: Id : 1, {_}: add b a =<= add a b [] by huntinton_1
+22317: Order:
+22317: kbo
+22317: Leaf order:
+22317: b 2 0 2 1,2
+22317: a 2 0 2 2,2
+22317: inverse 7 1 0
+22317: add 8 2 2 0,2
+NO CLASH, using fixed ground order
+22318: Facts:
+22318: Id : 2, {_}:
+ inverse
+ (add (inverse (add (inverse (add ?2 ?3)) ?4))
+ (inverse
+ (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
+22318: Goal:
+22318: Id : 1, {_}: add b a =<= add a b [] by huntinton_1
+22318: Order:
+22318: lpo
+22318: Leaf order:
+22318: b 2 0 2 1,2
+22318: a 2 0 2 2,2
+22318: inverse 7 1 0
+22318: add 8 2 2 0,2
+Statistics :
+Max weight : 70
+Found proof, 10.385052s
+% SZS status Unsatisfiable for BOO072-1.p
+% SZS output start CNFRefutation for BOO072-1.p
+Id : 3, {_}: inverse (add (inverse (add (inverse (add ?7 ?8)) ?9)) (inverse (add ?7 (inverse (add (inverse ?9) (inverse (add ?9 ?10))))))) =>= ?9 [10, 9, 8, 7] by dn1 ?7 ?8 ?9 ?10
+Id : 2, {_}: inverse (add (inverse (add (inverse (add ?2 ?3)) ?4)) (inverse (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) =>= ?4 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
+Id : 15, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?74)) ?75)) ?74)) ?76)) (inverse ?74))) ?74) =>= inverse ?74 [76, 75, 74] by Super 3 with 2 at 2,1,2
+Id : 20, {_}: inverse (add (inverse (add ?104 (inverse ?104))) ?104) =>= inverse ?104 [104] by Super 15 with 2 at 1,1,1,1,2
+Id : 99, {_}: inverse (add (inverse ?355) (inverse (add ?355 (inverse (add (inverse ?355) (inverse (add ?355 ?356))))))) =>= ?355 [356, 355] by Super 2 with 20 at 1,1,2
+Id : 136, {_}: inverse (add (inverse (add (inverse (add ?450 ?451)) ?452)) (inverse (add ?450 ?452))) =>= ?452 [452, 451, 450] by Super 2 with 99 at 2,1,2,1,2
+Id : 536, {_}: inverse (add (inverse (add (inverse (add ?1808 ?1809)) ?1810)) (inverse (add ?1808 ?1810))) =>= ?1810 [1810, 1809, 1808] by Super 2 with 99 at 2,1,2,1,2
+Id : 550, {_}: inverse (add (inverse (add ?1882 ?1883)) (inverse (add (inverse ?1882) ?1883))) =>= ?1883 [1883, 1882] by Super 536 with 99 at 1,1,1,1,2
+Id : 724, {_}: inverse (add ?2517 (inverse (add ?2518 (inverse (add (inverse ?2518) ?2517))))) =>= inverse (add (inverse ?2518) ?2517) [2518, 2517] by Super 136 with 550 at 1,1,2
+Id : 1584, {_}: inverse (add (inverse ?4978) (inverse (add ?4978 (inverse (add (inverse ?4978) (inverse ?4978)))))) =>= ?4978 [4978] by Super 99 with 724 at 2,1,2,1,2
+Id : 1652, {_}: inverse (add (inverse ?4978) (inverse ?4978)) =>= ?4978 [4978] by Demod 1584 with 724 at 2
+Id : 763, {_}: inverse (add (inverse (add ?2736 ?2737)) (inverse (add (inverse ?2736) ?2737))) =>= ?2737 [2737, 2736] by Super 536 with 99 at 1,1,1,1,2
+Id : 144, {_}: inverse (add (inverse ?482) (inverse (add ?482 (inverse (add (inverse ?482) (inverse (add ?482 ?483))))))) =>= ?482 [483, 482] by Super 2 with 20 at 1,1,2
+Id : 155, {_}: inverse (add (inverse ?528) (inverse (add ?528 ?528))) =>= ?528 [528] by Super 144 with 99 at 2,1,2,1,2
+Id : 782, {_}: inverse (add (inverse (add ?2830 (inverse (add ?2830 ?2830)))) ?2830) =>= inverse (add ?2830 ?2830) [2830] by Super 763 with 155 at 2,1,2
+Id : 871, {_}: inverse (add (inverse (add ?3076 ?3076)) (inverse (add ?3076 ?3076))) =>= ?3076 [3076] by Super 136 with 782 at 1,1,2
+Id : 1724, {_}: add ?3076 ?3076 =>= ?3076 [3076] by Demod 871 with 1652 at 2
+Id : 1754, {_}: inverse (inverse ?5284) =>= ?5284 [5284] by Demod 1652 with 1724 at 1,2
+Id : 1761, {_}: inverse ?5314 =<= add (inverse (add ?5315 ?5314)) (inverse (add (inverse ?5315) ?5314)) [5315, 5314] by Super 1754 with 550 at 1,2
+Id : 1733, {_}: inverse (inverse ?4978) =>= ?4978 [4978] by Demod 1652 with 1724 at 1,2
+Id : 6, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?26)) ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Super 3 with 2 at 2,1,2
+Id : 1734, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add ?26 ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Demod 6 with 1733 at 1,1,1,1,1,1,1,1,1,1,2
+Id : 921, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse (add ?3102 ?3102))))) =>= inverse (add ?3102 ?3102) [3102] by Super 136 with 871 at 1,1,2
+Id : 1725, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse (add ?3102 ?3102) [3102] by Demod 921 with 1724 at 1,2,1,2,1,2
+Id : 1726, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse ?3102 [3102] by Demod 1725 with 1724 at 1,3
+Id : 1763, {_}: inverse (inverse ?5320) =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Super 1754 with 1726 at 1,2
+Id : 1786, {_}: ?5320 =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Demod 1763 with 1733 at 2
+Id : 2715, {_}: inverse (add (inverse (add (inverse ?7389) (inverse (inverse ?7389)))) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Super 724 with 1786 at 1,2,1,2,1,2
+Id : 2755, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2715 with 1733 at 2,1,1,1,2
+Id : 2756, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =?= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2755 with 1733 at 2,1,2,1,2
+Id : 2757, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =>= inverse (inverse ?7389) [7389] by Demod 2756 with 1786 at 1,3
+Id : 2758, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= inverse (inverse ?7389) [7389] by Demod 2757 with 1724 at 1,2,1,2
+Id : 2759, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= ?7389 [7389] by Demod 2758 with 1733 at 3
+Id : 2920, {_}: inverse ?7714 =<= add (inverse (add (inverse ?7714) ?7714)) (inverse ?7714) [7714] by Super 1733 with 2759 at 1,2
+Id : 3142, {_}: inverse (add (inverse (add (inverse (add (inverse (inverse ?8118)) ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Super 1734 with 2920 at 1,1,1,1,1,1,1,2
+Id : 3172, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3142 with 1733 at 1,1,1,1,1,1,2
+Id : 3173, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) ?8118)) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3172 with 1733 at 2,1,1,1,2
+Id : 8100, {_}: inverse (add (inverse (add (inverse (add ?15581 ?15582)) ?15581)) (inverse ?15581)) =>= ?15581 [15582, 15581] by Demod 3173 with 1733 at 3
+Id : 8144, {_}: inverse (add ?15759 (inverse (inverse (add ?15760 ?15759)))) =>= inverse (add ?15760 ?15759) [15760, 15759] by Super 8100 with 136 at 1,1,2
+Id : 8459, {_}: inverse (add ?16264 (add ?16265 ?16264)) =>= inverse (add ?16265 ?16264) [16265, 16264] by Demod 8144 with 1733 at 2,1,2
+Id : 1749, {_}: inverse (add (inverse (add (inverse ?5262) ?5263)) (inverse (add ?5262 ?5263))) =>= ?5263 [5263, 5262] by Super 550 with 1733 at 1,1,2,1,2
+Id : 5602, {_}: inverse ?11750 =<= add (inverse (add (inverse ?11751) ?11750)) (inverse (add ?11751 ?11750)) [11751, 11750] by Super 1733 with 1749 at 1,2
+Id : 8468, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =<= inverse (add (inverse (add (inverse ?16285) ?16286)) (inverse (add ?16285 ?16286))) [16286, 16285] by Super 8459 with 5602 at 2,1,2
+Id : 8598, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= inverse (inverse ?16286) [16286, 16285] by Demod 8468 with 5602 at 1,3
+Id : 8599, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= ?16286 [16286, 16285] by Demod 8598 with 1733 at 3
+Id : 8791, {_}: inverse ?16774 =<= add (inverse (add ?16775 ?16774)) (inverse ?16774) [16775, 16774] by Super 1733 with 8599 at 1,2
+Id : 10568, {_}: inverse (add (inverse (inverse ?20566)) (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Super 136 with 8791 at 1,1,1,2
+Id : 10805, {_}: inverse (add ?20566 (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Demod 10568 with 1733 at 1,1,2
+Id : 11153, {_}: inverse (inverse ?21486) =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Super 1733 with 10805 at 1,2
+Id : 11260, {_}: ?21486 =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Demod 11153 with 1733 at 2
+Id : 12127, {_}: inverse (inverse (add ?22871 (inverse (inverse ?22872)))) =<= add (inverse (add ?22872 (inverse (add ?22871 (inverse (inverse ?22872)))))) (inverse (inverse ?22872)) [22872, 22871] by Super 1761 with 11260 at 1,2,3
+Id : 12312, {_}: add ?22871 (inverse (inverse ?22872)) =<= add (inverse (add ?22872 (inverse (add ?22871 (inverse (inverse ?22872)))))) (inverse (inverse ?22872)) [22872, 22871] by Demod 12127 with 1733 at 2
+Id : 12313, {_}: add ?22871 (inverse (inverse ?22872)) =<= add (inverse (add ?22872 (inverse (add ?22871 ?22872)))) (inverse (inverse ?22872)) [22872, 22871] by Demod 12312 with 1733 at 2,1,2,1,1,3
+Id : 12314, {_}: add ?22871 (inverse (inverse ?22872)) =<= add (inverse (add ?22872 (inverse (add ?22871 ?22872)))) ?22872 [22872, 22871] by Demod 12313 with 1733 at 2,3
+Id : 12315, {_}: add ?22871 ?22872 =<= add (inverse (add ?22872 (inverse (add ?22871 ?22872)))) ?22872 [22872, 22871] by Demod 12314 with 1733 at 2,2
+Id : 12, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Super 2 with 6 at 2,1,2
+Id : 3710, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 12 with 1733 at 1,1,1,1,1,1,1,1,1,1,1,1,1,1,2
+Id : 3711, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3710 with 1733 at 2,1,1,1,1,1,1,1,2
+Id : 3712, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (add (inverse ?57) (inverse (add ?57 ?58)))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3711 with 1733 at 2,1,2
+Id : 10590, {_}: inverse (add (inverse (inverse ?20667)) (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Super 3712 with 8791 at 1,1,1,2
+Id : 10753, {_}: inverse (add ?20667 (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10590 with 1733 at 1,1,2
+Id : 10754, {_}: inverse (add ?20667 (add ?20667 (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10753 with 1733 at 1,2,1,2
+Id : 15430, {_}: inverse (inverse ?28103) =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Super 1733 with 10754 at 1,2
+Id : 15735, {_}: ?28103 =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Demod 15430 with 1733 at 2
+Id : 1762, {_}: inverse (inverse (add (inverse ?5317) ?5318)) =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Super 1754 with 724 at 1,2
+Id : 1785, {_}: add (inverse ?5317) ?5318 =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Demod 1762 with 1733 at 2
+Id : 11176, {_}: inverse (add ?21600 (inverse (add ?21601 (inverse ?21600)))) =>= inverse ?21600 [21601, 21600] by Demod 10568 with 1733 at 1,1,2
+Id : 11183, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= inverse (inverse ?21642) [21643, 21642] by Super 11176 with 1733 at 2,1,2,1,2
+Id : 11564, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= ?21642 [21643, 21642] by Demod 11183 with 1733 at 3
+Id : 13294, {_}: inverse ?24726 =<= add (inverse ?24726) (inverse (add ?24727 ?24726)) [24727, 24726] by Super 1733 with 11564 at 1,2
+Id : 13313, {_}: inverse (add (inverse ?24792) (inverse (add ?24792 ?24793))) =<= add (inverse (add (inverse ?24792) (inverse (add ?24792 ?24793)))) ?24792 [24793, 24792] by Super 13294 with 3712 at 2,3
+Id : 16466, {_}: add (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) ?29660 =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Super 1785 with 13313 at 1,2,1,2,3
+Id : 16829, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Demod 16466 with 13313 at 2
+Id : 16830, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (add (inverse ?29660) (inverse (add ?29660 ?29661))))) [29661, 29660] by Demod 16829 with 1733 at 2,1,2,3
+Id : 16831, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) [29661, 29660] by Demod 16830 with 1724 at 1,2,3
+Id : 17624, {_}: ?31105 =<= add ?31105 (inverse (add (inverse ?31105) (inverse (add ?31105 ?31106)))) [31106, 31105] by Super 15735 with 16831 at 2,3
+Id : 17680, {_}: ?31105 =<= inverse (add (inverse ?31105) (inverse (add ?31105 ?31106))) [31106, 31105] by Demod 17624 with 16831 at 3
+Id : 18257, {_}: add ?31431 ?31432 =<= add (add ?31431 ?31432) ?31431 [31432, 31431] by Super 11260 with 17680 at 2,3
+Id : 18514, {_}: add (add ?31834 ?31835) ?31834 =<= add (inverse (add ?31834 (inverse (add ?31834 ?31835)))) ?31834 [31835, 31834] by Super 12315 with 18257 at 1,2,1,1,3
+Id : 19938, {_}: add ?34185 ?34186 =<= add (inverse (add ?34185 (inverse (add ?34185 ?34186)))) ?34185 [34186, 34185] by Demod 18514 with 18257 at 2
+Id : 8365, {_}: inverse (add ?15759 (add ?15760 ?15759)) =>= inverse (add ?15760 ?15759) [15760, 15759] by Demod 8144 with 1733 at 2,1,2
+Id : 8391, {_}: inverse (inverse (add ?15887 ?15888)) =<= add ?15888 (add ?15887 ?15888) [15888, 15887] by Super 1733 with 8365 at 1,2
+Id : 8543, {_}: add ?15887 ?15888 =<= add ?15888 (add ?15887 ?15888) [15888, 15887] by Demod 8391 with 1733 at 2
+Id : 15853, {_}: add ?28715 (add ?28715 (inverse (add (inverse ?28715) ?28716))) =?= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Super 8543 with 15735 at 2,3
+Id : 16108, {_}: ?28715 =<= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Demod 15853 with 15735 at 2
+Id : 18478, {_}: ?28715 =<= add ?28715 (inverse (add (inverse ?28715) ?28716)) [28716, 28715] by Demod 16108 with 18257 at 3
+Id : 18480, {_}: add (inverse ?5317) ?5318 =?= add ?5318 (inverse ?5317) [5318, 5317] by Demod 1785 with 18478 at 1,2,3
+Id : 20385, {_}: add ?34911 ?34912 =<= add (inverse (add (inverse (add ?34911 ?34912)) ?34911)) ?34911 [34912, 34911] by Super 19938 with 18480 at 1,1,3
+Id : 20390, {_}: add ?34925 (add ?34926 ?34925) =<= add (inverse (add (inverse (add ?34926 ?34925)) ?34925)) ?34925 [34926, 34925] by Super 20385 with 8543 at 1,1,1,1,3
+Id : 20500, {_}: add ?34926 ?34925 =<= add (inverse (add (inverse (add ?34926 ?34925)) ?34925)) ?34925 [34925, 34926] by Demod 20390 with 8543 at 2
+Id : 5906, {_}: inverse (add (inverse (inverse ?12265)) (inverse (add (inverse ?12266) (inverse (add ?12266 ?12265))))) =>= inverse (add ?12266 ?12265) [12266, 12265] by Super 136 with 5602 at 1,1,1,2
+Id : 6067, {_}: inverse (add ?12265 (inverse (add (inverse ?12266) (inverse (add ?12266 ?12265))))) =>= inverse (add ?12266 ?12265) [12266, 12265] by Demod 5906 with 1733 at 1,1,2
+Id : 15857, {_}: add (inverse ?28730) (add (inverse ?28730) (inverse (add (inverse (inverse ?28730)) ?28731))) =<= add (add (inverse ?28730) (inverse (add (inverse (inverse ?28730)) ?28731))) (inverse (add ?28730 (inverse (inverse ?28730)))) [28731, 28730] by Super 1785 with 15735 at 1,2,1,2,3
+Id : 16100, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add (inverse (inverse ?28730)) ?28731))) (inverse (add ?28730 (inverse (inverse ?28730)))) [28731, 28730] by Demod 15857 with 15735 at 2
+Id : 16101, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add ?28730 ?28731))) (inverse (add ?28730 (inverse (inverse ?28730)))) [28731, 28730] by Demod 16100 with 1733 at 1,1,2,1,3
+Id : 16102, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add ?28730 ?28731))) (inverse (add ?28730 ?28730)) [28731, 28730] by Demod 16101 with 1733 at 2,1,2,3
+Id : 16103, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add ?28730 ?28731))) (inverse ?28730) [28731, 28730] by Demod 16102 with 1724 at 1,2,3
+Id : 18477, {_}: inverse ?28730 =<= add (inverse ?28730) (inverse (add ?28730 ?28731)) [28731, 28730] by Demod 16103 with 18257 at 3
+Id : 21222, {_}: inverse (add ?12265 (inverse (inverse ?12266))) =>= inverse (add ?12266 ?12265) [12266, 12265] by Demod 6067 with 18477 at 1,2,1,2
+Id : 21223, {_}: inverse (add ?12265 ?12266) =?= inverse (add ?12266 ?12265) [12266, 12265] by Demod 21222 with 1733 at 2,1,2
+Id : 21386, {_}: add ?36951 ?36952 =<= add (inverse (add (inverse (add ?36952 ?36951)) ?36952)) ?36952 [36952, 36951] by Super 20500 with 21223 at 1,1,1,3
+Id : 19969, {_}: add ?34289 ?34290 =<= add (inverse (add (inverse (add ?34289 ?34290)) ?34289)) ?34289 [34290, 34289] by Super 19938 with 18480 at 1,1,3
+Id : 21454, {_}: add ?36951 ?36952 =?= add ?36952 ?36951 [36952, 36951] by Demod 21386 with 19969 at 3
+Id : 21981, {_}: add b a === add b a [] by Demod 1 with 21454 at 3
+Id : 1, {_}: add b a =<= add a b [] by huntinton_1
+% SZS output end CNFRefutation for BOO072-1.p
+22316: solved BOO072-1.p in 10.380648 using nrkbo
+22316: status Unsatisfiable for BOO072-1.p
+NO CLASH, using fixed ground order
+22328: Facts:
+22328: Id : 2, {_}:
+ inverse
+ (add (inverse (add (inverse (add ?2 ?3)) ?4))
+ (inverse
+ (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
+22328: Goal:
+22328: Id : 1, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2
+22328: Order:
+22328: nrkbo
+22328: Leaf order:
+22328: a 2 0 2 1,1,2
+22328: b 2 0 2 2,1,2
+22328: c 2 0 2 2,2
+22328: inverse 7 1 0
+22328: add 10 2 4 0,2
+NO CLASH, using fixed ground order
+22329: Facts:
+22329: Id : 2, {_}:
+ inverse
+ (add (inverse (add (inverse (add ?2 ?3)) ?4))
+ (inverse
+ (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
+22329: Goal:
+22329: Id : 1, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2
+22329: Order:
+22329: kbo
+22329: Leaf order:
+22329: a 2 0 2 1,1,2
+22329: b 2 0 2 2,1,2
+22329: c 2 0 2 2,2
+22329: inverse 7 1 0
+22329: add 10 2 4 0,2
+NO CLASH, using fixed ground order
+22330: Facts:
+22330: Id : 2, {_}:
+ inverse
+ (add (inverse (add (inverse (add ?2 ?3)) ?4))
+ (inverse
+ (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
+22330: Goal:
+22330: Id : 1, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2
+22330: Order:
+22330: lpo
+22330: Leaf order:
+22330: a 2 0 2 1,1,2
+22330: b 2 0 2 2,1,2
+22330: c 2 0 2 2,2
+22330: inverse 7 1 0
+22330: add 10 2 4 0,2
+% SZS status Timeout for BOO073-1.p
+NO CLASH, using fixed ground order
+22390: Facts:
+22390: Id : 2, {_}:
+ inverse
+ (add (inverse (add (inverse (add ?2 ?3)) ?4))
+ (inverse
+ (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
+22390: Goal:
+22390: Id : 1, {_}:
+ add (inverse (add (inverse a) b))
+ (inverse (add (inverse a) (inverse b)))
+ =>=
+ a
+ [] by huntinton_3
+22390: Order:
+22390: nrkbo
+22390: Leaf order:
+22390: b 2 0 2 2,1,1,2
+22390: a 3 0 3 1,1,1,1,2
+22390: inverse 12 1 5 0,1,2
+22390: add 9 2 3 0,2
+NO CLASH, using fixed ground order
+22391: Facts:
+22391: Id : 2, {_}:
+ inverse
+ (add (inverse (add (inverse (add ?2 ?3)) ?4))
+ (inverse
+ (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
+22391: Goal:
+22391: Id : 1, {_}:
+ add (inverse (add (inverse a) b))
+ (inverse (add (inverse a) (inverse b)))
+ =>=
+ a
+ [] by huntinton_3
+22391: Order:
+22391: kbo
+22391: Leaf order:
+22391: b 2 0 2 2,1,1,2
+22391: a 3 0 3 1,1,1,1,2
+22391: inverse 12 1 5 0,1,2
+22391: add 9 2 3 0,2
+NO CLASH, using fixed ground order
+22392: Facts:
+22392: Id : 2, {_}:
+ inverse
+ (add (inverse (add (inverse (add ?2 ?3)) ?4))
+ (inverse
+ (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5)))))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
+22392: Goal:
+22392: Id : 1, {_}:
+ add (inverse (add (inverse a) b))
+ (inverse (add (inverse a) (inverse b)))
+ =>=
+ a
+ [] by huntinton_3
+22392: Order:
+22392: lpo
+22392: Leaf order:
+22392: b 2 0 2 2,1,1,2
+22392: a 3 0 3 1,1,1,1,2
+22392: inverse 12 1 5 0,1,2
+22392: add 9 2 3 0,2
+Statistics :
+Max weight : 70
+Found proof, 9.195802s
+% SZS status Unsatisfiable for BOO074-1.p
+% SZS output start CNFRefutation for BOO074-1.p
+Id : 3, {_}: inverse (add (inverse (add (inverse (add ?7 ?8)) ?9)) (inverse (add ?7 (inverse (add (inverse ?9) (inverse (add ?9 ?10))))))) =>= ?9 [10, 9, 8, 7] by dn1 ?7 ?8 ?9 ?10
+Id : 2, {_}: inverse (add (inverse (add (inverse (add ?2 ?3)) ?4)) (inverse (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) =>= ?4 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5
+Id : 15, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?74)) ?75)) ?74)) ?76)) (inverse ?74))) ?74) =>= inverse ?74 [76, 75, 74] by Super 3 with 2 at 2,1,2
+Id : 20, {_}: inverse (add (inverse (add ?104 (inverse ?104))) ?104) =>= inverse ?104 [104] by Super 15 with 2 at 1,1,1,1,2
+Id : 99, {_}: inverse (add (inverse ?355) (inverse (add ?355 (inverse (add (inverse ?355) (inverse (add ?355 ?356))))))) =>= ?355 [356, 355] by Super 2 with 20 at 1,1,2
+Id : 136, {_}: inverse (add (inverse (add (inverse (add ?450 ?451)) ?452)) (inverse (add ?450 ?452))) =>= ?452 [452, 451, 450] by Super 2 with 99 at 2,1,2,1,2
+Id : 536, {_}: inverse (add (inverse (add (inverse (add ?1808 ?1809)) ?1810)) (inverse (add ?1808 ?1810))) =>= ?1810 [1810, 1809, 1808] by Super 2 with 99 at 2,1,2,1,2
+Id : 550, {_}: inverse (add (inverse (add ?1882 ?1883)) (inverse (add (inverse ?1882) ?1883))) =>= ?1883 [1883, 1882] by Super 536 with 99 at 1,1,1,1,2
+Id : 724, {_}: inverse (add ?2517 (inverse (add ?2518 (inverse (add (inverse ?2518) ?2517))))) =>= inverse (add (inverse ?2518) ?2517) [2518, 2517] by Super 136 with 550 at 1,1,2
+Id : 1584, {_}: inverse (add (inverse ?4978) (inverse (add ?4978 (inverse (add (inverse ?4978) (inverse ?4978)))))) =>= ?4978 [4978] by Super 99 with 724 at 2,1,2,1,2
+Id : 1652, {_}: inverse (add (inverse ?4978) (inverse ?4978)) =>= ?4978 [4978] by Demod 1584 with 724 at 2
+Id : 763, {_}: inverse (add (inverse (add ?2736 ?2737)) (inverse (add (inverse ?2736) ?2737))) =>= ?2737 [2737, 2736] by Super 536 with 99 at 1,1,1,1,2
+Id : 144, {_}: inverse (add (inverse ?482) (inverse (add ?482 (inverse (add (inverse ?482) (inverse (add ?482 ?483))))))) =>= ?482 [483, 482] by Super 2 with 20 at 1,1,2
+Id : 155, {_}: inverse (add (inverse ?528) (inverse (add ?528 ?528))) =>= ?528 [528] by Super 144 with 99 at 2,1,2,1,2
+Id : 782, {_}: inverse (add (inverse (add ?2830 (inverse (add ?2830 ?2830)))) ?2830) =>= inverse (add ?2830 ?2830) [2830] by Super 763 with 155 at 2,1,2
+Id : 871, {_}: inverse (add (inverse (add ?3076 ?3076)) (inverse (add ?3076 ?3076))) =>= ?3076 [3076] by Super 136 with 782 at 1,1,2
+Id : 1724, {_}: add ?3076 ?3076 =>= ?3076 [3076] by Demod 871 with 1652 at 2
+Id : 1754, {_}: inverse (inverse ?5284) =>= ?5284 [5284] by Demod 1652 with 1724 at 1,2
+Id : 1762, {_}: inverse (inverse (add (inverse ?5317) ?5318)) =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Super 1754 with 724 at 1,2
+Id : 1733, {_}: inverse (inverse ?4978) =>= ?4978 [4978] by Demod 1652 with 1724 at 1,2
+Id : 1785, {_}: add (inverse ?5317) ?5318 =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Demod 1762 with 1733 at 2
+Id : 6, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?26)) ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Super 3 with 2 at 2,1,2
+Id : 1734, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add ?26 ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Demod 6 with 1733 at 1,1,1,1,1,1,1,1,1,1,2
+Id : 921, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse (add ?3102 ?3102))))) =>= inverse (add ?3102 ?3102) [3102] by Super 136 with 871 at 1,1,2
+Id : 1725, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse (add ?3102 ?3102) [3102] by Demod 921 with 1724 at 1,2,1,2,1,2
+Id : 1726, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse ?3102 [3102] by Demod 1725 with 1724 at 1,3
+Id : 1763, {_}: inverse (inverse ?5320) =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Super 1754 with 1726 at 1,2
+Id : 1786, {_}: ?5320 =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Demod 1763 with 1733 at 2
+Id : 2715, {_}: inverse (add (inverse (add (inverse ?7389) (inverse (inverse ?7389)))) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Super 724 with 1786 at 1,2,1,2,1,2
+Id : 2755, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2715 with 1733 at 2,1,1,1,2
+Id : 2756, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =?= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2755 with 1733 at 2,1,2,1,2
+Id : 2757, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =>= inverse (inverse ?7389) [7389] by Demod 2756 with 1786 at 1,3
+Id : 2758, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= inverse (inverse ?7389) [7389] by Demod 2757 with 1724 at 1,2,1,2
+Id : 2759, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= ?7389 [7389] by Demod 2758 with 1733 at 3
+Id : 2920, {_}: inverse ?7714 =<= add (inverse (add (inverse ?7714) ?7714)) (inverse ?7714) [7714] by Super 1733 with 2759 at 1,2
+Id : 3142, {_}: inverse (add (inverse (add (inverse (add (inverse (inverse ?8118)) ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Super 1734 with 2920 at 1,1,1,1,1,1,1,2
+Id : 3172, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3142 with 1733 at 1,1,1,1,1,1,2
+Id : 3173, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) ?8118)) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3172 with 1733 at 2,1,1,1,2
+Id : 8100, {_}: inverse (add (inverse (add (inverse (add ?15581 ?15582)) ?15581)) (inverse ?15581)) =>= ?15581 [15582, 15581] by Demod 3173 with 1733 at 3
+Id : 8144, {_}: inverse (add ?15759 (inverse (inverse (add ?15760 ?15759)))) =>= inverse (add ?15760 ?15759) [15760, 15759] by Super 8100 with 136 at 1,1,2
+Id : 8365, {_}: inverse (add ?15759 (add ?15760 ?15759)) =>= inverse (add ?15760 ?15759) [15760, 15759] by Demod 8144 with 1733 at 2,1,2
+Id : 8391, {_}: inverse (inverse (add ?15887 ?15888)) =<= add ?15888 (add ?15887 ?15888) [15888, 15887] by Super 1733 with 8365 at 1,2
+Id : 8543, {_}: add ?15887 ?15888 =<= add ?15888 (add ?15887 ?15888) [15888, 15887] by Demod 8391 with 1733 at 2
+Id : 12, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Super 2 with 6 at 2,1,2
+Id : 3710, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 12 with 1733 at 1,1,1,1,1,1,1,1,1,1,1,1,1,1,2
+Id : 3711, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3710 with 1733 at 2,1,1,1,1,1,1,1,2
+Id : 3712, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (add (inverse ?57) (inverse (add ?57 ?58)))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3711 with 1733 at 2,1,2
+Id : 8459, {_}: inverse (add ?16264 (add ?16265 ?16264)) =>= inverse (add ?16265 ?16264) [16265, 16264] by Demod 8144 with 1733 at 2,1,2
+Id : 1749, {_}: inverse (add (inverse (add (inverse ?5262) ?5263)) (inverse (add ?5262 ?5263))) =>= ?5263 [5263, 5262] by Super 550 with 1733 at 1,1,2,1,2
+Id : 5602, {_}: inverse ?11750 =<= add (inverse (add (inverse ?11751) ?11750)) (inverse (add ?11751 ?11750)) [11751, 11750] by Super 1733 with 1749 at 1,2
+Id : 8468, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =<= inverse (add (inverse (add (inverse ?16285) ?16286)) (inverse (add ?16285 ?16286))) [16286, 16285] by Super 8459 with 5602 at 2,1,2
+Id : 8598, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= inverse (inverse ?16286) [16286, 16285] by Demod 8468 with 5602 at 1,3
+Id : 8599, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= ?16286 [16286, 16285] by Demod 8598 with 1733 at 3
+Id : 8791, {_}: inverse ?16774 =<= add (inverse (add ?16775 ?16774)) (inverse ?16774) [16775, 16774] by Super 1733 with 8599 at 1,2
+Id : 10590, {_}: inverse (add (inverse (inverse ?20667)) (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Super 3712 with 8791 at 1,1,1,2
+Id : 10753, {_}: inverse (add ?20667 (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10590 with 1733 at 1,1,2
+Id : 10754, {_}: inverse (add ?20667 (add ?20667 (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10753 with 1733 at 1,2,1,2
+Id : 15430, {_}: inverse (inverse ?28103) =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Super 1733 with 10754 at 1,2
+Id : 15735, {_}: ?28103 =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Demod 15430 with 1733 at 2
+Id : 15853, {_}: add ?28715 (add ?28715 (inverse (add (inverse ?28715) ?28716))) =?= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Super 8543 with 15735 at 2,3
+Id : 16108, {_}: ?28715 =<= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Demod 15853 with 15735 at 2
+Id : 10568, {_}: inverse (add (inverse (inverse ?20566)) (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Super 136 with 8791 at 1,1,1,2
+Id : 10805, {_}: inverse (add ?20566 (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Demod 10568 with 1733 at 1,1,2
+Id : 11153, {_}: inverse (inverse ?21486) =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Super 1733 with 10805 at 1,2
+Id : 11260, {_}: ?21486 =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Demod 11153 with 1733 at 2
+Id : 11176, {_}: inverse (add ?21600 (inverse (add ?21601 (inverse ?21600)))) =>= inverse ?21600 [21601, 21600] by Demod 10568 with 1733 at 1,1,2
+Id : 11183, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= inverse (inverse ?21642) [21643, 21642] by Super 11176 with 1733 at 2,1,2,1,2
+Id : 11564, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= ?21642 [21643, 21642] by Demod 11183 with 1733 at 3
+Id : 13294, {_}: inverse ?24726 =<= add (inverse ?24726) (inverse (add ?24727 ?24726)) [24727, 24726] by Super 1733 with 11564 at 1,2
+Id : 13313, {_}: inverse (add (inverse ?24792) (inverse (add ?24792 ?24793))) =<= add (inverse (add (inverse ?24792) (inverse (add ?24792 ?24793)))) ?24792 [24793, 24792] by Super 13294 with 3712 at 2,3
+Id : 16466, {_}: add (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) ?29660 =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Super 1785 with 13313 at 1,2,1,2,3
+Id : 16829, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Demod 16466 with 13313 at 2
+Id : 16830, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (add (inverse ?29660) (inverse (add ?29660 ?29661))))) [29661, 29660] by Demod 16829 with 1733 at 2,1,2,3
+Id : 16831, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) [29661, 29660] by Demod 16830 with 1724 at 1,2,3
+Id : 17624, {_}: ?31105 =<= add ?31105 (inverse (add (inverse ?31105) (inverse (add ?31105 ?31106)))) [31106, 31105] by Super 15735 with 16831 at 2,3
+Id : 17680, {_}: ?31105 =<= inverse (add (inverse ?31105) (inverse (add ?31105 ?31106))) [31106, 31105] by Demod 17624 with 16831 at 3
+Id : 18257, {_}: add ?31431 ?31432 =<= add (add ?31431 ?31432) ?31431 [31432, 31431] by Super 11260 with 17680 at 2,3
+Id : 18478, {_}: ?28715 =<= add ?28715 (inverse (add (inverse ?28715) ?28716)) [28716, 28715] by Demod 16108 with 18257 at 3
+Id : 18480, {_}: add (inverse ?5317) ?5318 =?= add ?5318 (inverse ?5317) [5318, 5317] by Demod 1785 with 18478 at 1,2,3
+Id : 1761, {_}: inverse ?5314 =<= add (inverse (add ?5315 ?5314)) (inverse (add (inverse ?5315) ?5314)) [5315, 5314] by Super 1754 with 550 at 1,2
+Id : 18617, {_}: a === a [] by Demod 18616 with 1733 at 2
+Id : 18616, {_}: inverse (inverse a) =>= a [] by Demod 18615 with 1761 at 2
+Id : 18615, {_}: add (inverse (add b (inverse a))) (inverse (add (inverse b) (inverse a))) =>= a [] by Demod 18614 with 18480 at 1,2,2
+Id : 18614, {_}: add (inverse (add b (inverse a))) (inverse (add (inverse a) (inverse b))) =>= a [] by Demod 1 with 18480 at 1,1,2
+Id : 1, {_}: add (inverse (add (inverse a) b)) (inverse (add (inverse a) (inverse b))) =>= a [] by huntinton_3
+% SZS output end CNFRefutation for BOO074-1.p
+22390: solved BOO074-1.p in 9.212575 using nrkbo
+22390: status Unsatisfiable for BOO074-1.p
+NO CLASH, using fixed ground order
+22397: Facts:
+22397: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+22397: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+22397: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b))
+ [] by strong_fixed_point
+22397: Goal:
+22397: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+22397: Order:
+22397: nrkbo
+22397: Leaf order:
+22397: strong_fixed_point 3 0 2 1,2
+22397: fixed_pt 3 0 3 2,2
+22397: w 4 0 0
+22397: b 6 0 0
+22397: apply 19 2 3 0,2
+NO CLASH, using fixed ground order
+22398: Facts:
+22398: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+22398: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+22398: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b))
+ [] by strong_fixed_point
+22398: Goal:
+22398: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+22398: Order:
+22398: kbo
+22398: Leaf order:
+22398: strong_fixed_point 3 0 2 1,2
+22398: fixed_pt 3 0 3 2,2
+22398: w 4 0 0
+22398: b 6 0 0
+22398: apply 19 2 3 0,2
+NO CLASH, using fixed ground order
+22399: Facts:
+22399: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+22399: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+22399: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b))
+ [] by strong_fixed_point
+22399: Goal:
+22399: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+22399: Order:
+22399: lpo
+22399: Leaf order:
+22399: strong_fixed_point 3 0 2 1,2
+22399: fixed_pt 3 0 3 2,2
+22399: w 4 0 0
+22399: b 6 0 0
+22399: apply 19 2 3 0,2
+% SZS status Timeout for COL003-12.p
+NO CLASH, using fixed ground order
+22420: Facts:
+22420: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+22420: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+22420: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply (apply b (apply (apply b (apply w w)) (apply b w))) b)) b
+ [] by strong_fixed_point
+22420: Goal:
+22420: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+22420: Order:
+22420: nrkbo
+22420: Leaf order:
+22420: strong_fixed_point 3 0 2 1,2
+22420: fixed_pt 3 0 3 2,2
+22420: w 4 0 0
+22420: b 7 0 0
+22420: apply 20 2 3 0,2
+NO CLASH, using fixed ground order
+22421: Facts:
+22421: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+22421: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+22421: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply (apply b (apply (apply b (apply w w)) (apply b w))) b)) b
+ [] by strong_fixed_point
+22421: Goal:
+22421: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+22421: Order:
+22421: kbo
+22421: Leaf order:
+22421: strong_fixed_point 3 0 2 1,2
+22421: fixed_pt 3 0 3 2,2
+22421: w 4 0 0
+22421: b 7 0 0
+22421: apply 20 2 3 0,2
+NO CLASH, using fixed ground order
+22422: Facts:
+22422: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+22422: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+22422: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply (apply b (apply (apply b (apply w w)) (apply b w))) b)) b
+ [] by strong_fixed_point
+22422: Goal:
+22422: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+22422: Order:
+22422: lpo
+22422: Leaf order:
+22422: strong_fixed_point 3 0 2 1,2
+22422: fixed_pt 3 0 3 2,2
+22422: w 4 0 0
+22422: b 7 0 0
+22422: apply 20 2 3 0,2
+% SZS status Timeout for COL003-17.p
+NO CLASH, using fixed ground order
+22445: Facts:
+22445: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+22445: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+22445: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply (apply b (apply (apply b (apply w w)) (apply b w)))
+ (apply (apply b b) b)
+ [] by strong_fixed_point
+22445: Goal:
+22445: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+22445: Order:
+22445: nrkbo
+22445: Leaf order:
+22445: strong_fixed_point 3 0 2 1,2
+22445: fixed_pt 3 0 3 2,2
+22445: w 4 0 0
+22445: b 7 0 0
+22445: apply 20 2 3 0,2
+NO CLASH, using fixed ground order
+22446: Facts:
+22446: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+22446: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+22446: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply (apply b (apply (apply b (apply w w)) (apply b w)))
+ (apply (apply b b) b)
+ [] by strong_fixed_point
+22446: Goal:
+22446: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+22446: Order:
+22446: kbo
+22446: Leaf order:
+22446: strong_fixed_point 3 0 2 1,2
+22446: fixed_pt 3 0 3 2,2
+22446: w 4 0 0
+22446: b 7 0 0
+22446: apply 20 2 3 0,2
+NO CLASH, using fixed ground order
+22447: Facts:
+22447: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+22447: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+22447: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply (apply b (apply (apply b (apply w w)) (apply b w)))
+ (apply (apply b b) b)
+ [] by strong_fixed_point
+22447: Goal:
+22447: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+22447: Order:
+22447: lpo
+22447: Leaf order:
+22447: strong_fixed_point 3 0 2 1,2
+22447: fixed_pt 3 0 3 2,2
+22447: w 4 0 0
+22447: b 7 0 0
+22447: apply 20 2 3 0,2
+% SZS status Timeout for COL003-18.p
+NO CLASH, using fixed ground order
+22471: Facts:
+22471: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+22471: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+22471: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply (apply b (apply w w)) (apply (apply b (apply b w)) b))) b
+ [] by strong_fixed_point
+22471: Goal:
+22471: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+22471: Order:
+22471: nrkbo
+22471: Leaf order:
+22471: strong_fixed_point 3 0 2 1,2
+22471: fixed_pt 3 0 3 2,2
+22471: w 4 0 0
+22471: b 7 0 0
+22471: apply 20 2 3 0,2
+NO CLASH, using fixed ground order
+22472: Facts:
+22472: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+22472: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+22472: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply (apply b (apply w w)) (apply (apply b (apply b w)) b))) b
+ [] by strong_fixed_point
+22472: Goal:
+22472: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+22472: Order:
+22472: kbo
+22472: Leaf order:
+22472: strong_fixed_point 3 0 2 1,2
+22472: fixed_pt 3 0 3 2,2
+22472: w 4 0 0
+22472: b 7 0 0
+22472: apply 20 2 3 0,2
+NO CLASH, using fixed ground order
+22473: Facts:
+22473: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+22473: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+22473: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply (apply b (apply w w)) (apply (apply b (apply b w)) b))) b
+ [] by strong_fixed_point
+22473: Goal:
+22473: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+22473: Order:
+22473: lpo
+22473: Leaf order:
+22473: strong_fixed_point 3 0 2 1,2
+22473: fixed_pt 3 0 3 2,2
+22473: w 4 0 0
+22473: b 7 0 0
+22473: apply 20 2 3 0,2
+% SZS status Timeout for COL003-19.p
+CLASH, statistics insufficient
+22495: Facts:
+22495: Id : 2, {_}:
+ apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4)
+ [4, 3] by o_definition ?3 ?4
+22495: Id : 3, {_}:
+ apply (apply (apply q1 ?6) ?7) ?8 =>= apply ?6 (apply ?8 ?7)
+ [8, 7, 6] by q1_definition ?6 ?7 ?8
+22495: Goal:
+22495: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
+22495: Order:
+22495: nrkbo
+22495: Leaf order:
+22495: o 1 0 0
+22495: q1 1 0 0
+22495: combinator 1 0 1 1,3
+22495: apply 10 2 1 0,3
+CLASH, statistics insufficient
+22496: Facts:
+22496: Id : 2, {_}:
+ apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4)
+ [4, 3] by o_definition ?3 ?4
+22496: Id : 3, {_}:
+ apply (apply (apply q1 ?6) ?7) ?8 =>= apply ?6 (apply ?8 ?7)
+ [8, 7, 6] by q1_definition ?6 ?7 ?8
+22496: Goal:
+22496: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
+22496: Order:
+22496: kbo
+22496: Leaf order:
+22496: o 1 0 0
+22496: q1 1 0 0
+22496: combinator 1 0 1 1,3
+22496: apply 10 2 1 0,3
+CLASH, statistics insufficient
+22497: Facts:
+22497: Id : 2, {_}:
+ apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4)
+ [4, 3] by o_definition ?3 ?4
+22497: Id : 3, {_}:
+ apply (apply (apply q1 ?6) ?7) ?8 =?= apply ?6 (apply ?8 ?7)
+ [8, 7, 6] by q1_definition ?6 ?7 ?8
+22497: Goal:
+22497: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
+22497: Order:
+22497: lpo
+22497: Leaf order:
+22497: o 1 0 0
+22497: q1 1 0 0
+22497: combinator 1 0 1 1,3
+22497: apply 10 2 1 0,3
+% SZS status Timeout for COL011-1.p
+CLASH, statistics insufficient
+22518: Facts:
+22518: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+22518: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
+22518: Id : 4, {_}:
+ apply (apply t ?9) ?10 =>= apply ?10 ?9
+ [10, 9] by t_definition ?9 ?10
+22518: Goal:
+22518: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+22518: Order:
+22518: nrkbo
+22518: Leaf order:
+22518: b 1 0 0
+22518: m 1 0 0
+22518: t 1 0 0
+22518: f 3 1 3 0,2,2
+22518: apply 13 2 3 0,2
+CLASH, statistics insufficient
+22519: Facts:
+22519: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+22519: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
+22519: Id : 4, {_}:
+ apply (apply t ?9) ?10 =>= apply ?10 ?9
+ [10, 9] by t_definition ?9 ?10
+22519: Goal:
+22519: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+22519: Order:
+22519: kbo
+22519: Leaf order:
+22519: b 1 0 0
+22519: m 1 0 0
+22519: t 1 0 0
+22519: f 3 1 3 0,2,2
+22519: apply 13 2 3 0,2
+CLASH, statistics insufficient
+22520: Facts:
+22520: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+22520: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
+22520: Id : 4, {_}:
+ apply (apply t ?9) ?10 =?= apply ?10 ?9
+ [10, 9] by t_definition ?9 ?10
+22520: Goal:
+22520: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+22520: Order:
+22520: lpo
+22520: Leaf order:
+22520: b 1 0 0
+22520: m 1 0 0
+22520: t 1 0 0
+22520: f 3 1 3 0,2,2
+22520: apply 13 2 3 0,2
+Goal subsumed
+Statistics :
+Max weight : 62
+Found proof, 0.520019s
+% SZS status Unsatisfiable for COL034-1.p
+% SZS output start CNFRefutation for COL034-1.p
+Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
+Id : 4, {_}: apply (apply t ?9) ?10 =>= apply ?10 ?9 [10, 9] by t_definition ?9 ?10
+Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
+Id : 11, {_}: apply m (apply (apply b ?29) ?30) =<= apply ?29 (apply ?30 (apply (apply b ?29) ?30)) [30, 29] by Super 2 with 3 at 2
+Id : 2545, {_}: apply (f (apply (apply b m) (apply (apply b (apply t m)) b))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply b (apply t m)) b)))) m)) === apply (f (apply (apply b m) (apply (apply b (apply t m)) b))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply b (apply t m)) b)))) m)) [] by Super 2544 with 11 at 2
+Id : 2544, {_}: apply ?1974 (apply (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976)))) ?1975) =<= apply (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976))) (apply ?1974 (apply (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976)))) ?1975)) [1975, 1976, 1974] by Demod 2294 with 4 at 2,2
+Id : 2294, {_}: apply ?1974 (apply (apply t ?1975) (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976))))) =<= apply (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976))) (apply ?1974 (apply (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976)))) ?1975)) [1976, 1975, 1974] by Super 53 with 4 at 2,2,3
+Id : 53, {_}: apply ?78 (apply ?79 (apply ?80 (f (apply (apply b ?78) (apply (apply b ?79) ?80))))) =<= apply (f (apply (apply b ?78) (apply (apply b ?79) ?80))) (apply ?78 (apply ?79 (apply ?80 (f (apply (apply b ?78) (apply (apply b ?79) ?80)))))) [80, 79, 78] by Demod 39 with 2 at 2,2
+Id : 39, {_}: apply ?78 (apply (apply (apply b ?79) ?80) (f (apply (apply b ?78) (apply (apply b ?79) ?80)))) =<= apply (f (apply (apply b ?78) (apply (apply b ?79) ?80))) (apply ?78 (apply ?79 (apply ?80 (f (apply (apply b ?78) (apply (apply b ?79) ?80)))))) [80, 79, 78] by Super 8 with 2 at 2,2,3
+Id : 8, {_}: apply ?20 (apply ?21 (f (apply (apply b ?20) ?21))) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Demod 7 with 2 at 2
+Id : 7, {_}: apply (apply (apply b ?20) ?21) (f (apply (apply b ?20) ?21)) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Super 1 with 2 at 2,3
+Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1
+% SZS output end CNFRefutation for COL034-1.p
+22518: solved COL034-1.p in 0.528032 using nrkbo
+22518: status Unsatisfiable for COL034-1.p
+CLASH, statistics insufficient
+22525: Facts:
+22525: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+22525: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+22525: Id : 4, {_}:
+ apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
+ [13, 12, 11] by c_definition ?11 ?12 ?13
+22525: Goal:
+22525: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+22525: Order:
+22525: nrkbo
+22525: Leaf order:
+22525: s 1 0 0
+22525: b 1 0 0
+22525: c 1 0 0
+22525: f 3 1 3 0,2,2
+22525: apply 19 2 3 0,2
+CLASH, statistics insufficient
+22526: Facts:
+22526: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+22526: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+22526: Id : 4, {_}:
+ apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
+ [13, 12, 11] by c_definition ?11 ?12 ?13
+22526: Goal:
+22526: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+22526: Order:
+22526: kbo
+22526: Leaf order:
+22526: s 1 0 0
+22526: b 1 0 0
+22526: c 1 0 0
+22526: f 3 1 3 0,2,2
+22526: apply 19 2 3 0,2
+CLASH, statistics insufficient
+22527: Facts:
+22527: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+22527: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+22527: Id : 4, {_}:
+ apply (apply (apply c ?11) ?12) ?13 =?= apply (apply ?11 ?13) ?12
+ [13, 12, 11] by c_definition ?11 ?12 ?13
+22527: Goal:
+22527: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+22527: Order:
+22527: lpo
+22527: Leaf order:
+22527: s 1 0 0
+22527: b 1 0 0
+22527: c 1 0 0
+22527: f 3 1 3 0,2,2
+22527: apply 19 2 3 0,2
+% SZS status Timeout for COL037-1.p
+CLASH, statistics insufficient
+22551: Facts:
+22551: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+22551: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
+22551: Id : 4, {_}:
+ apply (apply (apply c ?9) ?10) ?11 =>= apply (apply ?9 ?11) ?10
+ [11, 10, 9] by c_definition ?9 ?10 ?11
+22551: Goal:
+22551: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+22551: Order:
+22551: nrkbo
+22551: Leaf order:
+22551: b 1 0 0
+22551: m 1 0 0
+22551: c 1 0 0
+22551: f 3 1 3 0,2,2
+22551: apply 15 2 3 0,2
+CLASH, statistics insufficient
+22552: Facts:
+22552: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+22552: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
+22552: Id : 4, {_}:
+ apply (apply (apply c ?9) ?10) ?11 =>= apply (apply ?9 ?11) ?10
+ [11, 10, 9] by c_definition ?9 ?10 ?11
+22552: Goal:
+22552: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+22552: Order:
+22552: kbo
+22552: Leaf order:
+22552: b 1 0 0
+22552: m 1 0 0
+22552: c 1 0 0
+22552: f 3 1 3 0,2,2
+22552: apply 15 2 3 0,2
+CLASH, statistics insufficient
+22553: Facts:
+22553: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+22553: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
+22553: Id : 4, {_}:
+ apply (apply (apply c ?9) ?10) ?11 =?= apply (apply ?9 ?11) ?10
+ [11, 10, 9] by c_definition ?9 ?10 ?11
+22553: Goal:
+22553: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+22553: Order:
+22553: lpo
+22553: Leaf order:
+22553: b 1 0 0
+22553: m 1 0 0
+22553: c 1 0 0
+22553: f 3 1 3 0,2,2
+22553: apply 15 2 3 0,2
+Goal subsumed
+Statistics :
+Max weight : 54
+Found proof, 1.136025s
+% SZS status Unsatisfiable for COL041-1.p
+% SZS output start CNFRefutation for COL041-1.p
+Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
+Id : 4, {_}: apply (apply (apply c ?9) ?10) ?11 =>= apply (apply ?9 ?11) ?10 [11, 10, 9] by c_definition ?9 ?10 ?11
+Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
+Id : 11, {_}: apply m (apply (apply b ?30) ?31) =<= apply ?30 (apply ?31 (apply (apply b ?30) ?31)) [31, 30] by Super 2 with 3 at 2
+Id : 4380, {_}: apply (f (apply (apply b m) (apply (apply c b) m))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply c b) m)))) m)) === apply (f (apply (apply b m) (apply (apply c b) m))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply c b) m)))) m)) [] by Super 53 with 11 at 2
+Id : 53, {_}: apply ?91 (apply (apply ?92 (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) ?93) =<= apply (f (apply (apply b ?91) (apply (apply c ?92) ?93))) (apply ?91 (apply (apply ?92 (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) ?93)) [93, 92, 91] by Demod 39 with 4 at 2,2
+Id : 39, {_}: apply ?91 (apply (apply (apply c ?92) ?93) (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) =<= apply (f (apply (apply b ?91) (apply (apply c ?92) ?93))) (apply ?91 (apply (apply ?92 (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) ?93)) [93, 92, 91] by Super 8 with 4 at 2,2,3
+Id : 8, {_}: apply ?21 (apply ?22 (f (apply (apply b ?21) ?22))) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Demod 7 with 2 at 2
+Id : 7, {_}: apply (apply (apply b ?21) ?22) (f (apply (apply b ?21) ?22)) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Super 1 with 2 at 2,3
+Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1
+% SZS output end CNFRefutation for COL041-1.p
+22551: solved COL041-1.p in 1.14407 using nrkbo
+22551: status Unsatisfiable for COL041-1.p
+CLASH, statistics insufficient
+22558: Facts:
+22558: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+22558: Id : 3, {_}:
+ apply (apply (apply n ?7) ?8) ?9
+ =?=
+ apply (apply (apply ?7 ?9) ?8) ?9
+ [9, 8, 7] by n_definition ?7 ?8 ?9
+22558: Goal:
+22558: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+22558: Order:
+22558: nrkbo
+22558: Leaf order:
+22558: b 1 0 0
+22558: n 1 0 0
+22558: f 3 1 3 0,2,2
+22558: apply 14 2 3 0,2
+CLASH, statistics insufficient
+22559: Facts:
+22559: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+22559: Id : 3, {_}:
+ apply (apply (apply n ?7) ?8) ?9
+ =?=
+ apply (apply (apply ?7 ?9) ?8) ?9
+ [9, 8, 7] by n_definition ?7 ?8 ?9
+22559: Goal:
+22559: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+22559: Order:
+22559: kbo
+22559: Leaf order:
+22559: b 1 0 0
+22559: n 1 0 0
+22559: f 3 1 3 0,2,2
+22559: apply 14 2 3 0,2
+CLASH, statistics insufficient
+22560: Facts:
+22560: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+22560: Id : 3, {_}:
+ apply (apply (apply n ?7) ?8) ?9
+ =?=
+ apply (apply (apply ?7 ?9) ?8) ?9
+ [9, 8, 7] by n_definition ?7 ?8 ?9
+22560: Goal:
+22560: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+22560: Order:
+22560: lpo
+22560: Leaf order:
+22560: b 1 0 0
+22560: n 1 0 0
+22560: f 3 1 3 0,2,2
+22560: apply 14 2 3 0,2
+Goal subsumed
+Statistics :
+Max weight : 88
+Found proof, 25.425976s
+% SZS status Unsatisfiable for COL044-1.p
+% SZS output start CNFRefutation for COL044-1.p
+Id : 4, {_}: apply (apply (apply b ?11) ?12) ?13 =>= apply ?11 (apply ?12 ?13) [13, 12, 11] by b_definition ?11 ?12 ?13
+Id : 3, {_}: apply (apply (apply n ?7) ?8) ?9 =?= apply (apply (apply ?7 ?9) ?8) ?9 [9, 8, 7] by n_definition ?7 ?8 ?9
+Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
+Id : 8, {_}: apply (apply (apply n b) ?22) ?23 =?= apply ?23 (apply ?22 ?23) [23, 22] by Super 2 with 3 at 2
+Id : 5, {_}: apply ?15 (apply ?16 ?17) =?= apply ?15 (apply ?16 ?17) [17, 16, 15] by Super 4 with 2 at 2
+Id : 83, {_}: apply (apply (apply (apply n b) ?260) (apply b ?261)) ?262 =?= apply ?261 (apply (apply ?260 (apply b ?261)) ?262) [262, 261, 260] by Super 2 with 8 at 1,2
+Id : 24939, {_}: apply (apply (apply n b) (apply (apply (apply n (apply n b)) (apply b (apply n b))) (apply n (apply n b)))) (f (apply (apply (apply (apply n b) (apply n (apply n b))) (apply b (apply n b))) (apply n (apply n b)))) =?= apply (apply (apply n b) (apply (apply (apply n (apply n b)) (apply b (apply n b))) (apply n (apply n b)))) (f (apply (apply (apply (apply n b) (apply n (apply n b))) (apply b (apply n b))) (apply n (apply n b)))) [] by Super 24245 with 83 at 1,2
+Id : 24245, {_}: apply (apply (apply (apply ?35313 ?35314) ?35315) ?35314) (f (apply (apply (apply ?35313 ?35314) ?35315) ?35314)) =?= apply (apply (apply n b) (apply (apply (apply n ?35313) ?35315) ?35314)) (f (apply (apply (apply ?35313 ?35314) ?35315) ?35314)) [35315, 35314, 35313] by Super 153 with 3 at 2,1,3
+Id : 153, {_}: apply (apply ?460 ?461) (f (apply ?460 ?461)) =<= apply (apply (apply n b) (apply ?460 ?461)) (f (apply ?460 ?461)) [461, 460] by Super 115 with 5 at 1,3
+Id : 115, {_}: apply ?375 (f ?375) =<= apply (apply (apply n b) ?375) (f ?375) [375] by Super 1 with 8 at 3
+Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1
+% SZS output end CNFRefutation for COL044-1.p
+22559: solved COL044-1.p in 12.720795 using kbo
+22559: status Unsatisfiable for COL044-1.p
+CLASH, statistics insufficient
+22570: Facts:
+22570: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+CLASH, statistics insufficient
+22571: Facts:
+22571: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+22571: Id : 3, {_}:
+ apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
+ [8, 7] by w_definition ?7 ?8
+22571: Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
+22571: Goal:
+22571: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_strong_fixed_point ?1
+22571: Order:
+22571: kbo
+22571: Leaf order:
+22571: b 1 0 0
+22571: w 1 0 0
+22571: m 1 0 0
+22571: f 3 1 3 0,2,2
+22571: apply 14 2 3 0,2
+CLASH, statistics insufficient
+22572: Facts:
+22572: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+22572: Id : 3, {_}:
+ apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
+ [8, 7] by w_definition ?7 ?8
+22572: Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
+22572: Goal:
+22572: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_strong_fixed_point ?1
+22572: Order:
+22572: lpo
+22572: Leaf order:
+22572: b 1 0 0
+22572: w 1 0 0
+22572: m 1 0 0
+22572: f 3 1 3 0,2,2
+22572: apply 14 2 3 0,2
+22570: Id : 3, {_}:
+ apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
+ [8, 7] by w_definition ?7 ?8
+22570: Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
+22570: Goal:
+22570: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_strong_fixed_point ?1
+22570: Order:
+22570: nrkbo
+22570: Leaf order:
+22570: b 1 0 0
+22570: w 1 0 0
+22570: m 1 0 0
+22570: f 3 1 3 0,2,2
+22570: apply 14 2 3 0,2
+Goal subsumed
+Statistics :
+Max weight : 54
+Found proof, 12.496351s
+% SZS status Unsatisfiable for COL049-1.p
+% SZS output start CNFRefutation for COL049-1.p
+Id : 3, {_}: apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 [8, 7] by w_definition ?7 ?8
+Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10
+Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
+Id : 226, {_}: apply (apply w (apply b ?378)) ?379 =?= apply ?378 (apply ?379 ?379) [379, 378] by Super 2 with 3 at 2
+Id : 231, {_}: apply (apply w (apply b ?393)) ?394 =>= apply ?393 (apply m ?394) [394, 393] by Super 226 with 4 at 2,3
+Id : 289, {_}: apply m (apply w (apply b ?503)) =<= apply ?503 (apply m (apply w (apply b ?503))) [503] by Super 4 with 231 at 3
+Id : 15983, {_}: apply (f (apply (apply b m) (apply (apply b w) b))) (apply m (apply w (apply b (f (apply (apply b m) (apply (apply b w) b)))))) === apply (f (apply (apply b m) (apply (apply b w) b))) (apply m (apply w (apply b (f (apply (apply b m) (apply (apply b w) b)))))) [] by Super 72 with 289 at 2
+Id : 72, {_}: apply ?123 (apply ?124 (apply ?125 (f (apply (apply b ?123) (apply (apply b ?124) ?125))))) =<= apply (f (apply (apply b ?123) (apply (apply b ?124) ?125))) (apply ?123 (apply ?124 (apply ?125 (f (apply (apply b ?123) (apply (apply b ?124) ?125)))))) [125, 124, 123] by Demod 59 with 2 at 2,2
+Id : 59, {_}: apply ?123 (apply (apply (apply b ?124) ?125) (f (apply (apply b ?123) (apply (apply b ?124) ?125)))) =<= apply (f (apply (apply b ?123) (apply (apply b ?124) ?125))) (apply ?123 (apply ?124 (apply ?125 (f (apply (apply b ?123) (apply (apply b ?124) ?125)))))) [125, 124, 123] by Super 8 with 2 at 2,2,3
+Id : 8, {_}: apply ?20 (apply ?21 (f (apply (apply b ?20) ?21))) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Demod 7 with 2 at 2
+Id : 7, {_}: apply (apply (apply b ?20) ?21) (f (apply (apply b ?20) ?21)) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Super 1 with 2 at 2,3
+Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_strong_fixed_point ?1
+% SZS output end CNFRefutation for COL049-1.p
+22570: solved COL049-1.p in 6.296392 using nrkbo
+22570: status Unsatisfiable for COL049-1.p
+CLASH, statistics insufficient
+22586: Facts:
+22586: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+22586: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+22586: Id : 4, {_}:
+ apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
+ [13, 12, 11] by c_definition ?11 ?12 ?13
+22586: Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
+22586: Goal:
+22586: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_strong_fixed_point ?1
+22586: Order:
+22586: nrkbo
+22586: Leaf order:
+22586: s 1 0 0
+22586: b 1 0 0
+22586: c 1 0 0
+22586: i 1 0 0
+22586: f 3 1 3 0,2,2
+22586: apply 20 2 3 0,2
+CLASH, statistics insufficient
+22587: Facts:
+22587: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+22587: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+22587: Id : 4, {_}:
+ apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12
+ [13, 12, 11] by c_definition ?11 ?12 ?13
+22587: Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
+22587: Goal:
+22587: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_strong_fixed_point ?1
+22587: Order:
+22587: kbo
+22587: Leaf order:
+22587: s 1 0 0
+22587: b 1 0 0
+22587: c 1 0 0
+22587: i 1 0 0
+22587: f 3 1 3 0,2,2
+22587: apply 20 2 3 0,2
+CLASH, statistics insufficient
+22588: Facts:
+22588: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+22588: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+22588: Id : 4, {_}:
+ apply (apply (apply c ?11) ?12) ?13 =?= apply (apply ?11 ?13) ?12
+ [13, 12, 11] by c_definition ?11 ?12 ?13
+22588: Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
+22588: Goal:
+22588: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_strong_fixed_point ?1
+22588: Order:
+22588: lpo
+22588: Leaf order:
+22588: s 1 0 0
+22588: b 1 0 0
+22588: c 1 0 0
+22588: i 1 0 0
+22588: f 3 1 3 0,2,2
+22588: apply 20 2 3 0,2
+Goal subsumed
+Statistics :
+Max weight : 84
+Found proof, 2.121776s
+% SZS status Unsatisfiable for COL057-1.p
+% SZS output start CNFRefutation for COL057-1.p
+Id : 3, {_}: apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) [9, 8, 7] by b_definition ?7 ?8 ?9
+Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15
+Id : 2, {_}: apply (apply (apply s ?3) ?4) ?5 =?= apply (apply ?3 ?5) (apply ?4 ?5) [5, 4, 3] by s_definition ?3 ?4 ?5
+Id : 37, {_}: apply (apply (apply s i) ?141) ?142 =?= apply ?142 (apply ?141 ?142) [142, 141] by Super 2 with 5 at 1,3
+Id : 16, {_}: apply (apply (apply s (apply b ?64)) ?65) ?66 =?= apply ?64 (apply ?66 (apply ?65 ?66)) [66, 65, 64] by Super 2 with 3 at 3
+Id : 9068, {_}: apply (apply (apply (apply s (apply b (apply s i))) i) (apply (apply s (apply b (apply s i))) i)) (f (apply (apply (apply s (apply b (apply s i))) i) (apply i (apply (apply s (apply b (apply s i))) i)))) === apply (apply (apply (apply s (apply b (apply s i))) i) (apply (apply s (apply b (apply s i))) i)) (f (apply (apply (apply s (apply b (apply s i))) i) (apply i (apply (apply s (apply b (apply s i))) i)))) [] by Super 9059 with 5 at 2,1,2
+Id : 9059, {_}: apply (apply ?16932 (apply ?16933 ?16932)) (f (apply ?16932 (apply ?16933 ?16932))) =?= apply (apply (apply (apply s (apply b (apply s i))) ?16933) ?16932) (f (apply ?16932 (apply ?16933 ?16932))) [16933, 16932] by Super 9058 with 16 at 1,3
+Id : 9058, {_}: apply ?16930 (f ?16930) =<= apply (apply (apply s i) ?16930) (f ?16930) [16930] by Super 1 with 37 at 3
+Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_strong_fixed_point ?1
+% SZS output end CNFRefutation for COL057-1.p
+22586: solved COL057-1.p in 2.124132 using nrkbo
+22586: status Unsatisfiable for COL057-1.p
+NO CLASH, using fixed ground order
+22593: Facts:
+22593: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply
+ (multiply
+ (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
+ ?5) (inverse (multiply ?3 ?5))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
+22593: Goal:
+22593: Id : 1, {_}:
+ multiply a (multiply b c) =<= multiply (multiply a b) c
+ [] by prove_associativity
+22593: Order:
+22593: nrkbo
+22593: Leaf order:
+22593: a 2 0 2 1,2
+22593: b 2 0 2 1,2,2
+22593: c 2 0 2 2,2,2
+22593: inverse 5 1 0
+22593: multiply 10 2 4 0,2
+NO CLASH, using fixed ground order
+22594: Facts:
+22594: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply
+ (multiply
+ (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
+ ?5) (inverse (multiply ?3 ?5))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
+22594: Goal:
+22594: Id : 1, {_}:
+ multiply a (multiply b c) =<= multiply (multiply a b) c
+ [] by prove_associativity
+22594: Order:
+22594: kbo
+22594: Leaf order:
+22594: a 2 0 2 1,2
+22594: b 2 0 2 1,2,2
+22594: c 2 0 2 2,2,2
+22594: inverse 5 1 0
+22594: multiply 10 2 4 0,2
+NO CLASH, using fixed ground order
+22595: Facts:
+22595: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply
+ (multiply
+ (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
+ ?5) (inverse (multiply ?3 ?5))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
+22595: Goal:
+22595: Id : 1, {_}:
+ multiply a (multiply b c) =<= multiply (multiply a b) c
+ [] by prove_associativity
+22595: Order:
+22595: lpo
+22595: Leaf order:
+22595: a 2 0 2 1,2
+22595: b 2 0 2 1,2,2
+22595: c 2 0 2 2,2,2
+22595: inverse 5 1 0
+22595: multiply 10 2 4 0,2
+Statistics :
+Max weight : 62
+Found proof, 23.394494s
+% SZS status Unsatisfiable for GRP014-1.p
+% SZS output start CNFRefutation for GRP014-1.p
+Id : 2, {_}: multiply ?2 (inverse (multiply (multiply (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) ?5) (inverse (multiply ?3 ?5)))) =>= ?4 [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5
+Id : 3, {_}: multiply ?7 (inverse (multiply (multiply (inverse (multiply (inverse ?8) (multiply (inverse ?7) ?9))) ?10) (inverse (multiply ?8 ?10)))) =>= ?9 [10, 9, 8, 7] by group_axiom ?7 ?8 ?9 ?10
+Id : 6, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (inverse (multiply (inverse ?29) (multiply (inverse (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?27))) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 30, 29, 28, 27, 26] by Super 3 with 2 at 1,1,2,2
+Id : 5, {_}: multiply ?19 (inverse (multiply (multiply (inverse (multiply (inverse ?20) ?21)) ?22) (inverse (multiply ?20 ?22)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24) (inverse (multiply ?23 ?24))) [24, 23, 22, 21, 20, 19] by Super 3 with 2 at 2,1,1,1,1,2,2
+Id : 28, {_}: multiply (inverse ?215) (multiply ?215 (inverse (multiply (multiply (inverse (multiply (inverse ?216) ?217)) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 217, 216, 215] by Super 2 with 5 at 2,2
+Id : 29, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?220) (multiply (inverse (inverse ?221)) (multiply (inverse ?221) ?222)))) ?223) (inverse (multiply ?220 ?223))) =>= ?222 [223, 222, 221, 220] by Super 2 with 5 at 2
+Id : 287, {_}: multiply (inverse ?2293) (multiply ?2293 ?2294) =?= multiply (inverse (inverse ?2295)) (multiply (inverse ?2295) ?2294) [2295, 2294, 2293] by Super 28 with 29 at 2,2,2
+Id : 136, {_}: multiply (inverse ?1148) (multiply ?1148 ?1149) =?= multiply (inverse (inverse ?1150)) (multiply (inverse ?1150) ?1149) [1150, 1149, 1148] by Super 28 with 29 at 2,2,2
+Id : 301, {_}: multiply (inverse ?2384) (multiply ?2384 ?2385) =?= multiply (inverse ?2386) (multiply ?2386 ?2385) [2386, 2385, 2384] by Super 287 with 136 at 3
+Id : 356, {_}: multiply (inverse ?2583) (multiply ?2583 (inverse (multiply (multiply (inverse (multiply (inverse ?2584) (multiply ?2584 ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585, 2584, 2583] by Super 28 with 301 at 1,1,1,1,2,2,2
+Id : 679, {_}: multiply ?5168 (inverse (multiply (multiply (inverse (multiply (inverse ?5169) (multiply ?5169 ?5170))) ?5171) (inverse (multiply (inverse ?5168) ?5171)))) =>= ?5170 [5171, 5170, 5169, 5168] by Super 2 with 301 at 1,1,1,1,2,2
+Id : 2910, {_}: multiply ?23936 (inverse (multiply (multiply (inverse (multiply (inverse ?23937) (multiply ?23937 ?23938))) (multiply ?23936 ?23939)) (inverse (multiply (inverse ?23940) (multiply ?23940 ?23939))))) =>= ?23938 [23940, 23939, 23938, 23937, 23936] by Super 679 with 301 at 1,2,1,2,2
+Id : 2996, {_}: multiply (multiply (inverse ?24702) (multiply ?24702 ?24703)) (inverse (multiply ?24704 (inverse (multiply (inverse ?24705) (multiply ?24705 (inverse (multiply (multiply (inverse (multiply (inverse ?24706) ?24704)) ?24707) (inverse (multiply ?24706 ?24707))))))))) =>= ?24703 [24707, 24706, 24705, 24704, 24703, 24702] by Super 2910 with 28 at 1,1,2,2
+Id : 3034, {_}: multiply (multiply (inverse ?24702) (multiply ?24702 ?24703)) (inverse (multiply ?24704 (inverse ?24704))) =>= ?24703 [24704, 24703, 24702] by Demod 2996 with 28 at 1,2,1,2,2
+Id : 3426, {_}: multiply (inverse (multiply (inverse ?29536) (multiply ?29536 ?29537))) ?29537 =?= multiply (inverse (multiply (inverse ?29538) (multiply ?29538 ?29539))) ?29539 [29539, 29538, 29537, 29536] by Super 356 with 3034 at 2,2
+Id : 3726, {_}: multiply (inverse (inverse (multiply (inverse ?31745) (multiply ?31745 (inverse (multiply (multiply (inverse (multiply (inverse ?31746) ?31747)) ?31748) (inverse (multiply ?31746 ?31748)))))))) (multiply (inverse (multiply (inverse ?31749) (multiply ?31749 ?31750))) ?31750) =>= ?31747 [31750, 31749, 31748, 31747, 31746, 31745] by Super 28 with 3426 at 2,2
+Id : 3919, {_}: multiply (inverse (inverse ?31747)) (multiply (inverse (multiply (inverse ?31749) (multiply ?31749 ?31750))) ?31750) =>= ?31747 [31750, 31749, 31747] by Demod 3726 with 28 at 1,1,1,2
+Id : 91, {_}: multiply (inverse ?821) (multiply ?821 (inverse (multiply (multiply (inverse (multiply (inverse ?822) ?823)) ?824) (inverse (multiply ?822 ?824))))) =>= ?823 [824, 823, 822, 821] by Super 2 with 5 at 2,2
+Id : 107, {_}: multiply (inverse ?949) (multiply ?949 (multiply ?950 (inverse (multiply (multiply (inverse (multiply (inverse ?951) ?952)) ?953) (inverse (multiply ?951 ?953)))))) =>= multiply (inverse (inverse ?950)) ?952 [953, 952, 951, 950, 949] by Super 91 with 5 at 2,2,2
+Id : 3966, {_}: multiply (inverse (inverse (inverse ?33635))) ?33635 =?= multiply (inverse (inverse (inverse (multiply (inverse ?33636) (multiply ?33636 (inverse (multiply (multiply (inverse (multiply (inverse ?33637) ?33638)) ?33639) (inverse (multiply ?33637 ?33639))))))))) ?33638 [33639, 33638, 33637, 33636, 33635] by Super 107 with 3919 at 2,2
+Id : 4117, {_}: multiply (inverse (inverse (inverse ?33635))) ?33635 =?= multiply (inverse (inverse (inverse ?33638))) ?33638 [33638, 33635] by Demod 3966 with 28 at 1,1,1,1,3
+Id : 4346, {_}: multiply (inverse (inverse ?35898)) (multiply (inverse (multiply (inverse (inverse (inverse (inverse ?35899)))) (multiply (inverse (inverse (inverse ?35900))) ?35900))) ?35899) =>= ?35898 [35900, 35899, 35898] by Super 3919 with 4117 at 2,1,1,2,2
+Id : 3965, {_}: multiply (inverse ?33628) (multiply ?33628 (multiply ?33629 (inverse (multiply (multiply (inverse ?33630) ?33631) (inverse (multiply (inverse ?33630) ?33631)))))) =?= multiply (inverse (inverse ?33629)) (multiply (inverse (multiply (inverse ?33632) (multiply ?33632 ?33633))) ?33633) [33633, 33632, 33631, 33630, 33629, 33628] by Super 107 with 3919 at 1,1,1,1,2,2,2,2
+Id : 6632, {_}: multiply (inverse ?52916) (multiply ?52916 (multiply ?52917 (inverse (multiply (multiply (inverse ?52918) ?52919) (inverse (multiply (inverse ?52918) ?52919)))))) =>= ?52917 [52919, 52918, 52917, 52916] by Demod 3965 with 3919 at 3
+Id : 6641, {_}: multiply (inverse ?52992) (multiply ?52992 (multiply ?52993 (inverse (multiply (multiply (inverse ?52994) (inverse (multiply (multiply (inverse (multiply (inverse ?52995) (multiply (inverse (inverse ?52994)) ?52996))) ?52997) (inverse (multiply ?52995 ?52997))))) (inverse ?52996))))) =>= ?52993 [52997, 52996, 52995, 52994, 52993, 52992] by Super 6632 with 2 at 1,2,1,2,2,2,2
+Id : 6773, {_}: multiply (inverse ?52992) (multiply ?52992 (multiply ?52993 (inverse (multiply ?52996 (inverse ?52996))))) =>= ?52993 [52996, 52993, 52992] by Demod 6641 with 2 at 1,1,2,2,2,2
+Id : 6832, {_}: multiply (inverse (inverse ?53817)) (multiply (inverse ?53818) (multiply ?53818 (inverse (multiply ?53819 (inverse ?53819))))) =>= ?53817 [53819, 53818, 53817] by Super 4346 with 6773 at 1,1,2,2
+Id : 4, {_}: multiply ?12 (inverse (multiply (multiply (inverse (multiply (inverse ?13) (multiply (inverse ?12) ?14))) (inverse (multiply (multiply (inverse (multiply (inverse ?15) (multiply (inverse ?13) ?16))) ?17) (inverse (multiply ?15 ?17))))) (inverse ?16))) =>= ?14 [17, 16, 15, 14, 13, 12] by Super 3 with 2 at 1,2,1,2,2
+Id : 9, {_}: multiply ?44 (inverse (multiply (multiply (inverse (multiply (inverse ?45) ?46)) ?47) (inverse (multiply ?45 ?47)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?48) (multiply (inverse (inverse ?44)) ?46))) (inverse (multiply (multiply (inverse (multiply (inverse ?49) (multiply (inverse ?48) ?50))) ?51) (inverse (multiply ?49 ?51))))) (inverse ?50)) [51, 50, 49, 48, 47, 46, 45, 44] by Super 2 with 4 at 2,1,1,1,1,2,2
+Id : 7754, {_}: multiply ?63171 (inverse (multiply (multiply (inverse (multiply (inverse ?63172) (multiply (inverse ?63171) (inverse (multiply ?63173 (inverse ?63173)))))) ?63174) (inverse (multiply ?63172 ?63174)))) =?= inverse (multiply (multiply (inverse ?63175) (inverse (multiply (multiply (inverse (multiply (inverse ?63176) (multiply (inverse (inverse ?63175)) ?63177))) ?63178) (inverse (multiply ?63176 ?63178))))) (inverse ?63177)) [63178, 63177, 63176, 63175, 63174, 63173, 63172, 63171] by Super 9 with 6832 at 1,1,1,1,3
+Id : 7872, {_}: inverse (multiply ?63173 (inverse ?63173)) =?= inverse (multiply (multiply (inverse ?63175) (inverse (multiply (multiply (inverse (multiply (inverse ?63176) (multiply (inverse (inverse ?63175)) ?63177))) ?63178) (inverse (multiply ?63176 ?63178))))) (inverse ?63177)) [63178, 63177, 63176, 63175, 63173] by Demod 7754 with 2 at 2
+Id : 7873, {_}: inverse (multiply ?63173 (inverse ?63173)) =?= inverse (multiply ?63177 (inverse ?63177)) [63177, 63173] by Demod 7872 with 2 at 1,1,3
+Id : 8249, {_}: multiply (inverse (inverse (multiply ?66459 (inverse ?66459)))) (multiply (inverse ?66460) (multiply ?66460 (inverse (multiply ?66461 (inverse ?66461))))) =?= multiply ?66462 (inverse ?66462) [66462, 66461, 66460, 66459] by Super 6832 with 7873 at 1,1,2
+Id : 8282, {_}: multiply ?66459 (inverse ?66459) =?= multiply ?66462 (inverse ?66462) [66462, 66459] by Demod 8249 with 6832 at 2
+Id : 8520, {_}: multiply (multiply (inverse ?67970) (multiply ?67971 (inverse ?67971))) (inverse (multiply ?67972 (inverse ?67972))) =>= inverse ?67970 [67972, 67971, 67970] by Super 3034 with 8282 at 2,1,2
+Id : 380, {_}: multiply ?2743 (inverse (multiply (multiply (inverse ?2744) (multiply ?2744 ?2745)) (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745))))) =>= ?2747 [2747, 2746, 2745, 2744, 2743] by Super 2 with 301 at 1,1,2,2
+Id : 8912, {_}: multiply ?70596 (inverse (multiply (multiply (inverse ?70597) (multiply ?70597 (inverse (multiply ?70598 (inverse ?70598))))) (inverse (multiply ?70599 (inverse ?70599))))) =>= inverse (inverse ?70596) [70599, 70598, 70597, 70596] by Super 380 with 8520 at 2,1,2,1,2,2
+Id : 9021, {_}: multiply ?70596 (inverse (inverse (multiply ?70598 (inverse ?70598)))) =>= inverse (inverse ?70596) [70598, 70596] by Demod 8912 with 3034 at 1,2,2
+Id : 9165, {_}: multiply (inverse (inverse ?72171)) (multiply (inverse (multiply (inverse ?72172) (inverse (inverse ?72172)))) (inverse (inverse (multiply ?72173 (inverse ?72173))))) =>= ?72171 [72173, 72172, 72171] by Super 3919 with 9021 at 2,1,1,2,2
+Id : 10068, {_}: multiply (inverse (inverse ?76580)) (inverse (inverse (inverse (multiply (inverse ?76581) (inverse (inverse ?76581)))))) =>= ?76580 [76581, 76580] by Demod 9165 with 9021 at 2,2
+Id : 9180, {_}: multiply ?72234 (inverse ?72234) =?= inverse (inverse (inverse (multiply ?72235 (inverse ?72235)))) [72235, 72234] by Super 8282 with 9021 at 3
+Id : 10100, {_}: multiply (inverse (inverse ?76745)) (multiply ?76746 (inverse ?76746)) =>= ?76745 [76746, 76745] by Super 10068 with 9180 at 2,2
+Id : 10663, {_}: multiply ?82289 (inverse (multiply ?82290 (inverse ?82290))) =>= inverse (inverse ?82289) [82290, 82289] by Super 8520 with 10100 at 1,2
+Id : 10913, {_}: multiply (inverse (inverse ?83563)) (inverse (inverse (inverse (multiply (inverse ?83564) (multiply ?83564 (inverse (multiply ?83565 (inverse ?83565)))))))) =>= ?83563 [83565, 83564, 83563] by Super 3919 with 10663 at 2,2
+Id : 10892, {_}: inverse (inverse (multiply (inverse ?24702) (multiply ?24702 ?24703))) =>= ?24703 [24703, 24702] by Demod 3034 with 10663 at 2
+Id : 11238, {_}: multiply (inverse (inverse ?83563)) (inverse (inverse (multiply ?83565 (inverse ?83565)))) =>= ?83563 [83565, 83563] by Demod 10913 with 10892 at 1,2,2
+Id : 11239, {_}: inverse (inverse (inverse (inverse ?83563))) =>= ?83563 [83563] by Demod 11238 with 9021 at 2
+Id : 138, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1160) (multiply (inverse (inverse ?1161)) (multiply (inverse ?1161) ?1162)))) ?1163) (inverse (multiply ?1160 ?1163))) =>= ?1162 [1163, 1162, 1161, 1160] by Super 2 with 5 at 2
+Id : 145, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1213) (multiply (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?1214) (multiply (inverse (inverse ?1215)) (multiply (inverse ?1215) ?1216)))) ?1217) (inverse (multiply ?1214 ?1217))))) (multiply ?1216 ?1218)))) ?1219) (inverse (multiply ?1213 ?1219))) =>= ?1218 [1219, 1218, 1217, 1216, 1215, 1214, 1213] by Super 138 with 29 at 1,2,2,1,1,1,1,2
+Id : 168, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1213) (multiply (inverse ?1216) (multiply ?1216 ?1218)))) ?1219) (inverse (multiply ?1213 ?1219))) =>= ?1218 [1219, 1218, 1216, 1213] by Demod 145 with 29 at 1,1,2,1,1,1,1,2
+Id : 777, {_}: multiply (inverse ?5891) (multiply ?5891 (multiply ?5892 (inverse (multiply (multiply (inverse (multiply (inverse ?5893) ?5894)) ?5895) (inverse (multiply ?5893 ?5895)))))) =>= multiply (inverse (inverse ?5892)) ?5894 [5895, 5894, 5893, 5892, 5891] by Super 91 with 5 at 2,2,2
+Id : 813, {_}: multiply (inverse ?6211) (multiply ?6211 (multiply ?6212 ?6213)) =?= multiply (inverse (inverse ?6212)) (multiply (inverse ?6214) (multiply ?6214 ?6213)) [6214, 6213, 6212, 6211] by Super 777 with 168 at 2,2,2,2
+Id : 1401, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?11491) (multiply ?11491 (multiply ?11492 ?11493)))) ?11494) (inverse (multiply (inverse ?11492) ?11494))) =>= ?11493 [11494, 11493, 11492, 11491] by Super 168 with 813 at 1,1,1,1,2
+Id : 1427, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?11709) (multiply ?11709 (multiply (inverse ?11710) (multiply ?11710 ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711, 11710, 11709] by Super 1401 with 301 at 2,2,1,1,1,1,2
+Id : 10889, {_}: multiply (inverse ?52992) (multiply ?52992 (inverse (inverse ?52993))) =>= ?52993 [52993, 52992] by Demod 6773 with 10663 at 2,2,2
+Id : 11440, {_}: multiply (inverse ?85947) (multiply ?85947 ?85948) =>= inverse (inverse ?85948) [85948, 85947] by Super 10889 with 11239 at 2,2,2
+Id : 12070, {_}: inverse (multiply (multiply (inverse (inverse (inverse (multiply (inverse ?11710) (multiply ?11710 ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711, 11710] by Demod 1427 with 11440 at 1,1,1,1,2
+Id : 12071, {_}: inverse (multiply (multiply (inverse (inverse (inverse (inverse (inverse ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711] by Demod 12070 with 11440 at 1,1,1,1,1,1,2
+Id : 12086, {_}: inverse (multiply (multiply (inverse ?11711) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711] by Demod 12071 with 11239 at 1,1,1,2
+Id : 11284, {_}: multiply ?84907 (inverse (multiply (inverse (inverse (inverse ?84908))) ?84908)) =>= inverse (inverse ?84907) [84908, 84907] by Super 10663 with 11239 at 2,1,2,2
+Id : 12456, {_}: inverse (inverse (inverse (multiply (inverse ?89511) ?89512))) =>= multiply (inverse ?89512) ?89511 [89512, 89511] by Super 12086 with 11284 at 1,2
+Id : 12807, {_}: inverse (multiply (inverse ?89891) ?89892) =>= multiply (inverse ?89892) ?89891 [89892, 89891] by Super 11239 with 12456 at 1,2
+Id : 13084, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (inverse (multiply (inverse (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?27)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 6 with 12807 at 1,1,1,2,1,2,1,2,2
+Id : 13085, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13084 with 12807 at 1,1,1,1,2,1,2,1,2,2
+Id : 13086, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (inverse (multiply (inverse ?26) ?30)) ?28)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13085 with 12807 at 2,1,1,1,1,2,1,2,1,2,2
+Id : 13087, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13086 with 12807 at 1,2,1,1,1,1,2,1,2,1,2,2
+Id : 12072, {_}: multiply ?2743 (inverse (multiply (inverse (inverse ?2745)) (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745))))) =>= ?2747 [2747, 2746, 2745, 2743] by Demod 380 with 11440 at 1,1,2,2
+Id : 13068, {_}: multiply ?2743 (multiply (inverse (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745)))) (inverse ?2745)) =>= ?2747 [2745, 2747, 2746, 2743] by Demod 12072 with 12807 at 2,2
+Id : 358, {_}: multiply (inverse ?2595) (multiply ?2595 (inverse (multiply (multiply (inverse ?2596) (multiply ?2596 ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597, 2596, 2595] by Super 28 with 301 at 1,1,2,2,2
+Id : 12055, {_}: inverse (inverse (inverse (multiply (multiply (inverse ?2596) (multiply ?2596 ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597, 2596] by Demod 358 with 11440 at 2
+Id : 12056, {_}: inverse (inverse (inverse (multiply (inverse (inverse ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597] by Demod 12055 with 11440 at 1,1,1,1,2
+Id : 12778, {_}: multiply (inverse (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))) (inverse ?2597) =>= ?2599 [2597, 2599, 2598] by Demod 12056 with 12456 at 2
+Id : 13130, {_}: multiply ?2743 (multiply (inverse ?2743) ?2747) =>= ?2747 [2747, 2743] by Demod 13068 with 12778 at 2,2
+Id : 12068, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?2584) (multiply ?2584 ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585, 2584] by Demod 356 with 11440 at 2
+Id : 12069, {_}: inverse (inverse (inverse (multiply (multiply (inverse (inverse (inverse ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 12068 with 11440 at 1,1,1,1,1,1,2
+Id : 12343, {_}: inverse (inverse (inverse (inverse (inverse (multiply (inverse (inverse (inverse ?88665))) ?88666))))) =>= multiply (inverse (inverse (inverse ?88666))) ?88665 [88666, 88665] by Super 12069 with 11284 at 1,1,1,2
+Id : 12705, {_}: inverse (multiply (inverse (inverse (inverse ?88665))) ?88666) =>= multiply (inverse (inverse (inverse ?88666))) ?88665 [88666, 88665] by Demod 12343 with 11239 at 2
+Id : 13398, {_}: multiply (inverse ?88666) (inverse (inverse ?88665)) =?= multiply (inverse (inverse (inverse ?88666))) ?88665 [88665, 88666] by Demod 12705 with 12807 at 2
+Id : 13591, {_}: multiply (inverse ?93455) (inverse (inverse (multiply (inverse (inverse (inverse (inverse ?93455)))) ?93456))) =>= ?93456 [93456, 93455] by Super 13130 with 13398 at 2
+Id : 13688, {_}: multiply (inverse ?93455) (inverse (multiply (inverse ?93456) (inverse (inverse (inverse ?93455))))) =>= ?93456 [93456, 93455] by Demod 13591 with 12807 at 1,2,2
+Id : 13689, {_}: multiply (inverse ?93455) (multiply (inverse (inverse (inverse (inverse ?93455)))) ?93456) =>= ?93456 [93456, 93455] by Demod 13688 with 12807 at 2,2
+Id : 13690, {_}: multiply (inverse ?93455) (multiply ?93455 ?93456) =>= ?93456 [93456, 93455] by Demod 13689 with 11239 at 1,2,2
+Id : 13691, {_}: inverse (inverse ?93456) =>= ?93456 [93456] by Demod 13690 with 11440 at 2
+Id : 14259, {_}: inverse (multiply ?94937 ?94938) =<= multiply (inverse ?94938) (inverse ?94937) [94938, 94937] by Super 12807 with 13691 at 1,1,2
+Id : 14272, {_}: inverse (multiply ?94994 (inverse ?94995)) =>= multiply ?94995 (inverse ?94994) [94995, 94994] by Super 14259 with 13691 at 1,3
+Id : 15113, {_}: multiply ?26 (multiply (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31) (inverse (multiply ?29 ?31))))) (inverse ?27)) =>= ?30 [31, 29, 30, 27, 28, 26] by Demod 13087 with 14272 at 2,2
+Id : 15114, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31)))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 15113 with 14272 at 2,1,2,2
+Id : 14099, {_}: inverse (multiply ?94283 ?94284) =<= multiply (inverse ?94284) (inverse ?94283) [94284, 94283] by Super 12807 with 13691 at 1,1,2
+Id : 15376, {_}: multiply ?101449 (inverse (multiply ?101450 ?101449)) =>= inverse ?101450 [101450, 101449] by Super 13130 with 14099 at 2,2
+Id : 14196, {_}: multiply ?94524 (inverse (multiply ?94525 ?94524)) =>= inverse ?94525 [94525, 94524] by Super 13130 with 14099 at 2,2
+Id : 15386, {_}: multiply (inverse (multiply ?101486 ?101487)) (inverse (inverse ?101486)) =>= inverse ?101487 [101487, 101486] by Super 15376 with 14196 at 1,2,2
+Id : 15574, {_}: inverse (multiply (inverse ?101486) (multiply ?101486 ?101487)) =>= inverse ?101487 [101487, 101486] by Demod 15386 with 14099 at 2
+Id : 16040, {_}: multiply (inverse (multiply ?103094 ?103095)) ?103094 =>= inverse ?103095 [103095, 103094] by Demod 15574 with 12807 at 2
+Id : 12061, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?216) ?217)) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 217, 216] by Demod 28 with 11440 at 2
+Id : 13066, {_}: inverse (inverse (inverse (multiply (multiply (multiply (inverse ?217) ?216) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 216, 217] by Demod 12061 with 12807 at 1,1,1,1,1,2
+Id : 14035, {_}: inverse (multiply (multiply (multiply (inverse ?217) ?216) ?218) (inverse (multiply ?216 ?218))) =>= ?217 [218, 216, 217] by Demod 13066 with 13691 at 2
+Id : 15129, {_}: multiply (multiply ?216 ?218) (inverse (multiply (multiply (inverse ?217) ?216) ?218)) =>= ?217 [217, 218, 216] by Demod 14035 with 14272 at 2
+Id : 16059, {_}: multiply (inverse ?103200) (multiply ?103201 ?103202) =<= inverse (inverse (multiply (multiply (inverse ?103200) ?103201) ?103202)) [103202, 103201, 103200] by Super 16040 with 15129 at 1,1,2
+Id : 16156, {_}: multiply (inverse ?103200) (multiply ?103201 ?103202) =<= multiply (multiply (inverse ?103200) ?103201) ?103202 [103202, 103201, 103200] by Demod 16059 with 13691 at 3
+Id : 17066, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?30) ?26) ?28) ?29)) ?31)))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 15114 with 16156 at 1,1,2,2,1,2,2
+Id : 17067, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (multiply (inverse ?30) ?26) ?28) ?29) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17066 with 16156 at 1,2,2,1,2,2
+Id : 17068, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?30) (multiply ?26 ?28)) ?29) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17067 with 16156 at 1,1,2,1,2,2,1,2,2
+Id : 17069, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (inverse ?30) (multiply (multiply ?26 ?28) ?29)) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17068 with 16156 at 1,2,1,2,2,1,2,2
+Id : 17070, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (inverse ?30) (multiply (multiply (multiply ?26 ?28) ?29) ?31)))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17069 with 16156 at 2,1,2,2,1,2,2
+Id : 17075, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (inverse (multiply (inverse ?30) (multiply (multiply (multiply ?26 ?28) ?29) ?31))) ?27))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17070 with 12807 at 2,2,1,2,2
+Id : 17076, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (multiply (inverse (multiply (multiply (multiply ?26 ?28) ?29) ?31)) ?30) ?27))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17075 with 12807 at 1,2,2,1,2,2
+Id : 17077, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (inverse (multiply (multiply (multiply ?26 ?28) ?29) ?31)) (multiply ?30 ?27)))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17076 with 16156 at 2,2,1,2,2
+Id : 14023, {_}: multiply (inverse ?33635) ?33635 =?= multiply (inverse (inverse (inverse ?33638))) ?33638 [33638, 33635] by Demod 4117 with 13691 at 1,2
+Id : 14024, {_}: multiply (inverse ?33635) ?33635 =?= multiply (inverse ?33638) ?33638 [33638, 33635] by Demod 14023 with 13691 at 1,3
+Id : 14053, {_}: multiply (inverse ?93965) ?93965 =?= multiply ?93966 (inverse ?93966) [93966, 93965] by Super 14024 with 13691 at 1,3
+Id : 19206, {_}: multiply ?108859 (multiply (multiply ?108860 (multiply (multiply ?108861 ?108862) (multiply ?108863 (inverse ?108863)))) (inverse ?108862)) =>= multiply (multiply ?108859 ?108860) ?108861 [108863, 108862, 108861, 108860, 108859] by Super 17077 with 14053 at 2,2,1,2,2
+Id : 14021, {_}: multiply ?70596 (multiply ?70598 (inverse ?70598)) =>= inverse (inverse ?70596) [70598, 70596] by Demod 9021 with 13691 at 2,2
+Id : 14022, {_}: multiply ?70596 (multiply ?70598 (inverse ?70598)) =>= ?70596 [70598, 70596] by Demod 14021 with 13691 at 3
+Id : 19669, {_}: multiply ?108859 (multiply (multiply ?108860 (multiply ?108861 ?108862)) (inverse ?108862)) =>= multiply (multiply ?108859 ?108860) ?108861 [108862, 108861, 108860, 108859] by Demod 19206 with 14022 at 2,1,2,2
+Id : 14028, {_}: inverse (multiply (multiply (inverse (inverse (inverse ?2585))) ?2586) (inverse (multiply ?2587 ?2586))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 12069 with 13691 at 2
+Id : 14029, {_}: inverse (multiply (multiply (inverse ?2585) ?2586) (inverse (multiply ?2587 ?2586))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 14028 with 13691 at 1,1,1,2
+Id : 15108, {_}: multiply (multiply ?2587 ?2586) (inverse (multiply (inverse ?2585) ?2586)) =>= multiply ?2587 ?2585 [2585, 2586, 2587] by Demod 14029 with 14272 at 2
+Id : 15134, {_}: multiply (multiply ?2587 ?2586) (multiply (inverse ?2586) ?2585) =>= multiply ?2587 ?2585 [2585, 2586, 2587] by Demod 15108 with 12807 at 2,2
+Id : 15575, {_}: multiply (inverse (multiply ?101486 ?101487)) ?101486 =>= inverse ?101487 [101487, 101486] by Demod 15574 with 12807 at 2
+Id : 16032, {_}: multiply (multiply ?103052 (multiply ?103053 ?103054)) (inverse ?103054) =>= multiply ?103052 ?103053 [103054, 103053, 103052] by Super 15134 with 15575 at 2,2
+Id : 32860, {_}: multiply ?108859 (multiply ?108860 ?108861) =?= multiply (multiply ?108859 ?108860) ?108861 [108861, 108860, 108859] by Demod 19669 with 16032 at 2,2
+Id : 33337, {_}: multiply a (multiply b c) === multiply a (multiply b c) [] by Demod 1 with 32860 at 3
+Id : 1, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
+% SZS output end CNFRefutation for GRP014-1.p
+22593: solved GRP014-1.p in 11.760735 using nrkbo
+22593: status Unsatisfiable for GRP014-1.p
+CLASH, statistics insufficient
+22602: Facts:
+22602: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22602: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22602: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22602: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22602: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22602: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22602: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22602: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22602: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22602: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22602: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22602: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22602: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22602: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22602: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22602: Id : 17, {_}:
+ positive_part ?50 =<= least_upper_bound ?50 identity
+ [50] by lat4_1 ?50
+22602: Id : 18, {_}:
+ negative_part ?52 =<= greatest_lower_bound ?52 identity
+ [52] by lat4_2 ?52
+22602: Id : 19, {_}:
+ least_upper_bound ?54 (greatest_lower_bound ?55 ?56)
+ =<=
+ greatest_lower_bound (least_upper_bound ?54 ?55)
+ (least_upper_bound ?54 ?56)
+ [56, 55, 54] by lat4_3 ?54 ?55 ?56
+22602: Id : 20, {_}:
+ greatest_lower_bound ?58 (least_upper_bound ?59 ?60)
+ =<=
+ least_upper_bound (greatest_lower_bound ?58 ?59)
+ (greatest_lower_bound ?58 ?60)
+ [60, 59, 58] by lat4_4 ?58 ?59 ?60
+22602: Goal:
+22602: Id : 1, {_}:
+ a =<= multiply (positive_part a) (negative_part a)
+ [] by prove_lat4
+22602: Order:
+22602: nrkbo
+22602: Leaf order:
+22602: a 3 0 3 2
+22602: identity 4 0 0
+22602: inverse 1 1 0
+22602: positive_part 2 1 1 0,1,3
+22602: negative_part 2 1 1 0,2,3
+22602: greatest_lower_bound 19 2 0
+22602: least_upper_bound 19 2 0
+22602: multiply 19 2 1 0,3
+CLASH, statistics insufficient
+22603: Facts:
+22603: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22603: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22603: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22603: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22603: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22603: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22603: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22603: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22603: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22603: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22603: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22603: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22603: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22603: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22603: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22603: Id : 17, {_}:
+ positive_part ?50 =<= least_upper_bound ?50 identity
+ [50] by lat4_1 ?50
+22603: Id : 18, {_}:
+ negative_part ?52 =<= greatest_lower_bound ?52 identity
+ [52] by lat4_2 ?52
+22603: Id : 19, {_}:
+ least_upper_bound ?54 (greatest_lower_bound ?55 ?56)
+ =<=
+ greatest_lower_bound (least_upper_bound ?54 ?55)
+ (least_upper_bound ?54 ?56)
+ [56, 55, 54] by lat4_3 ?54 ?55 ?56
+22603: Id : 20, {_}:
+ greatest_lower_bound ?58 (least_upper_bound ?59 ?60)
+ =<=
+ least_upper_bound (greatest_lower_bound ?58 ?59)
+ (greatest_lower_bound ?58 ?60)
+ [60, 59, 58] by lat4_4 ?58 ?59 ?60
+22603: Goal:
+22603: Id : 1, {_}:
+ a =<= multiply (positive_part a) (negative_part a)
+ [] by prove_lat4
+22603: Order:
+22603: kbo
+22603: Leaf order:
+22603: a 3 0 3 2
+22603: identity 4 0 0
+22603: inverse 1 1 0
+22603: positive_part 2 1 1 0,1,3
+22603: negative_part 2 1 1 0,2,3
+22603: greatest_lower_bound 19 2 0
+22603: least_upper_bound 19 2 0
+22603: multiply 19 2 1 0,3
+CLASH, statistics insufficient
+22604: Facts:
+22604: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22604: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22604: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22604: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22604: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22604: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22604: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22604: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22604: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22604: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22604: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22604: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22604: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22604: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22604: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22604: Id : 17, {_}:
+ positive_part ?50 =>= least_upper_bound ?50 identity
+ [50] by lat4_1 ?50
+22604: Id : 18, {_}:
+ negative_part ?52 =>= greatest_lower_bound ?52 identity
+ [52] by lat4_2 ?52
+22604: Id : 19, {_}:
+ least_upper_bound ?54 (greatest_lower_bound ?55 ?56)
+ =<=
+ greatest_lower_bound (least_upper_bound ?54 ?55)
+ (least_upper_bound ?54 ?56)
+ [56, 55, 54] by lat4_3 ?54 ?55 ?56
+22604: Id : 20, {_}:
+ greatest_lower_bound ?58 (least_upper_bound ?59 ?60)
+ =>=
+ least_upper_bound (greatest_lower_bound ?58 ?59)
+ (greatest_lower_bound ?58 ?60)
+ [60, 59, 58] by lat4_4 ?58 ?59 ?60
+22604: Goal:
+22604: Id : 1, {_}:
+ a =<= multiply (positive_part a) (negative_part a)
+ [] by prove_lat4
+22604: Order:
+22604: lpo
+22604: Leaf order:
+22604: a 3 0 3 2
+22604: identity 4 0 0
+22604: inverse 1 1 0
+22604: positive_part 2 1 1 0,1,3
+22604: negative_part 2 1 1 0,2,3
+22604: greatest_lower_bound 19 2 0
+22604: least_upper_bound 19 2 0
+22604: multiply 19 2 1 0,3
+Statistics :
+Max weight : 20
+Found proof, 10.348100s
+% SZS status Unsatisfiable for GRP167-1.p
+% SZS output start CNFRefutation for GRP167-1.p
+Id : 185, {_}: multiply ?584 (greatest_lower_bound ?585 ?586) =<= greatest_lower_bound (multiply ?584 ?585) (multiply ?584 ?586) [586, 585, 584] by monotony_glb1 ?584 ?585 ?586
+Id : 218, {_}: multiply (least_upper_bound ?658 ?659) ?660 =<= least_upper_bound (multiply ?658 ?660) (multiply ?659 ?660) [660, 659, 658] by monotony_lub2 ?658 ?659 ?660
+Id : 11, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
+Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =?= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+Id : 12, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
+Id : 7, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =?= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
+Id : 250, {_}: multiply (greatest_lower_bound ?735 ?736) ?737 =<= greatest_lower_bound (multiply ?735 ?737) (multiply ?736 ?737) [737, 736, 735] by monotony_glb2 ?735 ?736 ?737
+Id : 16, {_}: multiply (greatest_lower_bound ?46 ?47) ?48 =<= greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+Id : 18, {_}: negative_part ?52 =<= greatest_lower_bound ?52 identity [52] by lat4_2 ?52
+Id : 364, {_}: greatest_lower_bound ?996 (least_upper_bound ?997 ?998) =<= least_upper_bound (greatest_lower_bound ?996 ?997) (greatest_lower_bound ?996 ?998) [998, 997, 996] by lat4_4 ?996 ?997 ?998
+Id : 17, {_}: positive_part ?50 =<= least_upper_bound ?50 identity [50] by lat4_1 ?50
+Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
+Id : 155, {_}: multiply ?513 (least_upper_bound ?514 ?515) =<= least_upper_bound (multiply ?513 ?514) (multiply ?513 ?515) [515, 514, 513] by monotony_lub1 ?513 ?514 ?515
+Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+Id : 25, {_}: multiply (multiply ?69 ?70) ?71 =?= multiply ?69 (multiply ?70 ?71) [71, 70, 69] by associativity ?69 ?70 ?71
+Id : 27, {_}: multiply (multiply ?76 (inverse ?77)) ?77 =>= multiply ?76 identity [77, 76] by Super 25 with 3 at 2,3
+Id : 643, {_}: multiply (multiply ?1439 (inverse ?1440)) ?1440 =>= multiply ?1439 identity [1440, 1439] by Super 25 with 3 at 2,3
+Id : 645, {_}: multiply identity ?1444 =<= multiply (inverse (inverse ?1444)) identity [1444] by Super 643 with 3 at 1,2
+Id : 656, {_}: ?1444 =<= multiply (inverse (inverse ?1444)) identity [1444] by Demod 645 with 2 at 2
+Id : 26, {_}: multiply (multiply ?73 identity) ?74 =>= multiply ?73 ?74 [74, 73] by Super 25 with 2 at 2,3
+Id : 1111, {_}: multiply ?2369 ?2370 =<= multiply (inverse (inverse ?2369)) ?2370 [2370, 2369] by Super 26 with 656 at 1,2
+Id : 2348, {_}: ?1444 =<= multiply ?1444 identity [1444] by Demod 656 with 1111 at 3
+Id : 2350, {_}: multiply (multiply ?76 (inverse ?77)) ?77 =>= ?76 [77, 76] by Demod 27 with 2348 at 3
+Id : 2372, {_}: inverse (inverse ?4335) =<= multiply ?4335 identity [4335] by Super 2348 with 1111 at 3
+Id : 2377, {_}: inverse (inverse ?4335) =>= ?4335 [4335] by Demod 2372 with 2348 at 3
+Id : 25971, {_}: multiply (multiply ?35046 ?35047) (inverse ?35047) =>= ?35046 [35047, 35046] by Super 2350 with 2377 at 2,1,2
+Id : 161, {_}: multiply (inverse ?536) (least_upper_bound ?536 ?537) =>= least_upper_bound identity (multiply (inverse ?536) ?537) [537, 536] by Super 155 with 3 at 1,3
+Id : 279, {_}: least_upper_bound identity ?790 =>= positive_part ?790 [790] by Super 6 with 17 at 3
+Id : 4991, {_}: multiply (inverse ?8728) (least_upper_bound ?8728 ?8729) =>= positive_part (multiply (inverse ?8728) ?8729) [8729, 8728] by Demod 161 with 279 at 3
+Id : 5015, {_}: multiply (inverse ?8798) (positive_part ?8798) =?= positive_part (multiply (inverse ?8798) identity) [8798] by Super 4991 with 17 at 2,2
+Id : 5066, {_}: multiply (inverse ?8872) (positive_part ?8872) =>= positive_part (inverse ?8872) [8872] by Demod 5015 with 2348 at 1,3
+Id : 5077, {_}: multiply ?8900 (positive_part (inverse ?8900)) =>= positive_part (inverse (inverse ?8900)) [8900] by Super 5066 with 2377 at 1,2
+Id : 5091, {_}: multiply ?8900 (positive_part (inverse ?8900)) =>= positive_part ?8900 [8900] by Demod 5077 with 2377 at 1,3
+Id : 25993, {_}: multiply (positive_part ?35122) (inverse (positive_part (inverse ?35122))) =>= ?35122 [35122] by Super 25971 with 5091 at 1,2
+Id : 2406, {_}: multiply (multiply ?4349 ?4350) (inverse ?4350) =>= ?4349 [4350, 4349] by Super 2350 with 2377 at 2,1,2
+Id : 4974, {_}: multiply (inverse ?536) (least_upper_bound ?536 ?537) =>= positive_part (multiply (inverse ?536) ?537) [537, 536] by Demod 161 with 279 at 3
+Id : 373, {_}: greatest_lower_bound ?1035 (least_upper_bound ?1036 identity) =<= least_upper_bound (greatest_lower_bound ?1035 ?1036) (negative_part ?1035) [1036, 1035] by Super 364 with 18 at 2,3
+Id : 397, {_}: greatest_lower_bound ?1035 (positive_part ?1036) =<= least_upper_bound (greatest_lower_bound ?1035 ?1036) (negative_part ?1035) [1036, 1035] by Demod 373 with 17 at 2,2
+Id : 256, {_}: multiply (greatest_lower_bound (inverse ?758) ?759) ?758 =>= greatest_lower_bound identity (multiply ?759 ?758) [759, 758] by Super 250 with 3 at 1,3
+Id : 296, {_}: greatest_lower_bound identity ?821 =>= negative_part ?821 [821] by Super 5 with 18 at 3
+Id : 17350, {_}: multiply (greatest_lower_bound (inverse ?24308) ?24309) ?24308 =>= negative_part (multiply ?24309 ?24308) [24309, 24308] by Demod 256 with 296 at 3
+Id : 17377, {_}: multiply (negative_part (inverse ?24398)) ?24398 =>= negative_part (multiply identity ?24398) [24398] by Super 17350 with 18 at 1,2
+Id : 17420, {_}: multiply (negative_part (inverse ?24398)) ?24398 =>= negative_part ?24398 [24398] by Demod 17377 with 2 at 1,3
+Id : 17441, {_}: multiply (greatest_lower_bound (negative_part (inverse ?24443)) ?24444) ?24443 =>= greatest_lower_bound (negative_part ?24443) (multiply ?24444 ?24443) [24444, 24443] by Super 16 with 17420 at 1,3
+Id : 455, {_}: greatest_lower_bound identity (greatest_lower_bound ?1150 ?1151) =>= greatest_lower_bound (negative_part ?1150) ?1151 [1151, 1150] by Super 7 with 296 at 1,3
+Id : 465, {_}: negative_part (greatest_lower_bound ?1150 ?1151) =>= greatest_lower_bound (negative_part ?1150) ?1151 [1151, 1150] by Demod 455 with 296 at 2
+Id : 299, {_}: greatest_lower_bound ?828 (greatest_lower_bound ?829 identity) =>= negative_part (greatest_lower_bound ?828 ?829) [829, 828] by Super 7 with 18 at 3
+Id : 309, {_}: greatest_lower_bound ?828 (negative_part ?829) =<= negative_part (greatest_lower_bound ?828 ?829) [829, 828] by Demod 299 with 18 at 2,2
+Id : 831, {_}: greatest_lower_bound ?1150 (negative_part ?1151) =?= greatest_lower_bound (negative_part ?1150) ?1151 [1151, 1150] by Demod 465 with 309 at 2
+Id : 17491, {_}: multiply (greatest_lower_bound (inverse ?24443) (negative_part ?24444)) ?24443 =>= greatest_lower_bound (negative_part ?24443) (multiply ?24444 ?24443) [24444, 24443] by Demod 17441 with 831 at 1,2
+Id : 17492, {_}: multiply (greatest_lower_bound (inverse ?24443) (negative_part ?24444)) ?24443 =>= greatest_lower_bound (multiply ?24444 ?24443) (negative_part ?24443) [24444, 24443] by Demod 17491 with 5 at 3
+Id : 17323, {_}: multiply (greatest_lower_bound (inverse ?758) ?759) ?758 =>= negative_part (multiply ?759 ?758) [759, 758] by Demod 256 with 296 at 3
+Id : 17493, {_}: negative_part (multiply (negative_part ?24444) ?24443) =<= greatest_lower_bound (multiply ?24444 ?24443) (negative_part ?24443) [24443, 24444] by Demod 17492 with 17323 at 2
+Id : 5044, {_}: multiply (inverse ?8798) (positive_part ?8798) =>= positive_part (inverse ?8798) [8798] by Demod 5015 with 2348 at 1,3
+Id : 25992, {_}: multiply (positive_part (inverse ?35120)) (inverse (positive_part ?35120)) =>= inverse ?35120 [35120] by Super 25971 with 5044 at 1,2
+Id : 65949, {_}: negative_part (multiply (negative_part (positive_part (inverse ?78239))) (inverse (positive_part ?78239))) =>= greatest_lower_bound (inverse ?78239) (negative_part (inverse (positive_part ?78239))) [78239] by Super 17493 with 25992 at 1,3
+Id : 285, {_}: greatest_lower_bound ?806 (positive_part ?806) =>= ?806 [806] by Super 12 with 17 at 2,2
+Id : 575, {_}: greatest_lower_bound (positive_part ?1304) ?1304 =>= ?1304 [1304] by Super 5 with 285 at 3
+Id : 424, {_}: least_upper_bound identity (least_upper_bound ?1119 ?1120) =>= least_upper_bound (positive_part ?1119) ?1120 [1120, 1119] by Super 8 with 279 at 1,3
+Id : 433, {_}: positive_part (least_upper_bound ?1119 ?1120) =>= least_upper_bound (positive_part ?1119) ?1120 [1120, 1119] by Demod 424 with 279 at 2
+Id : 282, {_}: least_upper_bound ?797 (least_upper_bound ?798 identity) =>= positive_part (least_upper_bound ?797 ?798) [798, 797] by Super 8 with 17 at 3
+Id : 292, {_}: least_upper_bound ?797 (positive_part ?798) =<= positive_part (least_upper_bound ?797 ?798) [798, 797] by Demod 282 with 17 at 2,2
+Id : 749, {_}: least_upper_bound ?1119 (positive_part ?1120) =?= least_upper_bound (positive_part ?1119) ?1120 [1120, 1119] by Demod 433 with 292 at 2
+Id : 758, {_}: least_upper_bound (positive_part (positive_part ?1606)) ?1606 =>= positive_part ?1606 [1606] by Super 9 with 749 at 2
+Id : 606, {_}: least_upper_bound ?1347 (positive_part ?1348) =<= positive_part (least_upper_bound ?1347 ?1348) [1348, 1347] by Demod 282 with 17 at 2,2
+Id : 616, {_}: least_upper_bound ?1379 (positive_part identity) =>= positive_part (positive_part ?1379) [1379] by Super 606 with 17 at 1,3
+Id : 278, {_}: positive_part identity =>= identity [] by Super 9 with 17 at 2
+Id : 628, {_}: least_upper_bound ?1379 identity =<= positive_part (positive_part ?1379) [1379] by Demod 616 with 278 at 2,2
+Id : 629, {_}: positive_part ?1379 =<= positive_part (positive_part ?1379) [1379] by Demod 628 with 17 at 2
+Id : 798, {_}: least_upper_bound (positive_part ?1606) ?1606 =>= positive_part ?1606 [1606] by Demod 758 with 629 at 1,2
+Id : 5005, {_}: multiply (inverse (positive_part ?8766)) (positive_part ?8766) =<= positive_part (multiply (inverse (positive_part ?8766)) ?8766) [8766] by Super 4991 with 798 at 2,2
+Id : 5040, {_}: identity =<= positive_part (multiply (inverse (positive_part ?8766)) ?8766) [8766] by Demod 5005 with 3 at 2
+Id : 5691, {_}: greatest_lower_bound identity (multiply (inverse (positive_part ?9483)) ?9483) =>= multiply (inverse (positive_part ?9483)) ?9483 [9483] by Super 575 with 5040 at 1,2
+Id : 5736, {_}: negative_part (multiply (inverse (positive_part ?9483)) ?9483) =>= multiply (inverse (positive_part ?9483)) ?9483 [9483] by Demod 5691 with 296 at 2
+Id : 770, {_}: least_upper_bound ?1642 (positive_part ?1643) =?= least_upper_bound (positive_part ?1642) ?1643 [1643, 1642] by Demod 433 with 292 at 2
+Id : 456, {_}: least_upper_bound identity (negative_part ?1153) =>= identity [1153] by Super 11 with 296 at 2,2
+Id : 464, {_}: positive_part (negative_part ?1153) =>= identity [1153] by Demod 456 with 279 at 2
+Id : 772, {_}: least_upper_bound (negative_part ?1647) (positive_part ?1648) =>= least_upper_bound identity ?1648 [1648, 1647] by Super 770 with 464 at 1,3
+Id : 812, {_}: least_upper_bound (negative_part ?1647) (positive_part ?1648) =>= positive_part ?1648 [1648, 1647] by Demod 772 with 279 at 3
+Id : 5068, {_}: multiply (inverse (negative_part ?8875)) identity =>= positive_part (inverse (negative_part ?8875)) [8875] by Super 5066 with 464 at 2,2
+Id : 5087, {_}: inverse (negative_part ?8875) =<= positive_part (inverse (negative_part ?8875)) [8875] by Demod 5068 with 2348 at 2
+Id : 5099, {_}: least_upper_bound (negative_part ?8914) (inverse (negative_part ?8915)) =>= positive_part (inverse (negative_part ?8915)) [8915, 8914] by Super 812 with 5087 at 2,2
+Id : 5137, {_}: least_upper_bound (inverse (negative_part ?8915)) (negative_part ?8914) =>= positive_part (inverse (negative_part ?8915)) [8914, 8915] by Demod 5099 with 6 at 2
+Id : 5138, {_}: least_upper_bound (inverse (negative_part ?8915)) (negative_part ?8914) =>= inverse (negative_part ?8915) [8914, 8915] by Demod 5137 with 5087 at 3
+Id : 7238, {_}: multiply (inverse (inverse (negative_part ?11513))) (inverse (negative_part ?11513)) =?= positive_part (multiply (inverse (inverse (negative_part ?11513))) (negative_part ?11514)) [11514, 11513] by Super 4974 with 5138 at 2,2
+Id : 7311, {_}: identity =<= positive_part (multiply (inverse (inverse (negative_part ?11513))) (negative_part ?11514)) [11514, 11513] by Demod 7238 with 3 at 2
+Id : 7312, {_}: identity =<= positive_part (multiply (negative_part ?11513) (negative_part ?11514)) [11514, 11513] by Demod 7311 with 2377 at 1,1,3
+Id : 11865, {_}: negative_part (multiply (inverse identity) (multiply (negative_part ?16875) (negative_part ?16876))) =<= multiply (inverse (positive_part (multiply (negative_part ?16875) (negative_part ?16876)))) (multiply (negative_part ?16875) (negative_part ?16876)) [16876, 16875] by Super 5736 with 7312 at 1,1,1,2
+Id : 2405, {_}: multiply ?4347 (inverse ?4347) =>= identity [4347] by Super 3 with 2377 at 1,2
+Id : 2415, {_}: identity =<= inverse identity [] by Super 2 with 2405 at 2
+Id : 11917, {_}: negative_part (multiply identity (multiply (negative_part ?16875) (negative_part ?16876))) =<= multiply (inverse (positive_part (multiply (negative_part ?16875) (negative_part ?16876)))) (multiply (negative_part ?16875) (negative_part ?16876)) [16876, 16875] by Demod 11865 with 2415 at 1,1,2
+Id : 11918, {_}: negative_part (multiply identity (multiply (negative_part ?16875) (negative_part ?16876))) =>= multiply (inverse identity) (multiply (negative_part ?16875) (negative_part ?16876)) [16876, 16875] by Demod 11917 with 7312 at 1,1,3
+Id : 11919, {_}: negative_part (multiply (negative_part ?16875) (negative_part ?16876)) =<= multiply (inverse identity) (multiply (negative_part ?16875) (negative_part ?16876)) [16876, 16875] by Demod 11918 with 2 at 1,2
+Id : 11920, {_}: negative_part (multiply (negative_part ?16875) (negative_part ?16876)) =<= multiply identity (multiply (negative_part ?16875) (negative_part ?16876)) [16876, 16875] by Demod 11919 with 2415 at 1,3
+Id : 13421, {_}: negative_part (multiply (negative_part ?18780) (negative_part ?18781)) =>= multiply (negative_part ?18780) (negative_part ?18781) [18781, 18780] by Demod 11920 with 2 at 3
+Id : 5075, {_}: multiply (inverse (positive_part ?8895)) (positive_part ?8895) =>= positive_part (inverse (positive_part ?8895)) [8895] by Super 5066 with 629 at 2,2
+Id : 5090, {_}: identity =<= positive_part (inverse (positive_part ?8895)) [8895] by Demod 5075 with 3 at 2
+Id : 5175, {_}: greatest_lower_bound identity (inverse (positive_part ?9005)) =>= inverse (positive_part ?9005) [9005] by Super 575 with 5090 at 1,2
+Id : 5216, {_}: negative_part (inverse (positive_part ?9005)) =>= inverse (positive_part ?9005) [9005] by Demod 5175 with 296 at 2
+Id : 13433, {_}: negative_part (multiply (negative_part ?18822) (inverse (positive_part ?18823))) =>= multiply (negative_part ?18822) (negative_part (inverse (positive_part ?18823))) [18823, 18822] by Super 13421 with 5216 at 2,1,2
+Id : 13543, {_}: negative_part (multiply (negative_part ?18822) (inverse (positive_part ?18823))) =>= multiply (negative_part ?18822) (inverse (positive_part ?18823)) [18823, 18822] by Demod 13433 with 5216 at 2,3
+Id : 66057, {_}: multiply (negative_part (positive_part (inverse ?78239))) (inverse (positive_part ?78239)) =>= greatest_lower_bound (inverse ?78239) (negative_part (inverse (positive_part ?78239))) [78239] by Demod 65949 with 13543 at 2
+Id : 66058, {_}: multiply (negative_part (positive_part (inverse ?78239))) (inverse (positive_part ?78239)) =>= greatest_lower_bound (inverse ?78239) (inverse (positive_part ?78239)) [78239] by Demod 66057 with 5216 at 2,3
+Id : 451, {_}: negative_part (least_upper_bound identity ?1143) =>= identity [1143] by Super 12 with 296 at 2
+Id : 469, {_}: negative_part (positive_part ?1143) =>= identity [1143] by Demod 451 with 279 at 1,2
+Id : 66059, {_}: multiply identity (inverse (positive_part ?78239)) =<= greatest_lower_bound (inverse ?78239) (inverse (positive_part ?78239)) [78239] by Demod 66058 with 469 at 1,2
+Id : 66060, {_}: inverse (positive_part ?78239) =<= greatest_lower_bound (inverse ?78239) (inverse (positive_part ?78239)) [78239] by Demod 66059 with 2 at 2
+Id : 66290, {_}: greatest_lower_bound (inverse ?78524) (positive_part (inverse (positive_part ?78524))) =>= least_upper_bound (inverse (positive_part ?78524)) (negative_part (inverse ?78524)) [78524] by Super 397 with 66060 at 1,3
+Id : 66456, {_}: greatest_lower_bound (inverse ?78524) identity =<= least_upper_bound (inverse (positive_part ?78524)) (negative_part (inverse ?78524)) [78524] by Demod 66290 with 5090 at 2,2
+Id : 66457, {_}: greatest_lower_bound identity (inverse ?78524) =<= least_upper_bound (inverse (positive_part ?78524)) (negative_part (inverse ?78524)) [78524] by Demod 66456 with 5 at 2
+Id : 66458, {_}: negative_part (inverse ?78524) =<= least_upper_bound (inverse (positive_part ?78524)) (negative_part (inverse ?78524)) [78524] by Demod 66457 with 296 at 2
+Id : 80743, {_}: multiply (inverse (inverse (positive_part ?90706))) (negative_part (inverse ?90706)) =<= positive_part (multiply (inverse (inverse (positive_part ?90706))) (negative_part (inverse ?90706))) [90706] by Super 4974 with 66458 at 2,2
+Id : 80871, {_}: multiply (positive_part ?90706) (negative_part (inverse ?90706)) =<= positive_part (multiply (inverse (inverse (positive_part ?90706))) (negative_part (inverse ?90706))) [90706] by Demod 80743 with 2377 at 1,2
+Id : 80872, {_}: multiply (positive_part ?90706) (negative_part (inverse ?90706)) =<= positive_part (multiply (positive_part ?90706) (negative_part (inverse ?90706))) [90706] by Demod 80871 with 2377 at 1,1,3
+Id : 224, {_}: multiply (least_upper_bound (inverse ?681) ?682) ?681 =>= least_upper_bound identity (multiply ?682 ?681) [682, 681] by Super 218 with 3 at 1,3
+Id : 15127, {_}: multiply (least_upper_bound (inverse ?21966) ?21967) ?21966 =>= positive_part (multiply ?21967 ?21966) [21967, 21966] by Demod 224 with 279 at 3
+Id : 5107, {_}: least_upper_bound (inverse (negative_part ?8933)) (positive_part ?8934) =>= least_upper_bound (inverse (negative_part ?8933)) ?8934 [8934, 8933] by Super 749 with 5087 at 1,3
+Id : 15147, {_}: multiply (least_upper_bound (inverse (negative_part ?22031)) ?22032) (negative_part ?22031) =>= positive_part (multiply (positive_part ?22032) (negative_part ?22031)) [22032, 22031] by Super 15127 with 5107 at 1,2
+Id : 15100, {_}: multiply (least_upper_bound (inverse ?681) ?682) ?681 =>= positive_part (multiply ?682 ?681) [682, 681] by Demod 224 with 279 at 3
+Id : 15182, {_}: positive_part (multiply ?22032 (negative_part ?22031)) =<= positive_part (multiply (positive_part ?22032) (negative_part ?22031)) [22031, 22032] by Demod 15147 with 15100 at 2
+Id : 80873, {_}: multiply (positive_part ?90706) (negative_part (inverse ?90706)) =<= positive_part (multiply ?90706 (negative_part (inverse ?90706))) [90706] by Demod 80872 with 15182 at 3
+Id : 191, {_}: multiply (inverse ?607) (greatest_lower_bound ?607 ?608) =>= greatest_lower_bound identity (multiply (inverse ?607) ?608) [608, 607] by Super 185 with 3 at 1,3
+Id : 14063, {_}: multiply (inverse ?19549) (greatest_lower_bound ?19549 ?19550) =>= negative_part (multiply (inverse ?19549) ?19550) [19550, 19549] by Demod 191 with 296 at 3
+Id : 14093, {_}: multiply (inverse ?19640) (negative_part ?19640) =?= negative_part (multiply (inverse ?19640) identity) [19640] by Super 14063 with 18 at 2,2
+Id : 14179, {_}: multiply (inverse ?19758) (negative_part ?19758) =>= negative_part (inverse ?19758) [19758] by Demod 14093 with 2348 at 1,3
+Id : 14205, {_}: multiply ?19826 (negative_part (inverse ?19826)) =>= negative_part (inverse (inverse ?19826)) [19826] by Super 14179 with 2377 at 1,2
+Id : 14261, {_}: multiply ?19826 (negative_part (inverse ?19826)) =>= negative_part ?19826 [19826] by Demod 14205 with 2377 at 1,3
+Id : 80874, {_}: multiply (positive_part ?90706) (negative_part (inverse ?90706)) =>= positive_part (negative_part ?90706) [90706] by Demod 80873 with 14261 at 1,3
+Id : 80875, {_}: multiply (positive_part ?90706) (negative_part (inverse ?90706)) =>= identity [90706] by Demod 80874 with 464 at 3
+Id : 81247, {_}: multiply identity (inverse (negative_part (inverse ?91006))) =>= positive_part ?91006 [91006] by Super 2406 with 80875 at 1,2
+Id : 81627, {_}: inverse (negative_part (inverse ?91433)) =>= positive_part ?91433 [91433] by Demod 81247 with 2 at 2
+Id : 81628, {_}: inverse (negative_part ?91435) =<= positive_part (inverse ?91435) [91435] by Super 81627 with 2377 at 1,1,2
+Id : 82425, {_}: multiply (positive_part ?35122) (inverse (inverse (negative_part ?35122))) =>= ?35122 [35122] by Demod 25993 with 81628 at 1,2,2
+Id : 82501, {_}: multiply (positive_part ?35122) (negative_part ?35122) =>= ?35122 [35122] by Demod 82425 with 2377 at 2,2
+Id : 82875, {_}: a === a [] by Demod 1 with 82501 at 3
+Id : 1, {_}: a =<= multiply (positive_part a) (negative_part a) [] by prove_lat4
+% SZS output end CNFRefutation for GRP167-1.p
+22602: solved GRP167-1.p in 10.376648 using nrkbo
+22602: status Unsatisfiable for GRP167-1.p
+CLASH, statistics insufficient
+22609: Facts:
+22609: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22609: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22609: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22609: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22609: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22609: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22609: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22609: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22609: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22609: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22609: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22609: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22609: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22609: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22609: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22609: Id : 17, {_}: inverse identity =>= identity [] by lat4_1
+22609: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51
+22609: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by lat4_3 ?53 ?54
+22609: Id : 20, {_}:
+ positive_part ?56 =<= least_upper_bound ?56 identity
+ [56] by lat4_4 ?56
+22609: Id : 21, {_}:
+ negative_part ?58 =<= greatest_lower_bound ?58 identity
+ [58] by lat4_5 ?58
+22609: Id : 22, {_}:
+ least_upper_bound ?60 (greatest_lower_bound ?61 ?62)
+ =<=
+ greatest_lower_bound (least_upper_bound ?60 ?61)
+ (least_upper_bound ?60 ?62)
+ [62, 61, 60] by lat4_6 ?60 ?61 ?62
+22609: Id : 23, {_}:
+ greatest_lower_bound ?64 (least_upper_bound ?65 ?66)
+ =<=
+ least_upper_bound (greatest_lower_bound ?64 ?65)
+ (greatest_lower_bound ?64 ?66)
+ [66, 65, 64] by lat4_7 ?64 ?65 ?66
+22609: Goal:
+22609: Id : 1, {_}:
+ a =<= multiply (positive_part a) (negative_part a)
+ [] by prove_lat4
+22609: Order:
+22609: nrkbo
+22609: Leaf order:
+22609: a 3 0 3 2
+22609: identity 6 0 0
+22609: positive_part 2 1 1 0,1,3
+22609: negative_part 2 1 1 0,2,3
+22609: inverse 7 1 0
+22609: greatest_lower_bound 19 2 0
+22609: least_upper_bound 19 2 0
+22609: multiply 21 2 1 0,3
+CLASH, statistics insufficient
+22610: Facts:
+22610: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22610: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22610: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22610: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22610: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+CLASH, statistics insufficient
+22611: Facts:
+22611: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22611: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22611: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22611: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22610: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22610: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22610: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22610: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22610: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22610: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22610: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22610: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22610: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22610: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22610: Id : 17, {_}: inverse identity =>= identity [] by lat4_1
+22610: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51
+22610: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by lat4_3 ?53 ?54
+22610: Id : 20, {_}:
+ positive_part ?56 =<= least_upper_bound ?56 identity
+ [56] by lat4_4 ?56
+22610: Id : 21, {_}:
+ negative_part ?58 =<= greatest_lower_bound ?58 identity
+ [58] by lat4_5 ?58
+22610: Id : 22, {_}:
+ least_upper_bound ?60 (greatest_lower_bound ?61 ?62)
+ =<=
+ greatest_lower_bound (least_upper_bound ?60 ?61)
+ (least_upper_bound ?60 ?62)
+ [62, 61, 60] by lat4_6 ?60 ?61 ?62
+22610: Id : 23, {_}:
+ greatest_lower_bound ?64 (least_upper_bound ?65 ?66)
+ =<=
+ least_upper_bound (greatest_lower_bound ?64 ?65)
+ (greatest_lower_bound ?64 ?66)
+ [66, 65, 64] by lat4_7 ?64 ?65 ?66
+22610: Goal:
+22610: Id : 1, {_}:
+ a =<= multiply (positive_part a) (negative_part a)
+ [] by prove_lat4
+22610: Order:
+22610: kbo
+22610: Leaf order:
+22610: a 3 0 3 2
+22610: identity 6 0 0
+22610: positive_part 2 1 1 0,1,3
+22610: negative_part 2 1 1 0,2,3
+22610: inverse 7 1 0
+22610: greatest_lower_bound 19 2 0
+22610: least_upper_bound 19 2 0
+22610: multiply 21 2 1 0,3
+22611: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22611: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22611: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22611: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22611: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22611: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22611: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22611: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22611: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22611: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22611: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22611: Id : 17, {_}: inverse identity =>= identity [] by lat4_1
+22611: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51
+22611: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by lat4_3 ?53 ?54
+22611: Id : 20, {_}:
+ positive_part ?56 =>= least_upper_bound ?56 identity
+ [56] by lat4_4 ?56
+22611: Id : 21, {_}:
+ negative_part ?58 =>= greatest_lower_bound ?58 identity
+ [58] by lat4_5 ?58
+22611: Id : 22, {_}:
+ least_upper_bound ?60 (greatest_lower_bound ?61 ?62)
+ =<=
+ greatest_lower_bound (least_upper_bound ?60 ?61)
+ (least_upper_bound ?60 ?62)
+ [62, 61, 60] by lat4_6 ?60 ?61 ?62
+22611: Id : 23, {_}:
+ greatest_lower_bound ?64 (least_upper_bound ?65 ?66)
+ =>=
+ least_upper_bound (greatest_lower_bound ?64 ?65)
+ (greatest_lower_bound ?64 ?66)
+ [66, 65, 64] by lat4_7 ?64 ?65 ?66
+22611: Goal:
+22611: Id : 1, {_}:
+ a =<= multiply (positive_part a) (negative_part a)
+ [] by prove_lat4
+22611: Order:
+22611: lpo
+22611: Leaf order:
+22611: a 3 0 3 2
+22611: identity 6 0 0
+22611: positive_part 2 1 1 0,1,3
+22611: negative_part 2 1 1 0,2,3
+22611: inverse 7 1 0
+22611: greatest_lower_bound 19 2 0
+22611: least_upper_bound 19 2 0
+22611: multiply 21 2 1 0,3
+Statistics :
+Max weight : 16
+Found proof, 6.082892s
+% SZS status Unsatisfiable for GRP167-2.p
+% SZS output start CNFRefutation for GRP167-2.p
+Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
+Id : 11, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
+Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =?= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+Id : 22, {_}: least_upper_bound ?60 (greatest_lower_bound ?61 ?62) =<= greatest_lower_bound (least_upper_bound ?60 ?61) (least_upper_bound ?60 ?62) [62, 61, 60] by lat4_6 ?60 ?61 ?62
+Id : 221, {_}: multiply (least_upper_bound ?664 ?665) ?666 =<= least_upper_bound (multiply ?664 ?666) (multiply ?665 ?666) [666, 665, 664] by monotony_lub2 ?664 ?665 ?666
+Id : 21, {_}: negative_part ?58 =<= greatest_lower_bound ?58 identity [58] by lat4_5 ?58
+Id : 14, {_}: multiply ?38 (greatest_lower_bound ?39 ?40) =<= greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
+Id : 20, {_}: positive_part ?56 =<= least_upper_bound ?56 identity [56] by lat4_4 ?56
+Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =<= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+Id : 19, {_}: inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) [54, 53] by lat4_3 ?53 ?54
+Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+Id : 17, {_}: inverse identity =>= identity [] by lat4_1
+Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+Id : 28, {_}: multiply (multiply ?75 ?76) ?77 =?= multiply ?75 (multiply ?76 ?77) [77, 76, 75] by associativity ?75 ?76 ?77
+Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51
+Id : 302, {_}: inverse (multiply ?849 ?850) =<= multiply (inverse ?850) (inverse ?849) [850, 849] by lat4_3 ?849 ?850
+Id : 1638, {_}: inverse (multiply ?3326 (inverse ?3327)) =>= multiply ?3327 (inverse ?3326) [3327, 3326] by Super 302 with 18 at 1,3
+Id : 30, {_}: multiply (multiply ?82 (inverse ?83)) ?83 =>= multiply ?82 identity [83, 82] by Super 28 with 3 at 2,3
+Id : 303, {_}: inverse (multiply identity ?852) =<= multiply (inverse ?852) identity [852] by Super 302 with 17 at 2,3
+Id : 587, {_}: inverse ?1361 =<= multiply (inverse ?1361) identity [1361] by Demod 303 with 2 at 1,2
+Id : 589, {_}: inverse (inverse ?1364) =<= multiply ?1364 identity [1364] by Super 587 with 18 at 1,3
+Id : 603, {_}: ?1364 =<= multiply ?1364 identity [1364] by Demod 589 with 18 at 2
+Id : 645, {_}: multiply (multiply ?82 (inverse ?83)) ?83 =>= ?82 [83, 82] by Demod 30 with 603 at 3
+Id : 1648, {_}: inverse ?3357 =<= multiply ?3358 (inverse (multiply ?3357 (inverse (inverse ?3358)))) [3358, 3357] by Super 1638 with 645 at 1,2
+Id : 306, {_}: inverse (multiply ?859 (inverse ?860)) =>= multiply ?860 (inverse ?859) [860, 859] by Super 302 with 18 at 1,3
+Id : 1667, {_}: inverse ?3357 =<= multiply ?3358 (multiply (inverse ?3358) (inverse ?3357)) [3358, 3357] by Demod 1648 with 306 at 2,3
+Id : 48018, {_}: inverse ?56639 =<= multiply ?56640 (inverse (multiply ?56639 ?56640)) [56640, 56639] by Demod 1667 with 19 at 2,3
+Id : 657, {_}: multiply ?1476 (least_upper_bound ?1477 identity) =?= least_upper_bound (multiply ?1476 ?1477) ?1476 [1477, 1476] by Super 13 with 603 at 2,3
+Id : 4078, {_}: multiply ?7362 (positive_part ?7363) =<= least_upper_bound (multiply ?7362 ?7363) ?7362 [7363, 7362] by Demod 657 with 20 at 2,2
+Id : 4080, {_}: multiply (inverse ?7367) (positive_part ?7367) =>= least_upper_bound identity (inverse ?7367) [7367] by Super 4078 with 3 at 1,3
+Id : 320, {_}: least_upper_bound identity ?881 =>= positive_part ?881 [881] by Super 6 with 20 at 3
+Id : 4115, {_}: multiply (inverse ?7367) (positive_part ?7367) =>= positive_part (inverse ?7367) [7367] by Demod 4080 with 320 at 3
+Id : 618, {_}: multiply (multiply ?1420 (inverse ?1421)) ?1421 =>= multiply ?1420 identity [1421, 1420] by Super 28 with 3 at 2,3
+Id : 620, {_}: multiply (multiply ?1425 ?1426) (inverse ?1426) =>= multiply ?1425 identity [1426, 1425] by Super 618 with 18 at 2,1,2
+Id : 34073, {_}: multiply (multiply ?41189 ?41190) (inverse ?41190) =>= ?41189 [41190, 41189] by Demod 620 with 603 at 3
+Id : 651, {_}: multiply ?1462 (greatest_lower_bound ?1463 identity) =?= greatest_lower_bound (multiply ?1462 ?1463) ?1462 [1463, 1462] by Super 14 with 603 at 2,3
+Id : 676, {_}: multiply ?1462 (negative_part ?1463) =<= greatest_lower_bound (multiply ?1462 ?1463) ?1462 [1463, 1462] by Demod 651 with 21 at 2,2
+Id : 227, {_}: multiply (least_upper_bound (inverse ?687) ?688) ?687 =>= least_upper_bound identity (multiply ?688 ?687) [688, 687] by Super 221 with 3 at 1,3
+Id : 14335, {_}: multiply (least_upper_bound (inverse ?21902) ?21903) ?21902 =>= positive_part (multiply ?21903 ?21902) [21903, 21902] by Demod 227 with 320 at 3
+Id : 14360, {_}: multiply (positive_part (inverse ?21984)) ?21984 =>= positive_part (multiply identity ?21984) [21984] by Super 14335 with 20 at 1,2
+Id : 14399, {_}: multiply (positive_part (inverse ?21984)) ?21984 =>= positive_part ?21984 [21984] by Demod 14360 with 2 at 1,3
+Id : 14409, {_}: multiply (positive_part (inverse ?22003)) (negative_part ?22003) =>= greatest_lower_bound (positive_part ?22003) (positive_part (inverse ?22003)) [22003] by Super 676 with 14399 at 1,3
+Id : 504, {_}: least_upper_bound identity (greatest_lower_bound ?1268 ?1269) =<= greatest_lower_bound (least_upper_bound identity ?1268) (positive_part ?1269) [1269, 1268] by Super 22 with 320 at 2,3
+Id : 513, {_}: positive_part (greatest_lower_bound ?1268 ?1269) =<= greatest_lower_bound (least_upper_bound identity ?1268) (positive_part ?1269) [1269, 1268] by Demod 504 with 320 at 2
+Id : 514, {_}: positive_part (greatest_lower_bound ?1268 ?1269) =<= greatest_lower_bound (positive_part ?1268) (positive_part ?1269) [1269, 1268] by Demod 513 with 320 at 1,3
+Id : 14487, {_}: multiply (positive_part (inverse ?22003)) (negative_part ?22003) =>= positive_part (greatest_lower_bound ?22003 (inverse ?22003)) [22003] by Demod 14409 with 514 at 3
+Id : 501, {_}: least_upper_bound identity (least_upper_bound ?1262 ?1263) =>= least_upper_bound (positive_part ?1262) ?1263 [1263, 1262] by Super 8 with 320 at 1,3
+Id : 518, {_}: positive_part (least_upper_bound ?1262 ?1263) =>= least_upper_bound (positive_part ?1262) ?1263 [1263, 1262] by Demod 501 with 320 at 2
+Id : 317, {_}: least_upper_bound ?872 (least_upper_bound ?873 identity) =>= positive_part (least_upper_bound ?872 ?873) [873, 872] by Super 8 with 20 at 3
+Id : 329, {_}: least_upper_bound ?872 (positive_part ?873) =<= positive_part (least_upper_bound ?872 ?873) [873, 872] by Demod 317 with 20 at 2,2
+Id : 975, {_}: least_upper_bound ?1262 (positive_part ?1263) =?= least_upper_bound (positive_part ?1262) ?1263 [1263, 1262] by Demod 518 with 329 at 2
+Id : 4147, {_}: multiply (inverse ?7493) (positive_part ?7493) =>= positive_part (inverse ?7493) [7493] by Demod 4080 with 320 at 3
+Id : 337, {_}: greatest_lower_bound identity ?912 =>= negative_part ?912 [912] by Super 5 with 21 at 3
+Id : 533, {_}: least_upper_bound identity (negative_part ?1296) =>= identity [1296] by Super 11 with 337 at 2,2
+Id : 549, {_}: positive_part (negative_part ?1296) =>= identity [1296] by Demod 533 with 320 at 2
+Id : 4149, {_}: multiply (inverse (negative_part ?7496)) identity =>= positive_part (inverse (negative_part ?7496)) [7496] by Super 4147 with 549 at 2,2
+Id : 4174, {_}: inverse (negative_part ?7496) =<= positive_part (inverse (negative_part ?7496)) [7496] by Demod 4149 with 603 at 2
+Id : 4193, {_}: least_upper_bound (inverse (negative_part ?7552)) (positive_part ?7553) =>= least_upper_bound (inverse (negative_part ?7552)) ?7553 [7553, 7552] by Super 975 with 4174 at 1,3
+Id : 14357, {_}: multiply (least_upper_bound (inverse (negative_part ?21975)) ?21976) (negative_part ?21975) =>= positive_part (multiply (positive_part ?21976) (negative_part ?21975)) [21976, 21975] by Super 14335 with 4193 at 1,2
+Id : 14303, {_}: multiply (least_upper_bound (inverse ?687) ?688) ?687 =>= positive_part (multiply ?688 ?687) [688, 687] by Demod 227 with 320 at 3
+Id : 14396, {_}: positive_part (multiply ?21976 (negative_part ?21975)) =<= positive_part (multiply (positive_part ?21976) (negative_part ?21975)) [21975, 21976] by Demod 14357 with 14303 at 2
+Id : 15618, {_}: positive_part (multiply (inverse ?23238) (negative_part ?23238)) =<= positive_part (positive_part (greatest_lower_bound ?23238 (inverse ?23238))) [23238] by Super 14396 with 14487 at 1,3
+Id : 4791, {_}: multiply ?8267 (negative_part ?8268) =<= greatest_lower_bound (multiply ?8267 ?8268) ?8267 [8268, 8267] by Demod 651 with 21 at 2,2
+Id : 4793, {_}: multiply (inverse ?8272) (negative_part ?8272) =>= greatest_lower_bound identity (inverse ?8272) [8272] by Super 4791 with 3 at 1,3
+Id : 4834, {_}: multiply (inverse ?8272) (negative_part ?8272) =>= negative_part (inverse ?8272) [8272] by Demod 4793 with 337 at 3
+Id : 15709, {_}: positive_part (negative_part (inverse ?23238)) =<= positive_part (positive_part (greatest_lower_bound ?23238 (inverse ?23238))) [23238] by Demod 15618 with 4834 at 1,2
+Id : 774, {_}: least_upper_bound ?1603 (positive_part ?1604) =<= positive_part (least_upper_bound ?1603 ?1604) [1604, 1603] by Demod 317 with 20 at 2,2
+Id : 784, {_}: least_upper_bound ?1635 (positive_part identity) =>= positive_part (positive_part ?1635) [1635] by Super 774 with 20 at 1,3
+Id : 322, {_}: positive_part identity =>= identity [] by Super 9 with 20 at 2
+Id : 796, {_}: least_upper_bound ?1635 identity =<= positive_part (positive_part ?1635) [1635] by Demod 784 with 322 at 2,2
+Id : 797, {_}: positive_part ?1635 =<= positive_part (positive_part ?1635) [1635] by Demod 796 with 20 at 2
+Id : 15710, {_}: positive_part (negative_part (inverse ?23238)) =<= positive_part (greatest_lower_bound ?23238 (inverse ?23238)) [23238] by Demod 15709 with 797 at 3
+Id : 15711, {_}: identity =<= positive_part (greatest_lower_bound ?23238 (inverse ?23238)) [23238] by Demod 15710 with 549 at 2
+Id : 15820, {_}: multiply (positive_part (inverse ?22003)) (negative_part ?22003) =>= identity [22003] by Demod 14487 with 15711 at 3
+Id : 34109, {_}: multiply identity (inverse (negative_part ?41304)) =>= positive_part (inverse ?41304) [41304] by Super 34073 with 15820 at 1,2
+Id : 34155, {_}: inverse (negative_part ?41304) =<= positive_part (inverse ?41304) [41304] by Demod 34109 with 2 at 2
+Id : 34195, {_}: multiply (inverse ?7367) (positive_part ?7367) =>= inverse (negative_part ?7367) [7367] by Demod 4115 with 34155 at 3
+Id : 48045, {_}: inverse (inverse ?56723) =<= multiply (positive_part ?56723) (inverse (inverse (negative_part ?56723))) [56723] by Super 48018 with 34195 at 1,2,3
+Id : 48126, {_}: ?56723 =<= multiply (positive_part ?56723) (inverse (inverse (negative_part ?56723))) [56723] by Demod 48045 with 18 at 2
+Id : 48127, {_}: ?56723 =<= multiply (positive_part ?56723) (negative_part ?56723) [56723] by Demod 48126 with 18 at 2,3
+Id : 48357, {_}: a === a [] by Demod 1 with 48127 at 3
+Id : 1, {_}: a =<= multiply (positive_part a) (negative_part a) [] by prove_lat4
+% SZS output end CNFRefutation for GRP167-2.p
+22609: solved GRP167-2.p in 6.08038 using nrkbo
+22609: status Unsatisfiable for GRP167-2.p
+NO CLASH, using fixed ground order
+22621: Facts:
+NO CLASH, using fixed ground order
+22622: Facts:
+22622: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22622: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22622: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22622: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22622: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22622: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22622: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22622: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22622: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22622: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22622: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22622: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22622: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22622: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22622: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22622: Id : 17, {_}: least_upper_bound identity a =>= a [] by p09a_1
+22622: Id : 18, {_}: least_upper_bound identity b =>= b [] by p09a_2
+22622: Id : 19, {_}: least_upper_bound identity c =>= c [] by p09a_3
+22622: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09a_4
+22622: Goal:
+22622: Id : 1, {_}:
+ greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
+ [] by prove_p09a
+22622: Order:
+22622: kbo
+22622: Leaf order:
+22622: b 4 0 1 1,2,2
+22622: c 4 0 2 2,2,2
+22622: a 5 0 2 1,2
+22622: identity 6 0 0
+22622: inverse 1 1 0
+22622: least_upper_bound 16 2 0
+22622: greatest_lower_bound 16 2 2 0,2
+22622: multiply 19 2 1 0,2,2
+NO CLASH, using fixed ground order
+22623: Facts:
+22623: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22623: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22623: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22623: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22623: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22623: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22623: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22623: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22623: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22623: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22623: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22623: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22623: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22623: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22623: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22623: Id : 17, {_}: least_upper_bound identity a =>= a [] by p09a_1
+22623: Id : 18, {_}: least_upper_bound identity b =>= b [] by p09a_2
+22623: Id : 19, {_}: least_upper_bound identity c =>= c [] by p09a_3
+22623: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09a_4
+22623: Goal:
+22623: Id : 1, {_}:
+ greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
+ [] by prove_p09a
+22623: Order:
+22623: lpo
+22623: Leaf order:
+22623: b 4 0 1 1,2,2
+22623: c 4 0 2 2,2,2
+22623: a 5 0 2 1,2
+22623: identity 6 0 0
+22623: inverse 1 1 0
+22623: least_upper_bound 16 2 0
+22623: greatest_lower_bound 16 2 2 0,2
+22623: multiply 19 2 1 0,2,2
+22621: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22621: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22621: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22621: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22621: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22621: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22621: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22621: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22621: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22621: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22621: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22621: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22621: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22621: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22621: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22621: Id : 17, {_}: least_upper_bound identity a =>= a [] by p09a_1
+22621: Id : 18, {_}: least_upper_bound identity b =>= b [] by p09a_2
+22621: Id : 19, {_}: least_upper_bound identity c =>= c [] by p09a_3
+22621: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09a_4
+22621: Goal:
+22621: Id : 1, {_}:
+ greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
+ [] by prove_p09a
+22621: Order:
+22621: nrkbo
+22621: Leaf order:
+22621: b 4 0 1 1,2,2
+22621: c 4 0 2 2,2,2
+22621: a 5 0 2 1,2
+22621: identity 6 0 0
+22621: inverse 1 1 0
+22621: least_upper_bound 16 2 0
+22621: greatest_lower_bound 16 2 2 0,2
+22621: multiply 19 2 1 0,2,2
+% SZS status Timeout for GRP178-1.p
+NO CLASH, using fixed ground order
+22657: Facts:
+22657: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22657: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22657: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22657: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22657: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22657: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22657: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22657: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22657: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22657: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22657: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22657: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22657: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22657: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22657: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22657: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1
+22657: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2
+22657: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3
+22657: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09b_4
+22657: Goal:
+22657: Id : 1, {_}:
+ greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
+ [] by prove_p09b
+22657: Order:
+22657: nrkbo
+22657: Leaf order:
+22657: b 3 0 1 1,2,2
+22657: c 3 0 2 2,2,2
+22657: a 4 0 2 1,2
+22657: identity 9 0 0
+22657: inverse 1 1 0
+22657: least_upper_bound 13 2 0
+22657: multiply 19 2 1 0,2,2
+22657: greatest_lower_bound 19 2 2 0,2
+NO CLASH, using fixed ground order
+22658: Facts:
+22658: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22658: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22658: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22658: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22658: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22658: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22658: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22658: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22658: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22658: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22658: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22658: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22658: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22658: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22658: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22658: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1
+22658: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2
+22658: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3
+22658: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09b_4
+22658: Goal:
+22658: Id : 1, {_}:
+ greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
+ [] by prove_p09b
+22658: Order:
+22658: kbo
+22658: Leaf order:
+22658: b 3 0 1 1,2,2
+22658: c 3 0 2 2,2,2
+22658: a 4 0 2 1,2
+22658: identity 9 0 0
+22658: inverse 1 1 0
+22658: least_upper_bound 13 2 0
+22658: multiply 19 2 1 0,2,2
+22658: greatest_lower_bound 19 2 2 0,2
+NO CLASH, using fixed ground order
+22659: Facts:
+22659: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22659: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22659: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22659: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22659: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22659: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22659: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22659: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22659: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22659: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22659: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22659: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22659: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22659: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22659: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22659: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1
+22659: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2
+22659: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3
+22659: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09b_4
+22659: Goal:
+22659: Id : 1, {_}:
+ greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
+ [] by prove_p09b
+22659: Order:
+22659: lpo
+22659: Leaf order:
+22659: b 3 0 1 1,2,2
+22659: c 3 0 2 2,2,2
+22659: a 4 0 2 1,2
+22659: identity 9 0 0
+22659: inverse 1 1 0
+22659: least_upper_bound 13 2 0
+22659: multiply 19 2 1 0,2,2
+22659: greatest_lower_bound 19 2 2 0,2
+% SZS status Timeout for GRP178-2.p
+CLASH, statistics insufficient
+22685: Facts:
+22685: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22685: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22685: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22685: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22685: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22685: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22685: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22685: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22685: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22685: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22685: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22685: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22685: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22685: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22685: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22685: Id : 17, {_}:
+ greatest_lower_bound a c =>= greatest_lower_bound b c
+ [] by p12x_1
+22685: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_2
+22685: Id : 19, {_}:
+ inverse (greatest_lower_bound ?52 ?53)
+ =<=
+ least_upper_bound (inverse ?52) (inverse ?53)
+ [53, 52] by p12x_3 ?52 ?53
+22685: Id : 20, {_}:
+ inverse (least_upper_bound ?55 ?56)
+ =<=
+ greatest_lower_bound (inverse ?55) (inverse ?56)
+ [56, 55] by p12x_4 ?55 ?56
+22685: Goal:
+22685: Id : 1, {_}: a =>= b [] by prove_p12x
+22685: Order:
+22685: nrkbo
+22685: Leaf order:
+22685: identity 2 0 0
+22685: a 3 0 1 2
+22685: b 3 0 1 3
+22685: c 4 0 0
+22685: inverse 7 1 0
+22685: greatest_lower_bound 17 2 0
+22685: least_upper_bound 17 2 0
+22685: multiply 18 2 0
+CLASH, statistics insufficient
+22686: Facts:
+22686: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22686: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22686: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22686: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22686: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+CLASH, statistics insufficient
+22687: Facts:
+22687: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22687: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22687: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22687: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22687: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22687: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22686: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22686: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22686: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22686: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22686: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22686: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22686: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22686: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22686: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22686: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22686: Id : 17, {_}:
+ greatest_lower_bound a c =>= greatest_lower_bound b c
+ [] by p12x_1
+22686: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_2
+22686: Id : 19, {_}:
+ inverse (greatest_lower_bound ?52 ?53)
+ =<=
+ least_upper_bound (inverse ?52) (inverse ?53)
+ [53, 52] by p12x_3 ?52 ?53
+22686: Id : 20, {_}:
+ inverse (least_upper_bound ?55 ?56)
+ =<=
+ greatest_lower_bound (inverse ?55) (inverse ?56)
+ [56, 55] by p12x_4 ?55 ?56
+22686: Goal:
+22686: Id : 1, {_}: a =>= b [] by prove_p12x
+22686: Order:
+22686: kbo
+22686: Leaf order:
+22686: identity 2 0 0
+22686: a 3 0 1 2
+22686: b 3 0 1 3
+22686: c 4 0 0
+22686: inverse 7 1 0
+22686: greatest_lower_bound 17 2 0
+22686: least_upper_bound 17 2 0
+22686: multiply 18 2 0
+22687: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22687: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22687: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22687: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22687: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22687: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22687: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22687: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22687: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22687: Id : 17, {_}:
+ greatest_lower_bound a c =>= greatest_lower_bound b c
+ [] by p12x_1
+22687: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_2
+22687: Id : 19, {_}:
+ inverse (greatest_lower_bound ?52 ?53)
+ =>=
+ least_upper_bound (inverse ?52) (inverse ?53)
+ [53, 52] by p12x_3 ?52 ?53
+22687: Id : 20, {_}:
+ inverse (least_upper_bound ?55 ?56)
+ =>=
+ greatest_lower_bound (inverse ?55) (inverse ?56)
+ [56, 55] by p12x_4 ?55 ?56
+22687: Goal:
+22687: Id : 1, {_}: a =>= b [] by prove_p12x
+22687: Order:
+22687: lpo
+22687: Leaf order:
+22687: identity 2 0 0
+22687: a 3 0 1 2
+22687: b 3 0 1 3
+22687: c 4 0 0
+22687: inverse 7 1 0
+22687: greatest_lower_bound 17 2 0
+22687: least_upper_bound 17 2 0
+22687: multiply 18 2 0
+% SZS status Timeout for GRP181-3.p
+NO CLASH, using fixed ground order
+22714: Facts:
+22714: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22714: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22714: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22714: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22714: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22714: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22714: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22714: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22714: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22714: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22714: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22714: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22714: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22714: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22714: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22714: Id : 17, {_}: inverse identity =>= identity [] by p21_1
+22714: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p21_2 ?51
+22714: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p21_3 ?53 ?54
+22714: Goal:
+22714: Id : 1, {_}:
+ multiply (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =>=
+ multiply (inverse (greatest_lower_bound a identity))
+ (least_upper_bound a identity)
+ [] by prove_p21
+22714: Order:
+22714: nrkbo
+22714: Leaf order:
+22714: a 4 0 4 1,1,2
+22714: identity 8 0 4 2,1,2
+22714: inverse 9 1 2 0,2,2
+22714: least_upper_bound 15 2 2 0,1,2
+22714: greatest_lower_bound 15 2 2 0,1,2,2
+22714: multiply 22 2 2 0,2
+NO CLASH, using fixed ground order
+22715: Facts:
+22715: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22715: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22715: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22715: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22715: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22715: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22715: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22715: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22715: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22715: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22715: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22715: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22715: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22715: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22715: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22715: Id : 17, {_}: inverse identity =>= identity [] by p21_1
+22715: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p21_2 ?51
+22715: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p21_3 ?53 ?54
+22715: Goal:
+22715: Id : 1, {_}:
+ multiply (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =<=
+ multiply (inverse (greatest_lower_bound a identity))
+ (least_upper_bound a identity)
+ [] by prove_p21
+22715: Order:
+22715: kbo
+22715: Leaf order:
+22715: a 4 0 4 1,1,2
+22715: identity 8 0 4 2,1,2
+22715: inverse 9 1 2 0,2,2
+22715: least_upper_bound 15 2 2 0,1,2
+22715: greatest_lower_bound 15 2 2 0,1,2,2
+22715: multiply 22 2 2 0,2
+NO CLASH, using fixed ground order
+22716: Facts:
+22716: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22716: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22716: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22716: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22716: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22716: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22716: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22716: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22716: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22716: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22716: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22716: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22716: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22716: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22716: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22716: Id : 17, {_}: inverse identity =>= identity [] by p21_1
+22716: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p21_2 ?51
+22716: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p21_3 ?53 ?54
+22716: Goal:
+22716: Id : 1, {_}:
+ multiply (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =<=
+ multiply (inverse (greatest_lower_bound a identity))
+ (least_upper_bound a identity)
+ [] by prove_p21
+22716: Order:
+22716: lpo
+22716: Leaf order:
+22716: a 4 0 4 1,1,2
+22716: identity 8 0 4 2,1,2
+22716: inverse 9 1 2 0,2,2
+22716: least_upper_bound 15 2 2 0,1,2
+22716: greatest_lower_bound 15 2 2 0,1,2,2
+22716: multiply 22 2 2 0,2
+% SZS status Timeout for GRP184-2.p
+NO CLASH, using fixed ground order
+22807: Facts:
+22807: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22807: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22807: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22807: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22807: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22807: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22807: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22807: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22807: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22807: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22807: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22807: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22807: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22807: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22807: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22807: Goal:
+22807: Id : 1, {_}:
+ least_upper_bound (least_upper_bound (multiply a b) identity)
+ (multiply (least_upper_bound a identity)
+ (least_upper_bound b identity))
+ =>=
+ multiply (least_upper_bound a identity)
+ (least_upper_bound b identity)
+ [] by prove_p22a
+22807: Order:
+22807: nrkbo
+22807: Leaf order:
+22807: a 3 0 3 1,1,1,2
+22807: b 3 0 3 2,1,1,2
+22807: identity 7 0 5 2,1,2
+22807: inverse 1 1 0
+22807: greatest_lower_bound 13 2 0
+22807: least_upper_bound 19 2 6 0,2
+22807: multiply 21 2 3 0,1,1,2
+NO CLASH, using fixed ground order
+22808: Facts:
+22808: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22808: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22808: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22808: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22808: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22808: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22808: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22808: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22808: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22808: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22808: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22808: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22808: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22808: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22808: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22808: Goal:
+22808: Id : 1, {_}:
+ least_upper_bound (least_upper_bound (multiply a b) identity)
+ (multiply (least_upper_bound a identity)
+ (least_upper_bound b identity))
+ =>=
+ multiply (least_upper_bound a identity)
+ (least_upper_bound b identity)
+ [] by prove_p22a
+22808: Order:
+22808: kbo
+22808: Leaf order:
+22808: a 3 0 3 1,1,1,2
+22808: b 3 0 3 2,1,1,2
+22808: identity 7 0 5 2,1,2
+22808: inverse 1 1 0
+22808: greatest_lower_bound 13 2 0
+22808: least_upper_bound 19 2 6 0,2
+22808: multiply 21 2 3 0,1,1,2
+NO CLASH, using fixed ground order
+22809: Facts:
+22809: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22809: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22809: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22809: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22809: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22809: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22809: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22809: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22809: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22809: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22809: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22809: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22809: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22809: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22809: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22809: Goal:
+22809: Id : 1, {_}:
+ least_upper_bound (least_upper_bound (multiply a b) identity)
+ (multiply (least_upper_bound a identity)
+ (least_upper_bound b identity))
+ =>=
+ multiply (least_upper_bound a identity)
+ (least_upper_bound b identity)
+ [] by prove_p22a
+22809: Order:
+22809: lpo
+22809: Leaf order:
+22809: a 3 0 3 1,1,1,2
+22809: b 3 0 3 2,1,1,2
+22809: identity 7 0 5 2,1,2
+22809: inverse 1 1 0
+22809: greatest_lower_bound 13 2 0
+22809: least_upper_bound 19 2 6 0,2
+22809: multiply 21 2 3 0,1,1,2
+Statistics :
+Max weight : 21
+Found proof, 1.740382s
+% SZS status Unsatisfiable for GRP185-1.p
+% SZS output start CNFRefutation for GRP185-1.p
+Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+Id : 21, {_}: multiply (multiply ?57 ?58) ?59 =>= multiply ?57 (multiply ?58 ?59) [59, 58, 57] by associativity ?57 ?58 ?59
+Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
+Id : 23, {_}: multiply identity ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Super 21 with 3 at 1,2
+Id : 482, {_}: ?594 =<= multiply (inverse ?595) (multiply ?595 ?594) [595, 594] by Demod 23 with 2 at 2
+Id : 484, {_}: ?599 =<= multiply (inverse (inverse ?599)) identity [599] by Super 482 with 3 at 2,3
+Id : 27, {_}: ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Demod 23 with 2 at 2
+Id : 490, {_}: multiply ?621 ?622 =<= multiply (inverse (inverse ?621)) ?622 [622, 621] by Super 482 with 27 at 2,3
+Id : 725, {_}: ?599 =<= multiply ?599 identity [599] by Demod 484 with 490 at 3
+Id : 73, {_}: least_upper_bound ?180 (least_upper_bound ?180 ?181) =>= least_upper_bound ?180 ?181 [181, 180] by Super 8 with 9 at 1,3
+Id : 57, {_}: least_upper_bound ?143 (least_upper_bound ?144 ?145) =?= least_upper_bound ?144 (least_upper_bound ?145 ?143) [145, 144, 143] by Super 6 with 8 at 3
+Id : 3011, {_}: least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b))) === least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b))) [] by Demod 3010 with 73 at 2,2,2
+Id : 3010, {_}: least_upper_bound b (least_upper_bound a (least_upper_bound identity (least_upper_bound identity (multiply a b)))) =>= least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b))) [] by Demod 3009 with 8 at 2,2
+Id : 3009, {_}: least_upper_bound b (least_upper_bound (least_upper_bound a identity) (least_upper_bound identity (multiply a b))) =>= least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b))) [] by Demod 3008 with 8 at 2
+Id : 3008, {_}: least_upper_bound (least_upper_bound b (least_upper_bound a identity)) (least_upper_bound identity (multiply a b)) =>= least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b))) [] by Demod 3007 with 8 at 2,3
+Id : 3007, {_}: least_upper_bound (least_upper_bound b (least_upper_bound a identity)) (least_upper_bound identity (multiply a b)) =>= least_upper_bound b (least_upper_bound (least_upper_bound a identity) (multiply a b)) [] by Demod 3006 with 57 at 2
+Id : 3006, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a identity))) =>= least_upper_bound b (least_upper_bound (least_upper_bound a identity) (multiply a b)) [] by Demod 3005 with 8 at 3
+Id : 3005, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a identity))) =>= least_upper_bound (least_upper_bound b (least_upper_bound a identity)) (multiply a b) [] by Demod 3004 with 2 at 2,2,2,2,2
+Id : 3004, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a (multiply identity identity)))) =>= least_upper_bound (least_upper_bound b (least_upper_bound a identity)) (multiply a b) [] by Demod 3003 with 725 at 1,2,2,2,2
+Id : 3003, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound (least_upper_bound b (least_upper_bound a identity)) (multiply a b) [] by Demod 3002 with 2 at 1,2,2,2
+Id : 3002, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound (least_upper_bound b (least_upper_bound a identity)) (multiply a b) [] by Demod 3001 with 6 at 3
+Id : 3001, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a identity)) [] by Demod 3000 with 73 at 2,2
+Id : 3000, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a identity)) [] by Demod 2999 with 2 at 2,2,2,3
+Id : 2999, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a (multiply identity identity))) [] by Demod 2998 with 725 at 1,2,2,3
+Id : 2998, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) (multiply identity identity))) [] by Demod 2997 with 2 at 1,2,3
+Id : 2997, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))) [] by Demod 2996 with 8 at 2,2,2
+Id : 2996, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))) [] by Demod 2995 with 8 at 3
+Id : 2995, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)) [] by Demod 2994 with 15 at 2,2,2,2
+Id : 2994, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)) [] by Demod 2993 with 15 at 1,2,2,2
+Id : 2993, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)) [] by Demod 2992 with 15 at 2,3
+Id : 2992, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (multiply (least_upper_bound a identity) identity) [] by Demod 2991 with 15 at 1,3
+Id : 2991, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity) [] by Demod 2990 with 13 at 2,2,2
+Id : 2990, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) =>= least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity) [] by Demod 2989 with 13 at 3
+Id : 2989, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 56 with 8 at 2
+Id : 56, {_}: least_upper_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 1 with 6 at 1,2
+Id : 1, {_}: least_upper_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by prove_p22a
+% SZS output end CNFRefutation for GRP185-1.p
+22809: solved GRP185-1.p in 0.852052 using lpo
+22809: status Unsatisfiable for GRP185-1.p
+NO CLASH, using fixed ground order
+22814: Facts:
+NO CLASH, using fixed ground order
+22815: Facts:
+22815: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22815: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22815: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22815: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22815: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22815: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22815: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+NO CLASH, using fixed ground order
+22816: Facts:
+22816: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22816: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22816: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22816: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22816: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22816: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22816: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22816: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22814: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22815: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22814: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+22815: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22815: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22815: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22814: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+22814: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+22814: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+22815: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22814: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+22815: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22814: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+22814: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+22814: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22814: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22814: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22814: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22814: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22814: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22814: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22814: Id : 17, {_}: inverse identity =>= identity [] by p22a_1
+22814: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
+22814: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p22a_3 ?53 ?54
+22814: Goal:
+22814: Id : 1, {_}:
+ least_upper_bound (least_upper_bound (multiply a b) identity)
+ (multiply (least_upper_bound a identity)
+ (least_upper_bound b identity))
+ =>=
+ multiply (least_upper_bound a identity)
+ (least_upper_bound b identity)
+ [] by prove_p22a
+22814: Order:
+22814: nrkbo
+22814: Leaf order:
+22814: a 3 0 3 1,1,1,2
+22814: b 3 0 3 2,1,1,2
+22814: identity 9 0 5 2,1,2
+22814: inverse 7 1 0
+22814: greatest_lower_bound 13 2 0
+22814: least_upper_bound 19 2 6 0,2
+22814: multiply 23 2 3 0,1,1,2
+22816: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+22815: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22815: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22815: Id : 17, {_}: inverse identity =>= identity [] by p22a_1
+22815: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
+22815: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p22a_3 ?53 ?54
+22815: Goal:
+22815: Id : 1, {_}:
+ least_upper_bound (least_upper_bound (multiply a b) identity)
+ (multiply (least_upper_bound a identity)
+ (least_upper_bound b identity))
+ =>=
+ multiply (least_upper_bound a identity)
+ (least_upper_bound b identity)
+ [] by prove_p22a
+22815: Order:
+22815: kbo
+22815: Leaf order:
+22815: a 3 0 3 1,1,1,2
+22815: b 3 0 3 2,1,1,2
+22815: identity 9 0 5 2,1,2
+22815: inverse 7 1 0
+22815: greatest_lower_bound 13 2 0
+22815: least_upper_bound 19 2 6 0,2
+22815: multiply 23 2 3 0,1,1,2
+22816: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+22816: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+22816: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+22816: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+22816: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+22816: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+22816: Id : 17, {_}: inverse identity =>= identity [] by p22a_1
+22816: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
+22816: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p22a_3 ?53 ?54
+22816: Goal:
+22816: Id : 1, {_}:
+ least_upper_bound (least_upper_bound (multiply a b) identity)
+ (multiply (least_upper_bound a identity)
+ (least_upper_bound b identity))
+ =>=
+ multiply (least_upper_bound a identity)
+ (least_upper_bound b identity)
+ [] by prove_p22a
+22816: Order:
+22816: lpo
+22816: Leaf order:
+22816: a 3 0 3 1,1,1,2
+22816: b 3 0 3 2,1,1,2
+22816: identity 9 0 5 2,1,2
+22816: inverse 7 1 0
+22816: greatest_lower_bound 13 2 0
+22816: least_upper_bound 19 2 6 0,2
+22816: multiply 23 2 3 0,1,1,2
+Statistics :
+Max weight : 21
+Found proof, 4.698116s
+% SZS status Unsatisfiable for GRP185-2.p
+% SZS output start CNFRefutation for GRP185-2.p
+Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
+Id : 17, {_}: inverse identity =>= identity [] by p22a_1
+Id : 426, {_}: inverse (multiply ?520 ?521) =?= multiply (inverse ?521) (inverse ?520) [521, 520] by p22a_3 ?520 ?521
+Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+Id : 62, {_}: least_upper_bound ?157 (least_upper_bound ?158 ?159) =<= least_upper_bound (least_upper_bound ?157 ?158) ?159 [159, 158, 157] by associativity_of_lub ?157 ?158 ?159
+Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
+Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+Id : 63, {_}: least_upper_bound ?161 (least_upper_bound ?162 ?163) =<= least_upper_bound (least_upper_bound ?162 ?161) ?163 [163, 162, 161] by Super 62 with 6 at 1,3
+Id : 69, {_}: least_upper_bound ?161 (least_upper_bound ?162 ?163) =?= least_upper_bound ?162 (least_upper_bound ?161 ?163) [163, 162, 161] by Demod 63 with 8 at 3
+Id : 76, {_}: least_upper_bound ?186 (least_upper_bound ?186 ?187) =>= least_upper_bound ?186 ?187 [187, 186] by Super 8 with 9 at 1,3
+Id : 427, {_}: inverse (multiply identity ?523) =<= multiply (inverse ?523) identity [523] by Super 426 with 17 at 2,3
+Id : 481, {_}: inverse ?569 =<= multiply (inverse ?569) identity [569] by Demod 427 with 2 at 1,2
+Id : 483, {_}: inverse (inverse ?572) =<= multiply ?572 identity [572] by Super 481 with 18 at 1,3
+Id : 491, {_}: ?572 =<= multiply ?572 identity [572] by Demod 483 with 18 at 2
+Id : 60, {_}: least_upper_bound ?149 (least_upper_bound ?150 ?151) =?= least_upper_bound ?150 (least_upper_bound ?151 ?149) [151, 150, 149] by Super 6 with 8 at 3
+Id : 706, {_}: least_upper_bound ?667 (least_upper_bound ?667 ?668) =>= least_upper_bound ?667 ?668 [668, 667] by Super 8 with 9 at 1,3
+Id : 707, {_}: least_upper_bound ?670 (least_upper_bound ?671 ?670) =>= least_upper_bound ?670 ?671 [671, 670] by Super 706 with 6 at 2,2
+Id : 1184, {_}: least_upper_bound ?916 (least_upper_bound (least_upper_bound ?917 ?916) ?918) =?= least_upper_bound (least_upper_bound ?916 ?917) ?918 [918, 917, 916] by Super 8 with 707 at 1,3
+Id : 1214, {_}: least_upper_bound ?916 (least_upper_bound ?917 (least_upper_bound ?916 ?918)) =<= least_upper_bound (least_upper_bound ?916 ?917) ?918 [918, 917, 916] by Demod 1184 with 8 at 2,2
+Id : 1215, {_}: least_upper_bound ?916 (least_upper_bound ?917 (least_upper_bound ?916 ?918)) =>= least_upper_bound ?916 (least_upper_bound ?917 ?918) [918, 917, 916] by Demod 1214 with 8 at 3
+Id : 7862, {_}: least_upper_bound a (least_upper_bound b (least_upper_bound identity (multiply a b))) === least_upper_bound a (least_upper_bound b (least_upper_bound identity (multiply a b))) [] by Demod 7861 with 69 at 2
+Id : 7861, {_}: least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b))) =>= least_upper_bound a (least_upper_bound b (least_upper_bound identity (multiply a b))) [] by Demod 7860 with 60 at 2,2
+Id : 7860, {_}: least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) a)) =>= least_upper_bound a (least_upper_bound b (least_upper_bound identity (multiply a b))) [] by Demod 7859 with 491 at 2,2,2,2
+Id : 7859, {_}: least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) (multiply a identity))) =>= least_upper_bound a (least_upper_bound b (least_upper_bound identity (multiply a b))) [] by Demod 7858 with 69 at 3
+Id : 7858, {_}: least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) (multiply a identity))) =>= least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b))) [] by Demod 7857 with 1215 at 2,2
+Id : 7857, {_}: least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound identity (multiply a identity)))) =>= least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b))) [] by Demod 7856 with 60 at 2,3
+Id : 7856, {_}: least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound identity (multiply a identity)))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) a)) [] by Demod 7855 with 69 at 2
+Id : 7855, {_}: least_upper_bound identity (least_upper_bound b (least_upper_bound (multiply a b) (least_upper_bound identity (multiply a identity)))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) a)) [] by Demod 7854 with 491 at 2,2,2,3
+Id : 7854, {_}: least_upper_bound identity (least_upper_bound b (least_upper_bound (multiply a b) (least_upper_bound identity (multiply a identity)))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) (multiply a identity))) [] by Demod 7853 with 69 at 2,2
+Id : 7853, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound identity (multiply a identity)))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) (multiply a identity))) [] by Demod 7852 with 69 at 2,3
+Id : 7852, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound identity (multiply a identity)))) =>= least_upper_bound b (least_upper_bound (multiply a b) (least_upper_bound identity (multiply a identity))) [] by Demod 7851 with 76 at 2,2
+Id : 7851, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound identity (multiply a identity))))) =>= least_upper_bound b (least_upper_bound (multiply a b) (least_upper_bound identity (multiply a identity))) [] by Demod 7850 with 69 at 3
+Id : 7850, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound identity (multiply a identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound identity (multiply a identity))) [] by Demod 509 with 69 at 2
+Id : 509, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound identity (multiply a identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound identity (multiply a identity))) [] by Demod 508 with 6 at 2,2,2,2,2
+Id : 508, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) identity)))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound identity (multiply a identity))) [] by Demod 507 with 6 at 2,2,3
+Id : 507, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) identity)))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) identity)) [] by Demod 506 with 2 at 2,2,2,2,2,2
+Id : 506, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) (multiply identity identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) identity)) [] by Demod 505 with 2 at 1,2,2,2,2
+Id : 505, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) identity)) [] by Demod 504 with 2 at 2,2,2,3
+Id : 504, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) (multiply identity identity))) [] by Demod 503 with 2 at 1,2,3
+Id : 503, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))) [] by Demod 502 with 8 at 2,2,2
+Id : 502, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))) [] by Demod 501 with 8 at 3
+Id : 501, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)) [] by Demod 500 with 15 at 2,2,2,2
+Id : 500, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)) [] by Demod 499 with 15 at 1,2,2,2
+Id : 499, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)) [] by Demod 498 with 15 at 2,3
+Id : 498, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (multiply (least_upper_bound a identity) identity) [] by Demod 497 with 15 at 1,3
+Id : 497, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity) [] by Demod 496 with 13 at 2,2,2
+Id : 496, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (multiply (least_upper_bound a identity) (least_upper_bound b identity))) =>= least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity) [] by Demod 495 with 13 at 3
+Id : 495, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (multiply (least_upper_bound a identity) (least_upper_bound b identity))) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 1 with 8 at 2
+Id : 1, {_}: least_upper_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by prove_p22a
+% SZS output end CNFRefutation for GRP185-2.p
+22816: solved GRP185-2.p in 2.292143 using lpo
+22816: status Unsatisfiable for GRP185-2.p
+CLASH, statistics insufficient
+22828: Facts:
+22828: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22828: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+22828: Id : 4, {_}:
+ multiply ?6 (left_division ?6 ?7) =>= ?7
+ [7, 6] by multiply_left_division ?6 ?7
+22828: Id : 5, {_}:
+ left_division ?9 (multiply ?9 ?10) =>= ?10
+ [10, 9] by left_division_multiply ?9 ?10
+22828: Id : 6, {_}:
+ multiply (right_division ?12 ?13) ?13 =>= ?12
+ [13, 12] by multiply_right_division ?12 ?13
+22828: Id : 7, {_}:
+ right_division (multiply ?15 ?16) ?16 =>= ?15
+ [16, 15] by right_division_multiply ?15 ?16
+22828: Id : 8, {_}:
+ multiply ?18 (right_inverse ?18) =>= identity
+ [18] by right_inverse ?18
+22828: Id : 9, {_}:
+ multiply (left_inverse ?20) ?20 =>= identity
+ [20] by left_inverse ?20
+22828: Id : 10, {_}:
+ multiply (multiply ?22 (multiply ?23 ?24)) ?22
+ =?=
+ multiply (multiply ?22 ?23) (multiply ?24 ?22)
+ [24, 23, 22] by moufang1 ?22 ?23 ?24
+22828: Goal:
+22828: Id : 1, {_}:
+ multiply (multiply (multiply a b) c) b
+ =>=
+ multiply a (multiply b (multiply c b))
+ [] by prove_moufang2
+22828: Order:
+22828: nrkbo
+22828: Leaf order:
+22828: a 2 0 2 1,1,1,2
+22828: c 2 0 2 2,1,2
+22828: identity 4 0 0
+22828: b 4 0 4 2,1,1,2
+22828: right_inverse 1 1 0
+22828: left_inverse 1 1 0
+22828: left_division 2 2 0
+22828: right_division 2 2 0
+22828: multiply 20 2 6 0,2
+CLASH, statistics insufficient
+22829: Facts:
+22829: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22829: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+22829: Id : 4, {_}:
+ multiply ?6 (left_division ?6 ?7) =>= ?7
+ [7, 6] by multiply_left_division ?6 ?7
+22829: Id : 5, {_}:
+ left_division ?9 (multiply ?9 ?10) =>= ?10
+ [10, 9] by left_division_multiply ?9 ?10
+22829: Id : 6, {_}:
+ multiply (right_division ?12 ?13) ?13 =>= ?12
+ [13, 12] by multiply_right_division ?12 ?13
+22829: Id : 7, {_}:
+ right_division (multiply ?15 ?16) ?16 =>= ?15
+ [16, 15] by right_division_multiply ?15 ?16
+22829: Id : 8, {_}:
+ multiply ?18 (right_inverse ?18) =>= identity
+ [18] by right_inverse ?18
+22829: Id : 9, {_}:
+ multiply (left_inverse ?20) ?20 =>= identity
+ [20] by left_inverse ?20
+22829: Id : 10, {_}:
+ multiply (multiply ?22 (multiply ?23 ?24)) ?22
+ =>=
+ multiply (multiply ?22 ?23) (multiply ?24 ?22)
+ [24, 23, 22] by moufang1 ?22 ?23 ?24
+22829: Goal:
+22829: Id : 1, {_}:
+ multiply (multiply (multiply a b) c) b
+ =>=
+ multiply a (multiply b (multiply c b))
+ [] by prove_moufang2
+22829: Order:
+22829: kbo
+22829: Leaf order:
+22829: a 2 0 2 1,1,1,2
+22829: c 2 0 2 2,1,2
+22829: identity 4 0 0
+22829: b 4 0 4 2,1,1,2
+22829: right_inverse 1 1 0
+22829: left_inverse 1 1 0
+22829: left_division 2 2 0
+22829: right_division 2 2 0
+22829: multiply 20 2 6 0,2
+CLASH, statistics insufficient
+22830: Facts:
+22830: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22830: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+22830: Id : 4, {_}:
+ multiply ?6 (left_division ?6 ?7) =>= ?7
+ [7, 6] by multiply_left_division ?6 ?7
+22830: Id : 5, {_}:
+ left_division ?9 (multiply ?9 ?10) =>= ?10
+ [10, 9] by left_division_multiply ?9 ?10
+22830: Id : 6, {_}:
+ multiply (right_division ?12 ?13) ?13 =>= ?12
+ [13, 12] by multiply_right_division ?12 ?13
+22830: Id : 7, {_}:
+ right_division (multiply ?15 ?16) ?16 =>= ?15
+ [16, 15] by right_division_multiply ?15 ?16
+22830: Id : 8, {_}:
+ multiply ?18 (right_inverse ?18) =>= identity
+ [18] by right_inverse ?18
+22830: Id : 9, {_}:
+ multiply (left_inverse ?20) ?20 =>= identity
+ [20] by left_inverse ?20
+22830: Id : 10, {_}:
+ multiply (multiply ?22 (multiply ?23 ?24)) ?22
+ =>=
+ multiply (multiply ?22 ?23) (multiply ?24 ?22)
+ [24, 23, 22] by moufang1 ?22 ?23 ?24
+22830: Goal:
+22830: Id : 1, {_}:
+ multiply (multiply (multiply a b) c) b
+ =>=
+ multiply a (multiply b (multiply c b))
+ [] by prove_moufang2
+22830: Order:
+22830: lpo
+22830: Leaf order:
+22830: a 2 0 2 1,1,1,2
+22830: c 2 0 2 2,1,2
+22830: identity 4 0 0
+22830: b 4 0 4 2,1,1,2
+22830: right_inverse 1 1 0
+22830: left_inverse 1 1 0
+22830: left_division 2 2 0
+22830: right_division 2 2 0
+22830: multiply 20 2 6 0,2
+% SZS status Timeout for GRP200-1.p
+CLASH, statistics insufficient
+22867: Facts:
+22867: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22867: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+22867: Id : 4, {_}:
+ multiply ?6 (left_division ?6 ?7) =>= ?7
+ [7, 6] by multiply_left_division ?6 ?7
+22867: Id : 5, {_}:
+ left_division ?9 (multiply ?9 ?10) =>= ?10
+ [10, 9] by left_division_multiply ?9 ?10
+22867: Id : 6, {_}:
+ multiply (right_division ?12 ?13) ?13 =>= ?12
+ [13, 12] by multiply_right_division ?12 ?13
+22867: Id : 7, {_}:
+ right_division (multiply ?15 ?16) ?16 =>= ?15
+ [16, 15] by right_division_multiply ?15 ?16
+22867: Id : 8, {_}:
+ multiply ?18 (right_inverse ?18) =>= identity
+ [18] by right_inverse ?18
+22867: Id : 9, {_}:
+ multiply (left_inverse ?20) ?20 =>= identity
+ [20] by left_inverse ?20
+22867: Id : 10, {_}:
+ multiply (multiply (multiply ?22 ?23) ?24) ?23
+ =?=
+ multiply ?22 (multiply ?23 (multiply ?24 ?23))
+ [24, 23, 22] by moufang2 ?22 ?23 ?24
+22867: Goal:
+22867: Id : 1, {_}:
+ multiply (multiply (multiply a b) a) c
+ =>=
+ multiply a (multiply b (multiply a c))
+ [] by prove_moufang3
+22867: Order:
+22867: nrkbo
+22867: Leaf order:
+22867: b 2 0 2 2,1,1,2
+22867: c 2 0 2 2,2
+22867: identity 4 0 0
+22867: a 4 0 4 1,1,1,2
+22867: right_inverse 1 1 0
+22867: left_inverse 1 1 0
+22867: left_division 2 2 0
+22867: right_division 2 2 0
+22867: multiply 20 2 6 0,2
+CLASH, statistics insufficient
+22868: Facts:
+22868: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22868: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+22868: Id : 4, {_}:
+ multiply ?6 (left_division ?6 ?7) =>= ?7
+ [7, 6] by multiply_left_division ?6 ?7
+22868: Id : 5, {_}:
+ left_division ?9 (multiply ?9 ?10) =>= ?10
+ [10, 9] by left_division_multiply ?9 ?10
+22868: Id : 6, {_}:
+ multiply (right_division ?12 ?13) ?13 =>= ?12
+ [13, 12] by multiply_right_division ?12 ?13
+22868: Id : 7, {_}:
+ right_division (multiply ?15 ?16) ?16 =>= ?15
+ [16, 15] by right_division_multiply ?15 ?16
+22868: Id : 8, {_}:
+ multiply ?18 (right_inverse ?18) =>= identity
+ [18] by right_inverse ?18
+22868: Id : 9, {_}:
+ multiply (left_inverse ?20) ?20 =>= identity
+ [20] by left_inverse ?20
+22868: Id : 10, {_}:
+ multiply (multiply (multiply ?22 ?23) ?24) ?23
+ =>=
+ multiply ?22 (multiply ?23 (multiply ?24 ?23))
+ [24, 23, 22] by moufang2 ?22 ?23 ?24
+22868: Goal:
+22868: Id : 1, {_}:
+ multiply (multiply (multiply a b) a) c
+ =>=
+ multiply a (multiply b (multiply a c))
+ [] by prove_moufang3
+22868: Order:
+22868: kbo
+22868: Leaf order:
+22868: b 2 0 2 2,1,1,2
+22868: c 2 0 2 2,2
+22868: identity 4 0 0
+22868: a 4 0 4 1,1,1,2
+22868: right_inverse 1 1 0
+22868: left_inverse 1 1 0
+22868: left_division 2 2 0
+22868: right_division 2 2 0
+22868: multiply 20 2 6 0,2
+CLASH, statistics insufficient
+22869: Facts:
+22869: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22869: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+22869: Id : 4, {_}:
+ multiply ?6 (left_division ?6 ?7) =>= ?7
+ [7, 6] by multiply_left_division ?6 ?7
+22869: Id : 5, {_}:
+ left_division ?9 (multiply ?9 ?10) =>= ?10
+ [10, 9] by left_division_multiply ?9 ?10
+22869: Id : 6, {_}:
+ multiply (right_division ?12 ?13) ?13 =>= ?12
+ [13, 12] by multiply_right_division ?12 ?13
+22869: Id : 7, {_}:
+ right_division (multiply ?15 ?16) ?16 =>= ?15
+ [16, 15] by right_division_multiply ?15 ?16
+22869: Id : 8, {_}:
+ multiply ?18 (right_inverse ?18) =>= identity
+ [18] by right_inverse ?18
+22869: Id : 9, {_}:
+ multiply (left_inverse ?20) ?20 =>= identity
+ [20] by left_inverse ?20
+22869: Id : 10, {_}:
+ multiply (multiply (multiply ?22 ?23) ?24) ?23
+ =>=
+ multiply ?22 (multiply ?23 (multiply ?24 ?23))
+ [24, 23, 22] by moufang2 ?22 ?23 ?24
+22869: Goal:
+22869: Id : 1, {_}:
+ multiply (multiply (multiply a b) a) c
+ =>=
+ multiply a (multiply b (multiply a c))
+ [] by prove_moufang3
+22869: Order:
+22869: lpo
+22869: Leaf order:
+22869: b 2 0 2 2,1,1,2
+22869: c 2 0 2 2,2
+22869: identity 4 0 0
+22869: a 4 0 4 1,1,1,2
+22869: right_inverse 1 1 0
+22869: left_inverse 1 1 0
+22869: left_division 2 2 0
+22869: right_division 2 2 0
+22869: multiply 20 2 6 0,2
+Statistics :
+Max weight : 15
+Found proof, 24.434685s
+% SZS status Unsatisfiable for GRP201-1.p
+% SZS output start CNFRefutation for GRP201-1.p
+Id : 22, {_}: left_division ?48 (multiply ?48 ?49) =>= ?49 [49, 48] by left_division_multiply ?48 ?49
+Id : 8, {_}: multiply ?18 (right_inverse ?18) =>= identity [18] by right_inverse ?18
+Id : 6, {_}: multiply (right_division ?12 ?13) ?13 =>= ?12 [13, 12] by multiply_right_division ?12 ?13
+Id : 4, {_}: multiply ?6 (left_division ?6 ?7) =>= ?7 [7, 6] by multiply_left_division ?6 ?7
+Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+Id : 9, {_}: multiply (left_inverse ?20) ?20 =>= identity [20] by left_inverse ?20
+Id : 10, {_}: multiply (multiply (multiply ?22 ?23) ?24) ?23 =>= multiply ?22 (multiply ?23 (multiply ?24 ?23)) [24, 23, 22] by moufang2 ?22 ?23 ?24
+Id : 7, {_}: right_division (multiply ?15 ?16) ?16 =>= ?15 [16, 15] by right_division_multiply ?15 ?16
+Id : 5, {_}: left_division ?9 (multiply ?9 ?10) =>= ?10 [10, 9] by left_division_multiply ?9 ?10
+Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+Id : 54, {_}: multiply (multiply (multiply ?119 ?120) ?121) ?120 =>= multiply ?119 (multiply ?120 (multiply ?121 ?120)) [121, 120, 119] by moufang2 ?119 ?120 ?121
+Id : 55, {_}: multiply (multiply ?123 ?124) ?123 =<= multiply identity (multiply ?123 (multiply ?124 ?123)) [124, 123] by Super 54 with 2 at 1,1,2
+Id : 71, {_}: multiply (multiply ?123 ?124) ?123 =>= multiply ?123 (multiply ?124 ?123) [124, 123] by Demod 55 with 2 at 3
+Id : 897, {_}: right_division (multiply ?1221 (multiply ?1222 (multiply ?1223 ?1222))) ?1222 =>= multiply (multiply ?1221 ?1222) ?1223 [1223, 1222, 1221] by Super 7 with 10 at 1,2
+Id : 904, {_}: right_division (multiply ?1247 (multiply ?1248 identity)) ?1248 =>= multiply (multiply ?1247 ?1248) (left_inverse ?1248) [1248, 1247] by Super 897 with 9 at 2,2,1,2
+Id : 944, {_}: right_division (multiply ?1247 ?1248) ?1248 =<= multiply (multiply ?1247 ?1248) (left_inverse ?1248) [1248, 1247] by Demod 904 with 3 at 2,1,2
+Id : 945, {_}: ?1247 =<= multiply (multiply ?1247 ?1248) (left_inverse ?1248) [1248, 1247] by Demod 944 with 7 at 2
+Id : 1320, {_}: left_division (multiply ?1774 ?1775) ?1774 =>= left_inverse ?1775 [1775, 1774] by Super 5 with 945 at 2,2
+Id : 1325, {_}: left_division ?1787 ?1788 =<= left_inverse (left_division ?1788 ?1787) [1788, 1787] by Super 1320 with 4 at 1,2
+Id : 1124, {_}: ?1512 =<= multiply (multiply ?1512 ?1513) (left_inverse ?1513) [1513, 1512] by Demod 944 with 7 at 2
+Id : 1136, {_}: right_division ?1545 ?1546 =<= multiply ?1545 (left_inverse ?1546) [1546, 1545] by Super 1124 with 6 at 1,3
+Id : 1239, {_}: right_division (multiply (left_inverse ?1664) ?1665) ?1664 =<= multiply (left_inverse ?1664) (multiply ?1665 (left_inverse ?1664)) [1665, 1664] by Super 71 with 1136 at 2
+Id : 1291, {_}: right_division (multiply (left_inverse ?1664) ?1665) ?1664 =<= multiply (left_inverse ?1664) (right_division ?1665 ?1664) [1665, 1664] by Demod 1239 with 1136 at 2,3
+Id : 621, {_}: right_division (multiply ?874 (multiply ?875 ?874)) ?874 =>= multiply ?874 ?875 [875, 874] by Super 7 with 71 at 1,2
+Id : 2721, {_}: right_division (multiply (left_inverse ?3427) (multiply ?3427 (multiply ?3428 ?3427))) ?3427 =>= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3428, 3427] by Super 1291 with 621 at 2,3
+Id : 53, {_}: right_division (multiply ?115 (multiply ?116 (multiply ?117 ?116))) ?116 =>= multiply (multiply ?115 ?116) ?117 [117, 116, 115] by Super 7 with 10 at 1,2
+Id : 2757, {_}: multiply (multiply (left_inverse ?3427) ?3427) ?3428 =>= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3428, 3427] by Demod 2721 with 53 at 2
+Id : 2758, {_}: multiply identity ?3428 =<= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3427, 3428] by Demod 2757 with 9 at 1,2
+Id : 2759, {_}: ?3428 =<= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3427, 3428] by Demod 2758 with 2 at 2
+Id : 3344, {_}: left_division (left_inverse ?4254) ?4255 =>= multiply ?4254 ?4255 [4255, 4254] by Super 5 with 2759 at 2,2
+Id : 46, {_}: left_division (left_inverse ?101) identity =>= ?101 [101] by Super 5 with 9 at 2,2
+Id : 40, {_}: left_division ?91 identity =>= right_inverse ?91 [91] by Super 5 with 8 at 2,2
+Id : 425, {_}: right_inverse (left_inverse ?101) =>= ?101 [101] by Demod 46 with 40 at 2
+Id : 626, {_}: multiply (multiply ?892 ?893) ?892 =>= multiply ?892 (multiply ?893 ?892) [893, 892] by Demod 55 with 2 at 3
+Id : 633, {_}: multiply identity ?911 =<= multiply ?911 (multiply (right_inverse ?911) ?911) [911] by Super 626 with 8 at 1,2
+Id : 654, {_}: ?911 =<= multiply ?911 (multiply (right_inverse ?911) ?911) [911] by Demod 633 with 2 at 2
+Id : 727, {_}: left_division ?1053 ?1053 =<= multiply (right_inverse ?1053) ?1053 [1053] by Super 5 with 654 at 2,2
+Id : 24, {_}: left_division ?53 ?53 =>= identity [53] by Super 22 with 3 at 2,2
+Id : 754, {_}: identity =<= multiply (right_inverse ?1053) ?1053 [1053] by Demod 727 with 24 at 2
+Id : 784, {_}: right_division identity ?1115 =>= right_inverse ?1115 [1115] by Super 7 with 754 at 1,2
+Id : 45, {_}: right_division identity ?99 =>= left_inverse ?99 [99] by Super 7 with 9 at 1,2
+Id : 808, {_}: left_inverse ?1115 =<= right_inverse ?1115 [1115] by Demod 784 with 45 at 2
+Id : 829, {_}: left_inverse (left_inverse ?101) =>= ?101 [101] by Demod 425 with 808 at 2
+Id : 3348, {_}: left_division ?4266 ?4267 =<= multiply (left_inverse ?4266) ?4267 [4267, 4266] by Super 3344 with 829 at 1,2
+Id : 3417, {_}: multiply (multiply (left_division ?4342 ?4343) ?4344) ?4343 =<= multiply (left_inverse ?4342) (multiply ?4343 (multiply ?4344 ?4343)) [4344, 4343, 4342] by Super 10 with 3348 at 1,1,2
+Id : 3495, {_}: multiply (multiply (left_division ?4342 ?4343) ?4344) ?4343 =>= left_division ?4342 (multiply ?4343 (multiply ?4344 ?4343)) [4344, 4343, 4342] by Demod 3417 with 3348 at 3
+Id : 3351, {_}: left_division (left_division ?4274 ?4275) ?4276 =<= multiply (left_division ?4275 ?4274) ?4276 [4276, 4275, 4274] by Super 3344 with 1325 at 1,2
+Id : 9541, {_}: multiply (left_division (left_division ?4343 ?4342) ?4344) ?4343 =>= left_division ?4342 (multiply ?4343 (multiply ?4344 ?4343)) [4344, 4342, 4343] by Demod 3495 with 3351 at 1,2
+Id : 9542, {_}: left_division (left_division ?4344 (left_division ?4343 ?4342)) ?4343 =>= left_division ?4342 (multiply ?4343 (multiply ?4344 ?4343)) [4342, 4343, 4344] by Demod 9541 with 3351 at 2
+Id : 9554, {_}: left_division ?10951 (left_division ?10952 (left_division ?10951 ?10953)) =<= left_inverse (left_division ?10953 (multiply ?10951 (multiply ?10952 ?10951))) [10953, 10952, 10951] by Super 1325 with 9542 at 1,3
+Id : 27037, {_}: left_division ?28025 (left_division ?28026 (left_division ?28025 ?28027)) =<= left_division (multiply ?28025 (multiply ?28026 ?28025)) ?28027 [28027, 28026, 28025] by Demod 9554 with 1325 at 3
+Id : 27055, {_}: left_division (left_inverse ?28099) (left_division ?28100 (left_division (left_inverse ?28099) ?28101)) =>= left_division (multiply (left_inverse ?28099) (right_division ?28100 ?28099)) ?28101 [28101, 28100, 28099] by Super 27037 with 1136 at 2,1,3
+Id : 3143, {_}: left_division (left_inverse ?4011) ?4012 =>= multiply ?4011 ?4012 [4012, 4011] by Super 5 with 2759 at 2,2
+Id : 27191, {_}: multiply ?28099 (left_division ?28100 (left_division (left_inverse ?28099) ?28101)) =>= left_division (multiply (left_inverse ?28099) (right_division ?28100 ?28099)) ?28101 [28101, 28100, 28099] by Demod 27055 with 3143 at 2
+Id : 27192, {_}: multiply ?28099 (left_division ?28100 (left_division (left_inverse ?28099) ?28101)) =>= left_division (left_division ?28099 (right_division ?28100 ?28099)) ?28101 [28101, 28100, 28099] by Demod 27191 with 3348 at 1,3
+Id : 1117, {_}: right_division ?1491 (left_inverse ?1492) =>= multiply ?1491 ?1492 [1492, 1491] by Super 7 with 945 at 1,2
+Id : 1524, {_}: right_division ?2086 (left_division ?2087 ?2088) =<= multiply ?2086 (left_division ?2088 ?2087) [2088, 2087, 2086] by Super 1117 with 1325 at 2,2
+Id : 27193, {_}: right_division ?28099 (left_division (left_division (left_inverse ?28099) ?28101) ?28100) =>= left_division (left_division ?28099 (right_division ?28100 ?28099)) ?28101 [28100, 28101, 28099] by Demod 27192 with 1524 at 2
+Id : 3400, {_}: right_division (left_division ?1664 ?1665) ?1664 =<= multiply (left_inverse ?1664) (right_division ?1665 ?1664) [1665, 1664] by Demod 1291 with 3348 at 1,2
+Id : 3401, {_}: right_division (left_division ?1664 ?1665) ?1664 =<= left_division ?1664 (right_division ?1665 ?1664) [1665, 1664] by Demod 3400 with 3348 at 3
+Id : 27194, {_}: right_division ?28099 (left_division (left_division (left_inverse ?28099) ?28101) ?28100) =>= left_division (right_division (left_division ?28099 ?28100) ?28099) ?28101 [28100, 28101, 28099] by Demod 27193 with 3401 at 1,3
+Id : 40132, {_}: right_division ?42719 (left_division (multiply ?42719 ?42720) ?42721) =<= left_division (right_division (left_division ?42719 ?42721) ?42719) ?42720 [42721, 42720, 42719] by Demod 27194 with 3143 at 1,2,2
+Id : 1118, {_}: left_division (multiply ?1494 ?1495) ?1494 =>= left_inverse ?1495 [1495, 1494] by Super 5 with 945 at 2,2
+Id : 3133, {_}: left_division ?3978 (left_inverse ?3979) =>= left_inverse (multiply ?3979 ?3978) [3979, 3978] by Super 1118 with 2759 at 1,2
+Id : 40144, {_}: right_division ?42768 (left_division (multiply ?42768 ?42769) (left_inverse ?42770)) =<= left_division (right_division (left_inverse (multiply ?42770 ?42768)) ?42768) ?42769 [42770, 42769, 42768] by Super 40132 with 3133 at 1,1,3
+Id : 40468, {_}: right_division ?42768 (left_inverse (multiply ?42770 (multiply ?42768 ?42769))) =<= left_division (right_division (left_inverse (multiply ?42770 ?42768)) ?42768) ?42769 [42769, 42770, 42768] by Demod 40144 with 3133 at 2,2
+Id : 3414, {_}: right_division (left_inverse ?4334) ?4335 =<= left_division ?4334 (left_inverse ?4335) [4335, 4334] by Super 1136 with 3348 at 3
+Id : 3502, {_}: right_division (left_inverse ?4334) ?4335 =>= left_inverse (multiply ?4335 ?4334) [4335, 4334] by Demod 3414 with 3133 at 3
+Id : 40469, {_}: right_division ?42768 (left_inverse (multiply ?42770 (multiply ?42768 ?42769))) =<= left_division (left_inverse (multiply ?42768 (multiply ?42770 ?42768))) ?42769 [42769, 42770, 42768] by Demod 40468 with 3502 at 1,3
+Id : 40470, {_}: multiply ?42768 (multiply ?42770 (multiply ?42768 ?42769)) =<= left_division (left_inverse (multiply ?42768 (multiply ?42770 ?42768))) ?42769 [42769, 42770, 42768] by Demod 40469 with 1117 at 2
+Id : 40471, {_}: multiply ?42768 (multiply ?42770 (multiply ?42768 ?42769)) =<= multiply (multiply ?42768 (multiply ?42770 ?42768)) ?42769 [42769, 42770, 42768] by Demod 40470 with 3143 at 3
+Id : 50862, {_}: multiply a (multiply b (multiply a c)) =?= multiply a (multiply b (multiply a c)) [] by Demod 50861 with 40471 at 2
+Id : 50861, {_}: multiply (multiply a (multiply b a)) c =>= multiply a (multiply b (multiply a c)) [] by Demod 1 with 71 at 1,2
+Id : 1, {_}: multiply (multiply (multiply a b) a) c =>= multiply a (multiply b (multiply a c)) [] by prove_moufang3
+% SZS output end CNFRefutation for GRP201-1.p
+22868: solved GRP201-1.p in 12.232764 using kbo
+22868: status Unsatisfiable for GRP201-1.p
+CLASH, statistics insufficient
+22882: Facts:
+CLASH, statistics insufficient
+22883: Facts:
+22883: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22883: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+22883: Id : 4, {_}:
+ multiply ?6 (left_division ?6 ?7) =>= ?7
+ [7, 6] by multiply_left_division ?6 ?7
+22883: Id : 5, {_}:
+ left_division ?9 (multiply ?9 ?10) =>= ?10
+ [10, 9] by left_division_multiply ?9 ?10
+22883: Id : 6, {_}:
+ multiply (right_division ?12 ?13) ?13 =>= ?12
+ [13, 12] by multiply_right_division ?12 ?13
+22883: Id : 7, {_}:
+ right_division (multiply ?15 ?16) ?16 =>= ?15
+ [16, 15] by right_division_multiply ?15 ?16
+22883: Id : 8, {_}:
+ multiply ?18 (right_inverse ?18) =>= identity
+ [18] by right_inverse ?18
+22883: Id : 9, {_}:
+ multiply (left_inverse ?20) ?20 =>= identity
+ [20] by left_inverse ?20
+22883: Id : 10, {_}:
+ multiply (multiply (multiply ?22 ?23) ?22) ?24
+ =>=
+ multiply ?22 (multiply ?23 (multiply ?22 ?24))
+ [24, 23, 22] by moufang3 ?22 ?23 ?24
+22883: Goal:
+22883: Id : 1, {_}:
+ multiply (multiply a (multiply b c)) a
+ =>=
+ multiply (multiply a b) (multiply c a)
+ [] by prove_moufang1
+22883: Order:
+22883: kbo
+22883: Leaf order:
+22883: b 2 0 2 1,2,1,2
+22883: c 2 0 2 2,2,1,2
+22883: identity 4 0 0
+22883: a 4 0 4 1,1,2
+22883: right_inverse 1 1 0
+22883: left_inverse 1 1 0
+22883: left_division 2 2 0
+22883: right_division 2 2 0
+22883: multiply 20 2 6 0,2
+22882: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22882: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+22882: Id : 4, {_}:
+ multiply ?6 (left_division ?6 ?7) =>= ?7
+ [7, 6] by multiply_left_division ?6 ?7
+22882: Id : 5, {_}:
+ left_division ?9 (multiply ?9 ?10) =>= ?10
+ [10, 9] by left_division_multiply ?9 ?10
+22882: Id : 6, {_}:
+ multiply (right_division ?12 ?13) ?13 =>= ?12
+ [13, 12] by multiply_right_division ?12 ?13
+22882: Id : 7, {_}:
+ right_division (multiply ?15 ?16) ?16 =>= ?15
+ [16, 15] by right_division_multiply ?15 ?16
+22882: Id : 8, {_}:
+ multiply ?18 (right_inverse ?18) =>= identity
+ [18] by right_inverse ?18
+22882: Id : 9, {_}:
+ multiply (left_inverse ?20) ?20 =>= identity
+ [20] by left_inverse ?20
+22882: Id : 10, {_}:
+ multiply (multiply (multiply ?22 ?23) ?22) ?24
+ =?=
+ multiply ?22 (multiply ?23 (multiply ?22 ?24))
+ [24, 23, 22] by moufang3 ?22 ?23 ?24
+22882: Goal:
+22882: Id : 1, {_}:
+ multiply (multiply a (multiply b c)) a
+ =>=
+ multiply (multiply a b) (multiply c a)
+ [] by prove_moufang1
+22882: Order:
+22882: nrkbo
+22882: Leaf order:
+22882: b 2 0 2 1,2,1,2
+22882: c 2 0 2 2,2,1,2
+22882: identity 4 0 0
+22882: a 4 0 4 1,1,2
+22882: right_inverse 1 1 0
+22882: left_inverse 1 1 0
+22882: left_division 2 2 0
+22882: right_division 2 2 0
+22882: multiply 20 2 6 0,2
+CLASH, statistics insufficient
+22884: Facts:
+22884: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+22884: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+22884: Id : 4, {_}:
+ multiply ?6 (left_division ?6 ?7) =>= ?7
+ [7, 6] by multiply_left_division ?6 ?7
+22884: Id : 5, {_}:
+ left_division ?9 (multiply ?9 ?10) =>= ?10
+ [10, 9] by left_division_multiply ?9 ?10
+22884: Id : 6, {_}:
+ multiply (right_division ?12 ?13) ?13 =>= ?12
+ [13, 12] by multiply_right_division ?12 ?13
+22884: Id : 7, {_}:
+ right_division (multiply ?15 ?16) ?16 =>= ?15
+ [16, 15] by right_division_multiply ?15 ?16
+22884: Id : 8, {_}:
+ multiply ?18 (right_inverse ?18) =>= identity
+ [18] by right_inverse ?18
+22884: Id : 9, {_}:
+ multiply (left_inverse ?20) ?20 =>= identity
+ [20] by left_inverse ?20
+22884: Id : 10, {_}:
+ multiply (multiply (multiply ?22 ?23) ?22) ?24
+ =>=
+ multiply ?22 (multiply ?23 (multiply ?22 ?24))
+ [24, 23, 22] by moufang3 ?22 ?23 ?24
+22884: Goal:
+22884: Id : 1, {_}:
+ multiply (multiply a (multiply b c)) a
+ =>=
+ multiply (multiply a b) (multiply c a)
+ [] by prove_moufang1
+22884: Order:
+22884: lpo
+22884: Leaf order:
+22884: b 2 0 2 1,2,1,2
+22884: c 2 0 2 2,2,1,2
+22884: identity 4 0 0
+22884: a 4 0 4 1,1,2
+22884: right_inverse 1 1 0
+22884: left_inverse 1 1 0
+22884: left_division 2 2 0
+22884: right_division 2 2 0
+22884: multiply 20 2 6 0,2
+Statistics :
+Max weight : 20
+Found proof, 29.906330s
+% SZS status Unsatisfiable for GRP202-1.p
+% SZS output start CNFRefutation for GRP202-1.p
+Id : 56, {_}: multiply (multiply (multiply ?126 ?127) ?126) ?128 =>= multiply ?126 (multiply ?127 (multiply ?126 ?128)) [128, 127, 126] by moufang3 ?126 ?127 ?128
+Id : 4, {_}: multiply ?6 (left_division ?6 ?7) =>= ?7 [7, 6] by multiply_left_division ?6 ?7
+Id : 9, {_}: multiply (left_inverse ?20) ?20 =>= identity [20] by left_inverse ?20
+Id : 22, {_}: left_division ?48 (multiply ?48 ?49) =>= ?49 [49, 48] by left_division_multiply ?48 ?49
+Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+Id : 5, {_}: left_division ?9 (multiply ?9 ?10) =>= ?10 [10, 9] by left_division_multiply ?9 ?10
+Id : 8, {_}: multiply ?18 (right_inverse ?18) =>= identity [18] by right_inverse ?18
+Id : 6, {_}: multiply (right_division ?12 ?13) ?13 =>= ?12 [13, 12] by multiply_right_division ?12 ?13
+Id : 7, {_}: right_division (multiply ?15 ?16) ?16 =>= ?15 [16, 15] by right_division_multiply ?15 ?16
+Id : 10, {_}: multiply (multiply (multiply ?22 ?23) ?22) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by moufang3 ?22 ?23 ?24
+Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+Id : 53, {_}: multiply ?115 (multiply ?116 (multiply ?115 identity)) =>= multiply (multiply ?115 ?116) ?115 [116, 115] by Super 3 with 10 at 2
+Id : 70, {_}: multiply ?115 (multiply ?116 ?115) =<= multiply (multiply ?115 ?116) ?115 [116, 115] by Demod 53 with 3 at 2,2,2
+Id : 894, {_}: right_division (multiply ?1099 (multiply ?1100 ?1099)) ?1099 =>= multiply ?1099 ?1100 [1100, 1099] by Super 7 with 70 at 1,2
+Id : 900, {_}: right_division (multiply ?1115 ?1116) ?1115 =<= multiply ?1115 (right_division ?1116 ?1115) [1116, 1115] by Super 894 with 6 at 2,1,2
+Id : 55, {_}: right_division (multiply ?122 (multiply ?123 (multiply ?122 ?124))) ?124 =>= multiply (multiply ?122 ?123) ?122 [124, 123, 122] by Super 7 with 10 at 1,2
+Id : 2577, {_}: right_division (multiply ?3478 (multiply ?3479 (multiply ?3478 ?3480))) ?3480 =>= multiply ?3478 (multiply ?3479 ?3478) [3480, 3479, 3478] by Demod 55 with 70 at 3
+Id : 647, {_}: multiply ?831 (multiply ?832 ?831) =<= multiply (multiply ?831 ?832) ?831 [832, 831] by Demod 53 with 3 at 2,2,2
+Id : 654, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= multiply identity ?850 [850] by Super 647 with 8 at 1,3
+Id : 677, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= ?850 [850] by Demod 654 with 2 at 3
+Id : 765, {_}: left_division ?991 ?991 =<= multiply (right_inverse ?991) ?991 [991] by Super 5 with 677 at 2,2
+Id : 24, {_}: left_division ?53 ?53 =>= identity [53] by Super 22 with 3 at 2,2
+Id : 791, {_}: identity =<= multiply (right_inverse ?991) ?991 [991] by Demod 765 with 24 at 2
+Id : 819, {_}: right_division identity ?1047 =>= right_inverse ?1047 [1047] by Super 7 with 791 at 1,2
+Id : 45, {_}: right_division identity ?99 =>= left_inverse ?99 [99] by Super 7 with 9 at 1,2
+Id : 846, {_}: left_inverse ?1047 =<= right_inverse ?1047 [1047] by Demod 819 with 45 at 2
+Id : 861, {_}: multiply ?18 (left_inverse ?18) =>= identity [18] by Demod 8 with 846 at 2,2
+Id : 2586, {_}: right_division (multiply ?3513 (multiply ?3514 identity)) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Super 2577 with 861 at 2,2,1,2
+Id : 2645, {_}: right_division (multiply ?3513 ?3514) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Demod 2586 with 3 at 2,1,2
+Id : 2833, {_}: right_division (multiply (left_inverse ?3781) (multiply ?3781 ?3782)) (left_inverse ?3781) =>= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Super 900 with 2645 at 2,3
+Id : 52, {_}: multiply ?111 (multiply ?112 (multiply ?111 (left_division (multiply (multiply ?111 ?112) ?111) ?113))) =>= ?113 [113, 112, 111] by Super 4 with 10 at 2
+Id : 969, {_}: multiply ?1216 (multiply ?1217 (multiply ?1216 (left_division (multiply ?1216 (multiply ?1217 ?1216)) ?1218))) =>= ?1218 [1218, 1217, 1216] by Demod 52 with 70 at 1,2,2,2,2
+Id : 976, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division (multiply ?1242 identity) ?1243))) =>= ?1243 [1243, 1242] by Super 969 with 9 at 2,1,2,2,2,2
+Id : 1036, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division ?1242 ?1243))) =>= ?1243 [1243, 1242] by Demod 976 with 3 at 1,2,2,2,2
+Id : 1037, {_}: multiply ?1242 (multiply (left_inverse ?1242) ?1243) =>= ?1243 [1243, 1242] by Demod 1036 with 4 at 2,2,2
+Id : 1172, {_}: left_division ?1548 ?1549 =<= multiply (left_inverse ?1548) ?1549 [1549, 1548] by Super 5 with 1037 at 2,2
+Id : 2879, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =<= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2833 with 1172 at 1,2
+Id : 2880, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =>= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2879 with 1172 at 3
+Id : 2881, {_}: right_division ?3782 (left_inverse ?3781) =<= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3781, 3782] by Demod 2880 with 5 at 1,2
+Id : 2882, {_}: right_division ?3782 (left_inverse ?3781) =>= multiply ?3782 ?3781 [3781, 3782] by Demod 2881 with 5 at 3
+Id : 1389, {_}: right_division (left_division ?1827 ?1828) ?1828 =>= left_inverse ?1827 [1828, 1827] by Super 7 with 1172 at 1,2
+Id : 28, {_}: left_division (right_division ?62 ?63) ?62 =>= ?63 [63, 62] by Super 5 with 6 at 2,2
+Id : 1395, {_}: right_division ?1844 ?1845 =<= left_inverse (right_division ?1845 ?1844) [1845, 1844] by Super 1389 with 28 at 1,2
+Id : 3679, {_}: multiply (multiply ?4879 ?4880) ?4881 =<= multiply ?4880 (multiply (left_division ?4880 ?4879) (multiply ?4880 ?4881)) [4881, 4880, 4879] by Super 56 with 4 at 1,1,2
+Id : 3684, {_}: multiply (multiply ?4897 ?4898) (left_division ?4898 ?4899) =>= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Super 3679 with 4 at 2,2,3
+Id : 2950, {_}: right_division (left_inverse ?3910) ?3911 =>= left_inverse (multiply ?3911 ?3910) [3911, 3910] by Super 1395 with 2882 at 1,3
+Id : 3037, {_}: left_inverse (multiply (left_inverse ?4021) ?4022) =>= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Super 2882 with 2950 at 2
+Id : 3056, {_}: left_inverse (left_division ?4021 ?4022) =<= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Demod 3037 with 1172 at 1,2
+Id : 3057, {_}: left_inverse (left_division ?4021 ?4022) =>= left_division ?4022 ?4021 [4022, 4021] by Demod 3056 with 1172 at 3
+Id : 3222, {_}: right_division ?4224 (left_division ?4225 ?4226) =<= multiply ?4224 (left_division ?4226 ?4225) [4226, 4225, 4224] by Super 2882 with 3057 at 2,2
+Id : 8079, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Demod 3684 with 3222 at 2
+Id : 3218, {_}: left_division (left_division ?4210 ?4211) ?4212 =<= multiply (left_division ?4211 ?4210) ?4212 [4212, 4211, 4210] by Super 1172 with 3057 at 1,3
+Id : 8080, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (left_division (left_division ?4897 ?4898) ?4899) [4899, 4898, 4897] by Demod 8079 with 3218 at 2,3
+Id : 8081, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =>= right_division ?4898 (left_division ?4899 (left_division ?4897 ?4898)) [4899, 4898, 4897] by Demod 8080 with 3222 at 3
+Id : 8094, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= left_inverse (right_division ?9767 (left_division ?9766 (left_division ?9768 ?9767))) [9768, 9767, 9766] by Super 1395 with 8081 at 1,3
+Id : 8159, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= right_division (left_division ?9766 (left_division ?9768 ?9767)) ?9767 [9768, 9767, 9766] by Demod 8094 with 1395 at 3
+Id : 23778, {_}: right_division (left_division ?25246 (left_inverse ?25247)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25247, 25246] by Super 2882 with 8159 at 2
+Id : 2960, {_}: right_division ?3937 (left_inverse ?3938) =>= multiply ?3937 ?3938 [3938, 3937] by Demod 2881 with 5 at 3
+Id : 46, {_}: left_division (left_inverse ?101) identity =>= ?101 [101] by Super 5 with 9 at 2,2
+Id : 40, {_}: left_division ?91 identity =>= right_inverse ?91 [91] by Super 5 with 8 at 2,2
+Id : 426, {_}: right_inverse (left_inverse ?101) =>= ?101 [101] by Demod 46 with 40 at 2
+Id : 864, {_}: left_inverse (left_inverse ?101) =>= ?101 [101] by Demod 426 with 846 at 2
+Id : 2964, {_}: right_division ?3949 ?3950 =<= multiply ?3949 (left_inverse ?3950) [3950, 3949] by Super 2960 with 864 at 2,2
+Id : 3107, {_}: left_division ?4125 (left_inverse ?4126) =>= right_division (left_inverse ?4125) ?4126 [4126, 4125] by Super 1172 with 2964 at 3
+Id : 3145, {_}: left_division ?4125 (left_inverse ?4126) =>= left_inverse (multiply ?4126 ?4125) [4126, 4125] by Demod 3107 with 2950 at 3
+Id : 23925, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23778 with 3145 at 1,2
+Id : 23926, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23925 with 2964 at 2,2
+Id : 23927, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25248, 25246, 25247] by Demod 23926 with 3218 at 3
+Id : 23928, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23927 with 2950 at 2
+Id : 23929, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23928 with 3145 at 1,1,3
+Id : 1175, {_}: multiply ?1556 (multiply (left_inverse ?1556) ?1557) =>= ?1557 [1557, 1556] by Demod 1036 with 4 at 2,2,2
+Id : 1185, {_}: multiply ?1584 ?1585 =<= left_division (left_inverse ?1584) ?1585 [1585, 1584] by Super 1175 with 4 at 2,2
+Id : 1426, {_}: multiply (right_division ?1873 ?1874) ?1875 =>= left_division (right_division ?1874 ?1873) ?1875 [1875, 1874, 1873] by Super 1185 with 1395 at 1,3
+Id : 23930, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25248, 25247] by Demod 23929 with 1426 at 1,2
+Id : 23931, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =>= left_division (multiply (multiply ?25247 ?25248) ?25246) ?25247 [25246, 25248, 25247] by Demod 23930 with 1185 at 1,3
+Id : 37380, {_}: left_division (multiply ?37773 ?37774) (right_division ?37773 ?37775) =<= left_division (multiply (multiply ?37773 ?37775) ?37774) ?37773 [37775, 37774, 37773] by Demod 23931 with 3057 at 2
+Id : 37397, {_}: left_division (multiply ?37844 ?37845) (right_division ?37844 (left_inverse ?37846)) =>= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Super 37380 with 2964 at 1,1,3
+Id : 37604, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Demod 37397 with 2882 at 2,2
+Id : 37605, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (left_division (right_division ?37846 ?37844) ?37845) ?37844 [37846, 37845, 37844] by Demod 37604 with 1426 at 1,3
+Id : 8101, {_}: right_division (multiply ?9794 ?9795) (left_division ?9796 ?9795) =>= right_division ?9795 (left_division ?9796 (left_division ?9794 ?9795)) [9796, 9795, 9794] by Demod 8080 with 3222 at 3
+Id : 8114, {_}: right_division (multiply ?9845 (left_inverse ?9846)) (left_inverse (multiply ?9846 ?9847)) =>= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Super 8101 with 3145 at 2,2
+Id : 8186, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Demod 8114 with 2882 at 2
+Id : 8187, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8186 with 2950 at 3
+Id : 8188, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8187 with 2964 at 1,2
+Id : 8189, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9846, 9845] by Demod 8188 with 3218 at 1,3
+Id : 8190, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9845, 9846] by Demod 8189 with 1426 at 2
+Id : 8191, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) [9847, 9845, 9846] by Demod 8190 with 3057 at 3
+Id : 8192, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_inverse (multiply ?9846 ?9845)) ?9847) [9847, 9845, 9846] by Demod 8191 with 3145 at 1,2,3
+Id : 24138, {_}: left_division (right_division ?25824 ?25825) (multiply ?25824 ?25826) =>= left_division ?25824 (multiply (multiply ?25824 ?25825) ?25826) [25826, 25825, 25824] by Demod 8192 with 1185 at 2,3
+Id : 24175, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =<= left_division ?25977 (multiply (multiply ?25977 (left_inverse ?25978)) ?25979) [25979, 25978, 25977] by Super 24138 with 2882 at 1,2
+Id : 24394, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (multiply (right_division ?25977 ?25978) ?25979) [25979, 25978, 25977] by Demod 24175 with 2964 at 1,2,3
+Id : 24395, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (left_division (right_division ?25978 ?25977) ?25979) [25979, 25978, 25977] by Demod 24394 with 1426 at 2,3
+Id : 47972, {_}: left_division ?49234 (left_division (right_division ?49235 ?49234) ?49236) =<= left_division (left_division (right_division ?49236 ?49234) ?49235) ?49234 [49236, 49235, 49234] by Demod 37605 with 24395 at 2
+Id : 1255, {_}: multiply (left_inverse ?1641) (multiply ?1642 (left_inverse ?1641)) =>= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Super 70 with 1172 at 1,3
+Id : 1319, {_}: left_division ?1641 (multiply ?1642 (left_inverse ?1641)) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1255 with 1172 at 2
+Id : 3086, {_}: left_division ?1641 (right_division ?1642 ?1641) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1319 with 2964 at 2,2
+Id : 3087, {_}: left_division ?1641 (right_division ?1642 ?1641) =>= right_division (left_division ?1641 ?1642) ?1641 [1642, 1641] by Demod 3086 with 2964 at 3
+Id : 48040, {_}: left_division ?49524 (left_division (right_division (right_division ?49525 (right_division ?49526 ?49524)) ?49524) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Super 47972 with 3087 at 1,3
+Id : 59, {_}: multiply (multiply ?136 ?137) ?138 =<= multiply ?137 (multiply (left_division ?137 ?136) (multiply ?137 ?138)) [138, 137, 136] by Super 56 with 4 at 1,1,2
+Id : 3668, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= multiply (left_division ?4830 ?4831) (multiply ?4830 ?4832) [4832, 4831, 4830] by Super 5 with 59 at 2,2
+Id : 7892, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= left_division (left_division ?4831 ?4830) (multiply ?4830 ?4832) [4832, 4831, 4830] by Demod 3668 with 3218 at 3
+Id : 7900, {_}: left_inverse (left_division ?9488 (multiply (multiply ?9489 ?9488) ?9490)) =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9489, 9488] by Super 3057 with 7892 at 1,2
+Id : 7969, {_}: left_division (multiply (multiply ?9489 ?9488) ?9490) ?9488 =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9488, 9489] by Demod 7900 with 3057 at 2
+Id : 22647, {_}: left_division (multiply (left_inverse ?23598) ?23599) (left_division ?23600 (left_inverse ?23598)) =>= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Super 3145 with 7969 at 2
+Id : 22730, {_}: left_division (left_division ?23598 ?23599) (left_division ?23600 (left_inverse ?23598)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22647 with 1172 at 1,2
+Id : 22731, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22730 with 3145 at 2,2
+Id : 22732, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23600, 23599, 23598] by Demod 22731 with 2964 at 1,2,1,3
+Id : 22733, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23599, 23600, 23598] by Demod 22732 with 3145 at 2
+Id : 22734, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22733 with 1426 at 2,1,3
+Id : 22735, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =<= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22734 with 3222 at 1,2
+Id : 22736, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =>= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23599, 23600, 23598] by Demod 22735 with 3222 at 1,3
+Id : 22737, {_}: right_division (left_division ?23599 ?23598) (multiply ?23598 ?23600) =<= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23600, 23598, 23599] by Demod 22736 with 1395 at 2
+Id : 33406, {_}: right_division (left_division ?33402 ?33403) (multiply ?33403 ?33404) =<= right_division (left_division ?33402 (right_division ?33403 ?33404)) ?33403 [33404, 33403, 33402] by Demod 22737 with 1395 at 3
+Id : 33487, {_}: right_division (left_division (left_inverse ?33737) ?33738) (multiply ?33738 ?33739) =>= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Super 33406 with 1185 at 1,3
+Id : 33773, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Demod 33487 with 1185 at 1,2
+Id : 2967, {_}: right_division ?3957 (right_division ?3958 ?3959) =<= multiply ?3957 (right_division ?3959 ?3958) [3959, 3958, 3957] by Super 2960 with 1395 at 2,2
+Id : 33774, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (right_division ?33737 (right_division ?33739 ?33738)) ?33738 [33739, 33738, 33737] by Demod 33773 with 2967 at 1,3
+Id : 48410, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Demod 48040 with 33774 at 1,2,2
+Id : 640, {_}: multiply (multiply ?22 (multiply ?23 ?22)) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by Demod 10 with 70 at 1,2
+Id : 1260, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =<= multiply ?1655 (multiply (left_inverse ?1656) (multiply ?1655 ?1657)) [1657, 1656, 1655] by Super 640 with 1172 at 2,1,2
+Id : 1315, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1260 with 1172 at 2,3
+Id : 5054, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1315 with 3222 at 1,2
+Id : 5055, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5054 with 3222 at 3
+Id : 5056, {_}: left_division (right_division (left_division ?1655 ?1656) ?1655) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5055 with 1426 at 2
+Id : 48411, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49526, 49525, 49524] by Demod 48410 with 5056 at 3
+Id : 3100, {_}: multiply (multiply (left_inverse ?4103) (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Super 640 with 2964 at 2,1,2
+Id : 3156, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3100 with 1172 at 1,2
+Id : 3157, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3156 with 1172 at 3
+Id : 3158, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3157 with 3087 at 1,2
+Id : 3159, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3158 with 1172 at 2,2,3
+Id : 3160, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3159 with 1426 at 2
+Id : 7103, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (right_division ?4104 (left_division ?4105 ?4103)) [4105, 4104, 4103] by Demod 3160 with 3222 at 2,3
+Id : 7119, {_}: left_division ?8435 (right_division ?8436 (left_division (left_inverse ?8437) ?8435)) =>= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Super 3145 with 7103 at 2
+Id : 7221, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Demod 7119 with 1185 at 2,2,2
+Id : 7222, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (right_division ?8437 (right_division (left_division ?8435 ?8436) ?8435)) [8437, 8436, 8435] by Demod 7221 with 2967 at 1,3
+Id : 7223, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =>= right_division (right_division (left_division ?8435 ?8436) ?8435) ?8437 [8437, 8436, 8435] by Demod 7222 with 1395 at 3
+Id : 21525, {_}: left_inverse (right_division (right_division (left_division ?22100 ?22101) ?22100) ?22102) =>= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22102, 22101, 22100] by Super 3057 with 7223 at 1,2
+Id : 21646, {_}: right_division ?22102 (right_division (left_division ?22100 ?22101) ?22100) =<= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22101, 22100, 22102] by Demod 21525 with 1395 at 2
+Id : 48412, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49525, 49526, 49524] by Demod 48411 with 21646 at 2,2
+Id : 48413, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49525, 49526, 49524] by Demod 48412 with 1426 at 1,2,3
+Id : 3103, {_}: left_division ?4114 (right_division ?4114 ?4115) =>= left_inverse ?4115 [4115, 4114] by Super 5 with 2964 at 2,2
+Id : 48414, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =<= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49524, 49525, 49526] by Demod 48413 with 3103 at 2
+Id : 48415, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48414 with 28 at 1,2,3
+Id : 48416, {_}: right_division ?49526 (left_division ?49526 (multiply ?49525 ?49524)) =<= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48415 with 1395 at 2
+Id : 52586, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= left_inverse (right_division ?54688 (left_division ?54688 (multiply ?54689 ?54690))) [54690, 54689, 54688] by Super 1395 with 48416 at 1,3
+Id : 52816, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= right_division (left_division ?54688 (multiply ?54689 ?54690)) ?54688 [54690, 54689, 54688] by Demod 52586 with 1395 at 3
+Id : 55129, {_}: right_division (left_division (left_inverse ?57654) ?57655) (right_division (left_inverse ?57654) ?57656) =>= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Super 2882 with 52816 at 2
+Id : 55322, {_}: right_division (multiply ?57654 ?57655) (right_division (left_inverse ?57654) ?57656) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55129 with 1185 at 1,2
+Id : 55323, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55322 with 2950 at 2,2
+Id : 55324, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55323 with 3218 at 3
+Id : 55325, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55324 with 2882 at 2
+Id : 55326, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_inverse (multiply ?57654 (multiply ?57655 ?57656))) ?57654 [57656, 57655, 57654] by Demod 55325 with 3145 at 1,3
+Id : 55327, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= multiply (multiply ?57654 (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55326 with 1185 at 3
+Id : 55328, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =>= multiply ?57654 (multiply (multiply ?57655 ?57656) ?57654) [57656, 57655, 57654] by Demod 55327 with 70 at 3
+Id : 57081, {_}: multiply a (multiply (multiply b c) a) =?= multiply a (multiply (multiply b c) a) [] by Demod 57080 with 55328 at 3
+Id : 57080, {_}: multiply a (multiply (multiply b c) a) =<= multiply (multiply a b) (multiply c a) [] by Demod 1 with 70 at 2
+Id : 1, {_}: multiply (multiply a (multiply b c)) a =>= multiply (multiply a b) (multiply c a) [] by prove_moufang1
+% SZS output end CNFRefutation for GRP202-1.p
+22883: solved GRP202-1.p in 14.88493 using kbo
+22883: status Unsatisfiable for GRP202-1.p
+NO CLASH, using fixed ground order
+22932: Facts:
+22932: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
+ (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
+ =>=
+ ?4
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+22932: Goal:
+22932: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+22932: Order:
+22932: nrkbo
+22932: Leaf order:
+22932: b2 2 0 2 1,1,1,2
+22932: a2 2 0 2 2,2
+22932: inverse 6 1 1 0,1,1,2
+22932: multiply 8 2 2 0,2
+NO CLASH, using fixed ground order
+22933: Facts:
+22933: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
+ (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
+ =>=
+ ?4
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+22933: Goal:
+22933: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+22933: Order:
+22933: kbo
+22933: Leaf order:
+22933: b2 2 0 2 1,1,1,2
+22933: a2 2 0 2 2,2
+22933: inverse 6 1 1 0,1,1,2
+22933: multiply 8 2 2 0,2
+NO CLASH, using fixed ground order
+22934: Facts:
+22934: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
+ (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
+ =>=
+ ?4
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+22934: Goal:
+22934: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+22934: Order:
+22934: lpo
+22934: Leaf order:
+22934: b2 2 0 2 1,1,1,2
+22934: a2 2 0 2 2,2
+22934: inverse 6 1 1 0,1,1,2
+22934: multiply 8 2 2 0,2
+% SZS status Timeout for GRP404-1.p
+NO CLASH, using fixed ground order
+23295: Facts:
+23295: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
+ (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
+ =>=
+ ?4
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+23295: Goal:
+23295: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+23295: Order:
+23295: nrkbo
+23295: Leaf order:
+23295: a3 2 0 2 1,1,2
+23295: b3 2 0 2 2,1,2
+23295: c3 2 0 2 2,2
+23295: inverse 5 1 0
+23295: multiply 10 2 4 0,2
+NO CLASH, using fixed ground order
+23296: Facts:
+23296: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
+ (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
+ =>=
+ ?4
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+23296: Goal:
+23296: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+23296: Order:
+23296: kbo
+23296: Leaf order:
+23296: a3 2 0 2 1,1,2
+23296: b3 2 0 2 2,1,2
+23296: c3 2 0 2 2,2
+23296: inverse 5 1 0
+23296: multiply 10 2 4 0,2
+NO CLASH, using fixed ground order
+23297: Facts:
+23297: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4))
+ (inverse (multiply ?3 (multiply (inverse ?3) ?3)))))
+ =>=
+ ?4
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+23297: Goal:
+23297: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+23297: Order:
+23297: lpo
+23297: Leaf order:
+23297: a3 2 0 2 1,1,2
+23297: b3 2 0 2 2,1,2
+23297: c3 2 0 2 2,2
+23297: inverse 5 1 0
+23297: multiply 10 2 4 0,2
+% SZS status Timeout for GRP405-1.p
+NO CLASH, using fixed ground order
+23512: Facts:
+NO CLASH, using fixed ground order
+23513: Facts:
+23513: Id : 2, {_}:
+ multiply
+ (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
+ (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+23513: Goal:
+23513: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+23513: Order:
+23513: kbo
+23513: Leaf order:
+23513: b2 2 0 2 1,1,1,2
+23513: a2 2 0 2 2,2
+23513: inverse 6 1 1 0,1,1,2
+23513: multiply 8 2 2 0,2
+NO CLASH, using fixed ground order
+23514: Facts:
+23514: Id : 2, {_}:
+ multiply
+ (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
+ (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+23514: Goal:
+23514: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+23514: Order:
+23514: lpo
+23514: Leaf order:
+23514: b2 2 0 2 1,1,1,2
+23514: a2 2 0 2 2,2
+23514: inverse 6 1 1 0,1,1,2
+23514: multiply 8 2 2 0,2
+23512: Id : 2, {_}:
+ multiply
+ (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
+ (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+23512: Goal:
+23512: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+23512: Order:
+23512: nrkbo
+23512: Leaf order:
+23512: b2 2 0 2 1,1,1,2
+23512: a2 2 0 2 2,2
+23512: inverse 6 1 1 0,1,1,2
+23512: multiply 8 2 2 0,2
+Statistics :
+Max weight : 71
+Found proof, 51.580663s
+% SZS status Unsatisfiable for GRP410-1.p
+% SZS output start CNFRefutation for GRP410-1.p
+Id : 3, {_}: multiply (multiply (inverse (multiply ?6 (inverse (multiply ?7 ?8)))) (multiply ?6 (inverse ?8))) (inverse (multiply (inverse ?8) ?8)) =>= ?7 [8, 7, 6] by single_axiom ?6 ?7 ?8
+Id : 2, {_}: multiply (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4)))) (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4)) =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
+Id : 5, {_}: multiply (multiply (inverse (multiply ?15 (inverse ?16))) (multiply ?15 (inverse (inverse (multiply (inverse ?17) ?17))))) (inverse (multiply (inverse (inverse (multiply (inverse ?17) ?17))) (inverse (multiply (inverse ?17) ?17)))) =?= multiply (inverse (multiply ?18 (inverse (multiply ?16 ?17)))) (multiply ?18 (inverse ?17)) [18, 17, 16, 15] by Super 3 with 2 at 1,2,1,1,1,2
+Id : 104, {_}: multiply (inverse (multiply ?498 (inverse (multiply (multiply ?499 (inverse (multiply (inverse ?500) ?500))) ?500)))) (multiply ?498 (inverse ?500)) =>= ?499 [500, 499, 498] by Super 2 with 5 at 2
+Id : 161, {_}: multiply (multiply (inverse (multiply ?829 (inverse ?830))) (multiply ?829 (inverse (multiply ?831 (inverse ?832))))) (inverse (multiply (inverse (multiply ?831 (inverse ?832))) (multiply ?831 (inverse ?832)))) =>= inverse (multiply ?831 (inverse (multiply (multiply ?830 (inverse (multiply (inverse ?832) ?832))) ?832))) [832, 831, 830, 829] by Super 2 with 104 at 1,2,1,1,1,2
+Id : 218, {_}: multiply (inverse (multiply ?1090 (inverse (multiply (inverse (multiply ?1091 (inverse (multiply (multiply ?1092 (inverse (multiply (inverse ?1093) ?1093))) ?1093)))) (multiply ?1091 (inverse ?1093)))))) (multiply ?1090 (inverse (multiply ?1091 (inverse ?1093)))) =?= multiply (inverse (multiply ?1094 (inverse ?1092))) (multiply ?1094 (inverse (multiply ?1091 (inverse ?1093)))) [1094, 1093, 1092, 1091, 1090] by Super 104 with 161 at 1,1,2,1,1,2
+Id : 846, {_}: multiply (inverse (multiply ?3342 (inverse ?3343))) (multiply ?3342 (inverse (multiply ?3344 (inverse ?3345)))) =?= multiply (inverse (multiply ?3346 (inverse ?3343))) (multiply ?3346 (inverse (multiply ?3344 (inverse ?3345)))) [3346, 3345, 3344, 3343, 3342] by Demod 218 with 104 at 1,2,1,1,2
+Id : 210, {_}: inverse (multiply ?1043 (inverse (multiply (multiply (multiply ?1044 (multiply ?1043 (inverse ?1045))) (inverse (multiply (inverse ?1045) ?1045))) ?1045))) =>= ?1044 [1045, 1044, 1043] by Super 2 with 161 at 2
+Id : 856, {_}: multiply (inverse (multiply ?3416 (inverse ?3417))) (multiply ?3416 (inverse (multiply ?3418 (inverse (multiply (multiply (multiply ?3419 (multiply ?3418 (inverse ?3420))) (inverse (multiply (inverse ?3420) ?3420))) ?3420))))) =?= multiply (inverse (multiply ?3421 (inverse ?3417))) (multiply ?3421 ?3419) [3421, 3420, 3419, 3418, 3417, 3416] by Super 846 with 210 at 2,2,3
+Id : 1213, {_}: multiply (inverse (multiply ?5198 (inverse ?5199))) (multiply ?5198 ?5200) =?= multiply (inverse (multiply ?5201 (inverse ?5199))) (multiply ?5201 ?5200) [5201, 5200, 5199, 5198] by Demod 856 with 210 at 2,2,2
+Id : 1228, {_}: multiply (inverse (multiply ?5296 (inverse (multiply ?5297 (inverse (multiply (multiply (multiply ?5298 (multiply ?5297 (inverse ?5299))) (inverse (multiply (inverse ?5299) ?5299))) ?5299)))))) (multiply ?5296 ?5300) =?= multiply (inverse (multiply ?5301 ?5298)) (multiply ?5301 ?5300) [5301, 5300, 5299, 5298, 5297, 5296] by Super 1213 with 210 at 2,1,1,3
+Id : 1288, {_}: multiply (inverse (multiply ?5296 ?5298)) (multiply ?5296 ?5300) =?= multiply (inverse (multiply ?5301 ?5298)) (multiply ?5301 ?5300) [5301, 5300, 5298, 5296] by Demod 1228 with 210 at 2,1,1,2
+Id : 1314, {_}: multiply (inverse (multiply ?5709 (inverse (multiply (multiply ?5710 (inverse (multiply (inverse (multiply ?5711 ?5712)) (multiply ?5711 ?5712)))) (multiply ?5713 ?5712))))) (multiply ?5709 (inverse (multiply ?5713 ?5712))) =>= ?5710 [5713, 5712, 5711, 5710, 5709] by Super 104 with 1288 at 1,2,1,1,2,1,1,2
+Id : 2743, {_}: multiply ?12126 (inverse (multiply (inverse (multiply ?12127 ?12128)) (multiply ?12127 ?12128))) =?= multiply ?12126 (inverse (multiply (inverse (multiply ?12129 ?12128)) (multiply ?12129 ?12128))) [12129, 12128, 12127, 12126] by Super 2 with 1314 at 1,2
+Id : 6, {_}: multiply (multiply (inverse ?20) (multiply (multiply (inverse (multiply ?21 (inverse (multiply ?20 ?22)))) (multiply ?21 (inverse ?22))) (inverse ?22))) (inverse (multiply (inverse ?22) ?22)) =>= inverse ?22 [22, 21, 20] by Super 3 with 2 at 1,1,1,2
+Id : 2747, {_}: multiply ?12151 (inverse (multiply (inverse (multiply ?12152 (inverse (multiply (inverse ?12153) ?12153)))) (multiply ?12152 (inverse (multiply (inverse ?12153) ?12153))))) =?= multiply ?12151 (inverse (multiply (inverse (multiply (multiply (inverse ?12154) (multiply (multiply (inverse (multiply ?12155 (inverse (multiply ?12154 ?12153)))) (multiply ?12155 (inverse ?12153))) (inverse ?12153))) (inverse (multiply (inverse ?12153) ?12153)))) (inverse ?12153))) [12155, 12154, 12153, 12152, 12151] by Super 2743 with 6 at 2,1,2,3
+Id : 3023, {_}: multiply ?13436 (inverse (multiply (inverse (multiply ?13437 (inverse (multiply (inverse ?13438) ?13438)))) (multiply ?13437 (inverse (multiply (inverse ?13438) ?13438))))) =>= multiply ?13436 (inverse (multiply (inverse (inverse ?13438)) (inverse ?13438))) [13438, 13437, 13436] by Demod 2747 with 6 at 1,1,1,2,3
+Id : 3033, {_}: multiply ?13495 (inverse (multiply (inverse (multiply (multiply (inverse (multiply ?13496 (inverse (multiply ?13497 ?13498)))) (multiply ?13496 (inverse ?13498))) (inverse (multiply (inverse ?13498) ?13498)))) ?13497)) =>= multiply ?13495 (inverse (multiply (inverse (inverse ?13498)) (inverse ?13498))) [13498, 13497, 13496, 13495] by Super 3023 with 2 at 2,1,2,2
+Id : 3493, {_}: multiply ?14948 (inverse (multiply (inverse ?14949) ?14949)) =?= multiply ?14948 (inverse (multiply (inverse (inverse ?14950)) (inverse ?14950))) [14950, 14949, 14948] by Demod 3033 with 2 at 1,1,1,2,2
+Id : 3250, {_}: multiply ?13495 (inverse (multiply (inverse ?13497) ?13497)) =?= multiply ?13495 (inverse (multiply (inverse (inverse ?13498)) (inverse ?13498))) [13498, 13497, 13495] by Demod 3033 with 2 at 1,1,1,2,2
+Id : 3510, {_}: multiply ?15042 (inverse (multiply (inverse ?15043) ?15043)) =?= multiply ?15042 (inverse (multiply (inverse ?15044) ?15044)) [15044, 15043, 15042] by Super 3493 with 3250 at 3
+Id : 3957, {_}: multiply (inverse (multiply ?16893 (inverse (multiply (multiply ?16894 (inverse (multiply (inverse ?16895) ?16895))) ?16896)))) (multiply ?16893 (inverse ?16896)) =>= ?16894 [16896, 16895, 16894, 16893] by Super 104 with 3510 at 1,1,2,1,1,2
+Id : 4003, {_}: multiply (multiply (inverse (multiply ?17133 (inverse (multiply ?17134 ?17135)))) (multiply ?17133 (inverse ?17135))) (inverse (multiply (inverse ?17136) ?17136)) =>= ?17134 [17136, 17135, 17134, 17133] by Super 2 with 3510 at 2
+Id : 4810, {_}: multiply (multiply (inverse ?21607) ?21607) (inverse (multiply (inverse (multiply (inverse ?21608) ?21608)) (multiply (inverse ?21608) ?21608))) =>= inverse (multiply (inverse ?21608) ?21608) [21608, 21607] by Super 6 with 4003 at 2,1,2
+Id : 1364, {_}: multiply (multiply (inverse (multiply ?5995 (inverse ?5996))) (multiply ?5995 (inverse (multiply ?5997 (inverse ?5998))))) (inverse (multiply (inverse (multiply ?5999 (inverse ?5998))) (multiply ?5999 (inverse ?5998)))) =>= inverse (multiply ?5997 (inverse (multiply (multiply ?5996 (inverse (multiply (inverse ?5998) ?5998))) ?5998))) [5999, 5998, 5997, 5996, 5995] by Super 161 with 1288 at 1,2,2
+Id : 4844, {_}: inverse (multiply ?21768 (inverse (multiply (multiply (multiply ?21768 (inverse ?21769)) (inverse (multiply (inverse ?21769) ?21769))) ?21769))) =>= inverse (multiply (inverse (inverse ?21769)) (inverse ?21769)) [21769, 21768] by Super 4810 with 1364 at 2
+Id : 21277, {_}: multiply (inverse (multiply (inverse (inverse ?53833)) (inverse ?53833))) (multiply ?53834 (inverse ?53833)) =>= multiply ?53834 (inverse ?53833) [53834, 53833] by Super 3957 with 4844 at 1,2
+Id : 21278, {_}: multiply (inverse (multiply (inverse (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838))))) (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))))) (multiply ?53839 ?53837) =>= multiply ?53839 (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))) [53839, 53838, 53837, 53836] by Super 21277 with 210 at 2,2,2
+Id : 21547, {_}: multiply (inverse (multiply (inverse ?53837) (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))))) (multiply ?53839 ?53837) =>= multiply ?53839 (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))) [53839, 53838, 53836, 53837] by Demod 21278 with 210 at 1,1,1,1,2
+Id : 21548, {_}: multiply (inverse (multiply (inverse ?53837) ?53837)) (multiply ?53839 ?53837) =?= multiply ?53839 (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))) [53838, 53836, 53839, 53837] by Demod 21547 with 210 at 2,1,1,2
+Id : 21549, {_}: multiply (inverse (multiply (inverse ?53837) ?53837)) (multiply ?53839 ?53837) =>= multiply ?53839 ?53837 [53839, 53837] by Demod 21548 with 210 at 2,3
+Id : 22063, {_}: multiply (inverse (multiply ?55325 ?55326)) (multiply ?55325 ?55326) =>= multiply (inverse ?55326) ?55326 [55326, 55325] by Super 1288 with 21549 at 3
+Id : 22073, {_}: multiply (inverse (multiply (inverse (multiply ?55370 (inverse (multiply (multiply ?55371 (inverse (multiply (inverse ?55372) ?55372))) ?55373)))) (multiply ?55370 (inverse ?55373)))) ?55371 =>= multiply (inverse (multiply ?55370 (inverse ?55373))) (multiply ?55370 (inverse ?55373)) [55373, 55372, 55371, 55370] by Super 22063 with 3957 at 2,2
+Id : 22230, {_}: multiply (inverse ?55371) ?55371 =?= multiply (inverse (multiply ?55370 (inverse ?55373))) (multiply ?55370 (inverse ?55373)) [55373, 55370, 55371] by Demod 22073 with 3957 at 1,1,2
+Id : 21784, {_}: multiply (inverse (multiply ?54500 ?54501)) (multiply ?54500 ?54501) =>= multiply (inverse ?54501) ?54501 [54501, 54500] by Super 1288 with 21549 at 3
+Id : 22543, {_}: multiply (inverse ?56820) ?56820 =?= multiply (inverse (inverse ?56821)) (inverse ?56821) [56821, 56820] by Demod 22230 with 21784 at 3
+Id : 22231, {_}: multiply (inverse ?55371) ?55371 =?= multiply (inverse (inverse ?55373)) (inverse ?55373) [55373, 55371] by Demod 22230 with 21784 at 3
+Id : 22585, {_}: multiply (inverse ?57023) ?57023 =?= multiply (inverse ?57024) ?57024 [57024, 57023] by Super 22543 with 22231 at 3
+Id : 22724, {_}: multiply (inverse (multiply (inverse ?57285) ?57285)) (multiply ?57286 ?57287) =>= multiply ?57286 ?57287 [57287, 57286, 57285] by Super 21549 with 22585 at 1,1,2
+Id : 23108, {_}: multiply (inverse (multiply ?58913 ?58914)) (multiply ?58913 ?58915) =>= multiply (inverse ?58914) ?58915 [58915, 58914, 58913] by Super 1288 with 22724 at 3
+Id : 23378, {_}: multiply (multiply (inverse (inverse (multiply ?17134 ?17135))) (inverse ?17135)) (inverse (multiply (inverse ?17136) ?17136)) =>= ?17134 [17136, 17135, 17134] by Demod 4003 with 23108 at 1,2
+Id : 1370, {_}: inverse (multiply ?6029 (inverse (multiply (multiply (multiply (inverse (multiply ?6030 ?6031)) (multiply ?6030 (inverse ?6032))) (inverse (multiply (inverse ?6032) ?6032))) ?6032))) =>= inverse (multiply ?6029 ?6031) [6032, 6031, 6030, 6029] by Super 210 with 1288 at 1,1,1,2,1,2
+Id : 4845, {_}: multiply (multiply (inverse ?21771) ?21771) (inverse (multiply (inverse ?21772) ?21772)) =?= inverse (multiply (inverse ?21773) ?21773) [21773, 21772, 21771] by Super 4810 with 3510 at 2
+Id : 7295, {_}: inverse (multiply ?28092 (inverse (multiply (inverse (multiply (inverse ?28093) ?28093)) ?28094))) =>= inverse (multiply ?28092 (inverse ?28094)) [28094, 28093, 28092] by Super 1370 with 4845 at 1,1,2,1,2
+Id : 22930, {_}: inverse (multiply (inverse ?58245) ?58245) =?= inverse (multiply (inverse (inverse (multiply (inverse (multiply (inverse ?58246) ?58246)) ?58247))) (inverse ?58247)) [58247, 58246, 58245] by Super 7295 with 22585 at 1,2
+Id : 8, {_}: multiply (multiply (inverse (multiply (multiply (inverse ?26) (multiply (multiply (inverse (multiply ?27 (inverse (multiply ?26 ?28)))) (multiply ?27 (inverse ?28))) (inverse ?28))) (inverse (multiply ?29 (multiply (inverse ?28) ?28))))) (inverse ?28)) (inverse (multiply (inverse (multiply (inverse ?28) ?28)) (multiply (inverse ?28) ?28))) =>= ?29 [29, 28, 27, 26] by Super 2 with 6 at 2,1,2
+Id : 7694, {_}: inverse (multiply ?30248 (inverse (multiply (inverse (multiply (inverse ?30249) ?30249)) ?30250))) =>= inverse (multiply ?30248 (inverse ?30250)) [30250, 30249, 30248] by Super 1370 with 4845 at 1,1,2,1,2
+Id : 9751, {_}: inverse (multiply ?34833 (inverse (multiply (inverse (multiply ?34834 ?34835)) (multiply ?34834 ?34836)))) =>= inverse (multiply ?34833 (inverse (multiply (inverse ?34835) ?34836))) [34836, 34835, 34834, 34833] by Super 7694 with 1288 at 1,2,1,2
+Id : 9799, {_}: inverse (multiply ?35157 (inverse (multiply (inverse (multiply ?35158 (inverse ?35159))) (multiply ?35158 ?35160)))) =?= inverse (multiply ?35157 (inverse (multiply (inverse (inverse (multiply (inverse (multiply (inverse ?35161) ?35161)) ?35159))) ?35160))) [35161, 35160, 35159, 35158, 35157] by Super 9751 with 7295 at 1,1,2,1,2
+Id : 7715, {_}: inverse (multiply ?30362 (inverse (multiply (inverse (multiply ?30363 ?30364)) (multiply ?30363 ?30365)))) =>= inverse (multiply ?30362 (inverse (multiply (inverse ?30364) ?30365))) [30365, 30364, 30363, 30362] by Super 7694 with 1288 at 1,2,1,2
+Id : 10327, {_}: inverse (multiply ?35157 (inverse (multiply (inverse (inverse ?35159)) ?35160))) =<= inverse (multiply ?35157 (inverse (multiply (inverse (inverse (multiply (inverse (multiply (inverse ?35161) ?35161)) ?35159))) ?35160))) [35161, 35160, 35159, 35157] by Demod 9799 with 7715 at 2
+Id : 14061, {_}: multiply (multiply (inverse (multiply (multiply (inverse ?43109) (multiply (multiply (inverse (multiply ?43110 (inverse (multiply ?43109 ?43111)))) (multiply ?43110 (inverse ?43111))) (inverse ?43111))) (inverse (multiply (inverse (inverse ?43112)) (multiply (inverse ?43111) ?43111))))) (inverse ?43111)) (inverse (multiply (inverse (multiply (inverse ?43111) ?43111)) (multiply (inverse ?43111) ?43111))) =?= inverse (inverse (multiply (inverse (multiply (inverse ?43113) ?43113)) ?43112)) [43113, 43112, 43111, 43110, 43109] by Super 8 with 10327 at 1,1,2
+Id : 14495, {_}: inverse (inverse ?43112) =<= inverse (inverse (multiply (inverse (multiply (inverse ?43113) ?43113)) ?43112)) [43113, 43112] by Demod 14061 with 8 at 2
+Id : 23770, {_}: inverse (multiply (inverse ?60796) ?60796) =?= inverse (multiply (inverse (inverse ?60797)) (inverse ?60797)) [60797, 60796] by Demod 22930 with 14495 at 1,1,3
+Id : 23801, {_}: inverse (multiply (inverse ?60931) ?60931) =?= inverse (multiply (inverse ?60932) ?60932) [60932, 60931] by Super 23770 with 22585 at 1,3
+Id : 25761, {_}: multiply (multiply (inverse (inverse (multiply (inverse ?63084) ?63084))) (inverse ?63085)) (inverse (multiply (inverse ?63086) ?63086)) =>= inverse ?63085 [63086, 63085, 63084] by Super 23378 with 23801 at 1,1,1,2
+Id : 27867, {_}: multiply (inverse (multiply (inverse ?66211) ?66211)) (inverse ?66212) =?= multiply (multiply (inverse (inverse (multiply (inverse ?66213) ?66213))) (inverse ?66212)) (inverse (multiply (inverse ?66214) ?66214)) [66214, 66213, 66212, 66211] by Super 22724 with 25761 at 2,2
+Id : 28152, {_}: multiply (inverse (multiply (inverse ?66849) ?66849)) (inverse ?66850) =>= inverse ?66850 [66850, 66849] by Demod 27867 with 25761 at 3
+Id : 28153, {_}: multiply (inverse (multiply (inverse ?66852) ?66852)) ?66853 =?= inverse (multiply ?66854 (inverse (multiply (multiply (multiply ?66853 (multiply ?66854 (inverse ?66855))) (inverse (multiply (inverse ?66855) ?66855))) ?66855))) [66855, 66854, 66853, 66852] by Super 28152 with 210 at 2,2
+Id : 28218, {_}: multiply (inverse (multiply (inverse ?66852) ?66852)) ?66853 =>= ?66853 [66853, 66852] by Demod 28153 with 210 at 3
+Id : 23366, {_}: multiply (inverse (inverse (multiply (multiply ?16894 (inverse (multiply (inverse ?16895) ?16895))) ?16896))) (inverse ?16896) =>= ?16894 [16896, 16895, 16894] by Demod 3957 with 23108 at 2
+Id : 28331, {_}: multiply (inverse (inverse (multiply (inverse (multiply (inverse ?67206) ?67206)) ?67207))) (inverse ?67207) =?= inverse (multiply (inverse ?67208) ?67208) [67208, 67207, 67206] by Super 23366 with 28218 at 1,1,1,1,2
+Id : 28438, {_}: multiply (inverse (inverse ?67207)) (inverse ?67207) =?= inverse (multiply (inverse ?67208) ?67208) [67208, 67207] by Demod 28331 with 28218 at 1,1,1,2
+Id : 28698, {_}: multiply (inverse (inverse (multiply (inverse ?68177) ?68177))) ?68178 =>= ?68178 [68178, 68177] by Super 28218 with 28438 at 1,1,2
+Id : 23375, {_}: multiply (multiply (inverse (inverse ?16)) (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (multiply (inverse (inverse (multiply (inverse ?17) ?17))) (inverse (multiply (inverse ?17) ?17)))) =?= multiply (inverse (multiply ?18 (inverse (multiply ?16 ?17)))) (multiply ?18 (inverse ?17)) [18, 17, 16] by Demod 5 with 23108 at 1,2
+Id : 23376, {_}: multiply (multiply (inverse (inverse ?16)) (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (multiply (inverse (inverse (multiply (inverse ?17) ?17))) (inverse (multiply (inverse ?17) ?17)))) =>= multiply (inverse (inverse (multiply ?16 ?17))) (inverse ?17) [17, 16] by Demod 23375 with 23108 at 3
+Id : 23410, {_}: multiply (multiply (inverse (inverse ?59640)) (inverse (inverse (multiply (inverse (multiply ?59641 ?59642)) (multiply ?59641 ?59642))))) (inverse (multiply (inverse (inverse (multiply (inverse (multiply ?59641 ?59642)) (multiply ?59641 ?59642)))) (inverse (multiply (inverse ?59642) ?59642)))) =>= multiply (inverse (inverse (multiply ?59640 (multiply ?59641 ?59642)))) (inverse (multiply ?59641 ?59642)) [59642, 59641, 59640] by Super 23376 with 23108 at 1,2,1,2,2
+Id : 23543, {_}: multiply (multiply (inverse (inverse ?59640)) (inverse (inverse (multiply (inverse ?59642) ?59642)))) (inverse (multiply (inverse (inverse (multiply (inverse (multiply ?59641 ?59642)) (multiply ?59641 ?59642)))) (inverse (multiply (inverse ?59642) ?59642)))) =>= multiply (inverse (inverse (multiply ?59640 (multiply ?59641 ?59642)))) (inverse (multiply ?59641 ?59642)) [59641, 59642, 59640] by Demod 23410 with 23108 at 1,1,2,1,2
+Id : 23544, {_}: multiply (multiply (inverse (inverse ?59640)) (inverse (inverse (multiply (inverse ?59642) ?59642)))) (inverse (multiply (inverse (inverse (multiply (inverse ?59642) ?59642))) (inverse (multiply (inverse ?59642) ?59642)))) =?= multiply (inverse (inverse (multiply ?59640 (multiply ?59641 ?59642)))) (inverse (multiply ?59641 ?59642)) [59641, 59642, 59640] by Demod 23543 with 23108 at 1,1,1,1,2,2
+Id : 23545, {_}: multiply (inverse (inverse (multiply ?59640 ?59642))) (inverse ?59642) =<= multiply (inverse (inverse (multiply ?59640 (multiply ?59641 ?59642)))) (inverse (multiply ?59641 ?59642)) [59641, 59642, 59640] by Demod 23544 with 23376 at 2
+Id : 26221, {_}: multiply (inverse (inverse (multiply ?63681 (multiply (inverse ?63682) ?63682)))) (inverse (multiply (inverse ?63683) ?63683)) =>= multiply (inverse (inverse (multiply ?63681 ?63682))) (inverse ?63682) [63683, 63682, 63681] by Super 3510 with 23545 at 3
+Id : 29246, {_}: multiply (inverse ?63085) (inverse (multiply (inverse ?63086) ?63086)) =>= inverse ?63085 [63086, 63085] by Demod 25761 with 28698 at 1,2
+Id : 29249, {_}: inverse (inverse (multiply ?63681 (multiply (inverse ?63682) ?63682))) =<= multiply (inverse (inverse (multiply ?63681 ?63682))) (inverse ?63682) [63682, 63681] by Demod 26221 with 29246 at 2
+Id : 29250, {_}: multiply (inverse (inverse (multiply ?17134 (multiply (inverse ?17135) ?17135)))) (inverse (multiply (inverse ?17136) ?17136)) =>= ?17134 [17136, 17135, 17134] by Demod 23378 with 29249 at 1,2
+Id : 29258, {_}: inverse (inverse (multiply ?17134 (multiply (inverse ?17135) ?17135))) =>= ?17134 [17135, 17134] by Demod 29250 with 29246 at 2
+Id : 29298, {_}: inverse (inverse (multiply ?68838 (inverse (multiply (inverse ?68839) ?68839)))) =>= ?68838 [68839, 68838] by Super 29258 with 28698 at 2,1,1,2
+Id : 29251, {_}: inverse (inverse (multiply (multiply ?16894 (inverse (multiply (inverse ?16895) ?16895))) (multiply (inverse ?16896) ?16896))) =>= ?16894 [16896, 16895, 16894] by Demod 23366 with 29249 at 2
+Id : 29259, {_}: multiply ?16894 (inverse (multiply (inverse ?16895) ?16895)) =>= ?16894 [16895, 16894] by Demod 29251 with 29258 at 2
+Id : 29399, {_}: inverse (inverse ?68838) =>= ?68838 [68838] by Demod 29298 with 29259 at 1,1,2
+Id : 32788, {_}: multiply (multiply (inverse ?68177) ?68177) ?68178 =>= ?68178 [68178, 68177] by Demod 28698 with 29399 at 1,2
+Id : 32852, {_}: a2 === a2 [] by Demod 1 with 32788 at 2
+Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
+% SZS output end CNFRefutation for GRP410-1.p
+23512: solved GRP410-1.p in 25.797611 using nrkbo
+23512: status Unsatisfiable for GRP410-1.p
+NO CLASH, using fixed ground order
+23552: Facts:
+23552: Id : 2, {_}:
+ multiply
+ (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
+ (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+23552: Goal:
+23552: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+23552: Order:
+23552: nrkbo
+23552: Leaf order:
+23552: a3 2 0 2 1,1,2
+23552: b3 2 0 2 2,1,2
+23552: c3 2 0 2 2,2
+23552: inverse 5 1 0
+23552: multiply 10 2 4 0,2
+NO CLASH, using fixed ground order
+23553: Facts:
+23553: Id : 2, {_}:
+ multiply
+ (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
+ (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+23553: Goal:
+23553: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+23553: Order:
+23553: kbo
+23553: Leaf order:
+23553: a3 2 0 2 1,1,2
+23553: b3 2 0 2 2,1,2
+23553: c3 2 0 2 2,2
+23553: inverse 5 1 0
+23553: multiply 10 2 4 0,2
+NO CLASH, using fixed ground order
+23554: Facts:
+23554: Id : 2, {_}:
+ multiply
+ (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4))))
+ (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+23554: Goal:
+23554: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+23554: Order:
+23554: lpo
+23554: Leaf order:
+23554: a3 2 0 2 1,1,2
+23554: b3 2 0 2 2,1,2
+23554: c3 2 0 2 2,2
+23554: inverse 5 1 0
+23554: multiply 10 2 4 0,2
+Statistics :
+Max weight : 83
+Found proof, 26.764346s
+% SZS status Unsatisfiable for GRP411-1.p
+% SZS output start CNFRefutation for GRP411-1.p
+Id : 3, {_}: multiply (multiply (inverse (multiply ?6 (inverse (multiply ?7 ?8)))) (multiply ?6 (inverse ?8))) (inverse (multiply (inverse ?8) ?8)) =>= ?7 [8, 7, 6] by single_axiom ?6 ?7 ?8
+Id : 2, {_}: multiply (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4)))) (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4)) =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
+Id : 5, {_}: multiply (multiply (inverse (multiply ?15 (inverse ?16))) (multiply ?15 (inverse (inverse (multiply (inverse ?17) ?17))))) (inverse (multiply (inverse (inverse (multiply (inverse ?17) ?17))) (inverse (multiply (inverse ?17) ?17)))) =?= multiply (inverse (multiply ?18 (inverse (multiply ?16 ?17)))) (multiply ?18 (inverse ?17)) [18, 17, 16, 15] by Super 3 with 2 at 1,2,1,1,1,2
+Id : 104, {_}: multiply (inverse (multiply ?498 (inverse (multiply (multiply ?499 (inverse (multiply (inverse ?500) ?500))) ?500)))) (multiply ?498 (inverse ?500)) =>= ?499 [500, 499, 498] by Super 2 with 5 at 2
+Id : 161, {_}: multiply (multiply (inverse (multiply ?829 (inverse ?830))) (multiply ?829 (inverse (multiply ?831 (inverse ?832))))) (inverse (multiply (inverse (multiply ?831 (inverse ?832))) (multiply ?831 (inverse ?832)))) =>= inverse (multiply ?831 (inverse (multiply (multiply ?830 (inverse (multiply (inverse ?832) ?832))) ?832))) [832, 831, 830, 829] by Super 2 with 104 at 1,2,1,1,1,2
+Id : 218, {_}: multiply (inverse (multiply ?1090 (inverse (multiply (inverse (multiply ?1091 (inverse (multiply (multiply ?1092 (inverse (multiply (inverse ?1093) ?1093))) ?1093)))) (multiply ?1091 (inverse ?1093)))))) (multiply ?1090 (inverse (multiply ?1091 (inverse ?1093)))) =?= multiply (inverse (multiply ?1094 (inverse ?1092))) (multiply ?1094 (inverse (multiply ?1091 (inverse ?1093)))) [1094, 1093, 1092, 1091, 1090] by Super 104 with 161 at 1,1,2,1,1,2
+Id : 846, {_}: multiply (inverse (multiply ?3342 (inverse ?3343))) (multiply ?3342 (inverse (multiply ?3344 (inverse ?3345)))) =?= multiply (inverse (multiply ?3346 (inverse ?3343))) (multiply ?3346 (inverse (multiply ?3344 (inverse ?3345)))) [3346, 3345, 3344, 3343, 3342] by Demod 218 with 104 at 1,2,1,1,2
+Id : 210, {_}: inverse (multiply ?1043 (inverse (multiply (multiply (multiply ?1044 (multiply ?1043 (inverse ?1045))) (inverse (multiply (inverse ?1045) ?1045))) ?1045))) =>= ?1044 [1045, 1044, 1043] by Super 2 with 161 at 2
+Id : 856, {_}: multiply (inverse (multiply ?3416 (inverse ?3417))) (multiply ?3416 (inverse (multiply ?3418 (inverse (multiply (multiply (multiply ?3419 (multiply ?3418 (inverse ?3420))) (inverse (multiply (inverse ?3420) ?3420))) ?3420))))) =?= multiply (inverse (multiply ?3421 (inverse ?3417))) (multiply ?3421 ?3419) [3421, 3420, 3419, 3418, 3417, 3416] by Super 846 with 210 at 2,2,3
+Id : 1213, {_}: multiply (inverse (multiply ?5198 (inverse ?5199))) (multiply ?5198 ?5200) =?= multiply (inverse (multiply ?5201 (inverse ?5199))) (multiply ?5201 ?5200) [5201, 5200, 5199, 5198] by Demod 856 with 210 at 2,2,2
+Id : 1238, {_}: multiply (inverse (multiply ?5362 (inverse (multiply (multiply (multiply ?5363 (multiply ?5364 (inverse ?5365))) (inverse (multiply (inverse ?5365) ?5365))) ?5365)))) (multiply ?5362 ?5366) =>= multiply ?5363 (multiply ?5364 ?5366) [5366, 5365, 5364, 5363, 5362] by Super 1213 with 210 at 1,3
+Id : 1228, {_}: multiply (inverse (multiply ?5296 (inverse (multiply ?5297 (inverse (multiply (multiply (multiply ?5298 (multiply ?5297 (inverse ?5299))) (inverse (multiply (inverse ?5299) ?5299))) ?5299)))))) (multiply ?5296 ?5300) =?= multiply (inverse (multiply ?5301 ?5298)) (multiply ?5301 ?5300) [5301, 5300, 5299, 5298, 5297, 5296] by Super 1213 with 210 at 2,1,1,3
+Id : 1288, {_}: multiply (inverse (multiply ?5296 ?5298)) (multiply ?5296 ?5300) =?= multiply (inverse (multiply ?5301 ?5298)) (multiply ?5301 ?5300) [5301, 5300, 5298, 5296] by Demod 1228 with 210 at 2,1,1,2
+Id : 1314, {_}: multiply (inverse (multiply ?5709 (inverse (multiply (multiply ?5710 (inverse (multiply (inverse (multiply ?5711 ?5712)) (multiply ?5711 ?5712)))) (multiply ?5713 ?5712))))) (multiply ?5709 (inverse (multiply ?5713 ?5712))) =>= ?5710 [5713, 5712, 5711, 5710, 5709] by Super 104 with 1288 at 1,2,1,1,2,1,1,2
+Id : 2743, {_}: multiply ?12126 (inverse (multiply (inverse (multiply ?12127 ?12128)) (multiply ?12127 ?12128))) =?= multiply ?12126 (inverse (multiply (inverse (multiply ?12129 ?12128)) (multiply ?12129 ?12128))) [12129, 12128, 12127, 12126] by Super 2 with 1314 at 1,2
+Id : 6, {_}: multiply (multiply (inverse ?20) (multiply (multiply (inverse (multiply ?21 (inverse (multiply ?20 ?22)))) (multiply ?21 (inverse ?22))) (inverse ?22))) (inverse (multiply (inverse ?22) ?22)) =>= inverse ?22 [22, 21, 20] by Super 3 with 2 at 1,1,1,2
+Id : 2747, {_}: multiply ?12151 (inverse (multiply (inverse (multiply ?12152 (inverse (multiply (inverse ?12153) ?12153)))) (multiply ?12152 (inverse (multiply (inverse ?12153) ?12153))))) =?= multiply ?12151 (inverse (multiply (inverse (multiply (multiply (inverse ?12154) (multiply (multiply (inverse (multiply ?12155 (inverse (multiply ?12154 ?12153)))) (multiply ?12155 (inverse ?12153))) (inverse ?12153))) (inverse (multiply (inverse ?12153) ?12153)))) (inverse ?12153))) [12155, 12154, 12153, 12152, 12151] by Super 2743 with 6 at 2,1,2,3
+Id : 3023, {_}: multiply ?13436 (inverse (multiply (inverse (multiply ?13437 (inverse (multiply (inverse ?13438) ?13438)))) (multiply ?13437 (inverse (multiply (inverse ?13438) ?13438))))) =>= multiply ?13436 (inverse (multiply (inverse (inverse ?13438)) (inverse ?13438))) [13438, 13437, 13436] by Demod 2747 with 6 at 1,1,1,2,3
+Id : 3033, {_}: multiply ?13495 (inverse (multiply (inverse (multiply (multiply (inverse (multiply ?13496 (inverse (multiply ?13497 ?13498)))) (multiply ?13496 (inverse ?13498))) (inverse (multiply (inverse ?13498) ?13498)))) ?13497)) =>= multiply ?13495 (inverse (multiply (inverse (inverse ?13498)) (inverse ?13498))) [13498, 13497, 13496, 13495] by Super 3023 with 2 at 2,1,2,2
+Id : 3493, {_}: multiply ?14948 (inverse (multiply (inverse ?14949) ?14949)) =?= multiply ?14948 (inverse (multiply (inverse (inverse ?14950)) (inverse ?14950))) [14950, 14949, 14948] by Demod 3033 with 2 at 1,1,1,2,2
+Id : 3250, {_}: multiply ?13495 (inverse (multiply (inverse ?13497) ?13497)) =?= multiply ?13495 (inverse (multiply (inverse (inverse ?13498)) (inverse ?13498))) [13498, 13497, 13495] by Demod 3033 with 2 at 1,1,1,2,2
+Id : 3510, {_}: multiply ?15042 (inverse (multiply (inverse ?15043) ?15043)) =?= multiply ?15042 (inverse (multiply (inverse ?15044) ?15044)) [15044, 15043, 15042] by Super 3493 with 3250 at 3
+Id : 3957, {_}: multiply (inverse (multiply ?16893 (inverse (multiply (multiply ?16894 (inverse (multiply (inverse ?16895) ?16895))) ?16896)))) (multiply ?16893 (inverse ?16896)) =>= ?16894 [16896, 16895, 16894, 16893] by Super 104 with 3510 at 1,1,2,1,1,2
+Id : 4003, {_}: multiply (multiply (inverse (multiply ?17133 (inverse (multiply ?17134 ?17135)))) (multiply ?17133 (inverse ?17135))) (inverse (multiply (inverse ?17136) ?17136)) =>= ?17134 [17136, 17135, 17134, 17133] by Super 2 with 3510 at 2
+Id : 4810, {_}: multiply (multiply (inverse ?21607) ?21607) (inverse (multiply (inverse (multiply (inverse ?21608) ?21608)) (multiply (inverse ?21608) ?21608))) =>= inverse (multiply (inverse ?21608) ?21608) [21608, 21607] by Super 6 with 4003 at 2,1,2
+Id : 1364, {_}: multiply (multiply (inverse (multiply ?5995 (inverse ?5996))) (multiply ?5995 (inverse (multiply ?5997 (inverse ?5998))))) (inverse (multiply (inverse (multiply ?5999 (inverse ?5998))) (multiply ?5999 (inverse ?5998)))) =>= inverse (multiply ?5997 (inverse (multiply (multiply ?5996 (inverse (multiply (inverse ?5998) ?5998))) ?5998))) [5999, 5998, 5997, 5996, 5995] by Super 161 with 1288 at 1,2,2
+Id : 4844, {_}: inverse (multiply ?21768 (inverse (multiply (multiply (multiply ?21768 (inverse ?21769)) (inverse (multiply (inverse ?21769) ?21769))) ?21769))) =>= inverse (multiply (inverse (inverse ?21769)) (inverse ?21769)) [21769, 21768] by Super 4810 with 1364 at 2
+Id : 21277, {_}: multiply (inverse (multiply (inverse (inverse ?53833)) (inverse ?53833))) (multiply ?53834 (inverse ?53833)) =>= multiply ?53834 (inverse ?53833) [53834, 53833] by Super 3957 with 4844 at 1,2
+Id : 21278, {_}: multiply (inverse (multiply (inverse (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838))))) (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))))) (multiply ?53839 ?53837) =>= multiply ?53839 (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))) [53839, 53838, 53837, 53836] by Super 21277 with 210 at 2,2,2
+Id : 21547, {_}: multiply (inverse (multiply (inverse ?53837) (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))))) (multiply ?53839 ?53837) =>= multiply ?53839 (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))) [53839, 53838, 53836, 53837] by Demod 21278 with 210 at 1,1,1,1,2
+Id : 21548, {_}: multiply (inverse (multiply (inverse ?53837) ?53837)) (multiply ?53839 ?53837) =?= multiply ?53839 (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))) [53838, 53836, 53839, 53837] by Demod 21547 with 210 at 2,1,1,2
+Id : 21549, {_}: multiply (inverse (multiply (inverse ?53837) ?53837)) (multiply ?53839 ?53837) =>= multiply ?53839 ?53837 [53839, 53837] by Demod 21548 with 210 at 2,3
+Id : 22063, {_}: multiply (inverse (multiply ?55325 ?55326)) (multiply ?55325 ?55326) =>= multiply (inverse ?55326) ?55326 [55326, 55325] by Super 1288 with 21549 at 3
+Id : 22073, {_}: multiply (inverse (multiply (inverse (multiply ?55370 (inverse (multiply (multiply ?55371 (inverse (multiply (inverse ?55372) ?55372))) ?55373)))) (multiply ?55370 (inverse ?55373)))) ?55371 =>= multiply (inverse (multiply ?55370 (inverse ?55373))) (multiply ?55370 (inverse ?55373)) [55373, 55372, 55371, 55370] by Super 22063 with 3957 at 2,2
+Id : 22230, {_}: multiply (inverse ?55371) ?55371 =?= multiply (inverse (multiply ?55370 (inverse ?55373))) (multiply ?55370 (inverse ?55373)) [55373, 55370, 55371] by Demod 22073 with 3957 at 1,1,2
+Id : 21784, {_}: multiply (inverse (multiply ?54500 ?54501)) (multiply ?54500 ?54501) =>= multiply (inverse ?54501) ?54501 [54501, 54500] by Super 1288 with 21549 at 3
+Id : 22543, {_}: multiply (inverse ?56820) ?56820 =?= multiply (inverse (inverse ?56821)) (inverse ?56821) [56821, 56820] by Demod 22230 with 21784 at 3
+Id : 22231, {_}: multiply (inverse ?55371) ?55371 =?= multiply (inverse (inverse ?55373)) (inverse ?55373) [55373, 55371] by Demod 22230 with 21784 at 3
+Id : 22585, {_}: multiply (inverse ?57023) ?57023 =?= multiply (inverse ?57024) ?57024 [57024, 57023] by Super 22543 with 22231 at 3
+Id : 22724, {_}: multiply (inverse (multiply (inverse ?57285) ?57285)) (multiply ?57286 ?57287) =>= multiply ?57286 ?57287 [57287, 57286, 57285] by Super 21549 with 22585 at 1,1,2
+Id : 23108, {_}: multiply (inverse (multiply ?58913 ?58914)) (multiply ?58913 ?58915) =>= multiply (inverse ?58914) ?58915 [58915, 58914, 58913] by Super 1288 with 22724 at 3
+Id : 23367, {_}: multiply (inverse (inverse (multiply (multiply (multiply ?5363 (multiply ?5364 (inverse ?5365))) (inverse (multiply (inverse ?5365) ?5365))) ?5365))) ?5366 =>= multiply ?5363 (multiply ?5364 ?5366) [5366, 5365, 5364, 5363] by Demod 1238 with 23108 at 2
+Id : 23366, {_}: multiply (inverse (inverse (multiply (multiply ?16894 (inverse (multiply (inverse ?16895) ?16895))) ?16896))) (inverse ?16896) =>= ?16894 [16896, 16895, 16894] by Demod 3957 with 23108 at 2
+Id : 23375, {_}: multiply (multiply (inverse (inverse ?16)) (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (multiply (inverse (inverse (multiply (inverse ?17) ?17))) (inverse (multiply (inverse ?17) ?17)))) =?= multiply (inverse (multiply ?18 (inverse (multiply ?16 ?17)))) (multiply ?18 (inverse ?17)) [18, 17, 16] by Demod 5 with 23108 at 1,2
+Id : 23376, {_}: multiply (multiply (inverse (inverse ?16)) (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (multiply (inverse (inverse (multiply (inverse ?17) ?17))) (inverse (multiply (inverse ?17) ?17)))) =>= multiply (inverse (inverse (multiply ?16 ?17))) (inverse ?17) [17, 16] by Demod 23375 with 23108 at 3
+Id : 23410, {_}: multiply (multiply (inverse (inverse ?59640)) (inverse (inverse (multiply (inverse (multiply ?59641 ?59642)) (multiply ?59641 ?59642))))) (inverse (multiply (inverse (inverse (multiply (inverse (multiply ?59641 ?59642)) (multiply ?59641 ?59642)))) (inverse (multiply (inverse ?59642) ?59642)))) =>= multiply (inverse (inverse (multiply ?59640 (multiply ?59641 ?59642)))) (inverse (multiply ?59641 ?59642)) [59642, 59641, 59640] by Super 23376 with 23108 at 1,2,1,2,2
+Id : 23543, {_}: multiply (multiply (inverse (inverse ?59640)) (inverse (inverse (multiply (inverse ?59642) ?59642)))) (inverse (multiply (inverse (inverse (multiply (inverse (multiply ?59641 ?59642)) (multiply ?59641 ?59642)))) (inverse (multiply (inverse ?59642) ?59642)))) =>= multiply (inverse (inverse (multiply ?59640 (multiply ?59641 ?59642)))) (inverse (multiply ?59641 ?59642)) [59641, 59642, 59640] by Demod 23410 with 23108 at 1,1,2,1,2
+Id : 23544, {_}: multiply (multiply (inverse (inverse ?59640)) (inverse (inverse (multiply (inverse ?59642) ?59642)))) (inverse (multiply (inverse (inverse (multiply (inverse ?59642) ?59642))) (inverse (multiply (inverse ?59642) ?59642)))) =?= multiply (inverse (inverse (multiply ?59640 (multiply ?59641 ?59642)))) (inverse (multiply ?59641 ?59642)) [59641, 59642, 59640] by Demod 23543 with 23108 at 1,1,1,1,2,2
+Id : 23545, {_}: multiply (inverse (inverse (multiply ?59640 ?59642))) (inverse ?59642) =<= multiply (inverse (inverse (multiply ?59640 (multiply ?59641 ?59642)))) (inverse (multiply ?59641 ?59642)) [59641, 59642, 59640] by Demod 23544 with 23376 at 2
+Id : 26221, {_}: multiply (inverse (inverse (multiply ?63681 (multiply (inverse ?63682) ?63682)))) (inverse (multiply (inverse ?63683) ?63683)) =>= multiply (inverse (inverse (multiply ?63681 ?63682))) (inverse ?63682) [63683, 63682, 63681] by Super 3510 with 23545 at 3
+Id : 23378, {_}: multiply (multiply (inverse (inverse (multiply ?17134 ?17135))) (inverse ?17135)) (inverse (multiply (inverse ?17136) ?17136)) =>= ?17134 [17136, 17135, 17134] by Demod 4003 with 23108 at 1,2
+Id : 1370, {_}: inverse (multiply ?6029 (inverse (multiply (multiply (multiply (inverse (multiply ?6030 ?6031)) (multiply ?6030 (inverse ?6032))) (inverse (multiply (inverse ?6032) ?6032))) ?6032))) =>= inverse (multiply ?6029 ?6031) [6032, 6031, 6030, 6029] by Super 210 with 1288 at 1,1,1,2,1,2
+Id : 4845, {_}: multiply (multiply (inverse ?21771) ?21771) (inverse (multiply (inverse ?21772) ?21772)) =?= inverse (multiply (inverse ?21773) ?21773) [21773, 21772, 21771] by Super 4810 with 3510 at 2
+Id : 7295, {_}: inverse (multiply ?28092 (inverse (multiply (inverse (multiply (inverse ?28093) ?28093)) ?28094))) =>= inverse (multiply ?28092 (inverse ?28094)) [28094, 28093, 28092] by Super 1370 with 4845 at 1,1,2,1,2
+Id : 22930, {_}: inverse (multiply (inverse ?58245) ?58245) =?= inverse (multiply (inverse (inverse (multiply (inverse (multiply (inverse ?58246) ?58246)) ?58247))) (inverse ?58247)) [58247, 58246, 58245] by Super 7295 with 22585 at 1,2
+Id : 8, {_}: multiply (multiply (inverse (multiply (multiply (inverse ?26) (multiply (multiply (inverse (multiply ?27 (inverse (multiply ?26 ?28)))) (multiply ?27 (inverse ?28))) (inverse ?28))) (inverse (multiply ?29 (multiply (inverse ?28) ?28))))) (inverse ?28)) (inverse (multiply (inverse (multiply (inverse ?28) ?28)) (multiply (inverse ?28) ?28))) =>= ?29 [29, 28, 27, 26] by Super 2 with 6 at 2,1,2
+Id : 7694, {_}: inverse (multiply ?30248 (inverse (multiply (inverse (multiply (inverse ?30249) ?30249)) ?30250))) =>= inverse (multiply ?30248 (inverse ?30250)) [30250, 30249, 30248] by Super 1370 with 4845 at 1,1,2,1,2
+Id : 9751, {_}: inverse (multiply ?34833 (inverse (multiply (inverse (multiply ?34834 ?34835)) (multiply ?34834 ?34836)))) =>= inverse (multiply ?34833 (inverse (multiply (inverse ?34835) ?34836))) [34836, 34835, 34834, 34833] by Super 7694 with 1288 at 1,2,1,2
+Id : 9799, {_}: inverse (multiply ?35157 (inverse (multiply (inverse (multiply ?35158 (inverse ?35159))) (multiply ?35158 ?35160)))) =?= inverse (multiply ?35157 (inverse (multiply (inverse (inverse (multiply (inverse (multiply (inverse ?35161) ?35161)) ?35159))) ?35160))) [35161, 35160, 35159, 35158, 35157] by Super 9751 with 7295 at 1,1,2,1,2
+Id : 7715, {_}: inverse (multiply ?30362 (inverse (multiply (inverse (multiply ?30363 ?30364)) (multiply ?30363 ?30365)))) =>= inverse (multiply ?30362 (inverse (multiply (inverse ?30364) ?30365))) [30365, 30364, 30363, 30362] by Super 7694 with 1288 at 1,2,1,2
+Id : 10327, {_}: inverse (multiply ?35157 (inverse (multiply (inverse (inverse ?35159)) ?35160))) =<= inverse (multiply ?35157 (inverse (multiply (inverse (inverse (multiply (inverse (multiply (inverse ?35161) ?35161)) ?35159))) ?35160))) [35161, 35160, 35159, 35157] by Demod 9799 with 7715 at 2
+Id : 14061, {_}: multiply (multiply (inverse (multiply (multiply (inverse ?43109) (multiply (multiply (inverse (multiply ?43110 (inverse (multiply ?43109 ?43111)))) (multiply ?43110 (inverse ?43111))) (inverse ?43111))) (inverse (multiply (inverse (inverse ?43112)) (multiply (inverse ?43111) ?43111))))) (inverse ?43111)) (inverse (multiply (inverse (multiply (inverse ?43111) ?43111)) (multiply (inverse ?43111) ?43111))) =?= inverse (inverse (multiply (inverse (multiply (inverse ?43113) ?43113)) ?43112)) [43113, 43112, 43111, 43110, 43109] by Super 8 with 10327 at 1,1,2
+Id : 14495, {_}: inverse (inverse ?43112) =<= inverse (inverse (multiply (inverse (multiply (inverse ?43113) ?43113)) ?43112)) [43113, 43112] by Demod 14061 with 8 at 2
+Id : 23770, {_}: inverse (multiply (inverse ?60796) ?60796) =?= inverse (multiply (inverse (inverse ?60797)) (inverse ?60797)) [60797, 60796] by Demod 22930 with 14495 at 1,1,3
+Id : 23801, {_}: inverse (multiply (inverse ?60931) ?60931) =?= inverse (multiply (inverse ?60932) ?60932) [60932, 60931] by Super 23770 with 22585 at 1,3
+Id : 25761, {_}: multiply (multiply (inverse (inverse (multiply (inverse ?63084) ?63084))) (inverse ?63085)) (inverse (multiply (inverse ?63086) ?63086)) =>= inverse ?63085 [63086, 63085, 63084] by Super 23378 with 23801 at 1,1,1,2
+Id : 27867, {_}: multiply (inverse (multiply (inverse ?66211) ?66211)) (inverse ?66212) =?= multiply (multiply (inverse (inverse (multiply (inverse ?66213) ?66213))) (inverse ?66212)) (inverse (multiply (inverse ?66214) ?66214)) [66214, 66213, 66212, 66211] by Super 22724 with 25761 at 2,2
+Id : 28152, {_}: multiply (inverse (multiply (inverse ?66849) ?66849)) (inverse ?66850) =>= inverse ?66850 [66850, 66849] by Demod 27867 with 25761 at 3
+Id : 28153, {_}: multiply (inverse (multiply (inverse ?66852) ?66852)) ?66853 =?= inverse (multiply ?66854 (inverse (multiply (multiply (multiply ?66853 (multiply ?66854 (inverse ?66855))) (inverse (multiply (inverse ?66855) ?66855))) ?66855))) [66855, 66854, 66853, 66852] by Super 28152 with 210 at 2,2
+Id : 28218, {_}: multiply (inverse (multiply (inverse ?66852) ?66852)) ?66853 =>= ?66853 [66853, 66852] by Demod 28153 with 210 at 3
+Id : 28331, {_}: multiply (inverse (inverse (multiply (inverse (multiply (inverse ?67206) ?67206)) ?67207))) (inverse ?67207) =?= inverse (multiply (inverse ?67208) ?67208) [67208, 67207, 67206] by Super 23366 with 28218 at 1,1,1,1,2
+Id : 28438, {_}: multiply (inverse (inverse ?67207)) (inverse ?67207) =?= inverse (multiply (inverse ?67208) ?67208) [67208, 67207] by Demod 28331 with 28218 at 1,1,1,2
+Id : 28698, {_}: multiply (inverse (inverse (multiply (inverse ?68177) ?68177))) ?68178 =>= ?68178 [68178, 68177] by Super 28218 with 28438 at 1,1,2
+Id : 29246, {_}: multiply (inverse ?63085) (inverse (multiply (inverse ?63086) ?63086)) =>= inverse ?63085 [63086, 63085] by Demod 25761 with 28698 at 1,2
+Id : 29249, {_}: inverse (inverse (multiply ?63681 (multiply (inverse ?63682) ?63682))) =<= multiply (inverse (inverse (multiply ?63681 ?63682))) (inverse ?63682) [63682, 63681] by Demod 26221 with 29246 at 2
+Id : 29251, {_}: inverse (inverse (multiply (multiply ?16894 (inverse (multiply (inverse ?16895) ?16895))) (multiply (inverse ?16896) ?16896))) =>= ?16894 [16896, 16895, 16894] by Demod 23366 with 29249 at 2
+Id : 29250, {_}: multiply (inverse (inverse (multiply ?17134 (multiply (inverse ?17135) ?17135)))) (inverse (multiply (inverse ?17136) ?17136)) =>= ?17134 [17136, 17135, 17134] by Demod 23378 with 29249 at 1,2
+Id : 29258, {_}: inverse (inverse (multiply ?17134 (multiply (inverse ?17135) ?17135))) =>= ?17134 [17135, 17134] by Demod 29250 with 29246 at 2
+Id : 29259, {_}: multiply ?16894 (inverse (multiply (inverse ?16895) ?16895)) =>= ?16894 [16895, 16894] by Demod 29251 with 29258 at 2
+Id : 29266, {_}: multiply (inverse (inverse (multiply (multiply ?5363 (multiply ?5364 (inverse ?5365))) ?5365))) ?5366 =>= multiply ?5363 (multiply ?5364 ?5366) [5366, 5365, 5364, 5363] by Demod 23367 with 29259 at 1,1,1,1,2
+Id : 29298, {_}: inverse (inverse (multiply ?68838 (inverse (multiply (inverse ?68839) ?68839)))) =>= ?68838 [68839, 68838] by Super 29258 with 28698 at 2,1,1,2
+Id : 29399, {_}: inverse (inverse ?68838) =>= ?68838 [68838] by Demod 29298 with 29259 at 1,1,2
+Id : 32787, {_}: multiply (multiply (multiply ?5363 (multiply ?5364 (inverse ?5365))) ?5365) ?5366 =>= multiply ?5363 (multiply ?5364 ?5366) [5366, 5365, 5364, 5363] by Demod 29266 with 29399 at 1,2
+Id : 32817, {_}: multiply (multiply (multiply ?69480 (multiply ?69481 ?69482)) (inverse ?69482)) ?69483 =>= multiply ?69480 (multiply ?69481 ?69483) [69483, 69482, 69481, 69480] by Super 32787 with 29399 at 2,2,1,1,2
+Id : 27049, {_}: multiply (inverse (inverse (multiply ?65328 (multiply (inverse ?65329) ?65329)))) (inverse (multiply (inverse ?65330) ?65330)) =>= multiply (inverse (inverse (multiply ?65328 ?65329))) (inverse ?65329) [65330, 65329, 65328] by Super 3510 with 23545 at 3
+Id : 27102, {_}: multiply (inverse (inverse (multiply (inverse ?65600) ?65600))) (inverse (multiply (inverse ?65601) ?65601)) =?= multiply (inverse (inverse (multiply (inverse (multiply (inverse ?65602) ?65602)) ?65600))) (inverse ?65600) [65602, 65601, 65600] by Super 27049 with 22724 at 1,1,1,2
+Id : 27480, {_}: multiply (inverse (inverse (multiply (inverse ?65600) ?65600))) (inverse (multiply (inverse ?65601) ?65601)) =>= multiply (inverse (inverse ?65600)) (inverse ?65600) [65601, 65600] by Demod 27102 with 14495 at 1,3
+Id : 27499, {_}: multiply (multiply (inverse (inverse ?16)) (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (multiply (inverse (inverse ?17)) (inverse ?17))) =>= multiply (inverse (inverse (multiply ?16 ?17))) (inverse ?17) [17, 16] by Demod 23376 with 27480 at 1,2,2
+Id : 28687, {_}: multiply (multiply (inverse (multiply (inverse (inverse ?68131)) (inverse ?68131))) (inverse (inverse (multiply (inverse ?68132) ?68132)))) (inverse (multiply (inverse (inverse ?68132)) (inverse ?68132))) =?= multiply (inverse (inverse (multiply (multiply (inverse ?68133) ?68133) ?68132))) (inverse ?68132) [68133, 68132, 68131] by Super 27499 with 28438 at 1,1,1,2
+Id : 28770, {_}: multiply (inverse (inverse (multiply (inverse ?68132) ?68132))) (inverse (multiply (inverse (inverse ?68132)) (inverse ?68132))) =?= multiply (inverse (inverse (multiply (multiply (inverse ?68133) ?68133) ?68132))) (inverse ?68132) [68133, 68132] by Demod 28687 with 28218 at 1,2
+Id : 9, {_}: multiply (multiply (inverse (multiply ?31 (inverse (inverse ?32)))) (multiply ?31 (inverse (inverse (multiply (inverse ?32) ?32))))) (inverse (multiply (inverse (inverse (multiply (inverse ?32) ?32))) (inverse (multiply (inverse ?32) ?32)))) =?= multiply (inverse ?33) (multiply (multiply (inverse (multiply ?34 (inverse (multiply ?33 ?32)))) (multiply ?34 (inverse ?32))) (inverse ?32)) [34, 33, 32, 31] by Super 2 with 6 at 1,2,1,1,1,2
+Id : 23370, {_}: multiply (multiply (inverse (inverse (inverse ?32))) (inverse (inverse (multiply (inverse ?32) ?32)))) (inverse (multiply (inverse (inverse (multiply (inverse ?32) ?32))) (inverse (multiply (inverse ?32) ?32)))) =?= multiply (inverse ?33) (multiply (multiply (inverse (multiply ?34 (inverse (multiply ?33 ?32)))) (multiply ?34 (inverse ?32))) (inverse ?32)) [34, 33, 32] by Demod 9 with 23108 at 1,2
+Id : 23371, {_}: multiply (multiply (inverse (inverse (inverse ?32))) (inverse (inverse (multiply (inverse ?32) ?32)))) (inverse (multiply (inverse (inverse (multiply (inverse ?32) ?32))) (inverse (multiply (inverse ?32) ?32)))) =?= multiply (inverse ?33) (multiply (multiply (inverse (inverse (multiply ?33 ?32))) (inverse ?32)) (inverse ?32)) [33, 32] by Demod 23370 with 23108 at 1,2,3
+Id : 23387, {_}: multiply (inverse (inverse (multiply (inverse ?32) ?32))) (inverse ?32) =<= multiply (inverse ?33) (multiply (multiply (inverse (inverse (multiply ?33 ?32))) (inverse ?32)) (inverse ?32)) [33, 32] by Demod 23371 with 23376 at 2
+Id : 25785, {_}: multiply (inverse (inverse (multiply (inverse ?63178) ?63178))) (inverse ?63178) =<= multiply (inverse (multiply (inverse ?63179) ?63179)) (multiply (multiply (inverse (inverse (multiply (multiply (inverse ?63180) ?63180) ?63178))) (inverse ?63178)) (inverse ?63178)) [63180, 63179, 63178] by Super 23387 with 23801 at 1,3
+Id : 25940, {_}: multiply (inverse (inverse (multiply (inverse ?63178) ?63178))) (inverse ?63178) =<= multiply (multiply (inverse (inverse (multiply (multiply (inverse ?63180) ?63180) ?63178))) (inverse ?63178)) (inverse ?63178) [63180, 63178] by Demod 25785 with 22724 at 3
+Id : 26391, {_}: multiply (inverse (inverse (multiply (multiply (inverse (inverse (multiply (inverse (multiply (inverse ?64074) ?64074)) (multiply (inverse ?64074) ?64074)))) (inverse (multiply (inverse ?64074) ?64074))) ?64075))) (inverse ?64075) =?= multiply (inverse (inverse (multiply (multiply (inverse ?64076) ?64076) (multiply (inverse ?64074) ?64074)))) (inverse (multiply (inverse ?64074) ?64074)) [64076, 64075, 64074] by Super 23366 with 25940 at 1,1,1,1,2
+Id : 26476, {_}: inverse (inverse (multiply (inverse (multiply (inverse ?64074) ?64074)) (multiply (inverse ?64074) ?64074))) =<= multiply (inverse (inverse (multiply (multiply (inverse ?64076) ?64076) (multiply (inverse ?64074) ?64074)))) (inverse (multiply (inverse ?64074) ?64074)) [64076, 64074] by Demod 26391 with 23366 at 2
+Id : 26477, {_}: inverse (inverse (multiply (inverse (multiply (inverse ?64074) ?64074)) (multiply (inverse ?64074) ?64074))) =?= multiply (inverse (inverse (multiply (multiply (inverse ?64076) ?64076) ?64074))) (inverse ?64074) [64076, 64074] by Demod 26476 with 23545 at 3
+Id : 26478, {_}: inverse (inverse (multiply (inverse ?64074) ?64074)) =<= multiply (inverse (inverse (multiply (multiply (inverse ?64076) ?64076) ?64074))) (inverse ?64074) [64076, 64074] by Demod 26477 with 14495 at 2
+Id : 28771, {_}: multiply (inverse (inverse (multiply (inverse ?68132) ?68132))) (inverse (multiply (inverse (inverse ?68132)) (inverse ?68132))) =>= inverse (inverse (multiply (inverse ?68132) ?68132)) [68132] by Demod 28770 with 26478 at 3
+Id : 28772, {_}: multiply (inverse (inverse ?68132)) (inverse ?68132) =>= inverse (inverse (multiply (inverse ?68132) ?68132)) [68132] by Demod 28771 with 27480 at 2
+Id : 28931, {_}: inverse (multiply ?21768 (inverse (multiply (multiply (multiply ?21768 (inverse ?21769)) (inverse (multiply (inverse ?21769) ?21769))) ?21769))) =>= inverse (inverse (inverse (multiply (inverse ?21769) ?21769))) [21769, 21768] by Demod 4844 with 28772 at 1,3
+Id : 29275, {_}: inverse (multiply ?21768 (inverse (multiply (multiply ?21768 (inverse ?21769)) ?21769))) =>= inverse (inverse (inverse (multiply (inverse ?21769) ?21769))) [21769, 21768] by Demod 28931 with 29259 at 1,1,2,1,2
+Id : 32786, {_}: inverse (multiply ?21768 (inverse (multiply (multiply ?21768 (inverse ?21769)) ?21769))) =>= inverse (multiply (inverse ?21769) ?21769) [21769, 21768] by Demod 29275 with 29399 at 3
+Id : 32802, {_}: inverse (multiply ?69432 (inverse (multiply (multiply ?69432 ?69433) (inverse ?69433)))) =>= inverse (multiply (inverse (inverse ?69433)) (inverse ?69433)) [69433, 69432] by Super 32786 with 29399 at 2,1,1,2,1,2
+Id : 21975, {_}: multiply (multiply (inverse (multiply ?5995 (inverse ?5996))) (multiply ?5995 (inverse (multiply ?5997 (inverse ?5998))))) (inverse (multiply (inverse (inverse ?5998)) (inverse ?5998))) =>= inverse (multiply ?5997 (inverse (multiply (multiply ?5996 (inverse (multiply (inverse ?5998) ?5998))) ?5998))) [5998, 5997, 5996, 5995] by Demod 1364 with 21784 at 1,2,2
+Id : 23386, {_}: multiply (multiply (inverse (inverse ?5996)) (inverse (multiply ?5997 (inverse ?5998)))) (inverse (multiply (inverse (inverse ?5998)) (inverse ?5998))) =>= inverse (multiply ?5997 (inverse (multiply (multiply ?5996 (inverse (multiply (inverse ?5998) ?5998))) ?5998))) [5998, 5997, 5996] by Demod 21975 with 23108 at 1,2
+Id : 28932, {_}: multiply (multiply (inverse (inverse ?5996)) (inverse (multiply ?5997 (inverse ?5998)))) (inverse (inverse (inverse (multiply (inverse ?5998) ?5998)))) =>= inverse (multiply ?5997 (inverse (multiply (multiply ?5996 (inverse (multiply (inverse ?5998) ?5998))) ?5998))) [5998, 5997, 5996] by Demod 23386 with 28772 at 1,2,2
+Id : 29265, {_}: multiply (multiply (inverse (inverse ?5996)) (inverse (multiply ?5997 (inverse ?5998)))) (inverse (inverse (inverse (multiply (inverse ?5998) ?5998)))) =>= inverse (multiply ?5997 (inverse (multiply ?5996 ?5998))) [5998, 5997, 5996] by Demod 28932 with 29259 at 1,1,2,1,3
+Id : 32767, {_}: multiply (multiply ?5996 (inverse (multiply ?5997 (inverse ?5998)))) (inverse (inverse (inverse (multiply (inverse ?5998) ?5998)))) =>= inverse (multiply ?5997 (inverse (multiply ?5996 ?5998))) [5998, 5997, 5996] by Demod 29265 with 29399 at 1,1,2
+Id : 32768, {_}: multiply (multiply ?5996 (inverse (multiply ?5997 (inverse ?5998)))) (inverse (multiply (inverse ?5998) ?5998)) =>= inverse (multiply ?5997 (inverse (multiply ?5996 ?5998))) [5998, 5997, 5996] by Demod 32767 with 29399 at 2,2
+Id : 32797, {_}: multiply ?5996 (inverse (multiply ?5997 (inverse ?5998))) =>= inverse (multiply ?5997 (inverse (multiply ?5996 ?5998))) [5998, 5997, 5996] by Demod 32768 with 29259 at 2
+Id : 32841, {_}: inverse (inverse (multiply (multiply ?69432 ?69433) (inverse (multiply ?69432 ?69433)))) =>= inverse (multiply (inverse (inverse ?69433)) (inverse ?69433)) [69433, 69432] by Demod 32802 with 32797 at 1,2
+Id : 32842, {_}: inverse (inverse (multiply (multiply ?69432 ?69433) (inverse (multiply ?69432 ?69433)))) =>= inverse (multiply ?69433 (inverse ?69433)) [69433, 69432] by Demod 32841 with 29399 at 1,1,3
+Id : 32843, {_}: multiply (multiply ?69432 ?69433) (inverse (multiply ?69432 ?69433)) =>= inverse (multiply ?69433 (inverse ?69433)) [69433, 69432] by Demod 32842 with 29399 at 2
+Id : 10, {_}: multiply (multiply (inverse (inverse ?36)) (multiply (multiply (inverse ?37) (multiply (multiply (inverse (multiply ?38 (inverse (multiply ?37 ?36)))) (multiply ?38 (inverse ?36))) (inverse ?36))) (inverse ?36))) (inverse (multiply (inverse ?36) ?36)) =>= inverse ?36 [38, 37, 36] by Super 2 with 6 at 1,1,1,2
+Id : 37, {_}: multiply (multiply (inverse (multiply (inverse (inverse ?174)) (multiply (multiply (inverse ?175) (multiply (multiply (inverse (multiply ?176 (inverse (multiply ?175 ?174)))) (multiply ?176 (inverse ?174))) (inverse ?174))) (inverse ?174)))) (multiply (multiply (inverse (multiply ?177 (inverse (inverse ?174)))) (multiply ?177 (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [177, 176, 175, 174] by Super 6 with 10 at 1,2,1,1,1,2,1,2
+Id : 23364, {_}: multiply (multiply (inverse (multiply (inverse (inverse ?174)) (multiply (multiply (inverse ?175) (multiply (multiply (inverse (inverse (multiply ?175 ?174))) (inverse ?174)) (inverse ?174))) (inverse ?174)))) (multiply (multiply (inverse (multiply ?177 (inverse (inverse ?174)))) (multiply ?177 (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [177, 175, 174] by Demod 37 with 23108 at 1,2,1,2,1,1,1,2
+Id : 23365, {_}: multiply (multiply (inverse (multiply (inverse (inverse ?174)) (multiply (multiply (inverse ?175) (multiply (multiply (inverse (inverse (multiply ?175 ?174))) (inverse ?174)) (inverse ?174))) (inverse ?174)))) (multiply (multiply (inverse (inverse (inverse ?174))) (inverse (inverse (multiply (inverse ?174) ?174)))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [175, 174] by Demod 23364 with 23108 at 1,2,1,2
+Id : 23401, {_}: multiply (multiply (inverse (multiply (inverse (inverse ?174)) (multiply (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse ?174)) (inverse ?174)))) (multiply (multiply (inverse (inverse (inverse ?174))) (inverse (inverse (multiply (inverse ?174) ?174)))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 23365 with 23387 at 1,2,1,1,1,2
+Id : 23402, {_}: multiply (multiply (inverse (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse ?174))) (multiply (multiply (inverse (inverse (inverse ?174))) (inverse (inverse (multiply (inverse ?174) ?174)))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 23401 with 23387 at 1,1,1,2
+Id : 27500, {_}: multiply (multiply (inverse (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse ?174))) (multiply (multiply (inverse (inverse (inverse ?174))) (inverse (inverse (multiply (inverse ?174) ?174)))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (multiply (inverse (inverse ?174)) (inverse ?174))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 23402 with 27480 at 1,2,2
+Id : 28930, {_}: multiply (multiply (inverse (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse ?174))) (multiply (multiply (inverse (inverse (inverse ?174))) (inverse (inverse (multiply (inverse ?174) ?174)))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (inverse (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 27500 with 28772 at 1,2,2
+Id : 29247, {_}: multiply (multiply (inverse (inverse ?174)) (multiply (multiply (inverse (inverse (inverse ?174))) (inverse (inverse (multiply (inverse ?174) ?174)))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (inverse (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 28930 with 28698 at 1,1,1,2
+Id : 32772, {_}: multiply (multiply ?174 (multiply (multiply (inverse (inverse (inverse ?174))) (inverse (inverse (multiply (inverse ?174) ?174)))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (inverse (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 29247 with 29399 at 1,1,2
+Id : 32773, {_}: multiply (multiply ?174 (multiply (multiply (inverse ?174) (inverse (inverse (multiply (inverse ?174) ?174)))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (inverse (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 32772 with 29399 at 1,1,2,1,2
+Id : 32774, {_}: multiply (multiply ?174 (multiply (multiply (inverse ?174) (multiply (inverse ?174) ?174)) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (inverse (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 32773 with 29399 at 2,1,2,1,2
+Id : 32775, {_}: multiply (multiply ?174 (multiply (multiply (inverse ?174) (multiply (inverse ?174) ?174)) (multiply (inverse ?174) ?174))) (inverse (inverse (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 32774 with 29399 at 2,2,1,2
+Id : 32776, {_}: multiply (multiply ?174 (multiply (multiply (inverse ?174) (multiply (inverse ?174) ?174)) (multiply (inverse ?174) ?174))) (inverse (multiply (inverse ?174) ?174)) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 32775 with 29399 at 2,2
+Id : 32777, {_}: multiply (multiply ?174 (multiply (multiply (inverse ?174) (multiply (inverse ?174) ?174)) (multiply (inverse ?174) ?174))) (inverse (multiply (inverse ?174) ?174)) =>= multiply (inverse ?174) ?174 [174] by Demod 32776 with 29399 at 3
+Id : 32792, {_}: multiply ?174 (multiply (multiply (inverse ?174) (multiply (inverse ?174) ?174)) (multiply (inverse ?174) ?174)) =>= multiply (inverse ?174) ?174 [174] by Demod 32777 with 29259 at 2
+Id : 28933, {_}: multiply (multiply (inverse (inverse ?16)) (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (inverse (inverse (multiply (inverse ?17) ?17)))) =>= multiply (inverse (inverse (multiply ?16 ?17))) (inverse ?17) [17, 16] by Demod 27499 with 28772 at 1,2,2
+Id : 29256, {_}: multiply (multiply (inverse (inverse ?16)) (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (inverse (inverse (multiply (inverse ?17) ?17)))) =>= inverse (inverse (multiply ?16 (multiply (inverse ?17) ?17))) [17, 16] by Demod 28933 with 29249 at 3
+Id : 29262, {_}: multiply (multiply (inverse (inverse ?16)) (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (inverse (inverse (multiply (inverse ?17) ?17)))) =>= ?16 [17, 16] by Demod 29256 with 29258 at 3
+Id : 32782, {_}: multiply (multiply ?16 (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (inverse (inverse (multiply (inverse ?17) ?17)))) =>= ?16 [17, 16] by Demod 29262 with 29399 at 1,1,2
+Id : 32783, {_}: multiply (multiply ?16 (multiply (inverse ?17) ?17)) (inverse (inverse (inverse (multiply (inverse ?17) ?17)))) =>= ?16 [17, 16] by Demod 32782 with 29399 at 2,1,2
+Id : 32784, {_}: multiply (multiply ?16 (multiply (inverse ?17) ?17)) (inverse (multiply (inverse ?17) ?17)) =>= ?16 [17, 16] by Demod 32783 with 29399 at 2,2
+Id : 32789, {_}: multiply ?16 (multiply (inverse ?17) ?17) =>= ?16 [17, 16] by Demod 32784 with 29259 at 2
+Id : 32793, {_}: multiply ?174 (multiply (inverse ?174) (multiply (inverse ?174) ?174)) =>= multiply (inverse ?174) ?174 [174] by Demod 32792 with 32789 at 2,2
+Id : 32794, {_}: multiply ?174 (inverse ?174) =?= multiply (inverse ?174) ?174 [174] by Demod 32793 with 32789 at 2,2
+Id : 32844, {_}: multiply (inverse (multiply ?69432 ?69433)) (multiply ?69432 ?69433) =>= inverse (multiply ?69433 (inverse ?69433)) [69433, 69432] by Demod 32843 with 32794 at 2
+Id : 32845, {_}: multiply (inverse ?69433) ?69433 =<= inverse (multiply ?69433 (inverse ?69433)) [69433] by Demod 32844 with 23108 at 2
+Id : 32878, {_}: inverse (multiply (inverse ?69602) ?69602) =>= multiply ?69602 (inverse ?69602) [69602] by Super 29399 with 32845 at 1,2
+Id : 32984, {_}: multiply ?16894 (multiply ?16895 (inverse ?16895)) =>= ?16894 [16895, 16894] by Demod 29259 with 32878 at 2,2
+Id : 38023, {_}: multiply ?72734 (multiply ?72735 (multiply ?72736 (inverse ?72736))) =?= multiply (multiply ?72734 (multiply ?72735 ?72737)) (inverse ?72737) [72737, 72736, 72735, 72734] by Super 32984 with 32817 at 2
+Id : 38122, {_}: multiply ?72734 ?72735 =<= multiply (multiply ?72734 (multiply ?72735 ?72737)) (inverse ?72737) [72737, 72735, 72734] by Demod 38023 with 32984 at 2,2
+Id : 40272, {_}: multiply (multiply ?69480 ?69481) ?69483 =?= multiply ?69480 (multiply ?69481 ?69483) [69483, 69481, 69480] by Demod 32817 with 38122 at 1,2
+Id : 40468, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 1 with 40272 at 2
+Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
+% SZS output end CNFRefutation for GRP411-1.p
+23552: solved GRP411-1.p in 26.617662 using nrkbo
+23552: status Unsatisfiable for GRP411-1.p
+NO CLASH, using fixed ground order
+23570: Facts:
+23570: Id : 2, {_}:
+ inverse
+ (multiply
+ (inverse
+ (multiply ?2
+ (inverse
+ (multiply (inverse ?3)
+ (inverse
+ (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
+ (multiply ?2 ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+23570: Goal:
+23570: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+23570: Order:
+23570: nrkbo
+23570: Leaf order:
+23570: b2 2 0 2 1,1,1,2
+23570: a2 2 0 2 2,2
+23570: inverse 8 1 1 0,1,1,2
+23570: multiply 8 2 2 0,2
+NO CLASH, using fixed ground order
+23571: Facts:
+23571: Id : 2, {_}:
+ inverse
+ (multiply
+ (inverse
+ (multiply ?2
+ (inverse
+ (multiply (inverse ?3)
+ (inverse
+ (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
+ (multiply ?2 ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+23571: Goal:
+23571: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+23571: Order:
+23571: kbo
+23571: Leaf order:
+23571: b2 2 0 2 1,1,1,2
+23571: a2 2 0 2 2,2
+23571: inverse 8 1 1 0,1,1,2
+23571: multiply 8 2 2 0,2
+NO CLASH, using fixed ground order
+23572: Facts:
+23572: Id : 2, {_}:
+ inverse
+ (multiply
+ (inverse
+ (multiply ?2
+ (inverse
+ (multiply (inverse ?3)
+ (inverse
+ (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
+ (multiply ?2 ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+23572: Goal:
+23572: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+23572: Order:
+23572: lpo
+23572: Leaf order:
+23572: b2 2 0 2 1,1,1,2
+23572: a2 2 0 2 2,2
+23572: inverse 8 1 1 0,1,1,2
+23572: multiply 8 2 2 0,2
+Statistics :
+Max weight : 117
+Found proof, 75.766748s
+% SZS status Unsatisfiable for GRP419-1.p
+% SZS output start CNFRefutation for GRP419-1.p
+Id : 3, {_}: inverse (multiply (inverse (multiply ?6 (inverse (multiply (inverse ?7) (inverse (multiply ?8 (inverse (multiply (inverse ?8) ?8)))))))) (multiply ?6 ?8)) =>= ?7 [8, 7, 6] by single_axiom ?6 ?7 ?8
+Id : 2, {_}: inverse (multiply (inverse (multiply ?2 (inverse (multiply (inverse ?3) (inverse (multiply ?4 (inverse (multiply (inverse ?4) ?4)))))))) (multiply ?2 ?4)) =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
+Id : 31, {_}: inverse (multiply (inverse (multiply ?219 (inverse (multiply (inverse ?220) (inverse (multiply (multiply (inverse (multiply ?221 (inverse (multiply (inverse ?222) (inverse (multiply ?223 (inverse (multiply (inverse ?223) ?223)))))))) (multiply ?221 ?223)) (inverse (multiply ?222 (multiply (inverse (multiply ?221 (inverse (multiply (inverse ?222) (inverse (multiply ?223 (inverse (multiply (inverse ?223) ?223)))))))) (multiply ?221 ?223)))))))))) (multiply ?219 (multiply (inverse (multiply ?221 (inverse (multiply (inverse ?222) (inverse (multiply ?223 (inverse (multiply (inverse ?223) ?223)))))))) (multiply ?221 ?223)))) =>= ?220 [223, 222, 221, 220, 219] by Super 3 with 2 at 1,1,2,1,2,1,2,1,1,1,2
+Id : 5, {_}: inverse (multiply (inverse (multiply ?16 (inverse (multiply ?17 (inverse (multiply ?18 (inverse (multiply (inverse ?18) ?18)))))))) (multiply ?16 ?18)) =?= multiply (inverse (multiply ?19 (inverse (multiply (inverse ?17) (inverse (multiply ?20 (inverse (multiply (inverse ?20) ?20)))))))) (multiply ?19 ?20) [20, 19, 18, 17, 16] by Super 3 with 2 at 1,1,2,1,1,1,2
+Id : 39, {_}: inverse (multiply (inverse (multiply ?290 (inverse (multiply (inverse ?291) (inverse (multiply (multiply (inverse (multiply ?292 (inverse (multiply (inverse ?293) (inverse (multiply ?294 (inverse (multiply (inverse ?294) ?294)))))))) (multiply ?292 ?294)) (inverse (multiply ?293 (multiply (inverse (multiply ?292 (inverse (multiply (inverse ?293) (inverse (multiply ?294 (inverse (multiply (inverse ?294) ?294)))))))) (multiply ?292 ?294)))))))))) (multiply ?290 (inverse (multiply (inverse (multiply ?295 (inverse (multiply ?293 (inverse (multiply ?296 (inverse (multiply (inverse ?296) ?296)))))))) (multiply ?295 ?296))))) =>= ?291 [296, 295, 294, 293, 292, 291, 290] by Super 31 with 5 at 2,2,1,2
+Id : 11, {_}: multiply (inverse (multiply ?51 (inverse (multiply (inverse (inverse ?52)) (inverse (multiply ?53 (inverse (multiply (inverse ?53) ?53)))))))) (multiply ?51 ?53) =>= ?52 [53, 52, 51] by Super 2 with 5 at 2
+Id : 131, {_}: inverse (multiply (inverse (multiply (inverse (multiply ?678 (inverse (multiply (inverse (inverse ?679)) (inverse (multiply ?680 (inverse (multiply (inverse ?680) ?680)))))))) (inverse (multiply (inverse ?681) (inverse (multiply (multiply ?678 ?680) (inverse (multiply (inverse (multiply ?678 ?680)) (multiply ?678 ?680))))))))) ?679) =>= ?681 [681, 680, 679, 678] by Super 2 with 11 at 2,1,2
+Id : 592, {_}: inverse (multiply (inverse (multiply ?3887 ?3888)) (multiply ?3887 ?3889)) =?= multiply (inverse (multiply ?3890 (inverse (multiply (inverse (inverse (inverse (multiply ?3889 (inverse (multiply (inverse ?3889) ?3889)))))) (inverse (multiply ?3891 (inverse (multiply (inverse ?3891) ?3891)))))))) (inverse (multiply (inverse ?3888) (inverse (multiply (multiply ?3890 ?3891) (inverse (multiply (inverse (multiply ?3890 ?3891)) (multiply ?3890 ?3891))))))) [3891, 3890, 3889, 3888, 3887] by Super 2 with 131 at 2,1,1,1,2
+Id : 1723, {_}: inverse (multiply (inverse (inverse (multiply (inverse (multiply ?12104 ?12105)) (multiply ?12104 ?12106)))) (inverse (multiply ?12106 (inverse (multiply (inverse ?12106) ?12106))))) =>= ?12105 [12106, 12105, 12104] by Super 131 with 592 at 1,1,1,2
+Id : 139, {_}: multiply (inverse (multiply ?714 (inverse (multiply (inverse (inverse ?715)) (inverse (multiply ?716 (inverse (multiply (inverse ?716) ?716)))))))) (multiply ?714 ?716) =>= ?715 [716, 715, 714] by Super 2 with 5 at 2
+Id : 140, {_}: multiply (inverse (multiply (inverse (multiply ?718 (inverse (multiply (inverse (inverse ?719)) (inverse (multiply ?720 (inverse (multiply (inverse ?720) ?720)))))))) (inverse (multiply (inverse (inverse ?721)) (inverse (multiply (multiply ?718 ?720) (inverse (multiply (inverse (multiply ?718 ?720)) (multiply ?718 ?720))))))))) ?719 =>= ?721 [721, 720, 719, 718] by Super 139 with 11 at 2,2
+Id : 1734, {_}: multiply (inverse (inverse (multiply (inverse (multiply ?12189 (inverse ?12190))) (multiply ?12189 ?12191)))) (inverse (multiply ?12191 (inverse (multiply (inverse ?12191) ?12191)))) =>= ?12190 [12191, 12190, 12189] by Super 140 with 592 at 1,1,2
+Id : 10, {_}: inverse (inverse (multiply (inverse (multiply ?47 (inverse (multiply ?48 (inverse (multiply ?49 (inverse (multiply (inverse ?49) ?49)))))))) (multiply ?47 ?49))) =>= ?48 [49, 48, 47] by Super 2 with 5 at 1,2
+Id : 1746, {_}: inverse (multiply (inverse (multiply ?12293 ?12294)) (multiply ?12293 ?12295)) =?= multiply (inverse (multiply ?12296 (inverse (multiply (inverse (inverse (inverse (multiply ?12295 (inverse (multiply (inverse ?12295) ?12295)))))) (inverse (multiply ?12297 (inverse (multiply (inverse ?12297) ?12297)))))))) (inverse (multiply (inverse ?12294) (inverse (multiply (multiply ?12296 ?12297) (inverse (multiply (inverse (multiply ?12296 ?12297)) (multiply ?12296 ?12297))))))) [12297, 12296, 12295, 12294, 12293] by Super 2 with 131 at 2,1,1,1,2
+Id : 1828, {_}: inverse (multiply (inverse (multiply ?13070 ?13071)) (multiply ?13070 ?13072)) =?= inverse (multiply (inverse (multiply ?13073 ?13071)) (multiply ?13073 ?13072)) [13073, 13072, 13071, 13070] by Super 1746 with 592 at 3
+Id : 6984, {_}: inverse (inverse (multiply (inverse (multiply ?54958 (inverse (multiply ?54959 (inverse (multiply (multiply ?54960 ?54961) (inverse (multiply (inverse (multiply ?54962 ?54961)) (multiply ?54962 ?54961))))))))) (multiply ?54958 (multiply ?54960 ?54961)))) =>= ?54959 [54962, 54961, 54960, 54959, 54958] by Super 10 with 1828 at 2,1,2,1,2,1,1,1,1,2
+Id : 6987, {_}: inverse (inverse (multiply (inverse (multiply ?54980 (inverse (multiply ?54981 (inverse (multiply (multiply (inverse (multiply (inverse (multiply ?54982 (inverse (multiply (inverse (inverse ?54983)) (inverse (multiply ?54984 (inverse (multiply (inverse ?54984) ?54984)))))))) (inverse (multiply (inverse (inverse ?54985)) (inverse (multiply (multiply ?54982 ?54984) (inverse (multiply (inverse (multiply ?54982 ?54984)) (multiply ?54982 ?54984))))))))) ?54983) (inverse (multiply (inverse (multiply ?54986 ?54983)) (multiply ?54986 ?54983))))))))) (multiply ?54980 ?54985))) =>= ?54981 [54986, 54985, 54984, 54983, 54982, 54981, 54980] by Super 6984 with 140 at 2,2,1,1,2
+Id : 7283, {_}: inverse (inverse (multiply (inverse (multiply ?56997 (inverse (multiply ?56998 (inverse (multiply ?56999 (inverse (multiply (inverse (multiply ?57000 ?57001)) (multiply ?57000 ?57001))))))))) (multiply ?56997 ?56999))) =>= ?56998 [57001, 57000, 56999, 56998, 56997] by Demod 6987 with 140 at 1,1,2,1,2,1,1,1,1,2
+Id : 7302, {_}: inverse (inverse (multiply (inverse (multiply ?57173 (inverse (multiply ?57174 (inverse (multiply ?57175 (inverse (multiply (inverse (multiply (inverse (multiply ?57176 (inverse (multiply (inverse (inverse ?57177)) (inverse (multiply ?57178 (inverse (multiply (inverse ?57178) ?57178)))))))) (multiply ?57176 ?57178))) ?57177)))))))) (multiply ?57173 ?57175))) =>= ?57174 [57178, 57177, 57176, 57175, 57174, 57173] by Super 7283 with 11 at 2,1,2,1,2,1,2,1,1,1,1,2
+Id : 7433, {_}: inverse (inverse (multiply (inverse (multiply ?57173 (inverse (multiply ?57174 (inverse (multiply ?57175 (inverse (multiply (inverse ?57177) ?57177)))))))) (multiply ?57173 ?57175))) =>= ?57174 [57177, 57175, 57174, 57173] by Demod 7302 with 2 at 1,1,2,1,2,1,2,1,1,1,1,2
+Id : 7485, {_}: multiply ?58076 (inverse (multiply ?58077 (inverse (multiply (inverse ?58077) ?58077)))) =?= multiply ?58076 (inverse (multiply ?58077 (inverse (multiply (inverse ?58078) ?58078)))) [58078, 58077, 58076] by Super 1734 with 7433 at 1,2
+Id : 8374, {_}: multiply (inverse (inverse (multiply (inverse (multiply ?64683 (inverse (multiply ?64684 (inverse (multiply (inverse ?64685) ?64685)))))) (multiply ?64683 ?64686)))) (inverse (multiply ?64686 (inverse (multiply (inverse ?64686) ?64686)))) =?= multiply ?64684 (inverse (multiply (inverse ?64684) ?64684)) [64686, 64685, 64684, 64683] by Super 1734 with 7485 at 1,1,1,1,1,2
+Id : 8749, {_}: multiply ?64684 (inverse (multiply (inverse ?64685) ?64685)) =?= multiply ?64684 (inverse (multiply (inverse ?64684) ?64684)) [64685, 64684] by Demod 8374 with 1734 at 2
+Id : 8815, {_}: inverse (multiply (inverse (inverse (multiply (inverse (multiply ?67872 (inverse (multiply (inverse ?67872) ?67872)))) (multiply ?67872 ?67873)))) (inverse (multiply ?67873 (inverse (multiply (inverse ?67873) ?67873))))) =?= inverse (multiply (inverse ?67874) ?67874) [67874, 67873, 67872] by Super 1723 with 8749 at 1,1,1,1,1,1,2
+Id : 9225, {_}: inverse (multiply (inverse ?67872) ?67872) =?= inverse (multiply (inverse ?67874) ?67874) [67874, 67872] by Demod 8815 with 1723 at 2
+Id : 9030, {_}: multiply (inverse (inverse (multiply (inverse (multiply ?69262 (inverse (multiply (inverse ?69262) ?69262)))) (multiply ?69262 ?69263)))) (inverse (multiply ?69263 (inverse (multiply (inverse ?69263) ?69263)))) =?= multiply (inverse ?69264) ?69264 [69264, 69263, 69262] by Super 1734 with 8749 at 1,1,1,1,1,2
+Id : 9183, {_}: multiply (inverse ?69262) ?69262 =?= multiply (inverse ?69264) ?69264 [69264, 69262] by Demod 9030 with 1734 at 2
+Id : 12179, {_}: inverse (multiply (inverse (inverse (multiply (inverse ?88672) ?88672))) (inverse (multiply ?88673 (inverse (multiply (inverse ?88673) ?88673))))) =>= ?88673 [88673, 88672] by Super 1723 with 9183 at 1,1,1,1,2
+Id : 12213, {_}: inverse (multiply (inverse (inverse (multiply (inverse ?88894) ?88894))) (inverse (multiply ?88895 (inverse (multiply (inverse ?88896) ?88896))))) =>= ?88895 [88896, 88895, 88894] by Super 12179 with 9183 at 1,2,1,2,1,2
+Id : 13701, {_}: inverse (multiply (inverse ?97964) ?97964) =?= inverse (inverse (multiply (inverse ?97965) ?97965)) [97965, 97964] by Super 9225 with 12213 at 3
+Id : 34411, {_}: inverse (multiply (inverse (multiply (inverse ?202408) ?202408)) (inverse (multiply ?202409 (inverse (multiply (inverse ?202409) ?202409))))) =>= ?202409 [202409, 202408] by Super 1723 with 13701 at 1,1,2
+Id : 9086, {_}: multiply ?69615 (inverse (multiply (inverse ?69616) ?69616)) =?= multiply ?69615 (inverse (multiply (inverse ?69615) ?69615)) [69616, 69615] by Demod 8374 with 1734 at 2
+Id : 9126, {_}: multiply ?69879 (inverse (multiply (inverse ?69880) ?69880)) =?= multiply ?69879 (inverse (multiply (inverse ?69881) ?69881)) [69881, 69880, 69879] by Super 9086 with 8749 at 3
+Id : 56, {_}: inverse (multiply (inverse (multiply ?444 (inverse (multiply (inverse ?445) (inverse (multiply (inverse (multiply (inverse (multiply ?446 (inverse (multiply ?447 (inverse (multiply ?448 (inverse (multiply (inverse ?448) ?448)))))))) (multiply ?446 ?448))) (inverse (multiply ?447 (multiply (inverse (multiply ?449 (inverse (multiply (inverse ?447) (inverse (multiply ?450 (inverse (multiply (inverse ?450) ?450)))))))) (multiply ?449 ?450)))))))))) (multiply ?444 (multiply (inverse (multiply ?449 (inverse (multiply (inverse ?447) (inverse (multiply ?450 (inverse (multiply (inverse ?450) ?450)))))))) (multiply ?449 ?450)))) =>= ?445 [450, 449, 448, 447, 446, 445, 444] by Super 31 with 5 at 1,1,2,1,2,1,1,1,2
+Id : 14563, {_}: inverse (multiply (inverse (multiply ?103053 (inverse (multiply (inverse (inverse (multiply (inverse ?103054) ?103054))) (inverse (multiply (inverse (multiply (inverse (multiply ?103055 (inverse (multiply ?103056 (inverse (multiply ?103057 (inverse (multiply (inverse ?103057) ?103057)))))))) (multiply ?103055 ?103057))) (inverse (multiply ?103056 (multiply (inverse (multiply ?103058 (inverse (multiply (inverse ?103056) (inverse (multiply ?103059 (inverse (multiply (inverse ?103059) ?103059)))))))) (multiply ?103058 ?103059)))))))))) (multiply ?103053 (multiply (inverse (multiply ?103058 (inverse (multiply (inverse ?103056) (inverse (multiply ?103059 (inverse (multiply (inverse ?103059) ?103059)))))))) (multiply ?103058 ?103059)))) =?= multiply (inverse ?103060) ?103060 [103060, 103059, 103058, 103057, 103056, 103055, 103054, 103053] by Super 56 with 13701 at 1,1,2,1,1,1,2
+Id : 14713, {_}: inverse (multiply (inverse ?103054) ?103054) =?= multiply (inverse ?103060) ?103060 [103060, 103054] by Demod 14563 with 56 at 2
+Id : 15410, {_}: multiply ?107836 (inverse (multiply (inverse ?107837) ?107837)) =?= multiply ?107836 (multiply (inverse ?107838) ?107838) [107838, 107837, 107836] by Super 9126 with 14713 at 2,3
+Id : 34485, {_}: inverse (multiply (inverse (multiply (inverse ?202808) ?202808)) (inverse (multiply (inverse (multiply (inverse ?202809) ?202809)) (inverse (multiply (inverse (inverse (multiply (inverse ?202809) ?202809))) (multiply (inverse ?202810) ?202810)))))) =>= inverse (multiply (inverse ?202809) ?202809) [202810, 202809, 202808] by Super 34411 with 15410 at 1,2,1,2,1,2
+Id : 14824, {_}: multiply (inverse ?103830) ?103830 =?= inverse (inverse (multiply (inverse ?103831) ?103831)) [103831, 103830] by Super 12213 with 14713 at 2
+Id : 24848, {_}: inverse (multiply (multiply (inverse ?160661) ?160661) (inverse (multiply ?160662 (inverse (multiply (inverse ?160662) ?160662))))) =>= ?160662 [160662, 160661] by Super 1723 with 14824 at 1,1,2
+Id : 25277, {_}: inverse (multiply (multiply (inverse ?163120) ?163120) (inverse (multiply ?163121 (multiply (inverse ?163122) ?163122)))) =>= ?163121 [163122, 163121, 163120] by Super 24848 with 14713 at 2,1,2,1,2
+Id : 25479, {_}: inverse (multiply (inverse (multiply (inverse ?164337) ?164337)) (inverse (multiply ?164338 (multiply (inverse ?164339) ?164339)))) =>= ?164338 [164339, 164338, 164337] by Super 25277 with 14713 at 1,1,2
+Id : 35006, {_}: inverse (multiply (inverse (multiply (inverse ?204646) ?204646)) (inverse (inverse (multiply (inverse ?204647) ?204647)))) =>= inverse (multiply (inverse ?204647) ?204647) [204647, 204646] by Demod 34485 with 25479 at 2,1,2
+Id : 35218, {_}: inverse (multiply (multiply (inverse ?205705) ?205705) (inverse (inverse (multiply (inverse ?205706) ?205706)))) =>= inverse (multiply (inverse ?205706) ?205706) [205706, 205705] by Super 35006 with 14713 at 1,1,2
+Id : 35602, {_}: inverse (multiply (inverse (multiply ?206697 (inverse (multiply (inverse (multiply (inverse ?206698) ?206698)) (inverse (multiply (multiply (inverse (multiply ?206699 (inverse (multiply (inverse ?206700) (inverse (multiply ?206701 (inverse (multiply (inverse ?206701) ?206701)))))))) (multiply ?206699 ?206701)) (inverse (multiply ?206700 (multiply (inverse (multiply ?206699 (inverse (multiply (inverse ?206700) (inverse (multiply ?206701 (inverse (multiply (inverse ?206701) ?206701)))))))) (multiply ?206699 ?206701)))))))))) (multiply ?206697 (inverse (multiply (inverse (multiply ?206702 (inverse (multiply ?206700 (inverse (multiply ?206703 (inverse (multiply (inverse ?206703) ?206703)))))))) (multiply ?206702 ?206703))))) =?= multiply (multiply (inverse ?206704) ?206704) (inverse (inverse (multiply (inverse ?206698) ?206698))) [206704, 206703, 206702, 206701, 206700, 206699, 206698, 206697] by Super 39 with 35218 at 1,1,2,1,1,1,2
+Id : 35866, {_}: multiply (inverse ?206698) ?206698 =<= multiply (multiply (inverse ?206704) ?206704) (inverse (inverse (multiply (inverse ?206698) ?206698))) [206704, 206698] by Demod 35602 with 39 at 2
+Id : 36115, {_}: inverse (multiply (inverse (multiply (multiply (inverse ?208195) ?208195) (inverse (multiply (inverse ?208196) (inverse (multiply (inverse (inverse (multiply (inverse ?208197) ?208197))) (inverse (multiply (inverse (inverse (inverse (multiply (inverse ?208197) ?208197)))) (inverse (inverse (multiply (inverse ?208197) ?208197))))))))))) (multiply (inverse ?208197) ?208197)) =>= ?208196 [208197, 208196, 208195] by Super 2 with 35866 at 2,1,2
+Id : 15929, {_}: inverse (multiply (multiply (inverse ?110579) ?110579) (inverse (multiply ?110580 (inverse (multiply (inverse ?110580) ?110580))))) =>= ?110580 [110580, 110579] by Super 1723 with 14824 at 1,1,2
+Id : 24931, {_}: inverse (multiply (multiply (inverse ?161104) ?161104) (inverse (multiply ?161105 (multiply (inverse ?161106) ?161106)))) =>= ?161105 [161106, 161105, 161104] by Super 24848 with 14713 at 2,1,2,1,2
+Id : 25816, {_}: inverse (multiply (multiply (inverse ?166039) ?166039) (inverse (multiply (inverse ?166040) ?166040))) =>= multiply (inverse ?166040) ?166040 [166040, 166039] by Super 15929 with 24931 at 2,1,2
+Id : 25967, {_}: inverse (multiply (inverse (inverse (multiply (inverse ?166851) ?166851))) (inverse (multiply (inverse ?166852) ?166852))) =>= multiply (inverse ?166852) ?166852 [166852, 166851] by Super 25816 with 14824 at 1,1,2
+Id : 36557, {_}: inverse (multiply (inverse (multiply (multiply (inverse ?208195) ?208195) (inverse (multiply (inverse ?208196) (multiply (inverse (inverse (inverse (multiply (inverse ?208197) ?208197)))) (inverse (inverse (multiply (inverse ?208197) ?208197)))))))) (multiply (inverse ?208197) ?208197)) =>= ?208196 [208197, 208196, 208195] by Demod 36115 with 25967 at 2,1,2,1,1,1,2
+Id : 36558, {_}: inverse (multiply (inverse ?208196) (multiply (inverse ?208197) ?208197)) =>= ?208196 [208197, 208196] by Demod 36557 with 24931 at 1,1,2
+Id : 37252, {_}: inverse (multiply (multiply (inverse ?211410) ?211410) ?211411) =>= inverse ?211411 [211411, 211410] by Super 24931 with 36558 at 2,1,2
+Id : 40835, {_}: inverse (multiply (inverse ?231064) (multiply (inverse ?231065) ?231065)) =?= multiply (multiply (inverse ?231066) ?231066) ?231064 [231066, 231065, 231064] by Super 36558 with 37252 at 1,1,2
+Id : 40960, {_}: ?231064 =<= multiply (multiply (inverse ?231066) ?231066) ?231064 [231066, 231064] by Demod 40835 with 36558 at 2
+Id : 42184, {_}: a2 === a2 [] by Demod 1 with 40960 at 2
+Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
+% SZS output end CNFRefutation for GRP419-1.p
+23570: solved GRP419-1.p in 75.644727 using nrkbo
+23570: status Unsatisfiable for GRP419-1.p
+NO CLASH, using fixed ground order
+23595: Facts:
+23595: Id : 2, {_}:
+ inverse
+ (multiply
+ (inverse
+ (multiply ?2
+ (inverse
+ (multiply (inverse ?3)
+ (multiply (inverse ?4)
+ (inverse (multiply (inverse ?4) ?4)))))))
+ (multiply ?2 ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+23595: Goal:
+23595: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+23595: Order:
+23595: nrkbo
+23595: Leaf order:
+23595: b2 2 0 2 1,1,1,2
+23595: a2 2 0 2 2,2
+23595: inverse 8 1 1 0,1,1,2
+23595: multiply 8 2 2 0,2
+NO CLASH, using fixed ground order
+23596: Facts:
+23596: Id : 2, {_}:
+ inverse
+ (multiply
+ (inverse
+ (multiply ?2
+ (inverse
+ (multiply (inverse ?3)
+ (multiply (inverse ?4)
+ (inverse (multiply (inverse ?4) ?4)))))))
+ (multiply ?2 ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+23596: Goal:
+23596: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+23596: Order:
+23596: kbo
+23596: Leaf order:
+23596: b2 2 0 2 1,1,1,2
+23596: a2 2 0 2 2,2
+23596: inverse 8 1 1 0,1,1,2
+23596: multiply 8 2 2 0,2
+NO CLASH, using fixed ground order
+23597: Facts:
+23597: Id : 2, {_}:
+ inverse
+ (multiply
+ (inverse
+ (multiply ?2
+ (inverse
+ (multiply (inverse ?3)
+ (multiply (inverse ?4)
+ (inverse (multiply (inverse ?4) ?4)))))))
+ (multiply ?2 ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+23597: Goal:
+23597: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+23597: Order:
+23597: lpo
+23597: Leaf order:
+23597: b2 2 0 2 1,1,1,2
+23597: a2 2 0 2 2,2
+23597: inverse 8 1 1 0,1,1,2
+23597: multiply 8 2 2 0,2
+% SZS status Timeout for GRP422-1.p
+NO CLASH, using fixed ground order
+23629: Facts:
+23629: Id : 2, {_}:
+ inverse
+ (multiply
+ (inverse
+ (multiply ?2
+ (inverse
+ (multiply (inverse ?3)
+ (multiply (inverse ?4)
+ (inverse (multiply (inverse ?4) ?4)))))))
+ (multiply ?2 ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+23629: Goal:
+23629: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+23629: Order:
+23629: nrkbo
+23629: Leaf order:
+23629: a3 2 0 2 1,1,2
+23629: b3 2 0 2 2,1,2
+23629: c3 2 0 2 2,2
+23629: inverse 7 1 0
+23629: multiply 10 2 4 0,2
+NO CLASH, using fixed ground order
+23630: Facts:
+23630: Id : 2, {_}:
+ inverse
+ (multiply
+ (inverse
+ (multiply ?2
+ (inverse
+ (multiply (inverse ?3)
+ (multiply (inverse ?4)
+ (inverse (multiply (inverse ?4) ?4)))))))
+ (multiply ?2 ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+23630: Goal:
+23630: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+23630: Order:
+23630: kbo
+23630: Leaf order:
+23630: a3 2 0 2 1,1,2
+23630: b3 2 0 2 2,1,2
+23630: c3 2 0 2 2,2
+23630: inverse 7 1 0
+23630: multiply 10 2 4 0,2
+NO CLASH, using fixed ground order
+23631: Facts:
+23631: Id : 2, {_}:
+ inverse
+ (multiply
+ (inverse
+ (multiply ?2
+ (inverse
+ (multiply (inverse ?3)
+ (multiply (inverse ?4)
+ (inverse (multiply (inverse ?4) ?4)))))))
+ (multiply ?2 ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+23631: Goal:
+23631: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+23631: Order:
+23631: lpo
+23631: Leaf order:
+23631: a3 2 0 2 1,1,2
+23631: b3 2 0 2 2,1,2
+23631: c3 2 0 2 2,2
+23631: inverse 7 1 0
+23631: multiply 10 2 4 0,2
+% SZS status Timeout for GRP423-1.p
+NO CLASH, using fixed ground order
+23653: Facts:
+23653: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply
+ (multiply
+ (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
+ ?5) (inverse (multiply ?3 ?5))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23653: Goal:
+23653: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+23653: Order:
+23653: nrkbo
+23653: Leaf order:
+23653: a3 2 0 2 1,1,2
+23653: b3 2 0 2 2,1,2
+23653: c3 2 0 2 2,2
+23653: inverse 5 1 0
+23653: multiply 10 2 4 0,2
+NO CLASH, using fixed ground order
+23654: Facts:
+23654: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply
+ (multiply
+ (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
+ ?5) (inverse (multiply ?3 ?5))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23654: Goal:
+23654: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+23654: Order:
+23654: kbo
+23654: Leaf order:
+23654: a3 2 0 2 1,1,2
+23654: b3 2 0 2 2,1,2
+23654: c3 2 0 2 2,2
+23654: inverse 5 1 0
+23654: multiply 10 2 4 0,2
+NO CLASH, using fixed ground order
+23655: Facts:
+23655: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply
+ (multiply
+ (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4)))
+ ?5) (inverse (multiply ?3 ?5))))
+ =>=
+ ?4
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23655: Goal:
+23655: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+23655: Order:
+23655: lpo
+23655: Leaf order:
+23655: a3 2 0 2 1,1,2
+23655: b3 2 0 2 2,1,2
+23655: c3 2 0 2 2,2
+23655: inverse 5 1 0
+23655: multiply 10 2 4 0,2
+Statistics :
+Max weight : 62
+Found proof, 11.852538s
+% SZS status Unsatisfiable for GRP429-1.p
+% SZS output start CNFRefutation for GRP429-1.p
+Id : 2, {_}: multiply ?2 (inverse (multiply (multiply (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) ?5) (inverse (multiply ?3 ?5)))) =>= ?4 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+Id : 3, {_}: multiply ?7 (inverse (multiply (multiply (inverse (multiply (inverse ?8) (multiply (inverse ?7) ?9))) ?10) (inverse (multiply ?8 ?10)))) =>= ?9 [10, 9, 8, 7] by single_axiom ?7 ?8 ?9 ?10
+Id : 6, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (inverse (multiply (inverse ?29) (multiply (inverse (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?27))) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 30, 29, 28, 27, 26] by Super 3 with 2 at 1,1,2,2
+Id : 5, {_}: multiply ?19 (inverse (multiply (multiply (inverse (multiply (inverse ?20) ?21)) ?22) (inverse (multiply ?20 ?22)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24) (inverse (multiply ?23 ?24))) [24, 23, 22, 21, 20, 19] by Super 3 with 2 at 2,1,1,1,1,2,2
+Id : 28, {_}: multiply (inverse ?215) (multiply ?215 (inverse (multiply (multiply (inverse (multiply (inverse ?216) ?217)) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 217, 216, 215] by Super 2 with 5 at 2,2
+Id : 29, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?220) (multiply (inverse (inverse ?221)) (multiply (inverse ?221) ?222)))) ?223) (inverse (multiply ?220 ?223))) =>= ?222 [223, 222, 221, 220] by Super 2 with 5 at 2
+Id : 287, {_}: multiply (inverse ?2293) (multiply ?2293 ?2294) =?= multiply (inverse (inverse ?2295)) (multiply (inverse ?2295) ?2294) [2295, 2294, 2293] by Super 28 with 29 at 2,2,2
+Id : 136, {_}: multiply (inverse ?1148) (multiply ?1148 ?1149) =?= multiply (inverse (inverse ?1150)) (multiply (inverse ?1150) ?1149) [1150, 1149, 1148] by Super 28 with 29 at 2,2,2
+Id : 301, {_}: multiply (inverse ?2384) (multiply ?2384 ?2385) =?= multiply (inverse ?2386) (multiply ?2386 ?2385) [2386, 2385, 2384] by Super 287 with 136 at 3
+Id : 356, {_}: multiply (inverse ?2583) (multiply ?2583 (inverse (multiply (multiply (inverse (multiply (inverse ?2584) (multiply ?2584 ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585, 2584, 2583] by Super 28 with 301 at 1,1,1,1,2,2,2
+Id : 679, {_}: multiply ?5168 (inverse (multiply (multiply (inverse (multiply (inverse ?5169) (multiply ?5169 ?5170))) ?5171) (inverse (multiply (inverse ?5168) ?5171)))) =>= ?5170 [5171, 5170, 5169, 5168] by Super 2 with 301 at 1,1,1,1,2,2
+Id : 2910, {_}: multiply ?23936 (inverse (multiply (multiply (inverse (multiply (inverse ?23937) (multiply ?23937 ?23938))) (multiply ?23936 ?23939)) (inverse (multiply (inverse ?23940) (multiply ?23940 ?23939))))) =>= ?23938 [23940, 23939, 23938, 23937, 23936] by Super 679 with 301 at 1,2,1,2,2
+Id : 2996, {_}: multiply (multiply (inverse ?24702) (multiply ?24702 ?24703)) (inverse (multiply ?24704 (inverse (multiply (inverse ?24705) (multiply ?24705 (inverse (multiply (multiply (inverse (multiply (inverse ?24706) ?24704)) ?24707) (inverse (multiply ?24706 ?24707))))))))) =>= ?24703 [24707, 24706, 24705, 24704, 24703, 24702] by Super 2910 with 28 at 1,1,2,2
+Id : 3034, {_}: multiply (multiply (inverse ?24702) (multiply ?24702 ?24703)) (inverse (multiply ?24704 (inverse ?24704))) =>= ?24703 [24704, 24703, 24702] by Demod 2996 with 28 at 1,2,1,2,2
+Id : 3426, {_}: multiply (inverse (multiply (inverse ?29536) (multiply ?29536 ?29537))) ?29537 =?= multiply (inverse (multiply (inverse ?29538) (multiply ?29538 ?29539))) ?29539 [29539, 29538, 29537, 29536] by Super 356 with 3034 at 2,2
+Id : 3726, {_}: multiply (inverse (inverse (multiply (inverse ?31745) (multiply ?31745 (inverse (multiply (multiply (inverse (multiply (inverse ?31746) ?31747)) ?31748) (inverse (multiply ?31746 ?31748)))))))) (multiply (inverse (multiply (inverse ?31749) (multiply ?31749 ?31750))) ?31750) =>= ?31747 [31750, 31749, 31748, 31747, 31746, 31745] by Super 28 with 3426 at 2,2
+Id : 3919, {_}: multiply (inverse (inverse ?31747)) (multiply (inverse (multiply (inverse ?31749) (multiply ?31749 ?31750))) ?31750) =>= ?31747 [31750, 31749, 31747] by Demod 3726 with 28 at 1,1,1,2
+Id : 91, {_}: multiply (inverse ?821) (multiply ?821 (inverse (multiply (multiply (inverse (multiply (inverse ?822) ?823)) ?824) (inverse (multiply ?822 ?824))))) =>= ?823 [824, 823, 822, 821] by Super 2 with 5 at 2,2
+Id : 107, {_}: multiply (inverse ?949) (multiply ?949 (multiply ?950 (inverse (multiply (multiply (inverse (multiply (inverse ?951) ?952)) ?953) (inverse (multiply ?951 ?953)))))) =>= multiply (inverse (inverse ?950)) ?952 [953, 952, 951, 950, 949] by Super 91 with 5 at 2,2,2
+Id : 3966, {_}: multiply (inverse (inverse (inverse ?33635))) ?33635 =?= multiply (inverse (inverse (inverse (multiply (inverse ?33636) (multiply ?33636 (inverse (multiply (multiply (inverse (multiply (inverse ?33637) ?33638)) ?33639) (inverse (multiply ?33637 ?33639))))))))) ?33638 [33639, 33638, 33637, 33636, 33635] by Super 107 with 3919 at 2,2
+Id : 4117, {_}: multiply (inverse (inverse (inverse ?33635))) ?33635 =?= multiply (inverse (inverse (inverse ?33638))) ?33638 [33638, 33635] by Demod 3966 with 28 at 1,1,1,1,3
+Id : 4346, {_}: multiply (inverse (inverse ?35898)) (multiply (inverse (multiply (inverse (inverse (inverse (inverse ?35899)))) (multiply (inverse (inverse (inverse ?35900))) ?35900))) ?35899) =>= ?35898 [35900, 35899, 35898] by Super 3919 with 4117 at 2,1,1,2,2
+Id : 3965, {_}: multiply (inverse ?33628) (multiply ?33628 (multiply ?33629 (inverse (multiply (multiply (inverse ?33630) ?33631) (inverse (multiply (inverse ?33630) ?33631)))))) =?= multiply (inverse (inverse ?33629)) (multiply (inverse (multiply (inverse ?33632) (multiply ?33632 ?33633))) ?33633) [33633, 33632, 33631, 33630, 33629, 33628] by Super 107 with 3919 at 1,1,1,1,2,2,2,2
+Id : 6632, {_}: multiply (inverse ?52916) (multiply ?52916 (multiply ?52917 (inverse (multiply (multiply (inverse ?52918) ?52919) (inverse (multiply (inverse ?52918) ?52919)))))) =>= ?52917 [52919, 52918, 52917, 52916] by Demod 3965 with 3919 at 3
+Id : 6641, {_}: multiply (inverse ?52992) (multiply ?52992 (multiply ?52993 (inverse (multiply (multiply (inverse ?52994) (inverse (multiply (multiply (inverse (multiply (inverse ?52995) (multiply (inverse (inverse ?52994)) ?52996))) ?52997) (inverse (multiply ?52995 ?52997))))) (inverse ?52996))))) =>= ?52993 [52997, 52996, 52995, 52994, 52993, 52992] by Super 6632 with 2 at 1,2,1,2,2,2,2
+Id : 6773, {_}: multiply (inverse ?52992) (multiply ?52992 (multiply ?52993 (inverse (multiply ?52996 (inverse ?52996))))) =>= ?52993 [52996, 52993, 52992] by Demod 6641 with 2 at 1,1,2,2,2,2
+Id : 6832, {_}: multiply (inverse (inverse ?53817)) (multiply (inverse ?53818) (multiply ?53818 (inverse (multiply ?53819 (inverse ?53819))))) =>= ?53817 [53819, 53818, 53817] by Super 4346 with 6773 at 1,1,2,2
+Id : 4, {_}: multiply ?12 (inverse (multiply (multiply (inverse (multiply (inverse ?13) (multiply (inverse ?12) ?14))) (inverse (multiply (multiply (inverse (multiply (inverse ?15) (multiply (inverse ?13) ?16))) ?17) (inverse (multiply ?15 ?17))))) (inverse ?16))) =>= ?14 [17, 16, 15, 14, 13, 12] by Super 3 with 2 at 1,2,1,2,2
+Id : 9, {_}: multiply ?44 (inverse (multiply (multiply (inverse (multiply (inverse ?45) ?46)) ?47) (inverse (multiply ?45 ?47)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?48) (multiply (inverse (inverse ?44)) ?46))) (inverse (multiply (multiply (inverse (multiply (inverse ?49) (multiply (inverse ?48) ?50))) ?51) (inverse (multiply ?49 ?51))))) (inverse ?50)) [51, 50, 49, 48, 47, 46, 45, 44] by Super 2 with 4 at 2,1,1,1,1,2,2
+Id : 7754, {_}: multiply ?63171 (inverse (multiply (multiply (inverse (multiply (inverse ?63172) (multiply (inverse ?63171) (inverse (multiply ?63173 (inverse ?63173)))))) ?63174) (inverse (multiply ?63172 ?63174)))) =?= inverse (multiply (multiply (inverse ?63175) (inverse (multiply (multiply (inverse (multiply (inverse ?63176) (multiply (inverse (inverse ?63175)) ?63177))) ?63178) (inverse (multiply ?63176 ?63178))))) (inverse ?63177)) [63178, 63177, 63176, 63175, 63174, 63173, 63172, 63171] by Super 9 with 6832 at 1,1,1,1,3
+Id : 7872, {_}: inverse (multiply ?63173 (inverse ?63173)) =?= inverse (multiply (multiply (inverse ?63175) (inverse (multiply (multiply (inverse (multiply (inverse ?63176) (multiply (inverse (inverse ?63175)) ?63177))) ?63178) (inverse (multiply ?63176 ?63178))))) (inverse ?63177)) [63178, 63177, 63176, 63175, 63173] by Demod 7754 with 2 at 2
+Id : 7873, {_}: inverse (multiply ?63173 (inverse ?63173)) =?= inverse (multiply ?63177 (inverse ?63177)) [63177, 63173] by Demod 7872 with 2 at 1,1,3
+Id : 8249, {_}: multiply (inverse (inverse (multiply ?66459 (inverse ?66459)))) (multiply (inverse ?66460) (multiply ?66460 (inverse (multiply ?66461 (inverse ?66461))))) =?= multiply ?66462 (inverse ?66462) [66462, 66461, 66460, 66459] by Super 6832 with 7873 at 1,1,2
+Id : 8282, {_}: multiply ?66459 (inverse ?66459) =?= multiply ?66462 (inverse ?66462) [66462, 66459] by Demod 8249 with 6832 at 2
+Id : 8520, {_}: multiply (multiply (inverse ?67970) (multiply ?67971 (inverse ?67971))) (inverse (multiply ?67972 (inverse ?67972))) =>= inverse ?67970 [67972, 67971, 67970] by Super 3034 with 8282 at 2,1,2
+Id : 380, {_}: multiply ?2743 (inverse (multiply (multiply (inverse ?2744) (multiply ?2744 ?2745)) (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745))))) =>= ?2747 [2747, 2746, 2745, 2744, 2743] by Super 2 with 301 at 1,1,2,2
+Id : 8912, {_}: multiply ?70596 (inverse (multiply (multiply (inverse ?70597) (multiply ?70597 (inverse (multiply ?70598 (inverse ?70598))))) (inverse (multiply ?70599 (inverse ?70599))))) =>= inverse (inverse ?70596) [70599, 70598, 70597, 70596] by Super 380 with 8520 at 2,1,2,1,2,2
+Id : 9021, {_}: multiply ?70596 (inverse (inverse (multiply ?70598 (inverse ?70598)))) =>= inverse (inverse ?70596) [70598, 70596] by Demod 8912 with 3034 at 1,2,2
+Id : 9165, {_}: multiply (inverse (inverse ?72171)) (multiply (inverse (multiply (inverse ?72172) (inverse (inverse ?72172)))) (inverse (inverse (multiply ?72173 (inverse ?72173))))) =>= ?72171 [72173, 72172, 72171] by Super 3919 with 9021 at 2,1,1,2,2
+Id : 10068, {_}: multiply (inverse (inverse ?76580)) (inverse (inverse (inverse (multiply (inverse ?76581) (inverse (inverse ?76581)))))) =>= ?76580 [76581, 76580] by Demod 9165 with 9021 at 2,2
+Id : 9180, {_}: multiply ?72234 (inverse ?72234) =?= inverse (inverse (inverse (multiply ?72235 (inverse ?72235)))) [72235, 72234] by Super 8282 with 9021 at 3
+Id : 10100, {_}: multiply (inverse (inverse ?76745)) (multiply ?76746 (inverse ?76746)) =>= ?76745 [76746, 76745] by Super 10068 with 9180 at 2,2
+Id : 10663, {_}: multiply ?82289 (inverse (multiply ?82290 (inverse ?82290))) =>= inverse (inverse ?82289) [82290, 82289] by Super 8520 with 10100 at 1,2
+Id : 10913, {_}: multiply (inverse (inverse ?83563)) (inverse (inverse (inverse (multiply (inverse ?83564) (multiply ?83564 (inverse (multiply ?83565 (inverse ?83565)))))))) =>= ?83563 [83565, 83564, 83563] by Super 3919 with 10663 at 2,2
+Id : 10892, {_}: inverse (inverse (multiply (inverse ?24702) (multiply ?24702 ?24703))) =>= ?24703 [24703, 24702] by Demod 3034 with 10663 at 2
+Id : 11238, {_}: multiply (inverse (inverse ?83563)) (inverse (inverse (multiply ?83565 (inverse ?83565)))) =>= ?83563 [83565, 83563] by Demod 10913 with 10892 at 1,2,2
+Id : 11239, {_}: inverse (inverse (inverse (inverse ?83563))) =>= ?83563 [83563] by Demod 11238 with 9021 at 2
+Id : 138, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1160) (multiply (inverse (inverse ?1161)) (multiply (inverse ?1161) ?1162)))) ?1163) (inverse (multiply ?1160 ?1163))) =>= ?1162 [1163, 1162, 1161, 1160] by Super 2 with 5 at 2
+Id : 145, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1213) (multiply (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?1214) (multiply (inverse (inverse ?1215)) (multiply (inverse ?1215) ?1216)))) ?1217) (inverse (multiply ?1214 ?1217))))) (multiply ?1216 ?1218)))) ?1219) (inverse (multiply ?1213 ?1219))) =>= ?1218 [1219, 1218, 1217, 1216, 1215, 1214, 1213] by Super 138 with 29 at 1,2,2,1,1,1,1,2
+Id : 168, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1213) (multiply (inverse ?1216) (multiply ?1216 ?1218)))) ?1219) (inverse (multiply ?1213 ?1219))) =>= ?1218 [1219, 1218, 1216, 1213] by Demod 145 with 29 at 1,1,2,1,1,1,1,2
+Id : 777, {_}: multiply (inverse ?5891) (multiply ?5891 (multiply ?5892 (inverse (multiply (multiply (inverse (multiply (inverse ?5893) ?5894)) ?5895) (inverse (multiply ?5893 ?5895)))))) =>= multiply (inverse (inverse ?5892)) ?5894 [5895, 5894, 5893, 5892, 5891] by Super 91 with 5 at 2,2,2
+Id : 813, {_}: multiply (inverse ?6211) (multiply ?6211 (multiply ?6212 ?6213)) =?= multiply (inverse (inverse ?6212)) (multiply (inverse ?6214) (multiply ?6214 ?6213)) [6214, 6213, 6212, 6211] by Super 777 with 168 at 2,2,2,2
+Id : 1401, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?11491) (multiply ?11491 (multiply ?11492 ?11493)))) ?11494) (inverse (multiply (inverse ?11492) ?11494))) =>= ?11493 [11494, 11493, 11492, 11491] by Super 168 with 813 at 1,1,1,1,2
+Id : 1427, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?11709) (multiply ?11709 (multiply (inverse ?11710) (multiply ?11710 ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711, 11710, 11709] by Super 1401 with 301 at 2,2,1,1,1,1,2
+Id : 10889, {_}: multiply (inverse ?52992) (multiply ?52992 (inverse (inverse ?52993))) =>= ?52993 [52993, 52992] by Demod 6773 with 10663 at 2,2,2
+Id : 11440, {_}: multiply (inverse ?85947) (multiply ?85947 ?85948) =>= inverse (inverse ?85948) [85948, 85947] by Super 10889 with 11239 at 2,2,2
+Id : 12070, {_}: inverse (multiply (multiply (inverse (inverse (inverse (multiply (inverse ?11710) (multiply ?11710 ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711, 11710] by Demod 1427 with 11440 at 1,1,1,1,2
+Id : 12071, {_}: inverse (multiply (multiply (inverse (inverse (inverse (inverse (inverse ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711] by Demod 12070 with 11440 at 1,1,1,1,1,1,2
+Id : 12086, {_}: inverse (multiply (multiply (inverse ?11711) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711] by Demod 12071 with 11239 at 1,1,1,2
+Id : 11284, {_}: multiply ?84907 (inverse (multiply (inverse (inverse (inverse ?84908))) ?84908)) =>= inverse (inverse ?84907) [84908, 84907] by Super 10663 with 11239 at 2,1,2,2
+Id : 12456, {_}: inverse (inverse (inverse (multiply (inverse ?89511) ?89512))) =>= multiply (inverse ?89512) ?89511 [89512, 89511] by Super 12086 with 11284 at 1,2
+Id : 12807, {_}: inverse (multiply (inverse ?89891) ?89892) =>= multiply (inverse ?89892) ?89891 [89892, 89891] by Super 11239 with 12456 at 1,2
+Id : 13084, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (inverse (multiply (inverse (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?27)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 6 with 12807 at 1,1,1,2,1,2,1,2,2
+Id : 13085, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13084 with 12807 at 1,1,1,1,2,1,2,1,2,2
+Id : 13086, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (inverse (multiply (inverse ?26) ?30)) ?28)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13085 with 12807 at 2,1,1,1,1,2,1,2,1,2,2
+Id : 13087, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13086 with 12807 at 1,2,1,1,1,1,2,1,2,1,2,2
+Id : 12072, {_}: multiply ?2743 (inverse (multiply (inverse (inverse ?2745)) (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745))))) =>= ?2747 [2747, 2746, 2745, 2743] by Demod 380 with 11440 at 1,1,2,2
+Id : 13068, {_}: multiply ?2743 (multiply (inverse (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745)))) (inverse ?2745)) =>= ?2747 [2745, 2747, 2746, 2743] by Demod 12072 with 12807 at 2,2
+Id : 358, {_}: multiply (inverse ?2595) (multiply ?2595 (inverse (multiply (multiply (inverse ?2596) (multiply ?2596 ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597, 2596, 2595] by Super 28 with 301 at 1,1,2,2,2
+Id : 12055, {_}: inverse (inverse (inverse (multiply (multiply (inverse ?2596) (multiply ?2596 ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597, 2596] by Demod 358 with 11440 at 2
+Id : 12056, {_}: inverse (inverse (inverse (multiply (inverse (inverse ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597] by Demod 12055 with 11440 at 1,1,1,1,2
+Id : 12778, {_}: multiply (inverse (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))) (inverse ?2597) =>= ?2599 [2597, 2599, 2598] by Demod 12056 with 12456 at 2
+Id : 13130, {_}: multiply ?2743 (multiply (inverse ?2743) ?2747) =>= ?2747 [2747, 2743] by Demod 13068 with 12778 at 2,2
+Id : 12068, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?2584) (multiply ?2584 ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585, 2584] by Demod 356 with 11440 at 2
+Id : 12069, {_}: inverse (inverse (inverse (multiply (multiply (inverse (inverse (inverse ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 12068 with 11440 at 1,1,1,1,1,1,2
+Id : 12343, {_}: inverse (inverse (inverse (inverse (inverse (multiply (inverse (inverse (inverse ?88665))) ?88666))))) =>= multiply (inverse (inverse (inverse ?88666))) ?88665 [88666, 88665] by Super 12069 with 11284 at 1,1,1,2
+Id : 12705, {_}: inverse (multiply (inverse (inverse (inverse ?88665))) ?88666) =>= multiply (inverse (inverse (inverse ?88666))) ?88665 [88666, 88665] by Demod 12343 with 11239 at 2
+Id : 13398, {_}: multiply (inverse ?88666) (inverse (inverse ?88665)) =?= multiply (inverse (inverse (inverse ?88666))) ?88665 [88665, 88666] by Demod 12705 with 12807 at 2
+Id : 13591, {_}: multiply (inverse ?93455) (inverse (inverse (multiply (inverse (inverse (inverse (inverse ?93455)))) ?93456))) =>= ?93456 [93456, 93455] by Super 13130 with 13398 at 2
+Id : 13688, {_}: multiply (inverse ?93455) (inverse (multiply (inverse ?93456) (inverse (inverse (inverse ?93455))))) =>= ?93456 [93456, 93455] by Demod 13591 with 12807 at 1,2,2
+Id : 13689, {_}: multiply (inverse ?93455) (multiply (inverse (inverse (inverse (inverse ?93455)))) ?93456) =>= ?93456 [93456, 93455] by Demod 13688 with 12807 at 2,2
+Id : 13690, {_}: multiply (inverse ?93455) (multiply ?93455 ?93456) =>= ?93456 [93456, 93455] by Demod 13689 with 11239 at 1,2,2
+Id : 13691, {_}: inverse (inverse ?93456) =>= ?93456 [93456] by Demod 13690 with 11440 at 2
+Id : 14259, {_}: inverse (multiply ?94937 ?94938) =<= multiply (inverse ?94938) (inverse ?94937) [94938, 94937] by Super 12807 with 13691 at 1,1,2
+Id : 14272, {_}: inverse (multiply ?94994 (inverse ?94995)) =>= multiply ?94995 (inverse ?94994) [94995, 94994] by Super 14259 with 13691 at 1,3
+Id : 15113, {_}: multiply ?26 (multiply (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31) (inverse (multiply ?29 ?31))))) (inverse ?27)) =>= ?30 [31, 29, 30, 27, 28, 26] by Demod 13087 with 14272 at 2,2
+Id : 15114, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31)))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 15113 with 14272 at 2,1,2,2
+Id : 14099, {_}: inverse (multiply ?94283 ?94284) =<= multiply (inverse ?94284) (inverse ?94283) [94284, 94283] by Super 12807 with 13691 at 1,1,2
+Id : 15376, {_}: multiply ?101449 (inverse (multiply ?101450 ?101449)) =>= inverse ?101450 [101450, 101449] by Super 13130 with 14099 at 2,2
+Id : 14196, {_}: multiply ?94524 (inverse (multiply ?94525 ?94524)) =>= inverse ?94525 [94525, 94524] by Super 13130 with 14099 at 2,2
+Id : 15386, {_}: multiply (inverse (multiply ?101486 ?101487)) (inverse (inverse ?101486)) =>= inverse ?101487 [101487, 101486] by Super 15376 with 14196 at 1,2,2
+Id : 15574, {_}: inverse (multiply (inverse ?101486) (multiply ?101486 ?101487)) =>= inverse ?101487 [101487, 101486] by Demod 15386 with 14099 at 2
+Id : 16040, {_}: multiply (inverse (multiply ?103094 ?103095)) ?103094 =>= inverse ?103095 [103095, 103094] by Demod 15574 with 12807 at 2
+Id : 12061, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?216) ?217)) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 217, 216] by Demod 28 with 11440 at 2
+Id : 13066, {_}: inverse (inverse (inverse (multiply (multiply (multiply (inverse ?217) ?216) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 216, 217] by Demod 12061 with 12807 at 1,1,1,1,1,2
+Id : 14035, {_}: inverse (multiply (multiply (multiply (inverse ?217) ?216) ?218) (inverse (multiply ?216 ?218))) =>= ?217 [218, 216, 217] by Demod 13066 with 13691 at 2
+Id : 15129, {_}: multiply (multiply ?216 ?218) (inverse (multiply (multiply (inverse ?217) ?216) ?218)) =>= ?217 [217, 218, 216] by Demod 14035 with 14272 at 2
+Id : 16059, {_}: multiply (inverse ?103200) (multiply ?103201 ?103202) =<= inverse (inverse (multiply (multiply (inverse ?103200) ?103201) ?103202)) [103202, 103201, 103200] by Super 16040 with 15129 at 1,1,2
+Id : 16156, {_}: multiply (inverse ?103200) (multiply ?103201 ?103202) =<= multiply (multiply (inverse ?103200) ?103201) ?103202 [103202, 103201, 103200] by Demod 16059 with 13691 at 3
+Id : 17066, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?30) ?26) ?28) ?29)) ?31)))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 15114 with 16156 at 1,1,2,2,1,2,2
+Id : 17067, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (multiply (inverse ?30) ?26) ?28) ?29) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17066 with 16156 at 1,2,2,1,2,2
+Id : 17068, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?30) (multiply ?26 ?28)) ?29) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17067 with 16156 at 1,1,2,1,2,2,1,2,2
+Id : 17069, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (inverse ?30) (multiply (multiply ?26 ?28) ?29)) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17068 with 16156 at 1,2,1,2,2,1,2,2
+Id : 17070, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (inverse ?30) (multiply (multiply (multiply ?26 ?28) ?29) ?31)))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17069 with 16156 at 2,1,2,2,1,2,2
+Id : 17075, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (inverse (multiply (inverse ?30) (multiply (multiply (multiply ?26 ?28) ?29) ?31))) ?27))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17070 with 12807 at 2,2,1,2,2
+Id : 17076, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (multiply (inverse (multiply (multiply (multiply ?26 ?28) ?29) ?31)) ?30) ?27))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17075 with 12807 at 1,2,2,1,2,2
+Id : 17077, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (inverse (multiply (multiply (multiply ?26 ?28) ?29) ?31)) (multiply ?30 ?27)))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17076 with 16156 at 2,2,1,2,2
+Id : 14023, {_}: multiply (inverse ?33635) ?33635 =?= multiply (inverse (inverse (inverse ?33638))) ?33638 [33638, 33635] by Demod 4117 with 13691 at 1,2
+Id : 14024, {_}: multiply (inverse ?33635) ?33635 =?= multiply (inverse ?33638) ?33638 [33638, 33635] by Demod 14023 with 13691 at 1,3
+Id : 14053, {_}: multiply (inverse ?93965) ?93965 =?= multiply ?93966 (inverse ?93966) [93966, 93965] by Super 14024 with 13691 at 1,3
+Id : 19206, {_}: multiply ?108859 (multiply (multiply ?108860 (multiply (multiply ?108861 ?108862) (multiply ?108863 (inverse ?108863)))) (inverse ?108862)) =>= multiply (multiply ?108859 ?108860) ?108861 [108863, 108862, 108861, 108860, 108859] by Super 17077 with 14053 at 2,2,1,2,2
+Id : 14021, {_}: multiply ?70596 (multiply ?70598 (inverse ?70598)) =>= inverse (inverse ?70596) [70598, 70596] by Demod 9021 with 13691 at 2,2
+Id : 14022, {_}: multiply ?70596 (multiply ?70598 (inverse ?70598)) =>= ?70596 [70598, 70596] by Demod 14021 with 13691 at 3
+Id : 19669, {_}: multiply ?108859 (multiply (multiply ?108860 (multiply ?108861 ?108862)) (inverse ?108862)) =>= multiply (multiply ?108859 ?108860) ?108861 [108862, 108861, 108860, 108859] by Demod 19206 with 14022 at 2,1,2,2
+Id : 14028, {_}: inverse (multiply (multiply (inverse (inverse (inverse ?2585))) ?2586) (inverse (multiply ?2587 ?2586))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 12069 with 13691 at 2
+Id : 14029, {_}: inverse (multiply (multiply (inverse ?2585) ?2586) (inverse (multiply ?2587 ?2586))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 14028 with 13691 at 1,1,1,2
+Id : 15108, {_}: multiply (multiply ?2587 ?2586) (inverse (multiply (inverse ?2585) ?2586)) =>= multiply ?2587 ?2585 [2585, 2586, 2587] by Demod 14029 with 14272 at 2
+Id : 15134, {_}: multiply (multiply ?2587 ?2586) (multiply (inverse ?2586) ?2585) =>= multiply ?2587 ?2585 [2585, 2586, 2587] by Demod 15108 with 12807 at 2,2
+Id : 15575, {_}: multiply (inverse (multiply ?101486 ?101487)) ?101486 =>= inverse ?101487 [101487, 101486] by Demod 15574 with 12807 at 2
+Id : 16032, {_}: multiply (multiply ?103052 (multiply ?103053 ?103054)) (inverse ?103054) =>= multiply ?103052 ?103053 [103054, 103053, 103052] by Super 15134 with 15575 at 2,2
+Id : 32860, {_}: multiply ?108859 (multiply ?108860 ?108861) =?= multiply (multiply ?108859 ?108860) ?108861 [108861, 108860, 108859] by Demod 19669 with 16032 at 2,2
+Id : 33337, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 1 with 32860 at 2
+Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
+% SZS output end CNFRefutation for GRP429-1.p
+23653: solved GRP429-1.p in 11.596724 using nrkbo
+23653: status Unsatisfiable for GRP429-1.p
+NO CLASH, using fixed ground order
+23669: Facts:
+23669: Id : 2, {_}:
+ inverse
+ (multiply ?2
+ (multiply ?3
+ (multiply (multiply ?4 (inverse ?4))
+ (inverse (multiply ?5 (multiply ?2 ?3))))))
+ =>=
+ ?5
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23669: Goal:
+23669: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+23669: Order:
+23669: nrkbo
+23669: Leaf order:
+23669: a3 2 0 2 1,1,2
+23669: b3 2 0 2 2,1,2
+23669: c3 2 0 2 2,2
+23669: inverse 3 1 0
+23669: multiply 10 2 4 0,2
+NO CLASH, using fixed ground order
+23670: Facts:
+23670: Id : 2, {_}:
+ inverse
+ (multiply ?2
+ (multiply ?3
+ (multiply (multiply ?4 (inverse ?4))
+ (inverse (multiply ?5 (multiply ?2 ?3))))))
+ =>=
+ ?5
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23670: Goal:
+23670: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+23670: Order:
+23670: kbo
+23670: Leaf order:
+23670: a3 2 0 2 1,1,2
+23670: b3 2 0 2 2,1,2
+23670: c3 2 0 2 2,2
+23670: inverse 3 1 0
+23670: multiply 10 2 4 0,2
+NO CLASH, using fixed ground order
+23671: Facts:
+23671: Id : 2, {_}:
+ inverse
+ (multiply ?2
+ (multiply ?3
+ (multiply (multiply ?4 (inverse ?4))
+ (inverse (multiply ?5 (multiply ?2 ?3))))))
+ =>=
+ ?5
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23671: Goal:
+23671: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+23671: Order:
+23671: lpo
+23671: Leaf order:
+23671: a3 2 0 2 1,1,2
+23671: b3 2 0 2 2,1,2
+23671: c3 2 0 2 2,2
+23671: inverse 3 1 0
+23671: multiply 10 2 4 0,2
+Statistics :
+Max weight : 52
+Found proof, 56.465480s
+% SZS status Unsatisfiable for GRP444-1.p
+% SZS output start CNFRefutation for GRP444-1.p
+Id : 3, {_}: inverse (multiply ?7 (multiply ?8 (multiply (multiply ?9 (inverse ?9)) (inverse (multiply ?10 (multiply ?7 ?8)))))) =>= ?10 [10, 9, 8, 7] by single_axiom ?7 ?8 ?9 ?10
+Id : 2, {_}: inverse (multiply ?2 (multiply ?3 (multiply (multiply ?4 (inverse ?4)) (inverse (multiply ?5 (multiply ?2 ?3)))))) =>= ?5 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+Id : 5, {_}: inverse (multiply ?18 (multiply ?19 (multiply (multiply (multiply ?20 (multiply ?21 (multiply (multiply ?22 (inverse ?22)) (inverse (multiply ?23 (multiply ?20 ?21)))))) ?23) (inverse (multiply ?24 (multiply ?18 ?19)))))) =>= ?24 [24, 23, 22, 21, 20, 19, 18] by Super 3 with 2 at 2,1,2,2,1,2
+Id : 4, {_}: inverse (multiply ?12 (multiply (multiply (multiply ?13 (inverse ?13)) (inverse (multiply ?14 (multiply ?15 ?12)))) (multiply (multiply ?16 (inverse ?16)) ?14))) =>= ?15 [16, 15, 14, 13, 12] by Super 3 with 2 at 2,2,2,1,2
+Id : 7, {_}: inverse (multiply (multiply (multiply ?28 (inverse ?28)) (inverse (multiply ?29 (multiply ?30 ?31)))) (multiply (multiply (multiply ?32 (inverse ?32)) ?29) (multiply (multiply ?33 (inverse ?33)) ?30))) =>= ?31 [33, 32, 31, 30, 29, 28] by Super 2 with 4 at 2,2,2,1,2
+Id : 9, {_}: inverse (multiply ?44 (multiply (multiply (multiply ?45 (inverse ?45)) (inverse (multiply ?46 (multiply ?47 ?44)))) (multiply (multiply ?48 (inverse ?48)) ?46))) =>= ?47 [48, 47, 46, 45, 44] by Super 3 with 2 at 2,2,2,1,2
+Id : 13, {_}: inverse (multiply (multiply (multiply ?76 (inverse ?76)) ?77) (multiply (multiply (multiply ?78 (inverse ?78)) ?79) (multiply (multiply ?80 (inverse ?80)) ?81))) =?= multiply (multiply ?82 (inverse ?82)) (inverse (multiply ?77 (multiply ?79 ?81))) [82, 81, 80, 79, 78, 77, 76] by Super 9 with 4 at 2,1,2,1,2
+Id : 178, {_}: multiply (multiply ?1864 (inverse ?1864)) (inverse (multiply (inverse (multiply ?1865 (multiply ?1866 ?1867))) (multiply ?1865 ?1866))) =>= ?1867 [1867, 1866, 1865, 1864] by Super 7 with 13 at 2
+Id : 184, {_}: multiply (multiply ?1909 (inverse ?1909)) (inverse (multiply ?1910 (multiply ?1911 (multiply (multiply ?1912 (inverse ?1912)) (inverse (multiply ?1913 (multiply ?1910 ?1911))))))) =?= multiply (multiply ?1914 (inverse ?1914)) ?1913 [1914, 1913, 1912, 1911, 1910, 1909] by Super 178 with 4 at 1,1,2,2
+Id : 205, {_}: multiply (multiply ?1909 (inverse ?1909)) ?1913 =?= multiply (multiply ?1914 (inverse ?1914)) ?1913 [1914, 1913, 1909] by Demod 184 with 2 at 2,2
+Id : 277, {_}: inverse (multiply ?2556 (multiply ?2557 (multiply (multiply (multiply ?2558 (multiply ?2559 (multiply (multiply ?2560 (inverse ?2560)) (inverse (multiply ?2561 (multiply ?2558 ?2559)))))) ?2561) (inverse (multiply (multiply ?2562 (inverse ?2562)) (multiply ?2556 ?2557)))))) =?= multiply ?2563 (inverse ?2563) [2563, 2562, 2561, 2560, 2559, 2558, 2557, 2556] by Super 5 with 205 at 1,2,2,2,1,2
+Id : 348, {_}: multiply ?2562 (inverse ?2562) =?= multiply ?2563 (inverse ?2563) [2563, 2562] by Demod 277 with 5 at 2
+Id : 1129, {_}: inverse (multiply ?9239 (multiply (inverse ?9239) (multiply (multiply ?9240 (inverse ?9240)) (inverse (multiply ?9241 (multiply ?9242 (inverse ?9242))))))) =>= ?9241 [9242, 9241, 9240, 9239] by Super 2 with 348 at 2,1,2,2,2,1,2
+Id : 86, {_}: multiply (multiply ?817 (inverse ?817)) (inverse (multiply (inverse (multiply ?818 (multiply ?819 ?820))) (multiply ?818 ?819))) =>= ?820 [820, 819, 818, 817] by Super 7 with 13 at 2
+Id : 1168, {_}: inverse (multiply ?9548 (multiply (inverse ?9548) ?9549)) =?= inverse (multiply ?9550 (multiply (inverse ?9550) ?9549)) [9550, 9549, 9548] by Super 1129 with 86 at 2,2,1,2
+Id : 3826, {_}: inverse (multiply (inverse ?28880) (multiply ?28881 (multiply (multiply ?28882 (inverse ?28882)) (inverse (multiply ?28883 (multiply (inverse ?28883) ?28881)))))) =>= ?28880 [28883, 28882, 28881, 28880] by Super 2 with 1168 at 2,2,2,1,2
+Id : 529, {_}: multiply (multiply ?4511 (inverse ?4511)) (inverse (multiply (inverse (multiply ?4512 (multiply (inverse ?4512) ?4513))) (multiply ?4514 (inverse ?4514)))) =>= ?4513 [4514, 4513, 4512, 4511] by Super 86 with 348 at 2,1,2,2
+Id : 3910, {_}: inverse (multiply (inverse ?29502) (multiply (inverse (inverse (inverse (multiply ?29503 (multiply (inverse ?29503) ?29504))))) ?29504)) =>= ?29502 [29504, 29503, 29502] by Super 3826 with 529 at 2,2,1,2
+Id : 5137, {_}: inverse (multiply (inverse (inverse (inverse (multiply ?39280 (multiply (inverse ?39280) ?39281))))) (multiply ?39281 (multiply (multiply ?39282 (inverse ?39282)) ?39283))) =>= inverse ?39283 [39283, 39282, 39281, 39280] by Super 2 with 3910 at 2,2,2,1,2
+Id : 17340, {_}: inverse (inverse (multiply ?127629 (multiply (inverse (inverse (inverse (multiply ?127630 (multiply (inverse ?127630) ?127631))))) ?127631))) =>= ?127629 [127631, 127630, 127629] by Super 2 with 5137 at 2
+Id : 5128, {_}: multiply (multiply ?39206 (inverse ?39206)) (multiply (inverse (inverse (inverse (multiply ?39207 (multiply (inverse ?39207) ?39208))))) (multiply ?39208 ?39209)) =>= ?39209 [39209, 39208, 39207, 39206] by Super 86 with 3910 at 2,2
+Id : 3928, {_}: inverse (multiply (inverse (multiply ?29660 (multiply (inverse ?29660) ?29661))) (multiply ?29662 (multiply (multiply ?29663 (inverse ?29663)) (inverse (multiply ?29664 (multiply (inverse ?29664) ?29662)))))) =?= multiply ?29665 (multiply (inverse ?29665) ?29661) [29665, 29664, 29663, 29662, 29661, 29660] by Super 3826 with 1168 at 1,1,2
+Id : 1246, {_}: inverse (multiply (inverse ?10029) (multiply ?10030 (multiply (multiply ?10031 (inverse ?10031)) (inverse (multiply ?10032 (multiply (inverse ?10032) ?10030)))))) =>= ?10029 [10032, 10031, 10030, 10029] by Super 2 with 1168 at 2,2,2,1,2
+Id : 3958, {_}: multiply ?29660 (multiply (inverse ?29660) ?29661) =?= multiply ?29665 (multiply (inverse ?29665) ?29661) [29665, 29661, 29660] by Demod 3928 with 1246 at 2
+Id : 531, {_}: multiply (multiply ?4521 (inverse ?4521)) (inverse (multiply (inverse (multiply ?4522 (multiply ?4523 (inverse ?4523)))) (multiply ?4522 ?4524))) =>= inverse ?4524 [4524, 4523, 4522, 4521] by Super 86 with 348 at 2,1,1,1,2,2
+Id : 737, {_}: multiply (multiply ?5774 (inverse ?5774)) (inverse (multiply (inverse (multiply ?5775 (multiply ?5776 (inverse ?5776)))) (multiply ?5775 ?5777))) =>= inverse ?5777 [5777, 5776, 5775, 5774] by Super 86 with 348 at 2,1,1,1,2,2
+Id : 1911, {_}: multiply (multiply ?15350 (inverse ?15350)) (inverse (multiply (inverse (multiply ?15351 (multiply ?15352 (inverse ?15352)))) (multiply ?15353 (inverse ?15353)))) =>= inverse (inverse ?15351) [15353, 15352, 15351, 15350] by Super 737 with 348 at 2,1,2,2
+Id : 1956, {_}: multiply (multiply ?15717 (inverse ?15717)) (inverse (multiply (inverse (multiply (multiply ?15718 (inverse ?15718)) (multiply ?15719 (inverse ?15719)))) (multiply ?15720 (inverse ?15720)))) =?= inverse (inverse (multiply ?15721 (inverse ?15721))) [15721, 15720, 15719, 15718, 15717] by Super 1911 with 205 at 1,1,1,2,2
+Id : 740, {_}: multiply (multiply ?5792 (inverse ?5792)) (inverse (multiply (inverse (multiply ?5793 (multiply ?5794 (inverse ?5794)))) (multiply ?5795 (inverse ?5795)))) =>= inverse (inverse ?5793) [5795, 5794, 5793, 5792] by Super 737 with 348 at 2,1,2,2
+Id : 2009, {_}: inverse (inverse (multiply ?15718 (inverse ?15718))) =?= inverse (inverse (multiply ?15721 (inverse ?15721))) [15721, 15718] by Demod 1956 with 740 at 2
+Id : 2083, {_}: multiply ?16427 (inverse ?16427) =?= multiply (inverse (multiply ?16428 (inverse ?16428))) (inverse (inverse (multiply ?16429 (inverse ?16429)))) [16429, 16428, 16427] by Super 348 with 2009 at 2,3
+Id : 2187, {_}: multiply (multiply ?17062 (inverse ?17062)) (inverse (multiply (inverse (multiply (inverse (multiply ?17063 (inverse ?17063))) (multiply ?17064 (inverse ?17064)))) (multiply ?17065 (inverse ?17065)))) =?= inverse (inverse (inverse (multiply ?17066 (inverse ?17066)))) [17066, 17065, 17064, 17063, 17062] by Super 531 with 2083 at 2,1,2,2
+Id : 2437, {_}: inverse (inverse (inverse (multiply ?17063 (inverse ?17063)))) =?= inverse (inverse (inverse (multiply ?17066 (inverse ?17066)))) [17066, 17063] by Demod 2187 with 740 at 2
+Id : 2507, {_}: multiply ?19079 (inverse ?19079) =?= multiply (inverse (inverse (multiply ?19080 (inverse ?19080)))) (inverse (inverse (inverse (multiply ?19081 (inverse ?19081))))) [19081, 19080, 19079] by Super 348 with 2437 at 2,3
+Id : 5155, {_}: multiply (multiply ?39417 (inverse ?39417)) (multiply (inverse (inverse (inverse (multiply ?39418 (multiply (inverse ?39418) ?39419))))) (multiply ?39420 (inverse ?39420))) =>= inverse ?39419 [39420, 39419, 39418, 39417] by Super 531 with 3910 at 2,2
+Id : 21348, {_}: inverse (inverse (inverse (multiply ?158881 (inverse ?158881)))) =?= multiply ?158882 (inverse ?158882) [158882, 158881] by Super 17340 with 5155 at 1,1,2
+Id : 21903, {_}: multiply ?162370 (inverse ?162370) =?= multiply (inverse (inverse (multiply ?162371 (inverse ?162371)))) (multiply ?162372 (inverse ?162372)) [162372, 162371, 162370] by Super 2507 with 21348 at 2,3
+Id : 27319, {_}: multiply ?194055 (multiply (inverse ?194055) (inverse (inverse (inverse (inverse (multiply ?194056 (inverse ?194056))))))) =?= multiply ?194057 (inverse ?194057) [194057, 194056, 194055] by Super 3958 with 21903 at 3
+Id : 38543, {_}: multiply (multiply ?266891 (inverse ?266891)) (multiply (inverse (inverse (inverse (multiply ?266892 (multiply (inverse ?266892) ?266893))))) (multiply ?266894 (inverse ?266894))) =?= multiply (inverse ?266893) (inverse (inverse (inverse (inverse (multiply ?266895 (inverse ?266895)))))) [266895, 266894, 266893, 266892, 266891] by Super 5128 with 27319 at 2,2,2
+Id : 39135, {_}: inverse ?270165 =<= multiply (inverse ?270165) (inverse (inverse (inverse (inverse (multiply ?270166 (inverse ?270166)))))) [270166, 270165] by Demod 38543 with 5155 at 2
+Id : 39578, {_}: inverse ?271815 =<= multiply (inverse ?271815) (inverse (multiply ?271816 (inverse ?271816))) [271816, 271815] by Super 39135 with 21348 at 1,2,3
+Id : 39704, {_}: inverse (multiply ?272432 (multiply ?272433 (multiply (multiply ?272434 (inverse ?272434)) (inverse (multiply ?272435 (multiply ?272432 ?272433)))))) =?= multiply ?272435 (inverse (multiply ?272436 (inverse ?272436))) [272436, 272435, 272434, 272433, 272432] by Super 39578 with 2 at 1,3
+Id : 39842, {_}: ?272435 =<= multiply ?272435 (inverse (multiply ?272436 (inverse ?272436))) [272436, 272435] by Demod 39704 with 2 at 2
+Id : 40136, {_}: inverse (inverse (multiply ?274147 (multiply (inverse (inverse (inverse (multiply ?274148 (inverse ?274148))))) (inverse (multiply ?274149 (inverse ?274149)))))) =>= ?274147 [274149, 274148, 274147] by Super 17340 with 39842 at 2,1,1,1,1,2,1,1,2
+Id : 42233, {_}: inverse (inverse (multiply ?290970 (inverse (inverse (inverse (multiply ?290971 (inverse ?290971))))))) =>= ?290970 [290971, 290970] by Demod 40136 with 39842 at 2,1,1,2
+Id : 42325, {_}: inverse (inverse (multiply ?291465 (inverse (inverse (inverse (inverse (inverse (inverse (multiply ?291466 (inverse ?291466)))))))))) =>= ?291465 [291466, 291465] by Super 42233 with 21348 at 1,1,1,2,1,1,2
+Id : 3911, {_}: inverse (multiply (inverse ?29506) (multiply (inverse (inverse (inverse (multiply ?29507 (multiply ?29508 (inverse ?29508)))))) (inverse (inverse ?29507)))) =>= ?29506 [29508, 29507, 29506] by Super 3826 with 740 at 2,2,1,2
+Id : 42355, {_}: inverse (inverse (multiply ?291566 (multiply ?291567 (inverse ?291567)))) =>= ?291566 [291567, 291566] by Super 42233 with 21348 at 2,1,1,2
+Id : 42465, {_}: inverse (multiply (inverse ?29506) (multiply (inverse ?29507) (inverse (inverse ?29507)))) =>= ?29506 [29507, 29506] by Demod 3911 with 42355 at 1,1,2,1,2
+Id : 42659, {_}: inverse (multiply (inverse ?292844) (multiply (inverse (inverse (multiply ?292845 (multiply ?292846 (inverse ?292846))))) (inverse ?292845))) =>= ?292844 [292846, 292845, 292844] by Super 42465 with 42355 at 1,2,2,1,2
+Id : 42797, {_}: inverse (multiply (inverse ?292844) (multiply ?292845 (inverse ?292845))) =>= ?292844 [292845, 292844] by Demod 42659 with 42355 at 1,2,1,2
+Id : 42874, {_}: multiply (multiply ?5792 (inverse ?5792)) (multiply ?5793 (multiply ?5794 (inverse ?5794))) =>= inverse (inverse ?5793) [5794, 5793, 5792] by Demod 740 with 42797 at 2,2
+Id : 46254, {_}: ?309013 =<= multiply ?309013 (inverse (multiply (inverse (multiply ?309014 (multiply ?309015 (inverse ?309015)))) ?309014)) [309015, 309014, 309013] by Super 39842 with 42355 at 2,1,2,3
+Id : 46402, {_}: ?309842 =<= multiply ?309842 (multiply (multiply ?309843 (inverse ?309843)) (multiply ?309844 (inverse ?309844))) [309844, 309843, 309842] by Super 46254 with 42797 at 2,3
+Id : 46563, {_}: multiply ?309963 (inverse ?309963) =?= inverse (inverse (multiply ?309964 (inverse ?309964))) [309964, 309963] by Super 42874 with 46402 at 2
+Id : 47597, {_}: inverse (inverse (multiply ?315584 (inverse (inverse (inverse (inverse (multiply ?315585 (inverse ?315585)))))))) =>= ?315584 [315585, 315584] by Super 42325 with 46563 at 1,1,1,1,2,1,1,2
+Id : 39281, {_}: inverse (multiply ?270847 (multiply ?270848 (multiply (multiply ?270849 (inverse ?270849)) (inverse (multiply ?270850 (multiply ?270847 ?270848)))))) =?= multiply ?270850 (inverse (inverse (inverse (inverse (multiply ?270851 (inverse ?270851)))))) [270851, 270850, 270849, 270848, 270847] by Super 39135 with 2 at 1,3
+Id : 39433, {_}: ?270850 =<= multiply ?270850 (inverse (inverse (inverse (inverse (multiply ?270851 (inverse ?270851)))))) [270851, 270850] by Demod 39281 with 2 at 2
+Id : 47849, {_}: inverse (inverse ?315584) =>= ?315584 [315584] by Demod 47597 with 39433 at 1,1,2
+Id : 48100, {_}: multiply (multiply ?5792 (inverse ?5792)) (multiply ?5793 (multiply ?5794 (inverse ?5794))) =>= ?5793 [5794, 5793, 5792] by Demod 42874 with 47849 at 3
+Id : 48103, {_}: multiply ?291465 (inverse (inverse (inverse (inverse (inverse (inverse (multiply ?291466 (inverse ?291466)))))))) =>= ?291465 [291466, 291465] by Demod 42325 with 47849 at 2
+Id : 48104, {_}: multiply ?291465 (inverse (inverse (inverse (inverse (multiply ?291466 (inverse ?291466)))))) =>= ?291465 [291466, 291465] by Demod 48103 with 47849 at 2,2
+Id : 48105, {_}: multiply ?291465 (inverse (inverse (multiply ?291466 (inverse ?291466)))) =>= ?291465 [291466, 291465] by Demod 48104 with 47849 at 2,2
+Id : 48106, {_}: multiply ?291465 (multiply ?291466 (inverse ?291466)) =>= ?291465 [291466, 291465] by Demod 48105 with 47849 at 2,2
+Id : 48126, {_}: multiply (multiply ?5792 (inverse ?5792)) ?5793 =>= ?5793 [5793, 5792] by Demod 48100 with 48106 at 2,2
+Id : 48146, {_}: inverse (multiply ?2 (multiply ?3 (inverse (multiply ?5 (multiply ?2 ?3))))) =>= ?5 [5, 3, 2] by Demod 2 with 48126 at 2,2,1,2
+Id : 48243, {_}: multiply (multiply (inverse ?316807) ?316807) ?316808 =>= ?316808 [316808, 316807] by Super 48126 with 47849 at 2,1,2
+Id : 48369, {_}: inverse (multiply (multiply (inverse ?317633) ?317633) (multiply ?317634 (inverse (multiply ?317635 ?317634)))) =>= ?317635 [317635, 317634, 317633] by Super 48146 with 48243 at 2,1,2,2,1,2
+Id : 48458, {_}: inverse (multiply ?317634 (inverse (multiply ?317635 ?317634))) =>= ?317635 [317635, 317634] by Demod 48369 with 48243 at 1,2
+Id : 49027, {_}: inverse ?319864 =<= multiply ?319865 (inverse (multiply ?319864 ?319865)) [319865, 319864] by Super 47849 with 48458 at 1,2
+Id : 48054, {_}: multiply (multiply ?39206 (inverse ?39206)) (multiply (inverse (multiply ?39207 (multiply (inverse ?39207) ?39208))) (multiply ?39208 ?39209)) =>= ?39209 [39209, 39208, 39207, 39206] by Demod 5128 with 47849 at 1,2,2
+Id : 48214, {_}: multiply (inverse (multiply ?39207 (multiply (inverse ?39207) ?39208))) (multiply ?39208 ?39209) =>= ?39209 [39209, 39208, 39207] by Demod 48054 with 48126 at 2
+Id : 42875, {_}: multiply (multiply ?4511 (inverse ?4511)) (multiply ?4512 (multiply (inverse ?4512) ?4513)) =>= ?4513 [4513, 4512, 4511] by Demod 529 with 42797 at 2,2
+Id : 48128, {_}: multiply ?4512 (multiply (inverse ?4512) ?4513) =>= ?4513 [4513, 4512] by Demod 42875 with 48126 at 2
+Id : 48215, {_}: multiply (inverse ?39208) (multiply ?39208 ?39209) =>= ?39209 [39209, 39208] by Demod 48214 with 48128 at 1,1,2
+Id : 49034, {_}: inverse (inverse ?319885) =<= multiply (multiply ?319885 ?319886) (inverse ?319886) [319886, 319885] by Super 49027 with 48215 at 1,2,3
+Id : 49824, {_}: ?323338 =<= multiply (multiply ?323338 ?323339) (inverse ?323339) [323339, 323338] by Demod 49034 with 47849 at 2
+Id : 48152, {_}: inverse (multiply (inverse (multiply ?818 (multiply ?819 ?820))) (multiply ?818 ?819)) =>= ?820 [820, 819, 818] by Demod 86 with 48126 at 2
+Id : 48896, {_}: inverse ?319286 =<= multiply ?319287 (inverse (multiply ?319286 ?319287)) [319287, 319286] by Super 47849 with 48458 at 1,2
+Id : 49169, {_}: multiply (inverse ?320479) (inverse ?320480) =>= inverse (multiply ?320480 ?320479) [320480, 320479] by Super 48215 with 48896 at 2,2
+Id : 49171, {_}: multiply (inverse ?320486) ?320487 =<= inverse (multiply (inverse ?320487) ?320486) [320487, 320486] by Super 49169 with 47849 at 2,2
+Id : 49369, {_}: multiply (inverse (multiply ?818 ?819)) (multiply ?818 (multiply ?819 ?820)) =>= ?820 [820, 819, 818] by Demod 48152 with 49171 at 2
+Id : 49850, {_}: inverse (multiply ?323494 ?323495) =<= multiply ?323496 (inverse (multiply ?323494 (multiply ?323495 ?323496))) [323496, 323495, 323494] by Super 49824 with 49369 at 1,3
+Id : 49041, {_}: inverse ?319906 =<= multiply (inverse (multiply ?319907 ?319906)) (inverse (inverse ?319907)) [319907, 319906] by Super 49027 with 48896 at 1,2,3
+Id : 49999, {_}: inverse ?323996 =<= multiply (inverse (multiply ?323997 ?323996)) ?323997 [323997, 323996] by Demod 49041 with 47849 at 2,3
+Id : 50016, {_}: inverse (multiply ?324063 (inverse (multiply ?324064 (multiply ?324065 ?324063)))) =>= multiply ?324064 ?324065 [324065, 324064, 324063] by Super 49999 with 48146 at 1,3
+Id : 49025, {_}: multiply ?319858 (inverse ?319859) =<= inverse (multiply ?319859 (inverse ?319858)) [319859, 319858] by Super 48128 with 48896 at 2,2
+Id : 53578, {_}: multiply (multiply ?332164 (multiply ?332165 ?332166)) (inverse ?332166) =>= multiply ?332164 ?332165 [332166, 332165, 332164] by Demod 50016 with 49025 at 2
+Id : 49088, {_}: inverse ?319906 =<= multiply (inverse (multiply ?319907 ?319906)) ?319907 [319907, 319906] by Demod 49041 with 47849 at 2,3
+Id : 53621, {_}: multiply (inverse ?332348) (inverse ?332349) =<= multiply (inverse (multiply (multiply ?332350 ?332349) ?332348)) ?332350 [332350, 332349, 332348] by Super 53578 with 49088 at 1,2
+Id : 48971, {_}: multiply (inverse ?319476) (inverse ?319477) =>= inverse (multiply ?319477 ?319476) [319477, 319476] by Super 48215 with 48896 at 2,2
+Id : 53698, {_}: inverse (multiply ?332349 ?332348) =<= multiply (inverse (multiply (multiply ?332350 ?332349) ?332348)) ?332350 [332350, 332348, 332349] by Demod 53621 with 48971 at 2
+Id : 55617, {_}: inverse (multiply (inverse (multiply (multiply (multiply ?335716 ?335717) ?335718) ?335719)) ?335716) =>= multiply ?335717 (inverse (inverse (multiply ?335718 ?335719))) [335719, 335718, 335717, 335716] by Super 49850 with 53698 at 1,2,3
+Id : 55728, {_}: multiply (inverse ?335716) (multiply (multiply (multiply ?335716 ?335717) ?335718) ?335719) =>= multiply ?335717 (inverse (inverse (multiply ?335718 ?335719))) [335719, 335718, 335717, 335716] by Demod 55617 with 49171 at 2
+Id : 55729, {_}: multiply (inverse ?335716) (multiply (multiply (multiply ?335716 ?335717) ?335718) ?335719) =>= multiply ?335717 (multiply ?335718 ?335719) [335719, 335718, 335717, 335716] by Demod 55728 with 47849 at 2,3
+Id : 53403, {_}: inverse (multiply ?331872 ?331873) =<= multiply ?331874 (inverse (multiply ?331872 (multiply ?331873 ?331874))) [331874, 331873, 331872] by Super 49824 with 49369 at 1,3
+Id : 49375, {_}: multiply (inverse ?321009) (multiply (inverse ?321010) ?321011) =>= inverse (multiply (multiply (inverse ?321011) ?321010) ?321009) [321011, 321010, 321009] by Super 48971 with 49171 at 2,2
+Id : 53436, {_}: inverse (multiply (inverse ?332006) (inverse ?332007)) =<= multiply ?332008 (inverse (inverse (multiply (multiply (inverse ?332008) ?332007) ?332006))) [332008, 332007, 332006] by Super 53403 with 49375 at 1,2,3
+Id : 53542, {_}: multiply ?332007 (inverse (inverse ?332006)) =<= multiply ?332008 (inverse (inverse (multiply (multiply (inverse ?332008) ?332007) ?332006))) [332008, 332006, 332007] by Demod 53436 with 49025 at 2
+Id : 53543, {_}: multiply ?332007 (inverse (inverse ?332006)) =<= multiply ?332008 (multiply (multiply (inverse ?332008) ?332007) ?332006) [332008, 332006, 332007] by Demod 53542 with 47849 at 2,3
+Id : 53544, {_}: multiply ?332007 ?332006 =<= multiply ?332008 (multiply (multiply (inverse ?332008) ?332007) ?332006) [332008, 332006, 332007] by Demod 53543 with 47849 at 2,2
+Id : 54357, {_}: multiply (inverse ?333550) (multiply ?333551 ?333552) =<= multiply (multiply (inverse ?333550) ?333551) ?333552 [333552, 333551, 333550] by Super 48215 with 53544 at 2,2
+Id : 53440, {_}: inverse (multiply (inverse (multiply (multiply ?332022 ?332023) ?332024)) ?332022) =>= multiply ?332023 (inverse (inverse ?332024)) [332024, 332023, 332022] by Super 53403 with 49088 at 1,2,3
+Id : 53553, {_}: multiply (inverse ?332022) (multiply (multiply ?332022 ?332023) ?332024) =>= multiply ?332023 (inverse (inverse ?332024)) [332024, 332023, 332022] by Demod 53440 with 49171 at 2
+Id : 53554, {_}: multiply (inverse ?332022) (multiply (multiply ?332022 ?332023) ?332024) =>= multiply ?332023 ?332024 [332024, 332023, 332022] by Demod 53553 with 47849 at 2,3
+Id : 54857, {_}: multiply (inverse ?334428) (multiply (multiply (multiply ?334428 ?334429) ?334430) ?334431) =>= multiply (multiply ?334429 ?334430) ?334431 [334431, 334430, 334429, 334428] by Super 54357 with 53554 at 1,3
+Id : 81835, {_}: multiply (multiply ?335717 ?335718) ?335719 =?= multiply ?335717 (multiply ?335718 ?335719) [335719, 335718, 335717] by Demod 55729 with 54857 at 2
+Id : 82672, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 1 with 81835 at 2
+Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
+% SZS output end CNFRefutation for GRP444-1.p
+23669: solved GRP444-1.p in 49.195074 using nrkbo
+23669: status Unsatisfiable for GRP444-1.p
+NO CLASH, using fixed ground order
+23734: Facts:
+23734: Id : 2, {_}:
+ divide
+ (divide (divide ?2 ?2)
+ (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
+ ?4
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+23734: Id : 3, {_}:
+ multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
+ [8, 7, 6] by multiply ?6 ?7 ?8
+23734: Id : 4, {_}:
+ inverse ?10 =<= divide (divide ?11 ?11) ?10
+ [11, 10] by inverse ?10 ?11
+23734: Goal:
+23734: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+23734: Order:
+23734: nrkbo
+23734: Leaf order:
+23734: b2 2 0 2 1,1,1,2
+23734: a2 2 0 2 2,2
+23734: inverse 2 1 1 0,1,1,2
+23734: multiply 3 2 2 0,2
+23734: divide 13 2 0
+NO CLASH, using fixed ground order
+23735: Facts:
+23735: Id : 2, {_}:
+ divide
+ (divide (divide ?2 ?2)
+ (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
+ ?4
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+23735: Id : 3, {_}:
+ multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
+ [8, 7, 6] by multiply ?6 ?7 ?8
+23735: Id : 4, {_}:
+ inverse ?10 =<= divide (divide ?11 ?11) ?10
+ [11, 10] by inverse ?10 ?11
+23735: Goal:
+23735: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+23735: Order:
+23735: kbo
+23735: Leaf order:
+23735: b2 2 0 2 1,1,1,2
+23735: a2 2 0 2 2,2
+23735: inverse 2 1 1 0,1,1,2
+23735: multiply 3 2 2 0,2
+23735: divide 13 2 0
+NO CLASH, using fixed ground order
+23736: Facts:
+23736: Id : 2, {_}:
+ divide
+ (divide (divide ?2 ?2)
+ (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
+ ?4
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+23736: Id : 3, {_}:
+ multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
+ [8, 7, 6] by multiply ?6 ?7 ?8
+23736: Id : 4, {_}:
+ inverse ?10 =<= divide (divide ?11 ?11) ?10
+ [11, 10] by inverse ?10 ?11
+23736: Goal:
+23736: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+23736: Order:
+23736: lpo
+23736: Leaf order:
+23736: b2 2 0 2 1,1,1,2
+23736: a2 2 0 2 2,2
+23736: inverse 2 1 1 0,1,1,2
+23736: multiply 3 2 2 0,2
+23736: divide 13 2 0
+Statistics :
+Max weight : 38
+Found proof, 0.373646s
+% SZS status Unsatisfiable for GRP452-1.p
+% SZS output start CNFRefutation for GRP452-1.p
+Id : 5, {_}: divide (divide (divide ?13 ?13) (divide ?13 (divide ?14 (divide (divide (divide ?13 ?13) ?13) ?15)))) ?15 =>= ?14 [15, 14, 13] by single_axiom ?13 ?14 ?15
+Id : 35, {_}: inverse ?90 =<= divide (divide ?91 ?91) ?90 [91, 90] by inverse ?90 ?91
+Id : 2, {_}: divide (divide (divide ?2 ?2) (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
+Id : 4, {_}: inverse ?10 =<= divide (divide ?11 ?11) ?10 [11, 10] by inverse ?10 ?11
+Id : 3, {_}: multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) [8, 7, 6] by multiply ?6 ?7 ?8
+Id : 29, {_}: multiply ?6 ?7 =<= divide ?6 (inverse ?7) [7, 6] by Demod 3 with 4 at 2,3
+Id : 41, {_}: multiply (divide ?104 ?104) ?105 =>= inverse (inverse ?105) [105, 104] by Super 29 with 4 at 3
+Id : 43, {_}: multiply (multiply (inverse ?110) ?110) ?111 =>= inverse (inverse ?111) [111, 110] by Super 41 with 29 at 1,2
+Id : 13, {_}: divide (multiply (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50))) ?50 =>= ?49 [50, 49, 48] by Super 2 with 3 at 1,2
+Id : 32, {_}: multiply (divide ?79 ?79) ?80 =>= inverse (inverse ?80) [80, 79] by Super 29 with 4 at 3
+Id : 205, {_}: divide (inverse (inverse (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 13 with 32 at 1,2
+Id : 206, {_}: divide (inverse (inverse (divide ?49 (divide (inverse (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 205 with 4 at 1,2,1,1,1,2
+Id : 36, {_}: inverse ?93 =<= divide (inverse (divide ?94 ?94)) ?93 [94, 93] by Super 35 with 4 at 1,3
+Id : 207, {_}: divide (inverse (inverse (divide ?49 (inverse ?50)))) ?50 =>= ?49 [50, 49] by Demod 206 with 36 at 2,1,1,1,2
+Id : 208, {_}: divide (inverse (inverse (multiply ?49 ?50))) ?50 =>= ?49 [50, 49] by Demod 207 with 29 at 1,1,1,2
+Id : 6, {_}: divide (divide (divide ?17 ?17) (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Super 5 with 2 at 2,2,1,2
+Id : 61, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 6 with 4 at 1,2
+Id : 62, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 61 with 4 at 3
+Id : 63, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 62 with 4 at 1,2,2,1,3
+Id : 68, {_}: divide (inverse (divide ?170 ?171)) ?172 =<= inverse (divide ?173 (divide ?171 (divide (inverse ?173) (divide (inverse ?170) ?172)))) [173, 172, 171, 170] by Demod 63 with 4 at 1,2,2,2,1,3
+Id : 75, {_}: divide (inverse (divide ?213 ?214)) ?215 =<= inverse (divide (divide ?216 ?216) (divide ?214 (inverse (divide (inverse ?213) ?215)))) [216, 215, 214, 213] by Super 68 with 36 at 2,2,1,3
+Id : 85, {_}: divide (inverse (divide ?213 ?214)) ?215 =<= inverse (inverse (divide ?214 (inverse (divide (inverse ?213) ?215)))) [215, 214, 213] by Demod 75 with 4 at 1,3
+Id : 329, {_}: divide (inverse (divide ?884 ?885)) ?886 =<= inverse (inverse (multiply ?885 (divide (inverse ?884) ?886))) [886, 885, 884] by Demod 85 with 29 at 1,1,3
+Id : 336, {_}: divide (inverse (divide (divide ?919 ?919) ?920)) ?921 =>= inverse (inverse (multiply ?920 (inverse ?921))) [921, 920, 919] by Super 329 with 36 at 2,1,1,3
+Id : 348, {_}: divide (inverse (inverse ?920)) ?921 =<= inverse (inverse (multiply ?920 (inverse ?921))) [921, 920] by Demod 336 with 4 at 1,1,2
+Id : 435, {_}: divide (inverse (inverse ?1126)) ?1127 =<= inverse (inverse (multiply ?1126 (inverse ?1127))) [1127, 1126] by Demod 336 with 4 at 1,1,2
+Id : 439, {_}: divide (inverse (inverse (divide ?1144 ?1144))) ?1145 =>= inverse (inverse (inverse (inverse (inverse ?1145)))) [1145, 1144] by Super 435 with 32 at 1,1,3
+Id : 46, {_}: inverse ?115 =<= divide (inverse (inverse (divide ?116 ?116))) ?115 [116, 115] by Super 4 with 36 at 1,3
+Id : 452, {_}: inverse ?1145 =<= inverse (inverse (inverse (inverse (inverse ?1145)))) [1145] by Demod 439 with 46 at 2
+Id : 461, {_}: multiply ?1187 (inverse (inverse (inverse (inverse ?1188)))) =>= divide ?1187 (inverse ?1188) [1188, 1187] by Super 29 with 452 at 2,3
+Id : 480, {_}: multiply ?1187 (inverse (inverse (inverse (inverse ?1188)))) =>= multiply ?1187 ?1188 [1188, 1187] by Demod 461 with 29 at 3
+Id : 490, {_}: divide (inverse (inverse ?1237)) (inverse (inverse (inverse ?1238))) =>= inverse (inverse (multiply ?1237 ?1238)) [1238, 1237] by Super 348 with 480 at 1,1,3
+Id : 543, {_}: multiply (inverse (inverse ?1237)) (inverse (inverse ?1238)) =>= inverse (inverse (multiply ?1237 ?1238)) [1238, 1237] by Demod 490 with 29 at 2
+Id : 564, {_}: divide (inverse (inverse (inverse (inverse ?1361)))) (inverse ?1362) =>= inverse (inverse (inverse (inverse (multiply ?1361 ?1362)))) [1362, 1361] by Super 348 with 543 at 1,1,3
+Id : 586, {_}: multiply (inverse (inverse (inverse (inverse ?1361)))) ?1362 =>= inverse (inverse (inverse (inverse (multiply ?1361 ?1362)))) [1362, 1361] by Demod 564 with 29 at 2
+Id : 608, {_}: divide (inverse (inverse (inverse (inverse (inverse (inverse (multiply ?1454 ?1455))))))) ?1455 =>= inverse (inverse (inverse (inverse ?1454))) [1455, 1454] by Super 208 with 586 at 1,1,1,2
+Id : 633, {_}: divide (inverse (inverse (multiply ?1454 ?1455))) ?1455 =>= inverse (inverse (inverse (inverse ?1454))) [1455, 1454] by Demod 608 with 452 at 1,2
+Id : 634, {_}: ?1454 =<= inverse (inverse (inverse (inverse ?1454))) [1454] by Demod 633 with 208 at 2
+Id : 755, {_}: multiply ?1763 (inverse (inverse (inverse ?1764))) =>= divide ?1763 ?1764 [1764, 1763] by Super 29 with 634 at 2,3
+Id : 797, {_}: divide (inverse (inverse ?1873)) (inverse (inverse ?1874)) =>= inverse (inverse (divide ?1873 ?1874)) [1874, 1873] by Super 348 with 755 at 1,1,3
+Id : 816, {_}: multiply (inverse (inverse ?1873)) (inverse ?1874) =>= inverse (inverse (divide ?1873 ?1874)) [1874, 1873] by Demod 797 with 29 at 2
+Id : 868, {_}: divide (inverse (inverse (inverse (inverse (divide ?1957 ?1958))))) (inverse ?1958) =>= inverse (inverse ?1957) [1958, 1957] by Super 208 with 816 at 1,1,1,2
+Id : 892, {_}: multiply (inverse (inverse (inverse (inverse (divide ?1957 ?1958))))) ?1958 =>= inverse (inverse ?1957) [1958, 1957] by Demod 868 with 29 at 2
+Id : 915, {_}: multiply (divide ?2055 ?2056) ?2056 =>= inverse (inverse ?2055) [2056, 2055] by Demod 892 with 634 at 1,2
+Id : 921, {_}: multiply (multiply ?2076 ?2077) (inverse ?2077) =>= inverse (inverse ?2076) [2077, 2076] by Super 915 with 29 at 1,2
+Id : 872, {_}: multiply (inverse (inverse ?1970)) (inverse ?1971) =>= inverse (inverse (divide ?1970 ?1971)) [1971, 1970] by Demod 797 with 29 at 2
+Id : 885, {_}: multiply ?2028 (inverse ?2029) =<= inverse (inverse (divide (inverse (inverse ?2028)) ?2029)) [2029, 2028] by Super 872 with 634 at 1,2
+Id : 86, {_}: divide (inverse (divide ?213 ?214)) ?215 =<= inverse (inverse (multiply ?214 (divide (inverse ?213) ?215))) [215, 214, 213] by Demod 85 with 29 at 1,1,3
+Id : 64, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (inverse ?17) ?19)))) [20, 19, 18, 17] by Demod 63 with 4 at 1,2,2,2,1,3
+Id : 893, {_}: multiply (divide ?1957 ?1958) ?1958 =>= inverse (inverse ?1957) [1958, 1957] by Demod 892 with 634 at 1,2
+Id : 910, {_}: inverse (inverse ?2040) =<= divide (divide ?2040 (inverse (inverse (inverse ?2041)))) ?2041 [2041, 2040] by Super 755 with 893 at 2
+Id : 1447, {_}: inverse (inverse ?3326) =<= divide (multiply ?3326 (inverse (inverse ?3327))) ?3327 [3327, 3326] by Demod 910 with 29 at 1,3
+Id : 51, {_}: multiply (inverse (inverse (divide ?133 ?133))) ?134 =>= inverse (inverse ?134) [134, 133] by Super 32 with 36 at 1,2
+Id : 1463, {_}: inverse (inverse (inverse (inverse (divide ?3389 ?3389)))) =?= divide (inverse (inverse (inverse (inverse ?3390)))) ?3390 [3390, 3389] by Super 1447 with 51 at 1,3
+Id : 1498, {_}: divide ?3389 ?3389 =?= divide (inverse (inverse (inverse (inverse ?3390)))) ?3390 [3390, 3389] by Demod 1463 with 634 at 2
+Id : 1499, {_}: divide ?3389 ?3389 =?= divide ?3390 ?3390 [3390, 3389] by Demod 1498 with 634 at 1,3
+Id : 1548, {_}: divide (inverse (divide ?3530 (divide (inverse ?3531) (divide (inverse ?3530) ?3532)))) ?3532 =?= inverse (divide ?3531 (divide ?3533 ?3533)) [3533, 3532, 3531, 3530] by Super 64 with 1499 at 2,1,3
+Id : 30, {_}: divide (inverse (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 2 with 4 at 1,2
+Id : 31, {_}: divide (inverse (divide ?2 (divide ?3 (divide (inverse ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 30 with 4 at 1,2,2,1,1,2
+Id : 1619, {_}: inverse ?3531 =<= inverse (divide ?3531 (divide ?3533 ?3533)) [3533, 3531] by Demod 1548 with 31 at 2
+Id : 1667, {_}: divide ?3815 (divide ?3816 ?3816) =>= inverse (inverse (inverse (inverse ?3815))) [3816, 3815] by Super 634 with 1619 at 1,1,1,3
+Id : 1711, {_}: divide ?3815 (divide ?3816 ?3816) =>= ?3815 [3816, 3815] by Demod 1667 with 634 at 3
+Id : 1774, {_}: divide (inverse (divide ?4058 ?4059)) (divide ?4060 ?4060) =>= inverse (inverse (multiply ?4059 (inverse ?4058))) [4060, 4059, 4058] by Super 86 with 1711 at 2,1,1,3
+Id : 1809, {_}: inverse (divide ?4058 ?4059) =<= inverse (inverse (multiply ?4059 (inverse ?4058))) [4059, 4058] by Demod 1774 with 1711 at 2
+Id : 1810, {_}: inverse (divide ?4058 ?4059) =<= divide (inverse (inverse ?4059)) ?4058 [4059, 4058] by Demod 1809 with 348 at 3
+Id : 1856, {_}: multiply ?2028 (inverse ?2029) =<= inverse (inverse (inverse (divide ?2029 ?2028))) [2029, 2028] by Demod 885 with 1810 at 1,1,3
+Id : 52, {_}: inverse ?136 =<= divide (inverse (divide ?137 ?137)) ?136 [137, 136] by Super 35 with 4 at 1,3
+Id : 55, {_}: inverse ?145 =<= divide (inverse (inverse (inverse (divide ?146 ?146)))) ?145 [146, 145] by Super 52 with 36 at 1,1,3
+Id : 1858, {_}: inverse ?145 =<= inverse (divide ?145 (inverse (divide ?146 ?146))) [146, 145] by Demod 55 with 1810 at 3
+Id : 1862, {_}: inverse ?145 =<= inverse (multiply ?145 (divide ?146 ?146)) [146, 145] by Demod 1858 with 29 at 1,3
+Id : 1778, {_}: multiply ?4073 (divide ?4074 ?4074) =>= inverse (inverse ?4073) [4074, 4073] by Super 893 with 1711 at 1,2
+Id : 2425, {_}: inverse ?145 =<= inverse (inverse (inverse ?145)) [145] by Demod 1862 with 1778 at 1,3
+Id : 2428, {_}: multiply ?2028 (inverse ?2029) =>= inverse (divide ?2029 ?2028) [2029, 2028] by Demod 1856 with 2425 at 3
+Id : 2431, {_}: inverse (divide ?2077 (multiply ?2076 ?2077)) =>= inverse (inverse ?2076) [2076, 2077] by Demod 921 with 2428 at 2
+Id : 1860, {_}: inverse (divide ?50 (multiply ?49 ?50)) =>= ?49 [49, 50] by Demod 208 with 1810 at 2
+Id : 2432, {_}: ?2076 =<= inverse (inverse ?2076) [2076] by Demod 2431 with 1860 at 2
+Id : 2437, {_}: multiply (multiply (inverse ?110) ?110) ?111 =>= ?111 [111, 110] by Demod 43 with 2432 at 3
+Id : 2539, {_}: a2 === a2 [] by Demod 1 with 2437 at 2
+Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
+% SZS output end CNFRefutation for GRP452-1.p
+23734: solved GRP452-1.p in 0.388023 using nrkbo
+23734: status Unsatisfiable for GRP452-1.p
+NO CLASH, using fixed ground order
+23741: Facts:
+23741: Id : 2, {_}:
+ divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
+ (divide (divide ?5 ?4) ?2)
+ =>=
+ ?3
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+NO CLASH, using fixed ground order
+23742: Facts:
+23742: Id : 2, {_}:
+ divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
+ (divide (divide ?5 ?4) ?2)
+ =>=
+ ?3
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23742: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+23742: Goal:
+23742: Id : 1, {_}:
+ multiply (inverse a1) a1 =<= multiply (inverse b1) b1
+ [] by prove_these_axioms_1
+23742: Order:
+23742: kbo
+23742: Leaf order:
+23742: a1 2 0 2 1,1,2
+23742: b1 2 0 2 1,1,3
+23742: inverse 4 1 2 0,1,2
+23742: multiply 3 2 2 0,2
+23742: divide 7 2 0
+NO CLASH, using fixed ground order
+23743: Facts:
+23743: Id : 2, {_}:
+ divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
+ (divide (divide ?5 ?4) ?2)
+ =>=
+ ?3
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23743: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+23743: Goal:
+23743: Id : 1, {_}:
+ multiply (inverse a1) a1 =<= multiply (inverse b1) b1
+ [] by prove_these_axioms_1
+23743: Order:
+23743: lpo
+23743: Leaf order:
+23743: a1 2 0 2 1,1,2
+23743: b1 2 0 2 1,1,3
+23743: inverse 4 1 2 0,1,2
+23743: multiply 3 2 2 0,2
+23743: divide 7 2 0
+23741: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+23741: Goal:
+23741: Id : 1, {_}:
+ multiply (inverse a1) a1 =<= multiply (inverse b1) b1
+ [] by prove_these_axioms_1
+23741: Order:
+23741: nrkbo
+23741: Leaf order:
+23741: a1 2 0 2 1,1,2
+23741: b1 2 0 2 1,1,3
+23741: inverse 4 1 2 0,1,2
+23741: multiply 3 2 2 0,2
+23741: divide 7 2 0
+% SZS status Timeout for GRP469-1.p
+NO CLASH, using fixed ground order
+23763: Facts:
+23763: Id : 2, {_}:
+ divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
+ (divide (divide ?5 ?4) ?2)
+ =>=
+ ?3
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23763: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+23763: Goal:
+23763: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+23763: Order:
+23763: nrkbo
+23763: Leaf order:
+23763: b2 2 0 2 1,1,1,2
+23763: a2 2 0 2 2,2
+23763: inverse 3 1 1 0,1,1,2
+23763: multiply 3 2 2 0,2
+23763: divide 7 2 0
+NO CLASH, using fixed ground order
+23764: Facts:
+23764: Id : 2, {_}:
+ divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
+ (divide (divide ?5 ?4) ?2)
+ =>=
+ ?3
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23764: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+23764: Goal:
+23764: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+23764: Order:
+23764: kbo
+23764: Leaf order:
+23764: b2 2 0 2 1,1,1,2
+23764: a2 2 0 2 2,2
+23764: inverse 3 1 1 0,1,1,2
+23764: multiply 3 2 2 0,2
+23764: divide 7 2 0
+NO CLASH, using fixed ground order
+23765: Facts:
+23765: Id : 2, {_}:
+ divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
+ (divide (divide ?5 ?4) ?2)
+ =>=
+ ?3
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23765: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+23765: Goal:
+23765: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+23765: Order:
+23765: lpo
+23765: Leaf order:
+23765: b2 2 0 2 1,1,1,2
+23765: a2 2 0 2 2,2
+23765: inverse 3 1 1 0,1,1,2
+23765: multiply 3 2 2 0,2
+23765: divide 7 2 0
+% SZS status Timeout for GRP470-1.p
+NO CLASH, using fixed ground order
+23801: Facts:
+23801: Id : 2, {_}:
+ divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
+ (divide (divide ?5 ?4) ?2)
+ =>=
+ ?3
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23801: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+23801: Goal:
+23801: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+23801: Order:
+23801: nrkbo
+23801: Leaf order:
+23801: a3 2 0 2 1,1,2
+23801: b3 2 0 2 2,1,2
+23801: c3 2 0 2 2,2
+23801: inverse 2 1 0
+23801: multiply 5 2 4 0,2
+23801: divide 7 2 0
+NO CLASH, using fixed ground order
+23802: Facts:
+23802: Id : 2, {_}:
+ divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
+ (divide (divide ?5 ?4) ?2)
+ =>=
+ ?3
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23802: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+23802: Goal:
+23802: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+23802: Order:
+23802: kbo
+23802: Leaf order:
+23802: a3 2 0 2 1,1,2
+23802: b3 2 0 2 2,1,2
+23802: c3 2 0 2 2,2
+23802: inverse 2 1 0
+23802: multiply 5 2 4 0,2
+23802: divide 7 2 0
+NO CLASH, using fixed ground order
+23803: Facts:
+23803: Id : 2, {_}:
+ divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5))))
+ (divide (divide ?5 ?4) ?2)
+ =>=
+ ?3
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23803: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+23803: Goal:
+23803: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+23803: Order:
+23803: lpo
+23803: Leaf order:
+23803: a3 2 0 2 1,1,2
+23803: b3 2 0 2 2,1,2
+23803: c3 2 0 2 2,2
+23803: inverse 2 1 0
+23803: multiply 5 2 4 0,2
+23803: divide 7 2 0
+% SZS status Timeout for GRP471-1.p
+NO CLASH, using fixed ground order
+23910: Facts:
+23910: Id : 2, {_}:
+ divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
+ (divide ?3 ?2)
+ =>=
+ ?5
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23910: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+23910: Goal:
+23910: Id : 1, {_}:
+ multiply (inverse a1) a1 =<= multiply (inverse b1) b1
+ [] by prove_these_axioms_1
+23910: Order:
+23910: nrkbo
+23910: Leaf order:
+23910: a1 2 0 2 1,1,2
+23910: b1 2 0 2 1,1,3
+23910: inverse 4 1 2 0,1,2
+23910: multiply 3 2 2 0,2
+23910: divide 7 2 0
+NO CLASH, using fixed ground order
+23911: Facts:
+23911: Id : 2, {_}:
+ divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
+ (divide ?3 ?2)
+ =>=
+ ?5
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23911: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+23911: Goal:
+23911: Id : 1, {_}:
+ multiply (inverse a1) a1 =<= multiply (inverse b1) b1
+ [] by prove_these_axioms_1
+23911: Order:
+23911: kbo
+23911: Leaf order:
+23911: a1 2 0 2 1,1,2
+23911: b1 2 0 2 1,1,3
+23911: inverse 4 1 2 0,1,2
+23911: multiply 3 2 2 0,2
+23911: divide 7 2 0
+NO CLASH, using fixed ground order
+23912: Facts:
+23912: Id : 2, {_}:
+ divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
+ (divide ?3 ?2)
+ =>=
+ ?5
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23912: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+23912: Goal:
+23912: Id : 1, {_}:
+ multiply (inverse a1) a1 =<= multiply (inverse b1) b1
+ [] by prove_these_axioms_1
+23912: Order:
+23912: lpo
+23912: Leaf order:
+23912: a1 2 0 2 1,1,2
+23912: b1 2 0 2 1,1,3
+23912: inverse 4 1 2 0,1,2
+23912: multiply 3 2 2 0,2
+23912: divide 7 2 0
+% SZS status Timeout for GRP475-1.p
+NO CLASH, using fixed ground order
+23945: Facts:
+23945: Id : 2, {_}:
+ divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
+ (divide ?3 ?2)
+ =>=
+ ?5
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23945: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+23945: Goal:
+23945: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+23945: Order:
+23945: nrkbo
+23945: Leaf order:
+23945: b2 2 0 2 1,1,1,2
+23945: a2 2 0 2 2,2
+23945: inverse 3 1 1 0,1,1,2
+23945: multiply 3 2 2 0,2
+23945: divide 7 2 0
+NO CLASH, using fixed ground order
+23946: Facts:
+23946: Id : 2, {_}:
+ divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
+ (divide ?3 ?2)
+ =>=
+ ?5
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23946: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+23946: Goal:
+23946: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+23946: Order:
+23946: kbo
+23946: Leaf order:
+23946: b2 2 0 2 1,1,1,2
+23946: a2 2 0 2 2,2
+23946: inverse 3 1 1 0,1,1,2
+23946: multiply 3 2 2 0,2
+23946: divide 7 2 0
+NO CLASH, using fixed ground order
+23947: Facts:
+23947: Id : 2, {_}:
+ divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
+ (divide ?3 ?2)
+ =>=
+ ?5
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23947: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+23947: Goal:
+23947: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+23947: Order:
+23947: lpo
+23947: Leaf order:
+23947: b2 2 0 2 1,1,1,2
+23947: a2 2 0 2 2,2
+23947: inverse 3 1 1 0,1,1,2
+23947: multiply 3 2 2 0,2
+23947: divide 7 2 0
+Statistics :
+Max weight : 50
+Found proof, 11.024829s
+% SZS status Unsatisfiable for GRP476-1.p
+% SZS output start CNFRefutation for GRP476-1.p
+Id : 2, {_}: divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) (divide ?3 ?2) =>= ?5 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+Id : 4, {_}: divide (inverse (divide (divide (divide ?10 ?11) ?12) (divide ?13 ?12))) (divide ?11 ?10) =>= ?13 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
+Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
+Id : 5, {_}: divide (inverse (divide (divide (divide (divide ?15 ?16) (inverse (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17)))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 2,2
+Id : 17, {_}: divide (inverse (divide (divide (multiply (divide ?15 ?16) (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 1,1,1,1,2
+Id : 18, {_}: multiply (inverse (divide (divide (multiply (divide ?64 ?65) (divide (divide (divide ?65 ?64) ?66) (divide (inverse ?67) ?66))) ?68) (divide ?69 ?68))) ?67 =>= ?69 [69, 68, 67, 66, 65, 64] by Super 3 with 17 at 3
+Id : 20, {_}: divide (inverse (divide (divide (divide ?80 ?81) ?82) ?83)) (divide ?81 ?80) =?= inverse (divide (divide (multiply (divide ?84 ?85) (divide (divide (divide ?85 ?84) ?86) (divide ?82 ?86))) ?87) (divide ?83 ?87)) [87, 86, 85, 84, 83, 82, 81, 80] by Super 2 with 17 at 2,1,1,2
+Id : 863, {_}: multiply (divide (inverse (divide (divide (divide ?4853 ?4854) (inverse ?4855)) ?4856)) (divide ?4854 ?4853)) ?4855 =>= ?4856 [4856, 4855, 4854, 4853] by Super 18 with 20 at 1,2
+Id : 978, {_}: multiply (divide (inverse (divide (multiply (divide ?4853 ?4854) ?4855) ?4856)) (divide ?4854 ?4853)) ?4855 =>= ?4856 [4856, 4855, 4854, 4853] by Demod 863 with 3 at 1,1,1,1,2
+Id : 1168, {_}: divide (divide (inverse (divide (divide (divide ?6497 ?6498) ?6499) ?6500)) (divide ?6498 ?6497)) ?6499 =>= ?6500 [6500, 6499, 6498, 6497] by Super 17 with 20 at 1,2
+Id : 1637, {_}: divide (divide (inverse (divide (divide (divide (inverse ?8641) ?8642) ?8643) ?8644)) (multiply ?8642 ?8641)) ?8643 =>= ?8644 [8644, 8643, 8642, 8641] by Super 1168 with 3 at 2,1,2
+Id : 1659, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?8819) ?8820) ?8821) ?8822)) (multiply (inverse ?8820) ?8819)) ?8821 =>= ?8822 [8822, 8821, 8820, 8819] by Super 1637 with 3 at 1,1,1,1,1,2
+Id : 7, {_}: divide (inverse (divide (divide ?29 ?30) (divide ?31 ?30))) (divide (divide ?32 ?33) (inverse (divide (divide (divide ?33 ?32) ?34) (divide ?29 ?34)))) =>= ?31 [34, 33, 32, 31, 30, 29] by Super 4 with 2 at 1,1,1,1,2
+Id : 292, {_}: divide (inverse (divide (divide ?1415 ?1416) (divide ?1417 ?1416))) (multiply (divide ?1418 ?1419) (divide (divide (divide ?1419 ?1418) ?1420) (divide ?1415 ?1420))) =>= ?1417 [1420, 1419, 1418, 1417, 1416, 1415] by Demod 7 with 3 at 2,2
+Id : 6, {_}: divide (inverse (divide (divide (divide ?22 ?23) (divide ?24 ?25)) ?26)) (divide ?23 ?22) =?= inverse (divide (divide (divide ?25 ?24) ?27) (divide ?26 ?27)) [27, 26, 25, 24, 23, 22] by Super 4 with 2 at 2,1,1,2
+Id : 117, {_}: inverse (divide (divide (divide ?560 ?561) ?562) (divide (divide ?563 (divide ?561 ?560)) ?562)) =>= ?563 [563, 562, 561, 560] by Super 2 with 6 at 2
+Id : 329, {_}: divide ?1764 (multiply (divide ?1765 ?1766) (divide (divide (divide ?1766 ?1765) ?1767) (divide (divide ?1768 ?1769) ?1767))) =>= divide ?1764 (divide ?1769 ?1768) [1769, 1768, 1767, 1766, 1765, 1764] by Super 292 with 117 at 1,2
+Id : 13692, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?74151) ?74152) ?74153) (divide ?74154 ?74155))) (multiply (inverse ?74152) ?74151)) ?74153 =?= multiply (divide ?74156 ?74157) (divide (divide (divide ?74157 ?74156) ?74158) (divide (divide ?74155 ?74154) ?74158)) [74158, 74157, 74156, 74155, 74154, 74153, 74152, 74151] by Super 1659 with 329 at 1,1,1,2
+Id : 13926, {_}: divide ?74154 ?74155 =<= multiply (divide ?74156 ?74157) (divide (divide (divide ?74157 ?74156) ?74158) (divide (divide ?74155 ?74154) ?74158)) [74158, 74157, 74156, 74155, 74154] by Demod 13692 with 1659 at 2
+Id : 1195, {_}: divide (divide (inverse (multiply (divide (divide ?6697 ?6698) ?6699) ?6700)) (divide ?6698 ?6697)) ?6699 =>= inverse ?6700 [6700, 6699, 6698, 6697] by Super 1168 with 3 at 1,1,1,2
+Id : 14284, {_}: divide (divide (inverse (divide ?76258 ?76259)) (divide ?76260 ?76261)) ?76262 =<= inverse (divide (divide (divide ?76262 (divide ?76261 ?76260)) ?76263) (divide (divide ?76259 ?76258) ?76263)) [76263, 76262, 76261, 76260, 76259, 76258] by Super 1195 with 13926 at 1,1,1,2
+Id : 14590, {_}: divide (divide (divide (inverse (divide ?77679 ?77680)) (divide ?77681 ?77682)) ?77683) (divide (divide ?77682 ?77681) ?77683) =>= divide ?77680 ?77679 [77683, 77682, 77681, 77680, 77679] by Super 2 with 14284 at 1,2
+Id : 21451, {_}: divide ?110293 ?110294 =<= multiply (divide (divide ?110293 ?110294) (inverse (divide ?110295 ?110296))) (divide ?110296 ?110295) [110296, 110295, 110294, 110293] by Super 13926 with 14590 at 2,3
+Id : 22065, {_}: divide ?114187 ?114188 =<= multiply (multiply (divide ?114187 ?114188) (divide ?114189 ?114190)) (divide ?114190 ?114189) [114190, 114189, 114188, 114187] by Demod 21451 with 3 at 1,3
+Id : 22122, {_}: divide (inverse (divide (divide (divide ?114646 ?114647) ?114648) (divide ?114649 ?114648))) (divide ?114647 ?114646) =?= multiply (multiply ?114649 (divide ?114650 ?114651)) (divide ?114651 ?114650) [114651, 114650, 114649, 114648, 114647, 114646] by Super 22065 with 2 at 1,1,3
+Id : 22268, {_}: ?114649 =<= multiply (multiply ?114649 (divide ?114650 ?114651)) (divide ?114651 ?114650) [114651, 114650, 114649] by Demod 22122 with 2 at 2
+Id : 202, {_}: inverse (divide (divide (divide ?946 ?947) ?948) (divide (divide ?949 (divide ?947 ?946)) ?948)) =>= ?949 [949, 948, 947, 946] by Super 2 with 6 at 2
+Id : 213, {_}: inverse (divide (divide (divide ?1024 ?1025) (inverse ?1026)) (multiply (divide ?1027 (divide ?1025 ?1024)) ?1026)) =>= ?1027 [1027, 1026, 1025, 1024] by Super 202 with 3 at 2,1,2
+Id : 232, {_}: inverse (divide (multiply (divide ?1024 ?1025) ?1026) (multiply (divide ?1027 (divide ?1025 ?1024)) ?1026)) =>= ?1027 [1027, 1026, 1025, 1024] by Demod 213 with 3 at 1,1,2
+Id : 21617, {_}: divide (divide (inverse (divide ?111842 ?111843)) (divide ?111843 ?111842)) (inverse (divide ?111844 ?111845)) =>= inverse (divide ?111845 ?111844) [111845, 111844, 111843, 111842] by Super 14284 with 14590 at 1,3
+Id : 21801, {_}: multiply (divide (inverse (divide ?111842 ?111843)) (divide ?111843 ?111842)) (divide ?111844 ?111845) =>= inverse (divide ?111845 ?111844) [111845, 111844, 111843, 111842] by Demod 21617 with 3 at 2
+Id : 24938, {_}: inverse (divide (inverse (divide ?127750 ?127751)) (multiply (divide ?127752 (divide (divide ?127753 ?127754) (inverse (divide ?127754 ?127753)))) (divide ?127751 ?127750))) =>= ?127752 [127754, 127753, 127752, 127751, 127750] by Super 232 with 21801 at 1,1,2
+Id : 9, {_}: divide (inverse (divide (divide (divide (inverse ?38) ?39) ?40) (divide ?41 ?40))) (multiply ?39 ?38) =>= ?41 [41, 40, 39, 38] by Super 2 with 3 at 2,2
+Id : 21516, {_}: divide (inverse (divide ?110895 ?110896)) (multiply (divide ?110897 ?110898) (divide ?110896 ?110895)) =>= divide ?110898 ?110897 [110898, 110897, 110896, 110895] by Super 9 with 14590 at 1,1,2
+Id : 25207, {_}: inverse (divide (divide (divide ?127753 ?127754) (inverse (divide ?127754 ?127753))) ?127752) =>= ?127752 [127752, 127754, 127753] by Demod 24938 with 21516 at 1,2
+Id : 25208, {_}: inverse (divide (multiply (divide ?127753 ?127754) (divide ?127754 ?127753)) ?127752) =>= ?127752 [127752, 127754, 127753] by Demod 25207 with 3 at 1,1,2
+Id : 25416, {_}: multiply (divide ?129668 (divide ?129669 ?129670)) (divide ?129669 ?129670) =>= ?129668 [129670, 129669, 129668] by Super 232 with 25208 at 2
+Id : 25599, {_}: divide ?130543 (divide ?130544 ?130545) =>= multiply ?130543 (divide ?130545 ?130544) [130545, 130544, 130543] by Super 22268 with 25416 at 1,3
+Id : 25966, {_}: multiply (multiply (inverse (divide (multiply (divide ?4853 ?4854) ?4855) ?4856)) (divide ?4853 ?4854)) ?4855 =>= ?4856 [4856, 4855, 4854, 4853] by Demod 978 with 25599 at 1,2
+Id : 26300, {_}: multiply (multiply (inverse (multiply (multiply (divide ?133704 ?133705) ?133706) (divide ?133707 ?133708))) (divide ?133704 ?133705)) ?133706 =>= divide ?133708 ?133707 [133708, 133707, 133706, 133705, 133704] by Super 25966 with 25599 at 1,1,1,2
+Id : 1261, {_}: multiply (divide (inverse (divide (multiply (divide ?6852 ?6853) ?6854) ?6855)) (divide ?6853 ?6852)) ?6854 =>= ?6855 [6855, 6854, 6853, 6852] by Demod 863 with 3 at 1,1,1,1,2
+Id : 1287, {_}: multiply (divide (inverse (multiply (multiply (divide ?7047 ?7048) ?7049) ?7050)) (divide ?7048 ?7047)) ?7049 =>= inverse ?7050 [7050, 7049, 7048, 7047] by Super 1261 with 3 at 1,1,1,2
+Id : 25965, {_}: multiply (multiply (inverse (multiply (multiply (divide ?7047 ?7048) ?7049) ?7050)) (divide ?7047 ?7048)) ?7049 =>= inverse ?7050 [7050, 7049, 7048, 7047] by Demod 1287 with 25599 at 1,2
+Id : 26721, {_}: inverse (divide ?134526 ?134527) =>= divide ?134527 ?134526 [134527, 134526] by Demod 26300 with 25965 at 2
+Id : 26764, {_}: inverse (multiply ?134789 ?134790) =<= divide (inverse ?134790) ?134789 [134790, 134789] by Super 26721 with 3 at 1,2
+Id : 26966, {_}: multiply (inverse ?135418) ?135419 =<= inverse (multiply (inverse ?135419) ?135418) [135419, 135418] by Super 3 with 26764 at 3
+Id : 26405, {_}: inverse (divide ?133707 ?133708) =>= divide ?133708 ?133707 [133708, 133707] by Demod 26300 with 25965 at 2
+Id : 26641, {_}: divide ?127752 (multiply (divide ?127753 ?127754) (divide ?127754 ?127753)) =>= ?127752 [127754, 127753, 127752] by Demod 25208 with 26405 at 2
+Id : 656, {_}: inverse (divide (divide (divide (inverse ?3361) ?3362) ?3363) (divide (divide ?3364 (multiply ?3362 ?3361)) ?3363)) =>= ?3364 [3364, 3363, 3362, 3361] by Super 202 with 3 at 2,1,2,1,2
+Id : 272, {_}: divide (inverse (divide (divide ?29 ?30) (divide ?31 ?30))) (multiply (divide ?32 ?33) (divide (divide (divide ?33 ?32) ?34) (divide ?29 ?34))) =>= ?31 [34, 33, 32, 31, 30, 29] by Demod 7 with 3 at 2,2
+Id : 661, {_}: inverse (divide (divide (divide (inverse (divide (divide (divide ?3396 ?3397) ?3398) (divide ?3399 ?3398))) (divide ?3397 ?3396)) ?3400) (divide ?3401 ?3400)) =?= inverse (divide (divide ?3399 ?3402) (divide ?3401 ?3402)) [3402, 3401, 3400, 3399, 3398, 3397, 3396] by Super 656 with 272 at 1,2,1,2
+Id : 5809, {_}: inverse (divide (divide ?31363 ?31364) (divide ?31365 ?31364)) =?= inverse (divide (divide ?31363 ?31366) (divide ?31365 ?31366)) [31366, 31365, 31364, 31363] by Demod 661 with 2 at 1,1,1,2
+Id : 5810, {_}: inverse (divide (divide ?31368 ?31369) (divide (inverse (divide (divide (divide ?31370 ?31371) ?31372) (divide ?31373 ?31372))) ?31369)) =>= inverse (divide (divide ?31368 (divide ?31371 ?31370)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Super 5809 with 2 at 2,1,3
+Id : 25948, {_}: inverse (multiply (divide ?31368 ?31369) (divide ?31369 (inverse (divide (divide (divide ?31370 ?31371) ?31372) (divide ?31373 ?31372))))) =>= inverse (divide (divide ?31368 (divide ?31371 ?31370)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 5810 with 25599 at 1,2
+Id : 25949, {_}: inverse (multiply (divide ?31368 ?31369) (divide ?31369 (inverse (divide (divide (divide ?31370 ?31371) ?31372) (divide ?31373 ?31372))))) =>= inverse (divide (multiply ?31368 (divide ?31370 ?31371)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 25948 with 25599 at 1,1,3
+Id : 25950, {_}: inverse (multiply (divide ?31368 ?31369) (divide ?31369 (inverse (multiply (divide (divide ?31370 ?31371) ?31372) (divide ?31372 ?31373))))) =>= inverse (divide (multiply ?31368 (divide ?31370 ?31371)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 25949 with 25599 at 1,2,2,1,2
+Id : 26071, {_}: inverse (multiply (divide ?31368 ?31369) (multiply ?31369 (multiply (divide (divide ?31370 ?31371) ?31372) (divide ?31372 ?31373)))) =>= inverse (divide (multiply ?31368 (divide ?31370 ?31371)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 25950 with 3 at 2,1,2
+Id : 26655, {_}: inverse (multiply (divide ?31368 ?31369) (multiply ?31369 (multiply (divide (divide ?31370 ?31371) ?31372) (divide ?31372 ?31373)))) =>= divide ?31373 (multiply ?31368 (divide ?31370 ?31371)) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 26071 with 26405 at 3
+Id : 5834, {_}: inverse (divide (divide (inverse (divide (divide (divide ?31556 ?31557) ?31558) (divide ?31559 ?31558))) ?31560) (divide ?31561 ?31560)) =>= inverse (divide ?31559 (divide ?31561 (divide ?31557 ?31556))) [31561, 31560, 31559, 31558, 31557, 31556] by Super 5809 with 2 at 1,1,3
+Id : 25943, {_}: inverse (multiply (divide (inverse (divide (divide (divide ?31556 ?31557) ?31558) (divide ?31559 ?31558))) ?31560) (divide ?31560 ?31561)) =>= inverse (divide ?31559 (divide ?31561 (divide ?31557 ?31556))) [31561, 31560, 31559, 31558, 31557, 31556] by Demod 5834 with 25599 at 1,2
+Id : 25944, {_}: inverse (multiply (divide (inverse (divide (divide (divide ?31556 ?31557) ?31558) (divide ?31559 ?31558))) ?31560) (divide ?31560 ?31561)) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31561, 31560, 31559, 31558, 31557, 31556] by Demod 25943 with 25599 at 1,3
+Id : 25945, {_}: inverse (multiply (divide (inverse (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) ?31560) (divide ?31560 ?31561)) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31561, 31560, 31559, 31558, 31557, 31556] by Demod 25944 with 25599 at 1,1,1,1,2
+Id : 26832, {_}: inverse (multiply (inverse (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559)))) (divide ?31560 ?31561)) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31561, 31559, 31558, 31557, 31556, 31560] by Demod 25945 with 26764 at 1,1,2
+Id : 27298, {_}: multiply (inverse (divide ?31560 ?31561)) (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31559, 31558, 31557, 31556, 31561, 31560] by Demod 26832 with 26966 at 2
+Id : 27299, {_}: multiply (divide ?31561 ?31560) (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31559, 31558, 31557, 31556, 31560, 31561] by Demod 27298 with 26405 at 1,2
+Id : 27300, {_}: inverse (inverse (multiply ?31373 (divide (divide ?31371 ?31370) ?31368))) =>= divide ?31373 (multiply ?31368 (divide ?31370 ?31371)) [31368, 31370, 31371, 31373] by Demod 26655 with 27299 at 1,2
+Id : 26900, {_}: inverse (inverse (multiply ?134958 ?134959)) =>= divide ?134958 (inverse ?134959) [134959, 134958] by Super 26405 with 26764 at 1,2
+Id : 27254, {_}: inverse (inverse (multiply ?134958 ?134959)) =>= multiply ?134958 ?134959 [134959, 134958] by Demod 26900 with 3 at 3
+Id : 27506, {_}: multiply ?31373 (divide (divide ?31371 ?31370) ?31368) =<= divide ?31373 (multiply ?31368 (divide ?31370 ?31371)) [31368, 31370, 31371, 31373] by Demod 27300 with 27254 at 2
+Id : 27507, {_}: multiply ?127752 (divide (divide ?127753 ?127754) (divide ?127753 ?127754)) =>= ?127752 [127754, 127753, 127752] by Demod 26641 with 27506 at 2
+Id : 27516, {_}: multiply ?127752 (multiply (divide ?127753 ?127754) (divide ?127754 ?127753)) =>= ?127752 [127754, 127753, 127752] by Demod 27507 with 25599 at 2,2
+Id : 22416, {_}: ?115848 =<= multiply (multiply ?115848 (divide ?115849 ?115850)) (divide ?115850 ?115849) [115850, 115849, 115848] by Demod 22122 with 2 at 2
+Id : 22472, {_}: ?116246 =<= multiply (multiply ?116246 (multiply ?116247 ?116248)) (divide (inverse ?116248) ?116247) [116248, 116247, 116246] by Super 22416 with 3 at 2,1,3
+Id : 26848, {_}: ?116246 =<= multiply (multiply ?116246 (multiply ?116247 ?116248)) (inverse (multiply ?116247 ?116248)) [116248, 116247, 116246] by Demod 22472 with 26764 at 2,3
+Id : 27552, {_}: inverse (inverse (multiply ?137012 ?137013)) =>= multiply ?137012 ?137013 [137013, 137012] by Demod 26900 with 3 at 3
+Id : 25980, {_}: multiply (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) (divide ?2 ?3) =>= ?5 [5, 4, 3, 2] by Demod 2 with 25599 at 2
+Id : 25981, {_}: multiply (inverse (multiply (divide (divide ?2 ?3) ?4) (divide ?4 ?5))) (divide ?2 ?3) =>= ?5 [5, 4, 3, 2] by Demod 25980 with 25599 at 1,1,2
+Id : 27556, {_}: inverse (inverse ?137032) =<= multiply (inverse (multiply (divide (divide ?137033 ?137034) ?137035) (divide ?137035 ?137032))) (divide ?137033 ?137034) [137035, 137034, 137033, 137032] by Super 27552 with 25981 at 1,1,2
+Id : 27632, {_}: inverse (inverse ?137032) =>= ?137032 [137032] by Demod 27556 with 25981 at 3
+Id : 27734, {_}: multiply ?137511 (inverse ?137512) =>= divide ?137511 ?137512 [137512, 137511] by Super 3 with 27632 at 2,3
+Id : 27823, {_}: ?116246 =<= divide (multiply ?116246 (multiply ?116247 ?116248)) (multiply ?116247 ?116248) [116248, 116247, 116246] by Demod 26848 with 27734 at 3
+Id : 22, {_}: divide (inverse (divide (divide (multiply (divide ?98 ?99) (divide (divide (divide ?99 ?98) ?100) (divide ?101 ?100))) ?102) (divide ?103 ?102))) ?101 =>= ?103 [103, 102, 101, 100, 99, 98] by Demod 5 with 3 at 1,1,1,1,2
+Id : 26, {_}: divide (inverse (divide (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137) (divide ?138 ?137))) (inverse (divide (divide (divide ?135 ?134) ?139) (divide ?136 ?139))) =>= ?138 [139, 138, 137, 136, 135, 134, 133, 132] by Super 22 with 2 at 2,2,1,1,1,1,2
+Id : 42, {_}: multiply (inverse (divide (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137) (divide ?138 ?137))) (divide (divide (divide ?135 ?134) ?139) (divide ?136 ?139)) =>= ?138 [139, 138, 137, 136, 135, 134, 133, 132] by Demod 26 with 3 at 2
+Id : 26984, {_}: inverse (multiply (divide ?135518 ?135519) ?135520) =<= multiply (inverse ?135520) (divide ?135519 ?135518) [135520, 135519, 135518] by Super 25599 with 26764 at 2
+Id : 31736, {_}: inverse (multiply (divide (divide ?136 ?139) (divide (divide ?135 ?134) ?139)) (divide (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137) (divide ?138 ?137))) =>= ?138 [138, 137, 133, 132, 134, 135, 139, 136] by Demod 42 with 26984 at 2
+Id : 26724, {_}: inverse (multiply ?134539 (divide ?134540 ?134541)) =>= divide (divide ?134541 ?134540) ?134539 [134541, 134540, 134539] by Super 26721 with 25599 at 1,2
+Id : 31737, {_}: divide (divide (divide ?138 ?137) (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137)) (divide (divide ?136 ?139) (divide (divide ?135 ?134) ?139)) =>= ?138 [139, 136, 135, 134, 133, 132, 137, 138] by Demod 31736 with 26724 at 2
+Id : 31738, {_}: multiply (divide (divide ?138 ?137) (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137)) (divide (divide (divide ?135 ?134) ?139) (divide ?136 ?139)) =>= ?138 [139, 136, 135, 134, 133, 132, 137, 138] by Demod 31737 with 25599 at 2
+Id : 31739, {_}: multiply (multiply (divide ?138 ?137) (divide ?137 (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)))) (divide (divide (divide ?135 ?134) ?139) (divide ?136 ?139)) =>= ?138 [139, 136, 135, 134, 133, 132, 137, 138] by Demod 31738 with 25599 at 1,2
+Id : 31740, {_}: multiply (multiply (divide ?138 ?137) (divide ?137 (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 136, 135, 134, 133, 132, 137, 138] by Demod 31739 with 25599 at 2,2
+Id : 31741, {_}: multiply (multiply (divide ?138 ?137) (multiply ?137 (divide (divide ?136 (divide (divide ?133 ?132) (divide ?134 ?135))) (divide ?132 ?133)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 135, 134, 132, 133, 136, 137, 138] by Demod 31740 with 27506 at 2,1,2
+Id : 31742, {_}: multiply (multiply (divide ?138 ?137) (multiply ?137 (multiply (divide ?136 (divide (divide ?133 ?132) (divide ?134 ?135))) (divide ?133 ?132)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 135, 134, 132, 133, 136, 137, 138] by Demod 31741 with 25599 at 2,2,1,2
+Id : 31743, {_}: multiply (multiply (divide ?138 ?137) (multiply ?137 (multiply (multiply ?136 (divide (divide ?134 ?135) (divide ?133 ?132))) (divide ?133 ?132)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 132, 133, 135, 134, 136, 137, 138] by Demod 31742 with 25599 at 1,2,2,1,2
+Id : 31744, {_}: multiply (multiply (divide ?138 ?137) (multiply ?137 (multiply (multiply ?136 (multiply (divide ?134 ?135) (divide ?132 ?133))) (divide ?133 ?132)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 133, 132, 135, 134, 136, 137, 138] by Demod 31743 with 25599 at 2,1,2,2,1,2
+Id : 31832, {_}: ?147291 =<= divide (multiply ?147291 (multiply (multiply (divide ?147292 ?147293) (multiply ?147293 (multiply (multiply ?147294 (multiply (divide ?147295 ?147296) (divide ?147297 ?147298))) (divide ?147298 ?147297)))) (multiply (divide (divide ?147296 ?147295) ?147299) (divide ?147299 ?147294)))) ?147292 [147299, 147298, 147297, 147296, 147295, 147294, 147293, 147292, 147291] by Super 27823 with 31744 at 2,3
+Id : 32203, {_}: ?147291 =<= divide (multiply ?147291 ?147292) ?147292 [147292, 147291] by Demod 31832 with 31744 at 2,1,3
+Id : 33094, {_}: inverse ?153200 =<= divide ?153201 (multiply ?153200 ?153201) [153201, 153200] by Super 26405 with 32203 at 1,2
+Id : 33479, {_}: multiply ?154885 (multiply (divide (multiply ?154886 ?154887) ?154887) (inverse ?154886)) =>= ?154885 [154887, 154886, 154885] by Super 27516 with 33094 at 2,2,2
+Id : 33980, {_}: multiply ?154885 (divide (divide (multiply ?154886 ?154887) ?154887) ?154886) =>= ?154885 [154887, 154886, 154885] by Demod 33479 with 27734 at 2,2
+Id : 33981, {_}: multiply ?154885 (divide ?154886 ?154886) =>= ?154885 [154886, 154885] by Demod 33980 with 32203 at 1,2,2
+Id : 34313, {_}: multiply (inverse (divide ?156478 ?156478)) ?156479 =>= inverse (inverse ?156479) [156479, 156478] by Super 26966 with 33981 at 1,3
+Id : 34773, {_}: multiply (divide ?156478 ?156478) ?156479 =>= inverse (inverse ?156479) [156479, 156478] by Demod 34313 with 26405 at 1,2
+Id : 36051, {_}: multiply (divide ?160644 ?160644) ?160645 =>= ?160645 [160645, 160644] by Demod 34773 with 27632 at 3
+Id : 36066, {_}: multiply (multiply (inverse ?160721) ?160721) ?160722 =>= ?160722 [160722, 160721] by Super 36051 with 3 at 1,2
+Id : 39894, {_}: a2 === a2 [] by Demod 1 with 36066 at 2
+Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
+% SZS output end CNFRefutation for GRP476-1.p
+23945: solved GRP476-1.p in 11.032689 using nrkbo
+23945: status Unsatisfiable for GRP476-1.p
+NO CLASH, using fixed ground order
+23952: Facts:
+23952: Id : 2, {_}:
+ divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
+ (divide ?3 ?2)
+ =>=
+ ?5
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23952: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+23952: Goal:
+23952: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+23952: Order:
+23952: nrkbo
+23952: Leaf order:
+23952: a3 2 0 2 1,1,2
+23952: b3 2 0 2 2,1,2
+23952: c3 2 0 2 2,2
+23952: inverse 2 1 0
+23952: multiply 5 2 4 0,2
+23952: divide 7 2 0
+NO CLASH, using fixed ground order
+23953: Facts:
+23953: Id : 2, {_}:
+ divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
+ (divide ?3 ?2)
+ =>=
+ ?5
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23953: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+23953: Goal:
+23953: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+23953: Order:
+23953: kbo
+23953: Leaf order:
+23953: a3 2 0 2 1,1,2
+23953: b3 2 0 2 2,1,2
+23953: c3 2 0 2 2,2
+23953: inverse 2 1 0
+23953: multiply 5 2 4 0,2
+23953: divide 7 2 0
+NO CLASH, using fixed ground order
+23954: Facts:
+23954: Id : 2, {_}:
+ divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4)))
+ (divide ?3 ?2)
+ =>=
+ ?5
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23954: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+23954: Goal:
+23954: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+23954: Order:
+23954: lpo
+23954: Leaf order:
+23954: a3 2 0 2 1,1,2
+23954: b3 2 0 2 2,1,2
+23954: c3 2 0 2 2,2
+23954: inverse 2 1 0
+23954: multiply 5 2 4 0,2
+23954: divide 7 2 0
+Statistics :
+Max weight : 50
+Found proof, 32.327095s
+% SZS status Unsatisfiable for GRP477-1.p
+% SZS output start CNFRefutation for GRP477-1.p
+Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
+Id : 2, {_}: divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) (divide ?3 ?2) =>= ?5 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+Id : 4, {_}: divide (inverse (divide (divide (divide ?10 ?11) ?12) (divide ?13 ?12))) (divide ?11 ?10) =>= ?13 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
+Id : 5, {_}: divide (inverse (divide (divide (divide (divide ?15 ?16) (inverse (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17)))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 2,2
+Id : 17, {_}: divide (inverse (divide (divide (multiply (divide ?15 ?16) (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 1,1,1,1,2
+Id : 20, {_}: divide (inverse (divide (divide (divide ?80 ?81) ?82) ?83)) (divide ?81 ?80) =?= inverse (divide (divide (multiply (divide ?84 ?85) (divide (divide (divide ?85 ?84) ?86) (divide ?82 ?86))) ?87) (divide ?83 ?87)) [87, 86, 85, 84, 83, 82, 81, 80] by Super 2 with 17 at 2,1,1,2
+Id : 1168, {_}: divide (divide (inverse (divide (divide (divide ?6497 ?6498) ?6499) ?6500)) (divide ?6498 ?6497)) ?6499 =>= ?6500 [6500, 6499, 6498, 6497] by Super 17 with 20 at 1,2
+Id : 1637, {_}: divide (divide (inverse (divide (divide (divide (inverse ?8641) ?8642) ?8643) ?8644)) (multiply ?8642 ?8641)) ?8643 =>= ?8644 [8644, 8643, 8642, 8641] by Super 1168 with 3 at 2,1,2
+Id : 1659, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?8819) ?8820) ?8821) ?8822)) (multiply (inverse ?8820) ?8819)) ?8821 =>= ?8822 [8822, 8821, 8820, 8819] by Super 1637 with 3 at 1,1,1,1,1,2
+Id : 7, {_}: divide (inverse (divide (divide ?29 ?30) (divide ?31 ?30))) (divide (divide ?32 ?33) (inverse (divide (divide (divide ?33 ?32) ?34) (divide ?29 ?34)))) =>= ?31 [34, 33, 32, 31, 30, 29] by Super 4 with 2 at 1,1,1,1,2
+Id : 292, {_}: divide (inverse (divide (divide ?1415 ?1416) (divide ?1417 ?1416))) (multiply (divide ?1418 ?1419) (divide (divide (divide ?1419 ?1418) ?1420) (divide ?1415 ?1420))) =>= ?1417 [1420, 1419, 1418, 1417, 1416, 1415] by Demod 7 with 3 at 2,2
+Id : 6, {_}: divide (inverse (divide (divide (divide ?22 ?23) (divide ?24 ?25)) ?26)) (divide ?23 ?22) =?= inverse (divide (divide (divide ?25 ?24) ?27) (divide ?26 ?27)) [27, 26, 25, 24, 23, 22] by Super 4 with 2 at 2,1,1,2
+Id : 117, {_}: inverse (divide (divide (divide ?560 ?561) ?562) (divide (divide ?563 (divide ?561 ?560)) ?562)) =>= ?563 [563, 562, 561, 560] by Super 2 with 6 at 2
+Id : 329, {_}: divide ?1764 (multiply (divide ?1765 ?1766) (divide (divide (divide ?1766 ?1765) ?1767) (divide (divide ?1768 ?1769) ?1767))) =>= divide ?1764 (divide ?1769 ?1768) [1769, 1768, 1767, 1766, 1765, 1764] by Super 292 with 117 at 1,2
+Id : 13692, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?74151) ?74152) ?74153) (divide ?74154 ?74155))) (multiply (inverse ?74152) ?74151)) ?74153 =?= multiply (divide ?74156 ?74157) (divide (divide (divide ?74157 ?74156) ?74158) (divide (divide ?74155 ?74154) ?74158)) [74158, 74157, 74156, 74155, 74154, 74153, 74152, 74151] by Super 1659 with 329 at 1,1,1,2
+Id : 13926, {_}: divide ?74154 ?74155 =<= multiply (divide ?74156 ?74157) (divide (divide (divide ?74157 ?74156) ?74158) (divide (divide ?74155 ?74154) ?74158)) [74158, 74157, 74156, 74155, 74154] by Demod 13692 with 1659 at 2
+Id : 1195, {_}: divide (divide (inverse (multiply (divide (divide ?6697 ?6698) ?6699) ?6700)) (divide ?6698 ?6697)) ?6699 =>= inverse ?6700 [6700, 6699, 6698, 6697] by Super 1168 with 3 at 1,1,1,2
+Id : 14284, {_}: divide (divide (inverse (divide ?76258 ?76259)) (divide ?76260 ?76261)) ?76262 =<= inverse (divide (divide (divide ?76262 (divide ?76261 ?76260)) ?76263) (divide (divide ?76259 ?76258) ?76263)) [76263, 76262, 76261, 76260, 76259, 76258] by Super 1195 with 13926 at 1,1,1,2
+Id : 14590, {_}: divide (divide (divide (inverse (divide ?77679 ?77680)) (divide ?77681 ?77682)) ?77683) (divide (divide ?77682 ?77681) ?77683) =>= divide ?77680 ?77679 [77683, 77682, 77681, 77680, 77679] by Super 2 with 14284 at 1,2
+Id : 21451, {_}: divide ?110293 ?110294 =<= multiply (divide (divide ?110293 ?110294) (inverse (divide ?110295 ?110296))) (divide ?110296 ?110295) [110296, 110295, 110294, 110293] by Super 13926 with 14590 at 2,3
+Id : 22065, {_}: divide ?114187 ?114188 =<= multiply (multiply (divide ?114187 ?114188) (divide ?114189 ?114190)) (divide ?114190 ?114189) [114190, 114189, 114188, 114187] by Demod 21451 with 3 at 1,3
+Id : 22122, {_}: divide (inverse (divide (divide (divide ?114646 ?114647) ?114648) (divide ?114649 ?114648))) (divide ?114647 ?114646) =?= multiply (multiply ?114649 (divide ?114650 ?114651)) (divide ?114651 ?114650) [114651, 114650, 114649, 114648, 114647, 114646] by Super 22065 with 2 at 1,1,3
+Id : 22416, {_}: ?115848 =<= multiply (multiply ?115848 (divide ?115849 ?115850)) (divide ?115850 ?115849) [115850, 115849, 115848] by Demod 22122 with 2 at 2
+Id : 22444, {_}: ?116047 =<= multiply (multiply ?116047 (divide (inverse ?116048) ?116049)) (multiply ?116049 ?116048) [116049, 116048, 116047] by Super 22416 with 3 at 2,3
+Id : 18, {_}: multiply (inverse (divide (divide (multiply (divide ?64 ?65) (divide (divide (divide ?65 ?64) ?66) (divide (inverse ?67) ?66))) ?68) (divide ?69 ?68))) ?67 =>= ?69 [69, 68, 67, 66, 65, 64] by Super 3 with 17 at 3
+Id : 863, {_}: multiply (divide (inverse (divide (divide (divide ?4853 ?4854) (inverse ?4855)) ?4856)) (divide ?4854 ?4853)) ?4855 =>= ?4856 [4856, 4855, 4854, 4853] by Super 18 with 20 at 1,2
+Id : 978, {_}: multiply (divide (inverse (divide (multiply (divide ?4853 ?4854) ?4855) ?4856)) (divide ?4854 ?4853)) ?4855 =>= ?4856 [4856, 4855, 4854, 4853] by Demod 863 with 3 at 1,1,1,1,2
+Id : 22268, {_}: ?114649 =<= multiply (multiply ?114649 (divide ?114650 ?114651)) (divide ?114651 ?114650) [114651, 114650, 114649] by Demod 22122 with 2 at 2
+Id : 202, {_}: inverse (divide (divide (divide ?946 ?947) ?948) (divide (divide ?949 (divide ?947 ?946)) ?948)) =>= ?949 [949, 948, 947, 946] by Super 2 with 6 at 2
+Id : 213, {_}: inverse (divide (divide (divide ?1024 ?1025) (inverse ?1026)) (multiply (divide ?1027 (divide ?1025 ?1024)) ?1026)) =>= ?1027 [1027, 1026, 1025, 1024] by Super 202 with 3 at 2,1,2
+Id : 232, {_}: inverse (divide (multiply (divide ?1024 ?1025) ?1026) (multiply (divide ?1027 (divide ?1025 ?1024)) ?1026)) =>= ?1027 [1027, 1026, 1025, 1024] by Demod 213 with 3 at 1,1,2
+Id : 21617, {_}: divide (divide (inverse (divide ?111842 ?111843)) (divide ?111843 ?111842)) (inverse (divide ?111844 ?111845)) =>= inverse (divide ?111845 ?111844) [111845, 111844, 111843, 111842] by Super 14284 with 14590 at 1,3
+Id : 21801, {_}: multiply (divide (inverse (divide ?111842 ?111843)) (divide ?111843 ?111842)) (divide ?111844 ?111845) =>= inverse (divide ?111845 ?111844) [111845, 111844, 111843, 111842] by Demod 21617 with 3 at 2
+Id : 24938, {_}: inverse (divide (inverse (divide ?127750 ?127751)) (multiply (divide ?127752 (divide (divide ?127753 ?127754) (inverse (divide ?127754 ?127753)))) (divide ?127751 ?127750))) =>= ?127752 [127754, 127753, 127752, 127751, 127750] by Super 232 with 21801 at 1,1,2
+Id : 9, {_}: divide (inverse (divide (divide (divide (inverse ?38) ?39) ?40) (divide ?41 ?40))) (multiply ?39 ?38) =>= ?41 [41, 40, 39, 38] by Super 2 with 3 at 2,2
+Id : 21516, {_}: divide (inverse (divide ?110895 ?110896)) (multiply (divide ?110897 ?110898) (divide ?110896 ?110895)) =>= divide ?110898 ?110897 [110898, 110897, 110896, 110895] by Super 9 with 14590 at 1,1,2
+Id : 25207, {_}: inverse (divide (divide (divide ?127753 ?127754) (inverse (divide ?127754 ?127753))) ?127752) =>= ?127752 [127752, 127754, 127753] by Demod 24938 with 21516 at 1,2
+Id : 25208, {_}: inverse (divide (multiply (divide ?127753 ?127754) (divide ?127754 ?127753)) ?127752) =>= ?127752 [127752, 127754, 127753] by Demod 25207 with 3 at 1,1,2
+Id : 25416, {_}: multiply (divide ?129668 (divide ?129669 ?129670)) (divide ?129669 ?129670) =>= ?129668 [129670, 129669, 129668] by Super 232 with 25208 at 2
+Id : 25599, {_}: divide ?130543 (divide ?130544 ?130545) =>= multiply ?130543 (divide ?130545 ?130544) [130545, 130544, 130543] by Super 22268 with 25416 at 1,3
+Id : 25966, {_}: multiply (multiply (inverse (divide (multiply (divide ?4853 ?4854) ?4855) ?4856)) (divide ?4853 ?4854)) ?4855 =>= ?4856 [4856, 4855, 4854, 4853] by Demod 978 with 25599 at 1,2
+Id : 26300, {_}: multiply (multiply (inverse (multiply (multiply (divide ?133704 ?133705) ?133706) (divide ?133707 ?133708))) (divide ?133704 ?133705)) ?133706 =>= divide ?133708 ?133707 [133708, 133707, 133706, 133705, 133704] by Super 25966 with 25599 at 1,1,1,2
+Id : 1261, {_}: multiply (divide (inverse (divide (multiply (divide ?6852 ?6853) ?6854) ?6855)) (divide ?6853 ?6852)) ?6854 =>= ?6855 [6855, 6854, 6853, 6852] by Demod 863 with 3 at 1,1,1,1,2
+Id : 1287, {_}: multiply (divide (inverse (multiply (multiply (divide ?7047 ?7048) ?7049) ?7050)) (divide ?7048 ?7047)) ?7049 =>= inverse ?7050 [7050, 7049, 7048, 7047] by Super 1261 with 3 at 1,1,1,2
+Id : 25965, {_}: multiply (multiply (inverse (multiply (multiply (divide ?7047 ?7048) ?7049) ?7050)) (divide ?7047 ?7048)) ?7049 =>= inverse ?7050 [7050, 7049, 7048, 7047] by Demod 1287 with 25599 at 1,2
+Id : 26721, {_}: inverse (divide ?134526 ?134527) =>= divide ?134527 ?134526 [134527, 134526] by Demod 26300 with 25965 at 2
+Id : 26764, {_}: inverse (multiply ?134789 ?134790) =<= divide (inverse ?134790) ?134789 [134790, 134789] by Super 26721 with 3 at 1,2
+Id : 26849, {_}: ?116047 =<= multiply (multiply ?116047 (inverse (multiply ?116049 ?116048))) (multiply ?116049 ?116048) [116048, 116049, 116047] by Demod 22444 with 26764 at 2,1,3
+Id : 26405, {_}: inverse (divide ?133707 ?133708) =>= divide ?133708 ?133707 [133708, 133707] by Demod 26300 with 25965 at 2
+Id : 26900, {_}: inverse (inverse (multiply ?134958 ?134959)) =>= divide ?134958 (inverse ?134959) [134959, 134958] by Super 26405 with 26764 at 1,2
+Id : 27552, {_}: inverse (inverse (multiply ?137012 ?137013)) =>= multiply ?137012 ?137013 [137013, 137012] by Demod 26900 with 3 at 3
+Id : 25980, {_}: multiply (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) (divide ?2 ?3) =>= ?5 [5, 4, 3, 2] by Demod 2 with 25599 at 2
+Id : 25981, {_}: multiply (inverse (multiply (divide (divide ?2 ?3) ?4) (divide ?4 ?5))) (divide ?2 ?3) =>= ?5 [5, 4, 3, 2] by Demod 25980 with 25599 at 1,1,2
+Id : 27556, {_}: inverse (inverse ?137032) =<= multiply (inverse (multiply (divide (divide ?137033 ?137034) ?137035) (divide ?137035 ?137032))) (divide ?137033 ?137034) [137035, 137034, 137033, 137032] by Super 27552 with 25981 at 1,1,2
+Id : 27632, {_}: inverse (inverse ?137032) =>= ?137032 [137032] by Demod 27556 with 25981 at 3
+Id : 27734, {_}: multiply ?137511 (inverse ?137512) =>= divide ?137511 ?137512 [137512, 137511] by Super 3 with 27632 at 2,3
+Id : 27821, {_}: ?116047 =<= multiply (divide ?116047 (multiply ?116049 ?116048)) (multiply ?116049 ?116048) [116048, 116049, 116047] by Demod 26849 with 27734 at 1,3
+Id : 22, {_}: divide (inverse (divide (divide (multiply (divide ?98 ?99) (divide (divide (divide ?99 ?98) ?100) (divide ?101 ?100))) ?102) (divide ?103 ?102))) ?101 =>= ?103 [103, 102, 101, 100, 99, 98] by Demod 5 with 3 at 1,1,1,1,2
+Id : 26, {_}: divide (inverse (divide (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137) (divide ?138 ?137))) (inverse (divide (divide (divide ?135 ?134) ?139) (divide ?136 ?139))) =>= ?138 [139, 138, 137, 136, 135, 134, 133, 132] by Super 22 with 2 at 2,2,1,1,1,1,2
+Id : 42, {_}: multiply (inverse (divide (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137) (divide ?138 ?137))) (divide (divide (divide ?135 ?134) ?139) (divide ?136 ?139)) =>= ?138 [139, 138, 137, 136, 135, 134, 133, 132] by Demod 26 with 3 at 2
+Id : 26984, {_}: inverse (multiply (divide ?135518 ?135519) ?135520) =<= multiply (inverse ?135520) (divide ?135519 ?135518) [135520, 135519, 135518] by Super 25599 with 26764 at 2
+Id : 31736, {_}: inverse (multiply (divide (divide ?136 ?139) (divide (divide ?135 ?134) ?139)) (divide (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137) (divide ?138 ?137))) =>= ?138 [138, 137, 133, 132, 134, 135, 139, 136] by Demod 42 with 26984 at 2
+Id : 26724, {_}: inverse (multiply ?134539 (divide ?134540 ?134541)) =>= divide (divide ?134541 ?134540) ?134539 [134541, 134540, 134539] by Super 26721 with 25599 at 1,2
+Id : 31737, {_}: divide (divide (divide ?138 ?137) (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137)) (divide (divide ?136 ?139) (divide (divide ?135 ?134) ?139)) =>= ?138 [139, 136, 135, 134, 133, 132, 137, 138] by Demod 31736 with 26724 at 2
+Id : 31738, {_}: multiply (divide (divide ?138 ?137) (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137)) (divide (divide (divide ?135 ?134) ?139) (divide ?136 ?139)) =>= ?138 [139, 136, 135, 134, 133, 132, 137, 138] by Demod 31737 with 25599 at 2
+Id : 31739, {_}: multiply (multiply (divide ?138 ?137) (divide ?137 (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)))) (divide (divide (divide ?135 ?134) ?139) (divide ?136 ?139)) =>= ?138 [139, 136, 135, 134, 133, 132, 137, 138] by Demod 31738 with 25599 at 1,2
+Id : 31740, {_}: multiply (multiply (divide ?138 ?137) (divide ?137 (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 136, 135, 134, 133, 132, 137, 138] by Demod 31739 with 25599 at 2,2
+Id : 656, {_}: inverse (divide (divide (divide (inverse ?3361) ?3362) ?3363) (divide (divide ?3364 (multiply ?3362 ?3361)) ?3363)) =>= ?3364 [3364, 3363, 3362, 3361] by Super 202 with 3 at 2,1,2,1,2
+Id : 272, {_}: divide (inverse (divide (divide ?29 ?30) (divide ?31 ?30))) (multiply (divide ?32 ?33) (divide (divide (divide ?33 ?32) ?34) (divide ?29 ?34))) =>= ?31 [34, 33, 32, 31, 30, 29] by Demod 7 with 3 at 2,2
+Id : 661, {_}: inverse (divide (divide (divide (inverse (divide (divide (divide ?3396 ?3397) ?3398) (divide ?3399 ?3398))) (divide ?3397 ?3396)) ?3400) (divide ?3401 ?3400)) =?= inverse (divide (divide ?3399 ?3402) (divide ?3401 ?3402)) [3402, 3401, 3400, 3399, 3398, 3397, 3396] by Super 656 with 272 at 1,2,1,2
+Id : 5809, {_}: inverse (divide (divide ?31363 ?31364) (divide ?31365 ?31364)) =?= inverse (divide (divide ?31363 ?31366) (divide ?31365 ?31366)) [31366, 31365, 31364, 31363] by Demod 661 with 2 at 1,1,1,2
+Id : 5810, {_}: inverse (divide (divide ?31368 ?31369) (divide (inverse (divide (divide (divide ?31370 ?31371) ?31372) (divide ?31373 ?31372))) ?31369)) =>= inverse (divide (divide ?31368 (divide ?31371 ?31370)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Super 5809 with 2 at 2,1,3
+Id : 25948, {_}: inverse (multiply (divide ?31368 ?31369) (divide ?31369 (inverse (divide (divide (divide ?31370 ?31371) ?31372) (divide ?31373 ?31372))))) =>= inverse (divide (divide ?31368 (divide ?31371 ?31370)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 5810 with 25599 at 1,2
+Id : 25949, {_}: inverse (multiply (divide ?31368 ?31369) (divide ?31369 (inverse (divide (divide (divide ?31370 ?31371) ?31372) (divide ?31373 ?31372))))) =>= inverse (divide (multiply ?31368 (divide ?31370 ?31371)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 25948 with 25599 at 1,1,3
+Id : 25950, {_}: inverse (multiply (divide ?31368 ?31369) (divide ?31369 (inverse (multiply (divide (divide ?31370 ?31371) ?31372) (divide ?31372 ?31373))))) =>= inverse (divide (multiply ?31368 (divide ?31370 ?31371)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 25949 with 25599 at 1,2,2,1,2
+Id : 26071, {_}: inverse (multiply (divide ?31368 ?31369) (multiply ?31369 (multiply (divide (divide ?31370 ?31371) ?31372) (divide ?31372 ?31373)))) =>= inverse (divide (multiply ?31368 (divide ?31370 ?31371)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 25950 with 3 at 2,1,2
+Id : 26655, {_}: inverse (multiply (divide ?31368 ?31369) (multiply ?31369 (multiply (divide (divide ?31370 ?31371) ?31372) (divide ?31372 ?31373)))) =>= divide ?31373 (multiply ?31368 (divide ?31370 ?31371)) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 26071 with 26405 at 3
+Id : 5834, {_}: inverse (divide (divide (inverse (divide (divide (divide ?31556 ?31557) ?31558) (divide ?31559 ?31558))) ?31560) (divide ?31561 ?31560)) =>= inverse (divide ?31559 (divide ?31561 (divide ?31557 ?31556))) [31561, 31560, 31559, 31558, 31557, 31556] by Super 5809 with 2 at 1,1,3
+Id : 25943, {_}: inverse (multiply (divide (inverse (divide (divide (divide ?31556 ?31557) ?31558) (divide ?31559 ?31558))) ?31560) (divide ?31560 ?31561)) =>= inverse (divide ?31559 (divide ?31561 (divide ?31557 ?31556))) [31561, 31560, 31559, 31558, 31557, 31556] by Demod 5834 with 25599 at 1,2
+Id : 25944, {_}: inverse (multiply (divide (inverse (divide (divide (divide ?31556 ?31557) ?31558) (divide ?31559 ?31558))) ?31560) (divide ?31560 ?31561)) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31561, 31560, 31559, 31558, 31557, 31556] by Demod 25943 with 25599 at 1,3
+Id : 25945, {_}: inverse (multiply (divide (inverse (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) ?31560) (divide ?31560 ?31561)) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31561, 31560, 31559, 31558, 31557, 31556] by Demod 25944 with 25599 at 1,1,1,1,2
+Id : 26832, {_}: inverse (multiply (inverse (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559)))) (divide ?31560 ?31561)) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31561, 31559, 31558, 31557, 31556, 31560] by Demod 25945 with 26764 at 1,1,2
+Id : 26966, {_}: multiply (inverse ?135418) ?135419 =<= inverse (multiply (inverse ?135419) ?135418) [135419, 135418] by Super 3 with 26764 at 3
+Id : 27298, {_}: multiply (inverse (divide ?31560 ?31561)) (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31559, 31558, 31557, 31556, 31561, 31560] by Demod 26832 with 26966 at 2
+Id : 27299, {_}: multiply (divide ?31561 ?31560) (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31559, 31558, 31557, 31556, 31560, 31561] by Demod 27298 with 26405 at 1,2
+Id : 27300, {_}: inverse (inverse (multiply ?31373 (divide (divide ?31371 ?31370) ?31368))) =>= divide ?31373 (multiply ?31368 (divide ?31370 ?31371)) [31368, 31370, 31371, 31373] by Demod 26655 with 27299 at 1,2
+Id : 27254, {_}: inverse (inverse (multiply ?134958 ?134959)) =>= multiply ?134958 ?134959 [134959, 134958] by Demod 26900 with 3 at 3
+Id : 27506, {_}: multiply ?31373 (divide (divide ?31371 ?31370) ?31368) =<= divide ?31373 (multiply ?31368 (divide ?31370 ?31371)) [31368, 31370, 31371, 31373] by Demod 27300 with 27254 at 2
+Id : 31741, {_}: multiply (multiply (divide ?138 ?137) (multiply ?137 (divide (divide ?136 (divide (divide ?133 ?132) (divide ?134 ?135))) (divide ?132 ?133)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 135, 134, 132, 133, 136, 137, 138] by Demod 31740 with 27506 at 2,1,2
+Id : 31742, {_}: multiply (multiply (divide ?138 ?137) (multiply ?137 (multiply (divide ?136 (divide (divide ?133 ?132) (divide ?134 ?135))) (divide ?133 ?132)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 135, 134, 132, 133, 136, 137, 138] by Demod 31741 with 25599 at 2,2,1,2
+Id : 31743, {_}: multiply (multiply (divide ?138 ?137) (multiply ?137 (multiply (multiply ?136 (divide (divide ?134 ?135) (divide ?133 ?132))) (divide ?133 ?132)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 132, 133, 135, 134, 136, 137, 138] by Demod 31742 with 25599 at 1,2,2,1,2
+Id : 31744, {_}: multiply (multiply (divide ?138 ?137) (multiply ?137 (multiply (multiply ?136 (multiply (divide ?134 ?135) (divide ?132 ?133))) (divide ?133 ?132)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 133, 132, 135, 134, 136, 137, 138] by Demod 31743 with 25599 at 2,1,2,2,1,2
+Id : 31835, {_}: ?147320 =<= multiply (divide ?147320 (multiply (multiply (divide ?147321 ?147322) (multiply ?147322 (multiply (multiply ?147323 (multiply (divide ?147324 ?147325) (divide ?147326 ?147327))) (divide ?147327 ?147326)))) (multiply (divide (divide ?147325 ?147324) ?147328) (divide ?147328 ?147323)))) ?147321 [147328, 147327, 147326, 147325, 147324, 147323, 147322, 147321, 147320] by Super 27821 with 31744 at 2,3
+Id : 32201, {_}: ?147320 =<= multiply (divide ?147320 ?147321) ?147321 [147321, 147320] by Demod 31835 with 31744 at 2,1,3
+Id : 835, {_}: divide (divide (inverse (divide (divide (divide ?4527 ?4528) ?4529) ?4530)) (divide ?4528 ?4527)) ?4529 =>= ?4530 [4530, 4529, 4528, 4527] by Super 17 with 20 at 1,2
+Id : 25994, {_}: divide (multiply (inverse (divide (divide (divide ?4527 ?4528) ?4529) ?4530)) (divide ?4527 ?4528)) ?4529 =>= ?4530 [4530, 4529, 4528, 4527] by Demod 835 with 25599 at 1,2
+Id : 26651, {_}: divide (multiply (divide ?4530 (divide (divide ?4527 ?4528) ?4529)) (divide ?4527 ?4528)) ?4529 =>= ?4530 [4529, 4528, 4527, 4530] by Demod 25994 with 26405 at 1,1,2
+Id : 26667, {_}: divide (multiply (multiply ?4530 (divide ?4529 (divide ?4527 ?4528))) (divide ?4527 ?4528)) ?4529 =>= ?4530 [4528, 4527, 4529, 4530] by Demod 26651 with 25599 at 1,1,2
+Id : 26668, {_}: divide (multiply (multiply ?4530 (multiply ?4529 (divide ?4528 ?4527))) (divide ?4527 ?4528)) ?4529 =>= ?4530 [4527, 4528, 4529, 4530] by Demod 26667 with 25599 at 2,1,1,2
+Id : 32718, {_}: divide (multiply ?151970 (divide ?151971 ?151972)) ?151973 =?= divide ?151970 (multiply ?151973 (divide ?151972 ?151971)) [151973, 151972, 151971, 151970] by Super 26668 with 32201 at 1,1,2
+Id : 42767, {_}: divide (multiply ?174190 (divide ?174191 ?174192)) ?174193 =>= multiply ?174190 (divide (divide ?174191 ?174192) ?174193) [174193, 174192, 174191, 174190] by Demod 32718 with 27506 at 3
+Id : 25986, {_}: inverse (divide (multiply (divide ?1024 ?1025) ?1026) (multiply (multiply ?1027 (divide ?1024 ?1025)) ?1026)) =>= ?1027 [1027, 1026, 1025, 1024] by Demod 232 with 25599 at 1,2,1,2
+Id : 26619, {_}: divide (multiply (multiply ?1027 (divide ?1024 ?1025)) ?1026) (multiply (divide ?1024 ?1025) ?1026) =>= ?1027 [1026, 1025, 1024, 1027] by Demod 25986 with 26405 at 2
+Id : 42770, {_}: divide (multiply ?174208 ?174209) ?174210 =<= multiply ?174208 (divide (divide (multiply (multiply ?174209 (divide ?174211 ?174212)) ?174213) (multiply (divide ?174211 ?174212) ?174213)) ?174210) [174213, 174212, 174211, 174210, 174209, 174208] by Super 42767 with 26619 at 2,1,2
+Id : 43287, {_}: divide (multiply ?174208 ?174209) ?174210 =>= multiply ?174208 (divide ?174209 ?174210) [174210, 174209, 174208] by Demod 42770 with 26619 at 1,2,3
+Id : 45294, {_}: multiply ?177592 ?177593 =<= multiply (multiply ?177592 (divide ?177593 ?177594)) ?177594 [177594, 177593, 177592] by Super 32201 with 43287 at 1,3
+Id : 25967, {_}: multiply (inverse (divide (divide (divide ?80 ?81) ?82) ?83)) (divide ?80 ?81) =?= inverse (divide (divide (multiply (divide ?84 ?85) (divide (divide (divide ?85 ?84) ?86) (divide ?82 ?86))) ?87) (divide ?83 ?87)) [87, 86, 85, 84, 83, 82, 81, 80] by Demod 20 with 25599 at 2
+Id : 25968, {_}: multiply (inverse (divide (divide (divide ?80 ?81) ?82) ?83)) (divide ?80 ?81) =?= inverse (multiply (divide (multiply (divide ?84 ?85) (divide (divide (divide ?85 ?84) ?86) (divide ?82 ?86))) ?87) (divide ?87 ?83)) [87, 86, 85, 84, 83, 82, 81, 80] by Demod 25967 with 25599 at 1,3
+Id : 25969, {_}: multiply (inverse (divide (divide (divide ?80 ?81) ?82) ?83)) (divide ?80 ?81) =?= inverse (multiply (divide (multiply (divide ?84 ?85) (multiply (divide (divide ?85 ?84) ?86) (divide ?86 ?82))) ?87) (divide ?87 ?83)) [87, 86, 85, 84, 83, 82, 81, 80] by Demod 25968 with 25599 at 2,1,1,1,3
+Id : 26616, {_}: multiply (divide ?83 (divide (divide ?80 ?81) ?82)) (divide ?80 ?81) =?= inverse (multiply (divide (multiply (divide ?84 ?85) (multiply (divide (divide ?85 ?84) ?86) (divide ?86 ?82))) ?87) (divide ?87 ?83)) [87, 86, 85, 84, 82, 81, 80, 83] by Demod 25969 with 26405 at 1,2
+Id : 26679, {_}: multiply (multiply ?83 (divide ?82 (divide ?80 ?81))) (divide ?80 ?81) =?= inverse (multiply (divide (multiply (divide ?84 ?85) (multiply (divide (divide ?85 ?84) ?86) (divide ?86 ?82))) ?87) (divide ?87 ?83)) [87, 86, 85, 84, 81, 80, 82, 83] by Demod 26616 with 25599 at 1,2
+Id : 26680, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =?= inverse (multiply (divide (multiply (divide ?84 ?85) (multiply (divide (divide ?85 ?84) ?86) (divide ?86 ?82))) ?87) (divide ?87 ?83)) [87, 86, 85, 84, 80, 81, 82, 83] by Demod 26679 with 25599 at 2,1,2
+Id : 28666, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =?= divide (divide ?83 ?87) (divide (multiply (divide ?84 ?85) (multiply (divide (divide ?85 ?84) ?86) (divide ?86 ?82))) ?87) [86, 85, 84, 87, 80, 81, 82, 83] by Demod 26680 with 26724 at 3
+Id : 28715, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =?= multiply (divide ?83 ?87) (divide ?87 (multiply (divide ?84 ?85) (multiply (divide (divide ?85 ?84) ?86) (divide ?86 ?82)))) [86, 85, 84, 87, 80, 81, 82, 83] by Demod 28666 with 25599 at 3
+Id : 28664, {_}: multiply (divide ?31561 ?31560) (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) =>= divide (divide ?31561 (divide ?31557 ?31556)) ?31559 [31559, 31558, 31557, 31556, 31560, 31561] by Demod 27299 with 26724 at 3
+Id : 28717, {_}: multiply (divide ?31561 ?31560) (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) =>= divide (multiply ?31561 (divide ?31556 ?31557)) ?31559 [31559, 31558, 31557, 31556, 31560, 31561] by Demod 28664 with 25599 at 1,3
+Id : 32902, {_}: divide (multiply ?151970 (divide ?151971 ?151972)) ?151973 =>= multiply ?151970 (divide (divide ?151971 ?151972) ?151973) [151973, 151972, 151971, 151970] by Demod 32718 with 27506 at 3
+Id : 42552, {_}: multiply (divide ?31561 ?31560) (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) =>= multiply ?31561 (divide (divide ?31556 ?31557) ?31559) [31559, 31558, 31557, 31556, 31560, 31561] by Demod 28717 with 32902 at 3
+Id : 10, {_}: divide (inverse (divide (divide (divide ?43 ?44) (inverse ?45)) (multiply ?46 ?45))) (divide ?44 ?43) =>= ?46 [46, 45, 44, 43] by Super 2 with 3 at 2,1,1,2
+Id : 58, {_}: divide (inverse (divide (multiply (divide ?293 ?294) ?295) (multiply ?296 ?295))) (divide ?294 ?293) =>= ?296 [296, 295, 294, 293] by Demod 10 with 3 at 1,1,1,2
+Id : 66, {_}: divide (inverse (divide (multiply (multiply ?349 ?350) ?351) (multiply ?352 ?351))) (divide (inverse ?350) ?349) =>= ?352 [352, 351, 350, 349] by Super 58 with 3 at 1,1,1,1,2
+Id : 5845, {_}: inverse (divide (divide (inverse (divide (multiply (multiply ?31653 ?31654) ?31655) (multiply ?31656 ?31655))) ?31657) (divide ?31658 ?31657)) =>= inverse (divide ?31656 (divide ?31658 (divide (inverse ?31654) ?31653))) [31658, 31657, 31656, 31655, 31654, 31653] by Super 5809 with 66 at 1,1,3
+Id : 25939, {_}: inverse (multiply (divide (inverse (divide (multiply (multiply ?31653 ?31654) ?31655) (multiply ?31656 ?31655))) ?31657) (divide ?31657 ?31658)) =>= inverse (divide ?31656 (divide ?31658 (divide (inverse ?31654) ?31653))) [31658, 31657, 31656, 31655, 31654, 31653] by Demod 5845 with 25599 at 1,2
+Id : 25940, {_}: inverse (multiply (divide (inverse (divide (multiply (multiply ?31653 ?31654) ?31655) (multiply ?31656 ?31655))) ?31657) (divide ?31657 ?31658)) =>= inverse (multiply ?31656 (divide (divide (inverse ?31654) ?31653) ?31658)) [31658, 31657, 31656, 31655, 31654, 31653] by Demod 25939 with 25599 at 1,3
+Id : 26656, {_}: inverse (multiply (divide (divide (multiply ?31656 ?31655) (multiply (multiply ?31653 ?31654) ?31655)) ?31657) (divide ?31657 ?31658)) =>= inverse (multiply ?31656 (divide (divide (inverse ?31654) ?31653) ?31658)) [31658, 31657, 31654, 31653, 31655, 31656] by Demod 25940 with 26405 at 1,1,1,2
+Id : 26874, {_}: inverse (multiply (divide (divide (multiply ?31656 ?31655) (multiply (multiply ?31653 ?31654) ?31655)) ?31657) (divide ?31657 ?31658)) =>= inverse (multiply ?31656 (divide (inverse (multiply ?31653 ?31654)) ?31658)) [31658, 31657, 31654, 31653, 31655, 31656] by Demod 26656 with 26764 at 1,2,1,3
+Id : 26875, {_}: inverse (multiply (divide (divide (multiply ?31656 ?31655) (multiply (multiply ?31653 ?31654) ?31655)) ?31657) (divide ?31657 ?31658)) =>= inverse (multiply ?31656 (inverse (multiply ?31658 (multiply ?31653 ?31654)))) [31658, 31657, 31654, 31653, 31655, 31656] by Demod 26874 with 26764 at 2,1,3
+Id : 11, {_}: divide (inverse (divide (divide (multiply ?48 ?49) ?50) (divide ?51 ?50))) (divide (inverse ?49) ?48) =>= ?51 [51, 50, 49, 48] by Super 2 with 3 at 1,1,1,1,2
+Id : 5813, {_}: inverse (divide (divide ?31391 ?31392) (divide (inverse (divide (divide (multiply ?31393 ?31394) ?31395) (divide ?31396 ?31395))) ?31392)) =>= inverse (divide (divide ?31391 (divide (inverse ?31394) ?31393)) ?31396) [31396, 31395, 31394, 31393, 31392, 31391] by Super 5809 with 11 at 2,1,3
+Id : 26012, {_}: inverse (multiply (divide ?31391 ?31392) (divide ?31392 (inverse (divide (divide (multiply ?31393 ?31394) ?31395) (divide ?31396 ?31395))))) =>= inverse (divide (divide ?31391 (divide (inverse ?31394) ?31393)) ?31396) [31396, 31395, 31394, 31393, 31392, 31391] by Demod 5813 with 25599 at 1,2
+Id : 26013, {_}: inverse (multiply (divide ?31391 ?31392) (divide ?31392 (inverse (divide (divide (multiply ?31393 ?31394) ?31395) (divide ?31396 ?31395))))) =>= inverse (divide (multiply ?31391 (divide ?31393 (inverse ?31394))) ?31396) [31396, 31395, 31394, 31393, 31392, 31391] by Demod 26012 with 25599 at 1,1,3
+Id : 26014, {_}: inverse (multiply (divide ?31391 ?31392) (divide ?31392 (inverse (multiply (divide (multiply ?31393 ?31394) ?31395) (divide ?31395 ?31396))))) =>= inverse (divide (multiply ?31391 (divide ?31393 (inverse ?31394))) ?31396) [31396, 31395, 31394, 31393, 31392, 31391] by Demod 26013 with 25599 at 1,2,2,1,2
+Id : 26060, {_}: inverse (multiply (divide ?31391 ?31392) (multiply ?31392 (multiply (divide (multiply ?31393 ?31394) ?31395) (divide ?31395 ?31396)))) =>= inverse (divide (multiply ?31391 (divide ?31393 (inverse ?31394))) ?31396) [31396, 31395, 31394, 31393, 31392, 31391] by Demod 26014 with 3 at 2,1,2
+Id : 26061, {_}: inverse (multiply (divide ?31391 ?31392) (multiply ?31392 (multiply (divide (multiply ?31393 ?31394) ?31395) (divide ?31395 ?31396)))) =>= inverse (divide (multiply ?31391 (multiply ?31393 ?31394)) ?31396) [31396, 31395, 31394, 31393, 31392, 31391] by Demod 26060 with 3 at 2,1,1,3
+Id : 26649, {_}: inverse (multiply (divide ?31391 ?31392) (multiply ?31392 (multiply (divide (multiply ?31393 ?31394) ?31395) (divide ?31395 ?31396)))) =>= divide ?31396 (multiply ?31391 (multiply ?31393 ?31394)) [31396, 31395, 31394, 31393, 31392, 31391] by Demod 26061 with 26405 at 3
+Id : 5837, {_}: inverse (divide (divide (inverse (divide (divide (multiply ?31579 ?31580) ?31581) (divide ?31582 ?31581))) ?31583) (divide ?31584 ?31583)) =>= inverse (divide ?31582 (divide ?31584 (divide (inverse ?31580) ?31579))) [31584, 31583, 31582, 31581, 31580, 31579] by Super 5809 with 11 at 1,1,3
+Id : 26017, {_}: inverse (multiply (divide (inverse (divide (divide (multiply ?31579 ?31580) ?31581) (divide ?31582 ?31581))) ?31583) (divide ?31583 ?31584)) =>= inverse (divide ?31582 (divide ?31584 (divide (inverse ?31580) ?31579))) [31584, 31583, 31582, 31581, 31580, 31579] by Demod 5837 with 25599 at 1,2
+Id : 26018, {_}: inverse (multiply (divide (inverse (divide (divide (multiply ?31579 ?31580) ?31581) (divide ?31582 ?31581))) ?31583) (divide ?31583 ?31584)) =>= inverse (multiply ?31582 (divide (divide (inverse ?31580) ?31579) ?31584)) [31584, 31583, 31582, 31581, 31580, 31579] by Demod 26017 with 25599 at 1,3
+Id : 26019, {_}: inverse (multiply (divide (inverse (multiply (divide (multiply ?31579 ?31580) ?31581) (divide ?31581 ?31582))) ?31583) (divide ?31583 ?31584)) =>= inverse (multiply ?31582 (divide (divide (inverse ?31580) ?31579) ?31584)) [31584, 31583, 31582, 31581, 31580, 31579] by Demod 26018 with 25599 at 1,1,1,1,2
+Id : 26844, {_}: inverse (multiply (inverse (multiply ?31583 (multiply (divide (multiply ?31579 ?31580) ?31581) (divide ?31581 ?31582)))) (divide ?31583 ?31584)) =>= inverse (multiply ?31582 (divide (divide (inverse ?31580) ?31579) ?31584)) [31584, 31582, 31581, 31580, 31579, 31583] by Demod 26019 with 26764 at 1,1,2
+Id : 26845, {_}: inverse (multiply (inverse (multiply ?31583 (multiply (divide (multiply ?31579 ?31580) ?31581) (divide ?31581 ?31582)))) (divide ?31583 ?31584)) =>= inverse (multiply ?31582 (divide (inverse (multiply ?31579 ?31580)) ?31584)) [31584, 31582, 31581, 31580, 31579, 31583] by Demod 26844 with 26764 at 1,2,1,3
+Id : 26846, {_}: inverse (multiply (inverse (multiply ?31583 (multiply (divide (multiply ?31579 ?31580) ?31581) (divide ?31581 ?31582)))) (divide ?31583 ?31584)) =>= inverse (multiply ?31582 (inverse (multiply ?31584 (multiply ?31579 ?31580)))) [31584, 31582, 31581, 31580, 31579, 31583] by Demod 26845 with 26764 at 2,1,3
+Id : 27296, {_}: multiply (inverse (divide ?31583 ?31584)) (multiply ?31583 (multiply (divide (multiply ?31579 ?31580) ?31581) (divide ?31581 ?31582))) =>= inverse (multiply ?31582 (inverse (multiply ?31584 (multiply ?31579 ?31580)))) [31582, 31581, 31580, 31579, 31584, 31583] by Demod 26846 with 26966 at 2
+Id : 27301, {_}: multiply (divide ?31584 ?31583) (multiply ?31583 (multiply (divide (multiply ?31579 ?31580) ?31581) (divide ?31581 ?31582))) =>= inverse (multiply ?31582 (inverse (multiply ?31584 (multiply ?31579 ?31580)))) [31582, 31581, 31580, 31579, 31583, 31584] by Demod 27296 with 26405 at 1,2
+Id : 27302, {_}: inverse (inverse (multiply ?31396 (inverse (multiply ?31391 (multiply ?31393 ?31394))))) =>= divide ?31396 (multiply ?31391 (multiply ?31393 ?31394)) [31394, 31393, 31391, 31396] by Demod 26649 with 27301 at 1,2
+Id : 27505, {_}: multiply ?31396 (inverse (multiply ?31391 (multiply ?31393 ?31394))) =>= divide ?31396 (multiply ?31391 (multiply ?31393 ?31394)) [31394, 31393, 31391, 31396] by Demod 27302 with 27254 at 2
+Id : 27520, {_}: inverse (multiply (divide (divide (multiply ?31656 ?31655) (multiply (multiply ?31653 ?31654) ?31655)) ?31657) (divide ?31657 ?31658)) =>= inverse (divide ?31656 (multiply ?31658 (multiply ?31653 ?31654))) [31658, 31657, 31654, 31653, 31655, 31656] by Demod 26875 with 27505 at 1,3
+Id : 27523, {_}: inverse (multiply (divide (divide (multiply ?31656 ?31655) (multiply (multiply ?31653 ?31654) ?31655)) ?31657) (divide ?31657 ?31658)) =>= divide (multiply ?31658 (multiply ?31653 ?31654)) ?31656 [31658, 31657, 31654, 31653, 31655, 31656] by Demod 27520 with 26405 at 3
+Id : 28682, {_}: divide (divide ?31658 ?31657) (divide (divide (multiply ?31656 ?31655) (multiply (multiply ?31653 ?31654) ?31655)) ?31657) =>= divide (multiply ?31658 (multiply ?31653 ?31654)) ?31656 [31654, 31653, 31655, 31656, 31657, 31658] by Demod 27523 with 26724 at 2
+Id : 28683, {_}: multiply (divide ?31658 ?31657) (divide ?31657 (divide (multiply ?31656 ?31655) (multiply (multiply ?31653 ?31654) ?31655))) =>= divide (multiply ?31658 (multiply ?31653 ?31654)) ?31656 [31654, 31653, 31655, 31656, 31657, 31658] by Demod 28682 with 25599 at 2
+Id : 28684, {_}: multiply (divide ?31658 ?31657) (multiply ?31657 (divide (multiply (multiply ?31653 ?31654) ?31655) (multiply ?31656 ?31655))) =>= divide (multiply ?31658 (multiply ?31653 ?31654)) ?31656 [31656, 31655, 31654, 31653, 31657, 31658] by Demod 28683 with 25599 at 2,2
+Id : 43520, {_}: multiply (divide ?31658 ?31657) (multiply ?31657 (multiply (multiply ?31653 ?31654) (divide ?31655 (multiply ?31656 ?31655)))) =>= divide (multiply ?31658 (multiply ?31653 ?31654)) ?31656 [31656, 31655, 31654, 31653, 31657, 31658] by Demod 28684 with 43287 at 2,2,2
+Id : 43521, {_}: multiply (divide ?31658 ?31657) (multiply ?31657 (multiply (multiply ?31653 ?31654) (divide ?31655 (multiply ?31656 ?31655)))) =>= multiply ?31658 (divide (multiply ?31653 ?31654) ?31656) [31656, 31655, 31654, 31653, 31657, 31658] by Demod 43520 with 43287 at 3
+Id : 43522, {_}: multiply (divide ?31658 ?31657) (multiply ?31657 (multiply (multiply ?31653 ?31654) (divide ?31655 (multiply ?31656 ?31655)))) =>= multiply ?31658 (multiply ?31653 (divide ?31654 ?31656)) [31656, 31655, 31654, 31653, 31657, 31658] by Demod 43521 with 43287 at 2,3
+Id : 22472, {_}: ?116246 =<= multiply (multiply ?116246 (multiply ?116247 ?116248)) (divide (inverse ?116248) ?116247) [116248, 116247, 116246] by Super 22416 with 3 at 2,1,3
+Id : 26848, {_}: ?116246 =<= multiply (multiply ?116246 (multiply ?116247 ?116248)) (inverse (multiply ?116247 ?116248)) [116248, 116247, 116246] by Demod 22472 with 26764 at 2,3
+Id : 27823, {_}: ?116246 =<= divide (multiply ?116246 (multiply ?116247 ?116248)) (multiply ?116247 ?116248) [116248, 116247, 116246] by Demod 26848 with 27734 at 3
+Id : 31832, {_}: ?147291 =<= divide (multiply ?147291 (multiply (multiply (divide ?147292 ?147293) (multiply ?147293 (multiply (multiply ?147294 (multiply (divide ?147295 ?147296) (divide ?147297 ?147298))) (divide ?147298 ?147297)))) (multiply (divide (divide ?147296 ?147295) ?147299) (divide ?147299 ?147294)))) ?147292 [147299, 147298, 147297, 147296, 147295, 147294, 147293, 147292, 147291] by Super 27823 with 31744 at 2,3
+Id : 32203, {_}: ?147291 =<= divide (multiply ?147291 ?147292) ?147292 [147292, 147291] by Demod 31832 with 31744 at 2,1,3
+Id : 33094, {_}: inverse ?153200 =<= divide ?153201 (multiply ?153200 ?153201) [153201, 153200] by Super 26405 with 32203 at 1,2
+Id : 43571, {_}: multiply (divide ?31658 ?31657) (multiply ?31657 (multiply (multiply ?31653 ?31654) (inverse ?31656))) =>= multiply ?31658 (multiply ?31653 (divide ?31654 ?31656)) [31656, 31654, 31653, 31657, 31658] by Demod 43522 with 33094 at 2,2,2,2
+Id : 43572, {_}: multiply (divide ?31658 ?31657) (multiply ?31657 (divide (multiply ?31653 ?31654) ?31656)) =>= multiply ?31658 (multiply ?31653 (divide ?31654 ?31656)) [31656, 31654, 31653, 31657, 31658] by Demod 43571 with 27734 at 2,2,2
+Id : 43573, {_}: multiply (divide ?31658 ?31657) (multiply ?31657 (multiply ?31653 (divide ?31654 ?31656))) =>= multiply ?31658 (multiply ?31653 (divide ?31654 ?31656)) [31656, 31654, 31653, 31657, 31658] by Demod 43572 with 43287 at 2,2,2
+Id : 43575, {_}: multiply ?31561 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559)) =>= multiply ?31561 (divide (divide ?31556 ?31557) ?31559) [31559, 31558, 31557, 31556, 31561] by Demod 42552 with 43573 at 2
+Id : 43578, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =?= multiply (divide ?83 ?87) (divide ?87 (multiply (divide ?84 ?85) (divide (divide ?85 ?84) ?82))) [85, 84, 87, 80, 81, 82, 83] by Demod 28715 with 43575 at 2,2,3
+Id : 43604, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =?= multiply (divide ?83 ?87) (multiply ?87 (divide (divide ?82 (divide ?85 ?84)) (divide ?84 ?85))) [84, 85, 87, 80, 81, 82, 83] by Demod 43578 with 27506 at 2,3
+Id : 243, {_}: inverse (divide (multiply (divide ?1104 ?1105) ?1106) (multiply (divide ?1107 (divide ?1105 ?1104)) ?1106)) =>= ?1107 [1107, 1106, 1105, 1104] by Demod 213 with 3 at 1,1,2
+Id : 748, {_}: inverse (divide (multiply (divide (inverse ?3864) ?3865) ?3866) (multiply (divide ?3867 (multiply ?3865 ?3864)) ?3866)) =>= ?3867 [3867, 3866, 3865, 3864] by Super 243 with 3 at 2,1,2,1,2
+Id : 753, {_}: inverse (divide (multiply (divide (inverse (divide (divide (divide ?3899 ?3900) ?3901) (divide ?3902 ?3901))) (divide ?3900 ?3899)) ?3903) (multiply ?3904 ?3903)) =?= inverse (divide (divide ?3902 ?3905) (divide ?3904 ?3905)) [3905, 3904, 3903, 3902, 3901, 3900, 3899] by Super 748 with 272 at 1,2,1,2
+Id : 773, {_}: inverse (divide (multiply ?3902 ?3903) (multiply ?3904 ?3903)) =?= inverse (divide (divide ?3902 ?3905) (divide ?3904 ?3905)) [3905, 3904, 3903, 3902] by Demod 753 with 2 at 1,1,1,2
+Id : 15665, {_}: inverse (divide (multiply (divide ?84988 (divide ?84989 ?84990)) ?84991) (multiply (divide ?84992 ?84993) ?84991)) =>= divide (divide (inverse (divide ?84993 ?84992)) (divide ?84990 ?84989)) ?84988 [84993, 84992, 84991, 84990, 84989, 84988] by Super 773 with 14284 at 3
+Id : 15692, {_}: inverse (divide (multiply (divide ?85261 (divide ?85262 ?85263)) ?85264) (multiply (multiply ?85265 ?85266) ?85264)) =>= divide (divide (inverse (divide (inverse ?85266) ?85265)) (divide ?85263 ?85262)) ?85261 [85266, 85265, 85264, 85263, 85262, 85261] by Super 15665 with 3 at 1,2,1,2
+Id : 25923, {_}: inverse (divide (multiply (multiply ?85261 (divide ?85263 ?85262)) ?85264) (multiply (multiply ?85265 ?85266) ?85264)) =>= divide (divide (inverse (divide (inverse ?85266) ?85265)) (divide ?85263 ?85262)) ?85261 [85266, 85265, 85264, 85262, 85263, 85261] by Demod 15692 with 25599 at 1,1,1,2
+Id : 25924, {_}: inverse (divide (multiply (multiply ?85261 (divide ?85263 ?85262)) ?85264) (multiply (multiply ?85265 ?85266) ?85264)) =>= divide (multiply (inverse (divide (inverse ?85266) ?85265)) (divide ?85262 ?85263)) ?85261 [85266, 85265, 85264, 85262, 85263, 85261] by Demod 25923 with 25599 at 1,3
+Id : 26606, {_}: divide (multiply (multiply ?85265 ?85266) ?85264) (multiply (multiply ?85261 (divide ?85263 ?85262)) ?85264) =>= divide (multiply (inverse (divide (inverse ?85266) ?85265)) (divide ?85262 ?85263)) ?85261 [85262, 85263, 85261, 85264, 85266, 85265] by Demod 25924 with 26405 at 2
+Id : 26607, {_}: divide (multiply (multiply ?85265 ?85266) ?85264) (multiply (multiply ?85261 (divide ?85263 ?85262)) ?85264) =>= divide (multiply (divide ?85265 (inverse ?85266)) (divide ?85262 ?85263)) ?85261 [85262, 85263, 85261, 85264, 85266, 85265] by Demod 26606 with 26405 at 1,1,3
+Id : 26682, {_}: divide (multiply (multiply ?85265 ?85266) ?85264) (multiply (multiply ?85261 (divide ?85263 ?85262)) ?85264) =>= divide (multiply (multiply ?85265 ?85266) (divide ?85262 ?85263)) ?85261 [85262, 85263, 85261, 85264, 85266, 85265] by Demod 26607 with 3 at 1,1,3
+Id : 42547, {_}: divide (multiply (multiply ?85265 ?85266) ?85264) (multiply (multiply ?85261 (divide ?85263 ?85262)) ?85264) =>= multiply (multiply ?85265 ?85266) (divide (divide ?85262 ?85263) ?85261) [85262, 85263, 85261, 85264, 85266, 85265] by Demod 26682 with 32902 at 3
+Id : 43537, {_}: multiply (multiply ?85265 ?85266) (divide ?85264 (multiply (multiply ?85261 (divide ?85263 ?85262)) ?85264)) =>= multiply (multiply ?85265 ?85266) (divide (divide ?85262 ?85263) ?85261) [85262, 85263, 85261, 85264, 85266, 85265] by Demod 42547 with 43287 at 2
+Id : 43538, {_}: multiply (multiply ?85265 ?85266) (inverse (multiply ?85261 (divide ?85263 ?85262))) =>= multiply (multiply ?85265 ?85266) (divide (divide ?85262 ?85263) ?85261) [85262, 85263, 85261, 85266, 85265] by Demod 43537 with 33094 at 2,2
+Id : 43539, {_}: divide (multiply ?85265 ?85266) (multiply ?85261 (divide ?85263 ?85262)) =>= multiply (multiply ?85265 ?85266) (divide (divide ?85262 ?85263) ?85261) [85262, 85263, 85261, 85266, 85265] by Demod 43538 with 27734 at 2
+Id : 43540, {_}: multiply ?85265 (divide ?85266 (multiply ?85261 (divide ?85263 ?85262))) =?= multiply (multiply ?85265 ?85266) (divide (divide ?85262 ?85263) ?85261) [85262, 85263, 85261, 85266, 85265] by Demod 43539 with 43287 at 2
+Id : 43541, {_}: multiply ?85265 (multiply ?85266 (divide (divide ?85262 ?85263) ?85261)) =?= multiply (multiply ?85265 ?85266) (divide (divide ?85262 ?85263) ?85261) [85261, 85263, 85262, 85266, 85265] by Demod 43540 with 27506 at 2,2
+Id : 43605, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =?= multiply (multiply (divide ?83 ?87) ?87) (divide (divide ?82 (divide ?85 ?84)) (divide ?84 ?85)) [84, 85, 87, 80, 81, 82, 83] by Demod 43604 with 43541 at 3
+Id : 43606, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =?= multiply ?83 (divide (divide ?82 (divide ?85 ?84)) (divide ?84 ?85)) [84, 85, 80, 81, 82, 83] by Demod 43605 with 32201 at 1,3
+Id : 43607, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =?= multiply ?83 (multiply (divide ?82 (divide ?85 ?84)) (divide ?85 ?84)) [84, 85, 80, 81, 82, 83] by Demod 43606 with 25599 at 2,3
+Id : 43608, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =>= multiply ?83 ?82 [80, 81, 82, 83] by Demod 43607 with 32201 at 2,3
+Id : 45322, {_}: multiply (multiply ?177731 (multiply ?177732 (divide ?177733 ?177734))) ?177734 =>= multiply (multiply ?177731 ?177732) ?177733 [177734, 177733, 177732, 177731] by Super 45294 with 43608 at 1,3
+Id : 45299, {_}: multiply ?177614 (multiply ?177615 ?177616) =<= multiply (multiply ?177614 (multiply ?177615 (divide ?177616 ?177617))) ?177617 [177617, 177616, 177615, 177614] by Super 45294 with 43287 at 2,1,3
+Id : 64505, {_}: multiply ?177731 (multiply ?177732 ?177733) =?= multiply (multiply ?177731 ?177732) ?177733 [177733, 177732, 177731] by Demod 45322 with 45299 at 2
+Id : 64928, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 1 with 64505 at 2
+Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
+% SZS output end CNFRefutation for GRP477-1.p
+23952: solved GRP477-1.p in 16.221013 using nrkbo
+23952: status Unsatisfiable for GRP477-1.p
+NO CLASH, using fixed ground order
+23966: Facts:
+23966: Id : 2, {_}:
+ divide
+ (inverse
+ (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
+ ?5
+ =>=
+ ?4
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23966: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+23966: Goal:
+23966: Id : 1, {_}:
+ multiply (inverse a1) a1 =<= multiply (inverse b1) b1
+ [] by prove_these_axioms_1
+23966: Order:
+23966: nrkbo
+23966: Leaf order:
+23966: a1 2 0 2 1,1,2
+23966: b1 2 0 2 1,1,3
+23966: inverse 4 1 2 0,1,2
+23966: multiply 3 2 2 0,2
+23966: divide 7 2 0
+NO CLASH, using fixed ground order
+23967: Facts:
+23967: Id : 2, {_}:
+ divide
+ (inverse
+ (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
+ ?5
+ =>=
+ ?4
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23967: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+23967: Goal:
+23967: Id : 1, {_}:
+ multiply (inverse a1) a1 =<= multiply (inverse b1) b1
+ [] by prove_these_axioms_1
+23967: Order:
+23967: kbo
+23967: Leaf order:
+23967: a1 2 0 2 1,1,2
+23967: b1 2 0 2 1,1,3
+23967: inverse 4 1 2 0,1,2
+23967: multiply 3 2 2 0,2
+23967: divide 7 2 0
+NO CLASH, using fixed ground order
+23968: Facts:
+23968: Id : 2, {_}:
+ divide
+ (inverse
+ (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
+ ?5
+ =>=
+ ?4
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23968: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+23968: Goal:
+23968: Id : 1, {_}:
+ multiply (inverse a1) a1 =<= multiply (inverse b1) b1
+ [] by prove_these_axioms_1
+23968: Order:
+23968: lpo
+23968: Leaf order:
+23968: a1 2 0 2 1,1,2
+23968: b1 2 0 2 1,1,3
+23968: inverse 4 1 2 0,1,2
+23968: multiply 3 2 2 0,2
+23968: divide 7 2 0
+% SZS status Timeout for GRP478-1.p
+NO CLASH, using fixed ground order
+23995: Facts:
+23995: Id : 2, {_}:
+ divide
+ (inverse
+ (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
+ ?5
+ =>=
+ ?4
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23995: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+23995: Goal:
+23995: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+23995: Order:
+23995: nrkbo
+23995: Leaf order:
+23995: b2 2 0 2 1,1,1,2
+23995: a2 2 0 2 2,2
+23995: inverse 3 1 1 0,1,1,2
+23995: multiply 3 2 2 0,2
+23995: divide 7 2 0
+NO CLASH, using fixed ground order
+23996: Facts:
+23996: Id : 2, {_}:
+ divide
+ (inverse
+ (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
+ ?5
+ =>=
+ ?4
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23996: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+23996: Goal:
+23996: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+23996: Order:
+23996: kbo
+23996: Leaf order:
+23996: b2 2 0 2 1,1,1,2
+23996: a2 2 0 2 2,2
+23996: inverse 3 1 1 0,1,1,2
+23996: multiply 3 2 2 0,2
+23996: divide 7 2 0
+NO CLASH, using fixed ground order
+23997: Facts:
+23997: Id : 2, {_}:
+ divide
+ (inverse
+ (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
+ ?5
+ =>=
+ ?4
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+23997: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+23997: Goal:
+23997: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+23997: Order:
+23997: lpo
+23997: Leaf order:
+23997: b2 2 0 2 1,1,1,2
+23997: a2 2 0 2 2,2
+23997: inverse 3 1 1 0,1,1,2
+23997: multiply 3 2 2 0,2
+23997: divide 7 2 0
+Statistics :
+Max weight : 78
+Found proof, 37.151334s
+% SZS status Unsatisfiable for GRP479-1.p
+% SZS output start CNFRefutation for GRP479-1.p
+Id : 2, {_}: divide (inverse (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) ?5 =>= ?4 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+Id : 4, {_}: divide (inverse (divide (divide (divide ?10 ?10) ?11) (divide ?12 (divide ?11 ?13)))) ?13 =>= ?12 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
+Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
+Id : 5, {_}: divide (inverse (divide (divide (divide ?15 ?15) (inverse (divide (divide (divide ?16 ?16) ?17) (divide ?18 (divide ?17 ?19))))) (divide ?20 ?18))) ?19 =>= ?20 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 2,2,1,1,2
+Id : 22, {_}: divide (inverse (divide (multiply (divide ?87 ?87) (divide (divide (divide ?88 ?88) ?89) (divide ?90 (divide ?89 ?91)))) (divide ?92 ?90))) ?91 =>= ?92 [92, 91, 90, 89, 88, 87] by Demod 5 with 3 at 1,1,1,2
+Id : 18, {_}: divide (inverse (divide (multiply (divide ?15 ?15) (divide (divide (divide ?16 ?16) ?17) (divide ?18 (divide ?17 ?19)))) (divide ?20 ?18))) ?19 =>= ?20 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 1,1,1,2
+Id : 30, {_}: divide (inverse (divide (multiply (divide ?157 ?157) (divide (divide (divide ?158 ?158) ?159) ?160)) (divide ?161 (inverse (divide (multiply (divide ?162 ?162) (divide (divide (divide ?163 ?163) ?164) (divide ?165 (divide ?164 (divide ?159 ?166))))) (divide ?160 ?165)))))) ?166 =>= ?161 [166, 165, 164, 163, 162, 161, 160, 159, 158, 157] by Super 22 with 18 at 2,2,1,1,1,2
+Id : 42, {_}: divide (inverse (divide (multiply (divide ?157 ?157) (divide (divide (divide ?158 ?158) ?159) ?160)) (multiply ?161 (divide (multiply (divide ?162 ?162) (divide (divide (divide ?163 ?163) ?164) (divide ?165 (divide ?164 (divide ?159 ?166))))) (divide ?160 ?165))))) ?166 =>= ?161 [166, 165, 164, 163, 162, 161, 160, 159, 158, 157] by Demod 30 with 3 at 2,1,1,2
+Id : 6, {_}: divide (inverse (divide (divide (divide ?22 ?22) ?23) ?24)) ?25 =?= inverse (divide (divide (divide ?26 ?26) ?27) (divide ?24 (divide ?27 (divide ?23 ?25)))) [27, 26, 25, 24, 23, 22] by Super 4 with 2 at 2,1,1,2
+Id : 202, {_}: divide (divide (inverse (divide (divide (divide ?974 ?974) ?975) ?976)) ?977) (divide ?975 ?977) =>= ?976 [977, 976, 975, 974] by Super 2 with 6 at 1,2
+Id : 208, {_}: divide (divide (inverse (divide (divide (divide ?1018 ?1018) ?1019) ?1020)) (inverse ?1021)) (multiply ?1019 ?1021) =>= ?1020 [1021, 1020, 1019, 1018] by Super 202 with 3 at 2,2
+Id : 372, {_}: divide (multiply (inverse (divide (divide (divide ?1664 ?1664) ?1665) ?1666)) ?1667) (multiply ?1665 ?1667) =>= ?1666 [1667, 1666, 1665, 1664] by Demod 208 with 3 at 1,2
+Id : 378, {_}: divide (multiply (inverse (divide (multiply (divide ?1702 ?1702) ?1703) ?1704)) ?1705) (multiply (inverse ?1703) ?1705) =>= ?1704 [1705, 1704, 1703, 1702] by Super 372 with 3 at 1,1,1,1,2
+Id : 8, {_}: divide (inverse (divide (divide (divide ?31 ?31) ?32) (divide ?33 (multiply ?32 ?34)))) (inverse ?34) =>= ?33 [34, 33, 32, 31] by Super 2 with 3 at 2,2,1,1,2
+Id : 15, {_}: multiply (inverse (divide (divide (divide ?31 ?31) ?32) (divide ?33 (multiply ?32 ?34)))) ?34 =>= ?33 [34, 33, 32, 31] by Demod 8 with 3 at 2
+Id : 86, {_}: divide (divide (inverse (divide (divide (divide ?404 ?404) ?405) ?406)) ?407) (divide ?405 ?407) =>= ?406 [407, 406, 405, 404] by Super 2 with 6 at 1,2
+Id : 193, {_}: multiply (inverse (divide ?902 (divide ?903 (multiply (divide ?904 (inverse (divide (divide (divide ?905 ?905) ?904) ?902))) ?906)))) ?906 =>= ?903 [906, 905, 904, 903, 902] by Super 15 with 86 at 1,1,1,2
+Id : 223, {_}: multiply (inverse (divide ?902 (divide ?903 (multiply (multiply ?904 (divide (divide (divide ?905 ?905) ?904) ?902)) ?906)))) ?906 =>= ?903 [906, 905, 904, 903, 902] by Demod 193 with 3 at 1,2,2,1,1,2
+Id : 88082, {_}: divide ?485240 (multiply (inverse ?485241) ?485242) =<= divide ?485240 (multiply (multiply ?485243 (divide (divide (divide ?485244 ?485244) ?485243) (multiply (divide ?485245 ?485245) ?485241))) ?485242) [485245, 485244, 485243, 485242, 485241, 485240] by Super 378 with 223 at 1,2
+Id : 89234, {_}: divide (inverse (divide (multiply (divide ?494319 ?494319) (divide (divide (divide ?494320 ?494320) ?494321) ?494322)) (multiply (inverse ?494323) (divide (multiply (divide ?494324 ?494324) (divide (divide (divide ?494325 ?494325) ?494326) (divide ?494327 (divide ?494326 (divide ?494321 ?494328))))) (divide ?494322 ?494327))))) ?494328 =?= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (multiply (divide ?494331 ?494331) ?494323)) [494331, 494330, 494329, 494328, 494327, 494326, 494325, 494324, 494323, 494322, 494321, 494320, 494319] by Super 42 with 88082 at 1,1,2
+Id : 89554, {_}: inverse ?494323 =<= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (multiply (divide ?494331 ?494331) ?494323)) [494331, 494330, 494329, 494323] by Demod 89234 with 42 at 2
+Id : 23, {_}: divide (inverse (divide (multiply (divide ?94 ?94) (divide (divide (divide ?95 ?95) ?96) (divide ?97 (divide ?96 ?98)))) ?99)) ?98 =?= inverse (divide (divide (divide ?100 ?100) ?101) (divide ?99 (divide ?101 ?97))) [101, 100, 99, 98, 97, 96, 95, 94] by Super 22 with 2 at 2,1,1,2
+Id : 1304, {_}: inverse (divide (divide (divide ?6515 ?6515) ?6516) (divide (divide ?6517 ?6518) (divide ?6516 ?6518))) =>= ?6517 [6518, 6517, 6516, 6515] by Super 18 with 23 at 2
+Id : 2998, {_}: inverse (divide (divide (multiply (inverse ?16319) ?16319) ?16320) (divide (divide ?16321 ?16322) (divide ?16320 ?16322))) =>= ?16321 [16322, 16321, 16320, 16319] by Super 1304 with 3 at 1,1,1,2
+Id : 3072, {_}: inverse (divide (multiply (multiply (inverse ?16865) ?16865) ?16866) (divide (divide ?16867 ?16868) (divide (inverse ?16866) ?16868))) =>= ?16867 [16868, 16867, 16866, 16865] by Super 2998 with 3 at 1,1,2
+Id : 1319, {_}: inverse (divide (divide (divide ?6630 ?6630) ?6631) (divide (divide ?6632 (inverse ?6633)) (multiply ?6631 ?6633))) =>= ?6632 [6633, 6632, 6631, 6630] by Super 1304 with 3 at 2,2,1,2
+Id : 1369, {_}: inverse (divide (divide (divide ?6630 ?6630) ?6631) (divide (multiply ?6632 ?6633) (multiply ?6631 ?6633))) =>= ?6632 [6633, 6632, 6631, 6630] by Demod 1319 with 3 at 1,2,1,2
+Id : 1389, {_}: multiply ?6881 (divide (divide (divide ?6882 ?6882) ?6883) (divide (multiply ?6884 ?6885) (multiply ?6883 ?6885))) =>= divide ?6881 ?6884 [6885, 6884, 6883, 6882, 6881] by Super 3 with 1369 at 2,3
+Id : 90512, {_}: multiply (inverse (divide ?497368 (divide ?497369 (inverse ?497370)))) (divide (divide (divide ?497371 ?497371) (multiply ?497372 (divide (divide (divide ?497373 ?497373) ?497372) ?497368))) (multiply (divide ?497374 ?497374) ?497370)) =>= ?497369 [497374, 497373, 497372, 497371, 497370, 497369, 497368] by Super 223 with 89554 at 2,2,1,1,2
+Id : 196, {_}: divide (inverse (divide (divide (divide ?925 ?925) ?926) (divide (inverse (divide (divide (divide ?927 ?927) ?928) ?929)) (divide ?926 ?930)))) ?930 =?= inverse (divide (divide (divide ?931 ?931) ?928) ?929) [931, 930, 929, 928, 927, 926, 925] by Super 6 with 86 at 2,1,3
+Id : 6409, {_}: inverse (divide (divide (divide ?34204 ?34204) ?34205) ?34206) =?= inverse (divide (divide (divide ?34207 ?34207) ?34205) ?34206) [34207, 34206, 34205, 34204] by Demod 196 with 2 at 2
+Id : 6420, {_}: inverse (divide (divide (divide ?34278 ?34278) (divide ?34279 (inverse (divide (divide (divide ?34280 ?34280) ?34279) ?34281)))) ?34282) =>= inverse (divide ?34281 ?34282) [34282, 34281, 34280, 34279, 34278] by Super 6409 with 86 at 1,1,3
+Id : 6497, {_}: inverse (divide (divide (divide ?34278 ?34278) (multiply ?34279 (divide (divide (divide ?34280 ?34280) ?34279) ?34281))) ?34282) =>= inverse (divide ?34281 ?34282) [34282, 34281, 34280, 34279, 34278] by Demod 6420 with 3 at 2,1,1,2
+Id : 28325, {_}: multiply ?153090 (divide (divide (divide ?153091 ?153091) (multiply ?153092 (divide (divide (divide ?153093 ?153093) ?153092) ?153094))) ?153095) =>= divide ?153090 (inverse (divide ?153094 ?153095)) [153095, 153094, 153093, 153092, 153091, 153090] by Super 3 with 6497 at 2,3
+Id : 28522, {_}: multiply ?153090 (divide (divide (divide ?153091 ?153091) (multiply ?153092 (divide (divide (divide ?153093 ?153093) ?153092) ?153094))) ?153095) =>= multiply ?153090 (divide ?153094 ?153095) [153095, 153094, 153093, 153092, 153091, 153090] by Demod 28325 with 3 at 3
+Id : 91190, {_}: multiply (inverse (divide ?497368 (divide ?497369 (inverse ?497370)))) (divide ?497368 (multiply (divide ?497374 ?497374) ?497370)) =>= ?497369 [497374, 497370, 497369, 497368] by Demod 90512 with 28522 at 2
+Id : 91665, {_}: multiply (inverse (divide ?503116 (multiply ?503117 ?503118))) (divide ?503116 (multiply (divide ?503119 ?503119) ?503118)) =>= ?503117 [503119, 503118, 503117, 503116] by Demod 91190 with 3 at 2,1,1,2
+Id : 231, {_}: divide (multiply (inverse (divide (divide (divide ?1018 ?1018) ?1019) ?1020)) ?1021) (multiply ?1019 ?1021) =>= ?1020 [1021, 1020, 1019, 1018] by Demod 208 with 3 at 1,2
+Id : 1057, {_}: inverse (divide (divide (divide ?5280 ?5280) ?5281) (divide (divide ?5282 ?5283) (divide ?5281 ?5283))) =>= ?5282 [5283, 5282, 5281, 5280] by Super 18 with 23 at 2
+Id : 1292, {_}: divide (divide ?6440 ?6441) (divide ?6442 ?6441) =?= divide (divide ?6440 ?6443) (divide ?6442 ?6443) [6443, 6442, 6441, 6440] by Super 86 with 1057 at 1,1,2
+Id : 2334, {_}: divide (multiply (inverse (divide (divide (divide ?12626 ?12626) ?12627) (divide ?12628 ?12627))) ?12629) (multiply ?12630 ?12629) =>= divide ?12628 ?12630 [12630, 12629, 12628, 12627, 12626] by Super 231 with 1292 at 1,1,1,2
+Id : 91784, {_}: multiply (inverse (divide (multiply (inverse (divide (divide (divide ?504066 ?504066) ?504067) (divide ?504068 ?504067))) ?504069) (multiply ?504070 ?504069))) (divide ?504068 (divide ?504071 ?504071)) =>= ?504070 [504071, 504070, 504069, 504068, 504067, 504066] by Super 91665 with 2334 at 2,2
+Id : 92186, {_}: multiply (inverse (divide ?504068 ?504070)) (divide ?504068 (divide ?504071 ?504071)) =>= ?504070 [504071, 504070, 504068] by Demod 91784 with 2334 at 1,1,2
+Id : 92346, {_}: ?505751 =<= divide (inverse (divide (divide (divide ?505752 ?505752) ?505753) ?505751)) ?505753 [505753, 505752, 505751] by Super 1389 with 92186 at 2
+Id : 93111, {_}: divide ?509269 (divide ?509270 ?509270) =>= ?509269 [509270, 509269] by Super 2 with 92346 at 2
+Id : 100321, {_}: inverse (multiply (multiply (inverse ?535124) ?535124) ?535125) =>= inverse ?535125 [535125, 535124] by Super 3072 with 93111 at 1,2
+Id : 100420, {_}: inverse (inverse ?535740) =<= inverse (divide (divide (divide ?535741 ?535741) (multiply (inverse ?535742) ?535742)) (multiply (divide ?535743 ?535743) ?535740)) [535743, 535742, 535741, 535740] by Super 100321 with 89554 at 1,2
+Id : 94282, {_}: divide ?515515 (divide ?515516 ?515516) =>= ?515515 [515516, 515515] by Super 2 with 92346 at 2
+Id : 94361, {_}: divide ?515973 (multiply (inverse ?515974) ?515974) =>= ?515973 [515974, 515973] by Super 94282 with 3 at 2,2
+Id : 100488, {_}: inverse (inverse ?535740) =<= inverse (divide (divide ?535741 ?535741) (multiply (divide ?535743 ?535743) ?535740)) [535743, 535741, 535740] by Demod 100420 with 94361 at 1,1,3
+Id : 93886, {_}: inverse (divide (divide ?513000 ?513000) ?513001) =>= ?513001 [513001, 513000] by Super 1369 with 93111 at 1,2
+Id : 100489, {_}: inverse (inverse ?535740) =<= multiply (divide ?535743 ?535743) ?535740 [535743, 535740] by Demod 100488 with 93886 at 3
+Id : 100491, {_}: inverse ?494323 =<= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (inverse (inverse ?494323))) [494330, 494329, 494323] by Demod 89554 with 100489 at 2,2,3
+Id : 100612, {_}: inverse ?494323 =<= multiply ?494329 (multiply (divide (divide ?494330 ?494330) ?494329) (inverse ?494323)) [494330, 494329, 494323] by Demod 100491 with 3 at 2,3
+Id : 1348, {_}: inverse (divide (multiply (divide ?6830 ?6830) ?6831) (divide (divide ?6832 ?6833) (divide (inverse ?6831) ?6833))) =>= ?6832 [6833, 6832, 6831, 6830] by Super 1304 with 3 at 1,1,2
+Id : 3107, {_}: multiply ?16917 (divide (multiply (divide ?16918 ?16918) ?16919) (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16918, 16917] by Super 3 with 1348 at 2,3
+Id : 100541, {_}: multiply ?16917 (divide (inverse (inverse ?16919)) (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16917] by Demod 3107 with 100489 at 1,2,2
+Id : 100747, {_}: inverse (inverse (divide (inverse (inverse ?536517)) (divide (divide ?536518 ?536519) (divide (inverse ?536517) ?536519)))) =?= divide (divide ?536520 ?536520) ?536518 [536520, 536519, 536518, 536517] by Super 100541 with 100489 at 2
+Id : 100526, {_}: inverse (divide (inverse (inverse ?6831)) (divide (divide ?6832 ?6833) (divide (inverse ?6831) ?6833))) =>= ?6832 [6833, 6832, 6831] by Demod 1348 with 100489 at 1,1,2
+Id : 100849, {_}: inverse ?536518 =<= divide (divide ?536520 ?536520) ?536518 [536520, 536518] by Demod 100747 with 100526 at 1,2
+Id : 101341, {_}: inverse ?494323 =<= multiply ?494329 (multiply (inverse ?494329) (inverse ?494323)) [494329, 494323] by Demod 100612 with 100849 at 1,2,3
+Id : 101328, {_}: inverse (inverse ?513001) =>= ?513001 [513001] by Demod 93886 with 100849 at 1,2
+Id : 101357, {_}: multiply ?16917 (divide ?16919 (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16917] by Demod 100541 with 101328 at 1,2,2
+Id : 210, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?1032) ?1032) ?1033) ?1034)) ?1035) (divide ?1033 ?1035) =>= ?1034 [1035, 1034, 1033, 1032] by Super 202 with 3 at 1,1,1,1,1,2
+Id : 2224, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?11772) ?11772) ?11773) (divide ?11774 ?11773))) ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774, 11773, 11772] by Super 210 with 1292 at 1,1,1,2
+Id : 778, {_}: divide (inverse (divide (divide (divide ?3892 ?3892) ?3893) (divide (inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896)) (divide ?3893 ?3897)))) ?3897 =?= inverse (divide (divide (divide ?3898 ?3898) ?3895) ?3896) [3898, 3897, 3896, 3895, 3894, 3893, 3892] by Super 6 with 210 at 2,1,3
+Id : 811, {_}: inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896) =?= inverse (divide (divide (divide ?3898 ?3898) ?3895) ?3896) [3898, 3896, 3895, 3894] by Demod 778 with 2 at 2
+Id : 101312, {_}: inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896) =>= inverse (divide (inverse ?3895) ?3896) [3896, 3895, 3894] by Demod 811 with 100849 at 1,1,3
+Id : 101430, {_}: divide (divide (inverse (divide (inverse ?11773) (divide ?11774 ?11773))) ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774, 11773] by Demod 2224 with 101312 at 1,1,2
+Id : 375, {_}: divide (multiply (inverse (divide (divide (multiply (inverse ?1685) ?1685) ?1686) ?1687)) ?1688) (multiply ?1686 ?1688) =>= ?1687 [1688, 1687, 1686, 1685] by Super 372 with 3 at 1,1,1,1,1,2
+Id : 2362, {_}: divide (multiply (inverse (divide (divide (multiply (inverse ?12860) ?12860) ?12861) (divide ?12862 ?12861))) ?12863) (multiply ?12864 ?12863) =>= divide ?12862 ?12864 [12864, 12863, 12862, 12861, 12860] by Super 375 with 1292 at 1,1,1,2
+Id : 101423, {_}: divide (multiply (inverse (divide (inverse ?12861) (divide ?12862 ?12861))) ?12863) (multiply ?12864 ?12863) =>= divide ?12862 ?12864 [12864, 12863, 12862, 12861] by Demod 2362 with 101312 at 1,1,2
+Id : 1298, {_}: divide (multiply ?6472 ?6473) (multiply ?6474 ?6473) =?= divide (divide ?6472 ?6475) (divide ?6474 ?6475) [6475, 6474, 6473, 6472] by Super 231 with 1057 at 1,1,2
+Id : 2653, {_}: divide (multiply (inverse (divide (multiply (divide ?14473 ?14473) ?14474) (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474, 14473] by Super 231 with 1298 at 1,1,1,2
+Id : 100505, {_}: divide (multiply (inverse (divide (inverse (inverse ?14474)) (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474] by Demod 2653 with 100489 at 1,1,1,1,2
+Id : 101382, {_}: divide (multiply (inverse (divide ?14474 (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474] by Demod 100505 with 101328 at 1,1,1,1,2
+Id : 101429, {_}: divide (multiply (inverse (divide (inverse ?1686) ?1687)) ?1688) (multiply ?1686 ?1688) =>= ?1687 [1688, 1687, 1686] by Demod 375 with 101312 at 1,1,2
+Id : 101386, {_}: ?535740 =<= multiply (divide ?535743 ?535743) ?535740 [535743, 535740] by Demod 100489 with 101328 at 2
+Id : 101594, {_}: ?537458 =<= multiply (inverse (divide ?537459 ?537459)) ?537458 [537459, 537458] by Super 101386 with 100849 at 1,3
+Id : 101980, {_}: divide ?538112 (multiply ?538113 ?538112) =>= inverse ?538113 [538113, 538112] by Super 101429 with 101594 at 1,2
+Id : 102412, {_}: divide (multiply (inverse (inverse ?14475)) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475] by Demod 101382 with 101980 at 1,1,1,2
+Id : 102413, {_}: divide (multiply ?14475 ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475] by Demod 102412 with 101328 at 1,1,2
+Id : 102434, {_}: divide (inverse (divide (inverse ?12861) (divide ?12862 ?12861))) ?12864 =>= divide ?12862 ?12864 [12864, 12862, 12861] by Demod 101423 with 102413 at 2
+Id : 102436, {_}: divide (divide ?11774 ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774] by Demod 101430 with 102434 at 1,2
+Id : 102441, {_}: multiply ?16917 (divide ?16919 (divide ?16920 (inverse ?16919))) =>= divide ?16917 ?16920 [16920, 16919, 16917] by Demod 101357 with 102436 at 2,2,2
+Id : 102470, {_}: multiply ?16917 (divide ?16919 (multiply ?16920 ?16919)) =>= divide ?16917 ?16920 [16920, 16919, 16917] by Demod 102441 with 3 at 2,2,2
+Id : 102471, {_}: multiply ?16917 (inverse ?16920) =>= divide ?16917 ?16920 [16920, 16917] by Demod 102470 with 101980 at 2,2
+Id : 102472, {_}: inverse ?494323 =<= multiply ?494329 (divide (inverse ?494329) ?494323) [494329, 494323] by Demod 101341 with 102471 at 2,3
+Id : 102516, {_}: inverse (multiply ?538987 (inverse ?538988)) =>= multiply ?538988 (inverse ?538987) [538988, 538987] by Super 102472 with 101980 at 2,3
+Id : 102787, {_}: inverse (divide ?538987 ?538988) =<= multiply ?538988 (inverse ?538987) [538988, 538987] by Demod 102516 with 102471 at 1,2
+Id : 102959, {_}: inverse (divide ?539857 ?539858) =>= divide ?539858 ?539857 [539858, 539857] by Demod 102787 with 102471 at 3
+Id : 102980, {_}: inverse (multiply ?539955 ?539956) =<= divide (inverse ?539956) ?539955 [539956, 539955] by Super 102959 with 3 at 1,2
+Id : 103330, {_}: multiply (inverse ?540510) ?540511 =<= inverse (multiply (inverse ?540511) ?540510) [540511, 540510] by Super 3 with 102980 at 3
+Id : 93587, {_}: multiply (inverse (divide ?504068 ?504070)) ?504068 =>= ?504070 [504070, 504068] by Demod 92186 with 93111 at 2,2
+Id : 96346, {_}: multiply ?522565 (divide ?522566 ?522566) =>= ?522565 [522566, 522565] by Super 93587 with 93886 at 1,2
+Id : 96425, {_}: multiply ?523023 (multiply (inverse ?523024) ?523024) =>= ?523023 [523024, 523023] by Super 96346 with 3 at 2,2
+Id : 103339, {_}: multiply (inverse (multiply (inverse ?540545) ?540545)) ?540546 =>= inverse (inverse ?540546) [540546, 540545] by Super 103330 with 96425 at 1,3
+Id : 103110, {_}: multiply (inverse ?540161) ?540162 =<= inverse (multiply (inverse ?540162) ?540161) [540162, 540161] by Super 3 with 102980 at 3
+Id : 103424, {_}: multiply (multiply (inverse ?540545) ?540545) ?540546 =>= inverse (inverse ?540546) [540546, 540545] by Demod 103339 with 103110 at 1,2
+Id : 103425, {_}: multiply (multiply (inverse ?540545) ?540545) ?540546 =>= ?540546 [540546, 540545] by Demod 103424 with 101328 at 3
+Id : 104863, {_}: a2 === a2 [] by Demod 1 with 103425 at 2
+Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2
+% SZS output end CNFRefutation for GRP479-1.p
+23995: solved GRP479-1.p in 37.162321 using nrkbo
+23995: status Unsatisfiable for GRP479-1.p
+NO CLASH, using fixed ground order
+24007: Facts:
+24007: Id : 2, {_}:
+ divide
+ (inverse
+ (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
+ ?5
+ =>=
+ ?4
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+24007: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+24007: Goal:
+24007: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+24007: Order:
+24007: nrkbo
+24007: Leaf order:
+24007: a3 2 0 2 1,1,2
+24007: b3 2 0 2 2,1,2
+24007: c3 2 0 2 2,2
+24007: inverse 2 1 0
+24007: multiply 5 2 4 0,2
+24007: divide 7 2 0
+NO CLASH, using fixed ground order
+24008: Facts:
+24008: Id : 2, {_}:
+ divide
+ (inverse
+ (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
+ ?5
+ =>=
+ ?4
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+24008: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+24008: Goal:
+24008: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+24008: Order:
+24008: kbo
+24008: Leaf order:
+24008: a3 2 0 2 1,1,2
+24008: b3 2 0 2 2,1,2
+24008: c3 2 0 2 2,2
+24008: inverse 2 1 0
+24008: multiply 5 2 4 0,2
+24008: divide 7 2 0
+NO CLASH, using fixed ground order
+24009: Facts:
+24009: Id : 2, {_}:
+ divide
+ (inverse
+ (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5))))
+ ?5
+ =>=
+ ?4
+ [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+24009: Id : 3, {_}:
+ multiply ?7 ?8 =<= divide ?7 (inverse ?8)
+ [8, 7] by multiply ?7 ?8
+24009: Goal:
+24009: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+24009: Order:
+24009: lpo
+24009: Leaf order:
+24009: a3 2 0 2 1,1,2
+24009: b3 2 0 2 2,1,2
+24009: c3 2 0 2 2,2
+24009: inverse 2 1 0
+24009: multiply 5 2 4 0,2
+24009: divide 7 2 0
+Statistics :
+Max weight : 78
+Found proof, 40.781292s
+% SZS status Unsatisfiable for GRP480-1.p
+% SZS output start CNFRefutation for GRP480-1.p
+Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8
+Id : 2, {_}: divide (inverse (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) ?5 =>= ?4 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5
+Id : 4, {_}: divide (inverse (divide (divide (divide ?10 ?10) ?11) (divide ?12 (divide ?11 ?13)))) ?13 =>= ?12 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13
+Id : 5, {_}: divide (inverse (divide (divide (divide ?15 ?15) (inverse (divide (divide (divide ?16 ?16) ?17) (divide ?18 (divide ?17 ?19))))) (divide ?20 ?18))) ?19 =>= ?20 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 2,2,1,1,2
+Id : 22, {_}: divide (inverse (divide (multiply (divide ?87 ?87) (divide (divide (divide ?88 ?88) ?89) (divide ?90 (divide ?89 ?91)))) (divide ?92 ?90))) ?91 =>= ?92 [92, 91, 90, 89, 88, 87] by Demod 5 with 3 at 1,1,1,2
+Id : 23, {_}: divide (inverse (divide (multiply (divide ?94 ?94) (divide (divide (divide ?95 ?95) ?96) (divide ?97 (divide ?96 ?98)))) ?99)) ?98 =?= inverse (divide (divide (divide ?100 ?100) ?101) (divide ?99 (divide ?101 ?97))) [101, 100, 99, 98, 97, 96, 95, 94] by Super 22 with 2 at 2,1,1,2
+Id : 18, {_}: divide (inverse (divide (multiply (divide ?15 ?15) (divide (divide (divide ?16 ?16) ?17) (divide ?18 (divide ?17 ?19)))) (divide ?20 ?18))) ?19 =>= ?20 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 1,1,1,2
+Id : 1304, {_}: inverse (divide (divide (divide ?6515 ?6515) ?6516) (divide (divide ?6517 ?6518) (divide ?6516 ?6518))) =>= ?6517 [6518, 6517, 6516, 6515] by Super 18 with 23 at 2
+Id : 2998, {_}: inverse (divide (divide (multiply (inverse ?16319) ?16319) ?16320) (divide (divide ?16321 ?16322) (divide ?16320 ?16322))) =>= ?16321 [16322, 16321, 16320, 16319] by Super 1304 with 3 at 1,1,1,2
+Id : 3072, {_}: inverse (divide (multiply (multiply (inverse ?16865) ?16865) ?16866) (divide (divide ?16867 ?16868) (divide (inverse ?16866) ?16868))) =>= ?16867 [16868, 16867, 16866, 16865] by Super 2998 with 3 at 1,1,2
+Id : 1319, {_}: inverse (divide (divide (divide ?6630 ?6630) ?6631) (divide (divide ?6632 (inverse ?6633)) (multiply ?6631 ?6633))) =>= ?6632 [6633, 6632, 6631, 6630] by Super 1304 with 3 at 2,2,1,2
+Id : 1369, {_}: inverse (divide (divide (divide ?6630 ?6630) ?6631) (divide (multiply ?6632 ?6633) (multiply ?6631 ?6633))) =>= ?6632 [6633, 6632, 6631, 6630] by Demod 1319 with 3 at 1,2,1,2
+Id : 1389, {_}: multiply ?6881 (divide (divide (divide ?6882 ?6882) ?6883) (divide (multiply ?6884 ?6885) (multiply ?6883 ?6885))) =>= divide ?6881 ?6884 [6885, 6884, 6883, 6882, 6881] by Super 3 with 1369 at 2,3
+Id : 8, {_}: divide (inverse (divide (divide (divide ?31 ?31) ?32) (divide ?33 (multiply ?32 ?34)))) (inverse ?34) =>= ?33 [34, 33, 32, 31] by Super 2 with 3 at 2,2,1,1,2
+Id : 15, {_}: multiply (inverse (divide (divide (divide ?31 ?31) ?32) (divide ?33 (multiply ?32 ?34)))) ?34 =>= ?33 [34, 33, 32, 31] by Demod 8 with 3 at 2
+Id : 6, {_}: divide (inverse (divide (divide (divide ?22 ?22) ?23) ?24)) ?25 =?= inverse (divide (divide (divide ?26 ?26) ?27) (divide ?24 (divide ?27 (divide ?23 ?25)))) [27, 26, 25, 24, 23, 22] by Super 4 with 2 at 2,1,1,2
+Id : 86, {_}: divide (divide (inverse (divide (divide (divide ?404 ?404) ?405) ?406)) ?407) (divide ?405 ?407) =>= ?406 [407, 406, 405, 404] by Super 2 with 6 at 1,2
+Id : 193, {_}: multiply (inverse (divide ?902 (divide ?903 (multiply (divide ?904 (inverse (divide (divide (divide ?905 ?905) ?904) ?902))) ?906)))) ?906 =>= ?903 [906, 905, 904, 903, 902] by Super 15 with 86 at 1,1,1,2
+Id : 223, {_}: multiply (inverse (divide ?902 (divide ?903 (multiply (multiply ?904 (divide (divide (divide ?905 ?905) ?904) ?902)) ?906)))) ?906 =>= ?903 [906, 905, 904, 903, 902] by Demod 193 with 3 at 1,2,2,1,1,2
+Id : 30, {_}: divide (inverse (divide (multiply (divide ?157 ?157) (divide (divide (divide ?158 ?158) ?159) ?160)) (divide ?161 (inverse (divide (multiply (divide ?162 ?162) (divide (divide (divide ?163 ?163) ?164) (divide ?165 (divide ?164 (divide ?159 ?166))))) (divide ?160 ?165)))))) ?166 =>= ?161 [166, 165, 164, 163, 162, 161, 160, 159, 158, 157] by Super 22 with 18 at 2,2,1,1,1,2
+Id : 42, {_}: divide (inverse (divide (multiply (divide ?157 ?157) (divide (divide (divide ?158 ?158) ?159) ?160)) (multiply ?161 (divide (multiply (divide ?162 ?162) (divide (divide (divide ?163 ?163) ?164) (divide ?165 (divide ?164 (divide ?159 ?166))))) (divide ?160 ?165))))) ?166 =>= ?161 [166, 165, 164, 163, 162, 161, 160, 159, 158, 157] by Demod 30 with 3 at 2,1,1,2
+Id : 202, {_}: divide (divide (inverse (divide (divide (divide ?974 ?974) ?975) ?976)) ?977) (divide ?975 ?977) =>= ?976 [977, 976, 975, 974] by Super 2 with 6 at 1,2
+Id : 208, {_}: divide (divide (inverse (divide (divide (divide ?1018 ?1018) ?1019) ?1020)) (inverse ?1021)) (multiply ?1019 ?1021) =>= ?1020 [1021, 1020, 1019, 1018] by Super 202 with 3 at 2,2
+Id : 372, {_}: divide (multiply (inverse (divide (divide (divide ?1664 ?1664) ?1665) ?1666)) ?1667) (multiply ?1665 ?1667) =>= ?1666 [1667, 1666, 1665, 1664] by Demod 208 with 3 at 1,2
+Id : 378, {_}: divide (multiply (inverse (divide (multiply (divide ?1702 ?1702) ?1703) ?1704)) ?1705) (multiply (inverse ?1703) ?1705) =>= ?1704 [1705, 1704, 1703, 1702] by Super 372 with 3 at 1,1,1,1,2
+Id : 88082, {_}: divide ?485240 (multiply (inverse ?485241) ?485242) =<= divide ?485240 (multiply (multiply ?485243 (divide (divide (divide ?485244 ?485244) ?485243) (multiply (divide ?485245 ?485245) ?485241))) ?485242) [485245, 485244, 485243, 485242, 485241, 485240] by Super 378 with 223 at 1,2
+Id : 89234, {_}: divide (inverse (divide (multiply (divide ?494319 ?494319) (divide (divide (divide ?494320 ?494320) ?494321) ?494322)) (multiply (inverse ?494323) (divide (multiply (divide ?494324 ?494324) (divide (divide (divide ?494325 ?494325) ?494326) (divide ?494327 (divide ?494326 (divide ?494321 ?494328))))) (divide ?494322 ?494327))))) ?494328 =?= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (multiply (divide ?494331 ?494331) ?494323)) [494331, 494330, 494329, 494328, 494327, 494326, 494325, 494324, 494323, 494322, 494321, 494320, 494319] by Super 42 with 88082 at 1,1,2
+Id : 89554, {_}: inverse ?494323 =<= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (multiply (divide ?494331 ?494331) ?494323)) [494331, 494330, 494329, 494323] by Demod 89234 with 42 at 2
+Id : 90512, {_}: multiply (inverse (divide ?497368 (divide ?497369 (inverse ?497370)))) (divide (divide (divide ?497371 ?497371) (multiply ?497372 (divide (divide (divide ?497373 ?497373) ?497372) ?497368))) (multiply (divide ?497374 ?497374) ?497370)) =>= ?497369 [497374, 497373, 497372, 497371, 497370, 497369, 497368] by Super 223 with 89554 at 2,2,1,1,2
+Id : 196, {_}: divide (inverse (divide (divide (divide ?925 ?925) ?926) (divide (inverse (divide (divide (divide ?927 ?927) ?928) ?929)) (divide ?926 ?930)))) ?930 =?= inverse (divide (divide (divide ?931 ?931) ?928) ?929) [931, 930, 929, 928, 927, 926, 925] by Super 6 with 86 at 2,1,3
+Id : 6409, {_}: inverse (divide (divide (divide ?34204 ?34204) ?34205) ?34206) =?= inverse (divide (divide (divide ?34207 ?34207) ?34205) ?34206) [34207, 34206, 34205, 34204] by Demod 196 with 2 at 2
+Id : 6420, {_}: inverse (divide (divide (divide ?34278 ?34278) (divide ?34279 (inverse (divide (divide (divide ?34280 ?34280) ?34279) ?34281)))) ?34282) =>= inverse (divide ?34281 ?34282) [34282, 34281, 34280, 34279, 34278] by Super 6409 with 86 at 1,1,3
+Id : 6497, {_}: inverse (divide (divide (divide ?34278 ?34278) (multiply ?34279 (divide (divide (divide ?34280 ?34280) ?34279) ?34281))) ?34282) =>= inverse (divide ?34281 ?34282) [34282, 34281, 34280, 34279, 34278] by Demod 6420 with 3 at 2,1,1,2
+Id : 28325, {_}: multiply ?153090 (divide (divide (divide ?153091 ?153091) (multiply ?153092 (divide (divide (divide ?153093 ?153093) ?153092) ?153094))) ?153095) =>= divide ?153090 (inverse (divide ?153094 ?153095)) [153095, 153094, 153093, 153092, 153091, 153090] by Super 3 with 6497 at 2,3
+Id : 28522, {_}: multiply ?153090 (divide (divide (divide ?153091 ?153091) (multiply ?153092 (divide (divide (divide ?153093 ?153093) ?153092) ?153094))) ?153095) =>= multiply ?153090 (divide ?153094 ?153095) [153095, 153094, 153093, 153092, 153091, 153090] by Demod 28325 with 3 at 3
+Id : 91190, {_}: multiply (inverse (divide ?497368 (divide ?497369 (inverse ?497370)))) (divide ?497368 (multiply (divide ?497374 ?497374) ?497370)) =>= ?497369 [497374, 497370, 497369, 497368] by Demod 90512 with 28522 at 2
+Id : 91665, {_}: multiply (inverse (divide ?503116 (multiply ?503117 ?503118))) (divide ?503116 (multiply (divide ?503119 ?503119) ?503118)) =>= ?503117 [503119, 503118, 503117, 503116] by Demod 91190 with 3 at 2,1,1,2
+Id : 231, {_}: divide (multiply (inverse (divide (divide (divide ?1018 ?1018) ?1019) ?1020)) ?1021) (multiply ?1019 ?1021) =>= ?1020 [1021, 1020, 1019, 1018] by Demod 208 with 3 at 1,2
+Id : 1057, {_}: inverse (divide (divide (divide ?5280 ?5280) ?5281) (divide (divide ?5282 ?5283) (divide ?5281 ?5283))) =>= ?5282 [5283, 5282, 5281, 5280] by Super 18 with 23 at 2
+Id : 1292, {_}: divide (divide ?6440 ?6441) (divide ?6442 ?6441) =?= divide (divide ?6440 ?6443) (divide ?6442 ?6443) [6443, 6442, 6441, 6440] by Super 86 with 1057 at 1,1,2
+Id : 2334, {_}: divide (multiply (inverse (divide (divide (divide ?12626 ?12626) ?12627) (divide ?12628 ?12627))) ?12629) (multiply ?12630 ?12629) =>= divide ?12628 ?12630 [12630, 12629, 12628, 12627, 12626] by Super 231 with 1292 at 1,1,1,2
+Id : 91784, {_}: multiply (inverse (divide (multiply (inverse (divide (divide (divide ?504066 ?504066) ?504067) (divide ?504068 ?504067))) ?504069) (multiply ?504070 ?504069))) (divide ?504068 (divide ?504071 ?504071)) =>= ?504070 [504071, 504070, 504069, 504068, 504067, 504066] by Super 91665 with 2334 at 2,2
+Id : 92186, {_}: multiply (inverse (divide ?504068 ?504070)) (divide ?504068 (divide ?504071 ?504071)) =>= ?504070 [504071, 504070, 504068] by Demod 91784 with 2334 at 1,1,2
+Id : 92346, {_}: ?505751 =<= divide (inverse (divide (divide (divide ?505752 ?505752) ?505753) ?505751)) ?505753 [505753, 505752, 505751] by Super 1389 with 92186 at 2
+Id : 93111, {_}: divide ?509269 (divide ?509270 ?509270) =>= ?509269 [509270, 509269] by Super 2 with 92346 at 2
+Id : 100321, {_}: inverse (multiply (multiply (inverse ?535124) ?535124) ?535125) =>= inverse ?535125 [535125, 535124] by Super 3072 with 93111 at 1,2
+Id : 100420, {_}: inverse (inverse ?535740) =<= inverse (divide (divide (divide ?535741 ?535741) (multiply (inverse ?535742) ?535742)) (multiply (divide ?535743 ?535743) ?535740)) [535743, 535742, 535741, 535740] by Super 100321 with 89554 at 1,2
+Id : 94282, {_}: divide ?515515 (divide ?515516 ?515516) =>= ?515515 [515516, 515515] by Super 2 with 92346 at 2
+Id : 94361, {_}: divide ?515973 (multiply (inverse ?515974) ?515974) =>= ?515973 [515974, 515973] by Super 94282 with 3 at 2,2
+Id : 100488, {_}: inverse (inverse ?535740) =<= inverse (divide (divide ?535741 ?535741) (multiply (divide ?535743 ?535743) ?535740)) [535743, 535741, 535740] by Demod 100420 with 94361 at 1,1,3
+Id : 93886, {_}: inverse (divide (divide ?513000 ?513000) ?513001) =>= ?513001 [513001, 513000] by Super 1369 with 93111 at 1,2
+Id : 100489, {_}: inverse (inverse ?535740) =<= multiply (divide ?535743 ?535743) ?535740 [535743, 535740] by Demod 100488 with 93886 at 3
+Id : 100522, {_}: divide (inverse (divide (inverse (inverse (divide (divide (divide ?95 ?95) ?96) (divide ?97 (divide ?96 ?98))))) ?99)) ?98 =?= inverse (divide (divide (divide ?100 ?100) ?101) (divide ?99 (divide ?101 ?97))) [101, 100, 99, 98, 97, 96, 95] by Demod 23 with 100489 at 1,1,1,2
+Id : 1348, {_}: inverse (divide (multiply (divide ?6830 ?6830) ?6831) (divide (divide ?6832 ?6833) (divide (inverse ?6831) ?6833))) =>= ?6832 [6833, 6832, 6831, 6830] by Super 1304 with 3 at 1,1,2
+Id : 3107, {_}: multiply ?16917 (divide (multiply (divide ?16918 ?16918) ?16919) (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16918, 16917] by Super 3 with 1348 at 2,3
+Id : 100541, {_}: multiply ?16917 (divide (inverse (inverse ?16919)) (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16917] by Demod 3107 with 100489 at 1,2,2
+Id : 100747, {_}: inverse (inverse (divide (inverse (inverse ?536517)) (divide (divide ?536518 ?536519) (divide (inverse ?536517) ?536519)))) =?= divide (divide ?536520 ?536520) ?536518 [536520, 536519, 536518, 536517] by Super 100541 with 100489 at 2
+Id : 100526, {_}: inverse (divide (inverse (inverse ?6831)) (divide (divide ?6832 ?6833) (divide (inverse ?6831) ?6833))) =>= ?6832 [6833, 6832, 6831] by Demod 1348 with 100489 at 1,1,2
+Id : 100849, {_}: inverse ?536518 =<= divide (divide ?536520 ?536520) ?536518 [536520, 536518] by Demod 100747 with 100526 at 1,2
+Id : 101259, {_}: divide (inverse (divide (inverse (inverse (divide (inverse ?96) (divide ?97 (divide ?96 ?98))))) ?99)) ?98 =?= inverse (divide (divide (divide ?100 ?100) ?101) (divide ?99 (divide ?101 ?97))) [101, 100, 99, 98, 97, 96] by Demod 100522 with 100849 at 1,1,1,1,1,1,2
+Id : 101260, {_}: divide (inverse (divide (inverse (inverse (divide (inverse ?96) (divide ?97 (divide ?96 ?98))))) ?99)) ?98 =?= inverse (divide (inverse ?101) (divide ?99 (divide ?101 ?97))) [101, 99, 98, 97, 96] by Demod 101259 with 100849 at 1,1,3
+Id : 101328, {_}: inverse (inverse ?513001) =>= ?513001 [513001] by Demod 93886 with 100849 at 1,2
+Id : 101498, {_}: divide (inverse (divide (divide (inverse ?96) (divide ?97 (divide ?96 ?98))) ?99)) ?98 =?= inverse (divide (inverse ?101) (divide ?99 (divide ?101 ?97))) [101, 99, 98, 97, 96] by Demod 101260 with 101328 at 1,1,1,2
+Id : 100491, {_}: inverse ?494323 =<= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (inverse (inverse ?494323))) [494330, 494329, 494323] by Demod 89554 with 100489 at 2,2,3
+Id : 100612, {_}: inverse ?494323 =<= multiply ?494329 (multiply (divide (divide ?494330 ?494330) ?494329) (inverse ?494323)) [494330, 494329, 494323] by Demod 100491 with 3 at 2,3
+Id : 101341, {_}: inverse ?494323 =<= multiply ?494329 (multiply (inverse ?494329) (inverse ?494323)) [494329, 494323] by Demod 100612 with 100849 at 1,2,3
+Id : 101357, {_}: multiply ?16917 (divide ?16919 (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16917] by Demod 100541 with 101328 at 1,2,2
+Id : 210, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?1032) ?1032) ?1033) ?1034)) ?1035) (divide ?1033 ?1035) =>= ?1034 [1035, 1034, 1033, 1032] by Super 202 with 3 at 1,1,1,1,1,2
+Id : 2224, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?11772) ?11772) ?11773) (divide ?11774 ?11773))) ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774, 11773, 11772] by Super 210 with 1292 at 1,1,1,2
+Id : 778, {_}: divide (inverse (divide (divide (divide ?3892 ?3892) ?3893) (divide (inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896)) (divide ?3893 ?3897)))) ?3897 =?= inverse (divide (divide (divide ?3898 ?3898) ?3895) ?3896) [3898, 3897, 3896, 3895, 3894, 3893, 3892] by Super 6 with 210 at 2,1,3
+Id : 811, {_}: inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896) =?= inverse (divide (divide (divide ?3898 ?3898) ?3895) ?3896) [3898, 3896, 3895, 3894] by Demod 778 with 2 at 2
+Id : 101312, {_}: inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896) =>= inverse (divide (inverse ?3895) ?3896) [3896, 3895, 3894] by Demod 811 with 100849 at 1,1,3
+Id : 101430, {_}: divide (divide (inverse (divide (inverse ?11773) (divide ?11774 ?11773))) ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774, 11773] by Demod 2224 with 101312 at 1,1,2
+Id : 375, {_}: divide (multiply (inverse (divide (divide (multiply (inverse ?1685) ?1685) ?1686) ?1687)) ?1688) (multiply ?1686 ?1688) =>= ?1687 [1688, 1687, 1686, 1685] by Super 372 with 3 at 1,1,1,1,1,2
+Id : 2362, {_}: divide (multiply (inverse (divide (divide (multiply (inverse ?12860) ?12860) ?12861) (divide ?12862 ?12861))) ?12863) (multiply ?12864 ?12863) =>= divide ?12862 ?12864 [12864, 12863, 12862, 12861, 12860] by Super 375 with 1292 at 1,1,1,2
+Id : 101423, {_}: divide (multiply (inverse (divide (inverse ?12861) (divide ?12862 ?12861))) ?12863) (multiply ?12864 ?12863) =>= divide ?12862 ?12864 [12864, 12863, 12862, 12861] by Demod 2362 with 101312 at 1,1,2
+Id : 1298, {_}: divide (multiply ?6472 ?6473) (multiply ?6474 ?6473) =?= divide (divide ?6472 ?6475) (divide ?6474 ?6475) [6475, 6474, 6473, 6472] by Super 231 with 1057 at 1,1,2
+Id : 2653, {_}: divide (multiply (inverse (divide (multiply (divide ?14473 ?14473) ?14474) (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474, 14473] by Super 231 with 1298 at 1,1,1,2
+Id : 100505, {_}: divide (multiply (inverse (divide (inverse (inverse ?14474)) (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474] by Demod 2653 with 100489 at 1,1,1,1,2
+Id : 101382, {_}: divide (multiply (inverse (divide ?14474 (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474] by Demod 100505 with 101328 at 1,1,1,1,2
+Id : 101429, {_}: divide (multiply (inverse (divide (inverse ?1686) ?1687)) ?1688) (multiply ?1686 ?1688) =>= ?1687 [1688, 1687, 1686] by Demod 375 with 101312 at 1,1,2
+Id : 101386, {_}: ?535740 =<= multiply (divide ?535743 ?535743) ?535740 [535743, 535740] by Demod 100489 with 101328 at 2
+Id : 101594, {_}: ?537458 =<= multiply (inverse (divide ?537459 ?537459)) ?537458 [537459, 537458] by Super 101386 with 100849 at 1,3
+Id : 101980, {_}: divide ?538112 (multiply ?538113 ?538112) =>= inverse ?538113 [538113, 538112] by Super 101429 with 101594 at 1,2
+Id : 102412, {_}: divide (multiply (inverse (inverse ?14475)) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475] by Demod 101382 with 101980 at 1,1,1,2
+Id : 102413, {_}: divide (multiply ?14475 ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475] by Demod 102412 with 101328 at 1,1,2
+Id : 102434, {_}: divide (inverse (divide (inverse ?12861) (divide ?12862 ?12861))) ?12864 =>= divide ?12862 ?12864 [12864, 12862, 12861] by Demod 101423 with 102413 at 2
+Id : 102436, {_}: divide (divide ?11774 ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774] by Demod 101430 with 102434 at 1,2
+Id : 102441, {_}: multiply ?16917 (divide ?16919 (divide ?16920 (inverse ?16919))) =>= divide ?16917 ?16920 [16920, 16919, 16917] by Demod 101357 with 102436 at 2,2,2
+Id : 102470, {_}: multiply ?16917 (divide ?16919 (multiply ?16920 ?16919)) =>= divide ?16917 ?16920 [16920, 16919, 16917] by Demod 102441 with 3 at 2,2,2
+Id : 102471, {_}: multiply ?16917 (inverse ?16920) =>= divide ?16917 ?16920 [16920, 16917] by Demod 102470 with 101980 at 2,2
+Id : 102472, {_}: inverse ?494323 =<= multiply ?494329 (divide (inverse ?494329) ?494323) [494329, 494323] by Demod 101341 with 102471 at 2,3
+Id : 102516, {_}: inverse (multiply ?538987 (inverse ?538988)) =>= multiply ?538988 (inverse ?538987) [538988, 538987] by Super 102472 with 101980 at 2,3
+Id : 102787, {_}: inverse (divide ?538987 ?538988) =<= multiply ?538988 (inverse ?538987) [538988, 538987] by Demod 102516 with 102471 at 1,2
+Id : 102788, {_}: inverse (divide ?538987 ?538988) =>= divide ?538988 ?538987 [538988, 538987] by Demod 102787 with 102471 at 3
+Id : 102815, {_}: divide (divide ?99 (divide (inverse ?96) (divide ?97 (divide ?96 ?98)))) ?98 =?= inverse (divide (inverse ?101) (divide ?99 (divide ?101 ?97))) [101, 98, 97, 96, 99] by Demod 101498 with 102788 at 1,2
+Id : 102816, {_}: divide (divide ?99 (divide (inverse ?96) (divide ?97 (divide ?96 ?98)))) ?98 =?= divide (divide ?99 (divide ?101 ?97)) (inverse ?101) [101, 98, 97, 96, 99] by Demod 102815 with 102788 at 3
+Id : 2390, {_}: divide (divide ?13180 ?13181) (divide ?13182 ?13181) =?= divide (divide ?13180 ?13183) (divide ?13182 ?13183) [13183, 13182, 13181, 13180] by Super 86 with 1057 at 1,1,2
+Id : 212, {_}: divide (divide (inverse (divide (multiply (divide ?1043 ?1043) ?1044) ?1045)) ?1046) (divide (inverse ?1044) ?1046) =>= ?1045 [1046, 1045, 1044, 1043] by Super 202 with 3 at 1,1,1,1,2
+Id : 2401, {_}: divide (divide ?13273 ?13274) (divide (divide (inverse (divide (multiply (divide ?13275 ?13275) ?13276) ?13277)) ?13278) ?13274) =>= divide (divide ?13273 (divide (inverse ?13276) ?13278)) ?13277 [13278, 13277, 13276, 13275, 13274, 13273] by Super 2390 with 212 at 2,3
+Id : 100530, {_}: divide (divide ?13273 ?13274) (divide (divide (inverse (divide (inverse (inverse ?13276)) ?13277)) ?13278) ?13274) =>= divide (divide ?13273 (divide (inverse ?13276) ?13278)) ?13277 [13278, 13277, 13276, 13274, 13273] by Demod 2401 with 100489 at 1,1,1,1,2,2
+Id : 101375, {_}: divide (divide ?13273 ?13274) (divide (divide (inverse (divide ?13276 ?13277)) ?13278) ?13274) =>= divide (divide ?13273 (divide (inverse ?13276) ?13278)) ?13277 [13278, 13277, 13276, 13274, 13273] by Demod 100530 with 101328 at 1,1,1,1,2,2
+Id : 102446, {_}: divide ?13273 (divide (inverse (divide ?13276 ?13277)) ?13278) =?= divide (divide ?13273 (divide (inverse ?13276) ?13278)) ?13277 [13278, 13277, 13276, 13273] by Demod 101375 with 102436 at 2
+Id : 102862, {_}: divide ?13273 (divide (divide ?13277 ?13276) ?13278) =<= divide (divide ?13273 (divide (inverse ?13276) ?13278)) ?13277 [13278, 13276, 13277, 13273] by Demod 102446 with 102788 at 1,2,2
+Id : 102906, {_}: divide ?99 (divide (divide ?98 ?96) (divide ?97 (divide ?96 ?98))) =?= divide (divide ?99 (divide ?101 ?97)) (inverse ?101) [101, 97, 96, 98, 99] by Demod 102816 with 102862 at 2
+Id : 102907, {_}: divide ?99 (divide (divide ?98 ?96) (divide ?97 (divide ?96 ?98))) =?= multiply (divide ?99 (divide ?101 ?97)) ?101 [101, 97, 96, 98, 99] by Demod 102906 with 3 at 3
+Id : 102924, {_}: multiply ?539666 (divide ?539667 ?539668) =<= divide ?539666 (divide ?539668 ?539667) [539668, 539667, 539666] by Super 102471 with 102788 at 2,2
+Id : 103472, {_}: multiply ?99 (divide (divide ?97 (divide ?96 ?98)) (divide ?98 ?96)) =?= multiply (divide ?99 (divide ?101 ?97)) ?101 [101, 98, 96, 97, 99] by Demod 102907 with 102924 at 2
+Id : 103473, {_}: multiply ?99 (divide (divide ?97 (divide ?96 ?98)) (divide ?98 ?96)) =?= multiply (multiply ?99 (divide ?97 ?101)) ?101 [101, 98, 96, 97, 99] by Demod 103472 with 102924 at 1,3
+Id : 103474, {_}: multiply ?99 (multiply (divide ?97 (divide ?96 ?98)) (divide ?96 ?98)) =?= multiply (multiply ?99 (divide ?97 ?101)) ?101 [101, 98, 96, 97, 99] by Demod 103473 with 102924 at 2,2
+Id : 103475, {_}: multiply ?99 (multiply (multiply ?97 (divide ?98 ?96)) (divide ?96 ?98)) =?= multiply (multiply ?99 (divide ?97 ?101)) ?101 [101, 96, 98, 97, 99] by Demod 103474 with 102924 at 1,2,2
+Id : 9, {_}: divide (inverse (divide (divide (multiply (inverse ?36) ?36) ?37) (divide ?38 (divide ?37 ?39)))) ?39 =>= ?38 [39, 38, 37, 36] by Super 2 with 3 at 1,1,1,1,2
+Id : 101427, {_}: divide (inverse (divide (inverse ?37) (divide ?38 (divide ?37 ?39)))) ?39 =>= ?38 [39, 38, 37] by Demod 9 with 101312 at 1,2
+Id : 102819, {_}: divide (divide (divide ?38 (divide ?37 ?39)) (inverse ?37)) ?39 =>= ?38 [39, 37, 38] by Demod 101427 with 102788 at 1,2
+Id : 102903, {_}: divide (multiply (divide ?38 (divide ?37 ?39)) ?37) ?39 =>= ?38 [39, 37, 38] by Demod 102819 with 3 at 1,2
+Id : 103476, {_}: divide (multiply (multiply ?38 (divide ?39 ?37)) ?37) ?39 =>= ?38 [37, 39, 38] by Demod 102903 with 102924 at 1,1,2
+Id : 2408, {_}: divide (divide ?13322 ?13323) (divide (multiply (inverse (divide (multiply (divide ?13324 ?13324) ?13325) ?13326)) ?13327) ?13323) =>= divide (divide ?13322 (multiply (inverse ?13325) ?13327)) ?13326 [13327, 13326, 13325, 13324, 13323, 13322] by Super 2390 with 378 at 2,3
+Id : 100531, {_}: divide (divide ?13322 ?13323) (divide (multiply (inverse (divide (inverse (inverse ?13325)) ?13326)) ?13327) ?13323) =>= divide (divide ?13322 (multiply (inverse ?13325) ?13327)) ?13326 [13327, 13326, 13325, 13323, 13322] by Demod 2408 with 100489 at 1,1,1,1,2,2
+Id : 101355, {_}: divide (divide ?13322 ?13323) (divide (multiply (inverse (divide ?13325 ?13326)) ?13327) ?13323) =>= divide (divide ?13322 (multiply (inverse ?13325) ?13327)) ?13326 [13327, 13326, 13325, 13323, 13322] by Demod 100531 with 101328 at 1,1,1,1,2,2
+Id : 102440, {_}: divide ?13322 (multiply (inverse (divide ?13325 ?13326)) ?13327) =?= divide (divide ?13322 (multiply (inverse ?13325) ?13327)) ?13326 [13327, 13326, 13325, 13322] by Demod 101355 with 102436 at 2
+Id : 102864, {_}: divide ?13322 (multiply (divide ?13326 ?13325) ?13327) =<= divide (divide ?13322 (multiply (inverse ?13325) ?13327)) ?13326 [13327, 13325, 13326, 13322] by Demod 102440 with 102788 at 1,2,2
+Id : 102611, {_}: divide ?539467 (multiply ?539468 ?539467) =>= inverse ?539468 [539468, 539467] by Super 101429 with 101594 at 1,2
+Id : 102625, {_}: divide (inverse ?539525) (divide ?539526 ?539525) =>= inverse ?539526 [539526, 539525] by Super 102611 with 102471 at 2,2
+Id : 103817, {_}: multiply (inverse ?539525) (divide ?539525 ?539526) =>= inverse ?539526 [539526, 539525] by Demod 102625 with 102924 at 2
+Id : 103831, {_}: divide ?541233 (multiply (divide ?541234 ?541235) (divide ?541235 ?541236)) =>= divide (divide ?541233 (inverse ?541236)) ?541234 [541236, 541235, 541234, 541233] by Super 102864 with 103817 at 2,1,3
+Id : 103478, {_}: multiply (divide ?11774 ?11775) (divide ?11775 ?11776) =>= divide ?11774 ?11776 [11776, 11775, 11774] by Demod 102436 with 102924 at 2
+Id : 103925, {_}: divide ?541233 (divide ?541234 ?541236) =<= divide (divide ?541233 (inverse ?541236)) ?541234 [541236, 541234, 541233] by Demod 103831 with 103478 at 2,2
+Id : 103926, {_}: divide ?541233 (divide ?541234 ?541236) =?= divide (multiply ?541233 ?541236) ?541234 [541236, 541234, 541233] by Demod 103925 with 3 at 1,3
+Id : 103927, {_}: multiply ?541233 (divide ?541236 ?541234) =<= divide (multiply ?541233 ?541236) ?541234 [541234, 541236, 541233] by Demod 103926 with 102924 at 2
+Id : 103998, {_}: multiply (multiply ?38 (divide ?39 ?37)) (divide ?37 ?39) =>= ?38 [37, 39, 38] by Demod 103476 with 103927 at 2
+Id : 104001, {_}: multiply ?99 ?97 =<= multiply (multiply ?99 (divide ?97 ?101)) ?101 [101, 97, 99] by Demod 103475 with 103998 at 2,2
+Id : 104034, {_}: multiply ?541526 (multiply ?541527 ?541528) =<= multiply (multiply ?541526 (multiply ?541527 (divide ?541528 ?541529))) ?541529 [541529, 541528, 541527, 541526] by Super 104001 with 103927 at 2,1,3
+Id : 44, {_}: multiply (inverse (divide (divide (divide ?198 ?198) ?199) (divide ?200 (multiply ?199 ?201)))) ?201 =>= ?200 [201, 200, 199, 198] by Demod 8 with 3 at 2
+Id : 46, {_}: multiply (inverse (divide (divide (divide ?210 ?210) ?211) ?212)) ?213 =?= inverse (divide (divide (divide ?214 ?214) ?215) (divide ?212 (divide ?215 (multiply ?211 ?213)))) [215, 214, 213, 212, 211, 210] by Super 44 with 2 at 2,1,1,2
+Id : 104145, {_}: multiply (divide ?212 (divide (divide ?210 ?210) ?211)) ?213 =?= inverse (divide (divide (divide ?214 ?214) ?215) (divide ?212 (divide ?215 (multiply ?211 ?213)))) [215, 214, 213, 211, 210, 212] by Demod 46 with 102788 at 1,2
+Id : 104146, {_}: multiply (divide ?212 (divide (divide ?210 ?210) ?211)) ?213 =?= divide (divide ?212 (divide ?215 (multiply ?211 ?213))) (divide (divide ?214 ?214) ?215) [214, 215, 213, 211, 210, 212] by Demod 104145 with 102788 at 3
+Id : 104147, {_}: multiply (multiply ?212 (divide ?211 (divide ?210 ?210))) ?213 =?= divide (divide ?212 (divide ?215 (multiply ?211 ?213))) (divide (divide ?214 ?214) ?215) [214, 215, 213, 210, 211, 212] by Demod 104146 with 102924 at 1,2
+Id : 104148, {_}: multiply (multiply ?212 (divide ?211 (divide ?210 ?210))) ?213 =?= multiply (divide ?212 (divide ?215 (multiply ?211 ?213))) (divide ?215 (divide ?214 ?214)) [214, 215, 213, 210, 211, 212] by Demod 104147 with 102924 at 3
+Id : 104149, {_}: multiply (multiply ?212 (multiply ?211 (divide ?210 ?210))) ?213 =?= multiply (divide ?212 (divide ?215 (multiply ?211 ?213))) (divide ?215 (divide ?214 ?214)) [214, 215, 213, 210, 211, 212] by Demod 104148 with 102924 at 2,1,2
+Id : 104150, {_}: multiply (multiply ?212 (multiply ?211 (divide ?210 ?210))) ?213 =?= multiply (multiply ?212 (divide (multiply ?211 ?213) ?215)) (divide ?215 (divide ?214 ?214)) [214, 215, 213, 210, 211, 212] by Demod 104149 with 102924 at 1,3
+Id : 104151, {_}: multiply (multiply ?212 (multiply ?211 (divide ?210 ?210))) ?213 =?= multiply (multiply ?212 (divide (multiply ?211 ?213) ?215)) (multiply ?215 (divide ?214 ?214)) [214, 215, 213, 210, 211, 212] by Demod 104150 with 102924 at 2,3
+Id : 93587, {_}: multiply (inverse (divide ?504068 ?504070)) ?504068 =>= ?504070 [504070, 504068] by Demod 92186 with 93111 at 2,2
+Id : 95434, {_}: multiply ?517965 (divide ?517966 ?517966) =>= ?517965 [517966, 517965] by Super 93587 with 93886 at 1,2
+Id : 104152, {_}: multiply (multiply ?212 ?211) ?213 =<= multiply (multiply ?212 (divide (multiply ?211 ?213) ?215)) (multiply ?215 (divide ?214 ?214)) [214, 215, 213, 211, 212] by Demod 104151 with 95434 at 2,1,2
+Id : 104153, {_}: multiply (multiply ?212 ?211) ?213 =<= multiply (multiply ?212 (multiply ?211 (divide ?213 ?215))) (multiply ?215 (divide ?214 ?214)) [214, 215, 213, 211, 212] by Demod 104152 with 103927 at 2,1,3
+Id : 104154, {_}: multiply (multiply ?212 ?211) ?213 =<= multiply (multiply ?212 (multiply ?211 (divide ?213 ?215))) ?215 [215, 213, 211, 212] by Demod 104153 with 95434 at 2,3
+Id : 115019, {_}: multiply ?541526 (multiply ?541527 ?541528) =?= multiply (multiply ?541526 ?541527) ?541528 [541528, 541527, 541526] by Demod 104034 with 104154 at 3
+Id : 115288, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 1 with 115019 at 2
+Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
+% SZS output end CNFRefutation for GRP480-1.p
+24007: solved GRP480-1.p in 40.758547 using nrkbo
+24007: status Unsatisfiable for GRP480-1.p
+NO CLASH, using fixed ground order
+24021: Facts:
+24021: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24021: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24021: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24021: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24021: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24021: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24021: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24021: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24021: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?26 ?27)
+ (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
+ [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
+24021: Goal:
+24021: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H58
+24021: Order:
+24021: nrkbo
+24021: Leaf order:
+24021: c 2 0 2 2,2,2
+24021: a 4 0 4 1,2
+24021: b 4 0 4 1,2,2
+24021: meet 17 2 4 0,2
+24021: join 19 2 4 0,2,2
+NO CLASH, using fixed ground order
+24022: Facts:
+24022: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24022: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24022: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24022: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24022: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24022: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24022: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24022: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24022: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?26 ?27)
+ (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
+ [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
+24022: Goal:
+24022: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H58
+24022: Order:
+24022: kbo
+24022: Leaf order:
+24022: c 2 0 2 2,2,2
+24022: a 4 0 4 1,2
+24022: b 4 0 4 1,2,2
+24022: meet 17 2 4 0,2
+24022: join 19 2 4 0,2,2
+NO CLASH, using fixed ground order
+24023: Facts:
+24023: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+24023: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+24023: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+24023: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+24023: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+24023: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+24023: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+24023: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+24023: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?26 ?27)
+ (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
+ [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
+24023: Goal:
+24023: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H58
+24023: Order:
+24023: lpo
+24023: Leaf order:
+24023: c 2 0 2 2,2,2
+24023: a 4 0 4 1,2
+24023: b 4 0 4 1,2,2
+24023: meet 17 2 4 0,2
+24023: join 19 2 4 0,2,2
+% SZS status Timeout for LAT168-1.p
+NO CLASH, using fixed ground order
+24053: Facts:
+24053: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+24053: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+24053: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+24053: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+24053: Goal:
+24053: Id : 1, {_}:
+ implies (implies (implies a b) (implies b a)) (implies b a) =>= truth
+ [] by prove_wajsberg_mv_4
+24053: Order:
+24053: kbo
+24053: Leaf order:
+24053: a 3 0 3 1,1,1,2
+24053: b 3 0 3 2,1,1,2
+24053: truth 4 0 1 3
+24053: not 2 1 0
+24053: implies 18 2 5 0,2
+NO CLASH, using fixed ground order
+24054: Facts:
+24054: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+24054: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+24054: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+24054: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+24054: Goal:
+24054: Id : 1, {_}:
+ implies (implies (implies a b) (implies b a)) (implies b a) =>= truth
+ [] by prove_wajsberg_mv_4
+24054: Order:
+24054: lpo
+24054: Leaf order:
+24054: a 3 0 3 1,1,1,2
+24054: b 3 0 3 2,1,1,2
+24054: truth 4 0 1 3
+24054: not 2 1 0
+24054: implies 18 2 5 0,2
+NO CLASH, using fixed ground order
+24052: Facts:
+24052: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+24052: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+24052: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+24052: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+24052: Goal:
+24052: Id : 1, {_}:
+ implies (implies (implies a b) (implies b a)) (implies b a) =>= truth
+ [] by prove_wajsberg_mv_4
+24052: Order:
+24052: nrkbo
+24052: Leaf order:
+24052: a 3 0 3 1,1,1,2
+24052: b 3 0 3 2,1,1,2
+24052: truth 4 0 1 3
+24052: not 2 1 0
+24052: implies 18 2 5 0,2
+% SZS status Timeout for LCL109-2.p
+NO CLASH, using fixed ground order
+24075: Facts:
+24075: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+24075: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+24075: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+24075: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+24075: Goal:
+24075: Id : 1, {_}:
+ implies x (implies y z) =<= implies y (implies x z)
+ [] by prove_wajsberg_lemma
+24075: Order:
+24075: nrkbo
+24075: Leaf order:
+24075: x 2 0 2 1,2
+24075: y 2 0 2 1,2,2
+24075: z 2 0 2 2,2,2
+24075: truth 3 0 0
+24075: not 2 1 0
+24075: implies 17 2 4 0,2
+NO CLASH, using fixed ground order
+24076: Facts:
+24076: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+24076: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+24076: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+24076: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+24076: Goal:
+24076: Id : 1, {_}:
+ implies x (implies y z) =<= implies y (implies x z)
+ [] by prove_wajsberg_lemma
+24076: Order:
+24076: kbo
+24076: Leaf order:
+24076: x 2 0 2 1,2
+24076: y 2 0 2 1,2,2
+24076: z 2 0 2 2,2,2
+24076: truth 3 0 0
+24076: not 2 1 0
+24076: implies 17 2 4 0,2
+NO CLASH, using fixed ground order
+24077: Facts:
+24077: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+24077: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+24077: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+24077: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+24077: Goal:
+24077: Id : 1, {_}:
+ implies x (implies y z) =<= implies y (implies x z)
+ [] by prove_wajsberg_lemma
+24077: Order:
+24077: lpo
+24077: Leaf order:
+24077: x 2 0 2 1,2
+24077: y 2 0 2 1,2,2
+24077: z 2 0 2 2,2,2
+24077: truth 3 0 0
+24077: not 2 1 0
+24077: implies 17 2 4 0,2
+% SZS status Timeout for LCL138-1.p
+NO CLASH, using fixed ground order
+24160: Facts:
+24160: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+24160: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+24160: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+24160: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+24160: Id : 6, {_}:
+ or ?14 ?15 =<= implies (not ?14) ?15
+ [15, 14] by or_definition ?14 ?15
+24160: Id : 7, {_}:
+ or (or ?17 ?18) ?19 =?= or ?17 (or ?18 ?19)
+ [19, 18, 17] by or_associativity ?17 ?18 ?19
+24160: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
+24160: Id : 9, {_}:
+ and ?24 ?25 =<= not (or (not ?24) (not ?25))
+ [25, 24] by and_definition ?24 ?25
+24160: Id : 10, {_}:
+ and (and ?27 ?28) ?29 =?= and ?27 (and ?28 ?29)
+ [29, 28, 27] by and_associativity ?27 ?28 ?29
+24160: Id : 11, {_}:
+ and ?31 ?32 =?= and ?32 ?31
+ [32, 31] by and_commutativity ?31 ?32
+24160: Id : 12, {_}:
+ xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
+ [35, 34] by xor_definition ?34 ?35
+24160: Id : 13, {_}:
+ xor ?37 ?38 =?= xor ?38 ?37
+ [38, 37] by xor_commutativity ?37 ?38
+24160: Id : 14, {_}:
+ and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
+ [41, 40] by and_star_definition ?40 ?41
+24160: Id : 15, {_}:
+ and_star (and_star ?43 ?44) ?45 =?= and_star ?43 (and_star ?44 ?45)
+ [45, 44, 43] by and_star_associativity ?43 ?44 ?45
+24160: Id : 16, {_}:
+ and_star ?47 ?48 =?= and_star ?48 ?47
+ [48, 47] by and_star_commutativity ?47 ?48
+24160: Id : 17, {_}: not truth =>= falsehood [] by false_definition
+24160: Goal:
+24160: Id : 1, {_}:
+ xor x (xor truth y) =<= xor (xor x truth) y
+ [] by prove_alternative_wajsberg_axiom
+24160: Order:
+24160: nrkbo
+24160: Leaf order:
+24160: falsehood 1 0 0
+24160: x 2 0 2 1,2
+24160: y 2 0 2 2,2,2
+24160: truth 6 0 2 1,2,2
+24160: not 12 1 0
+24160: and_star 7 2 0
+24160: xor 7 2 4 0,2
+24160: and 9 2 0
+24160: or 10 2 0
+24160: implies 14 2 0
+NO CLASH, using fixed ground order
+24161: Facts:
+24161: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+24161: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+24161: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+24161: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+24161: Id : 6, {_}:
+ or ?14 ?15 =<= implies (not ?14) ?15
+ [15, 14] by or_definition ?14 ?15
+24161: Id : 7, {_}:
+ or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
+ [19, 18, 17] by or_associativity ?17 ?18 ?19
+24161: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
+24161: Id : 9, {_}:
+ and ?24 ?25 =<= not (or (not ?24) (not ?25))
+ [25, 24] by and_definition ?24 ?25
+24161: Id : 10, {_}:
+ and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
+ [29, 28, 27] by and_associativity ?27 ?28 ?29
+24161: Id : 11, {_}:
+ and ?31 ?32 =?= and ?32 ?31
+ [32, 31] by and_commutativity ?31 ?32
+24161: Id : 12, {_}:
+ xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
+ [35, 34] by xor_definition ?34 ?35
+24161: Id : 13, {_}:
+ xor ?37 ?38 =?= xor ?38 ?37
+ [38, 37] by xor_commutativity ?37 ?38
+24161: Id : 14, {_}:
+ and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
+ [41, 40] by and_star_definition ?40 ?41
+24161: Id : 15, {_}:
+ and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45)
+ [45, 44, 43] by and_star_associativity ?43 ?44 ?45
+24161: Id : 16, {_}:
+ and_star ?47 ?48 =?= and_star ?48 ?47
+ [48, 47] by and_star_commutativity ?47 ?48
+24161: Id : 17, {_}: not truth =>= falsehood [] by false_definition
+24161: Goal:
+24161: Id : 1, {_}:
+ xor x (xor truth y) =<= xor (xor x truth) y
+ [] by prove_alternative_wajsberg_axiom
+24161: Order:
+24161: kbo
+24161: Leaf order:
+24161: falsehood 1 0 0
+24161: x 2 0 2 1,2
+24161: y 2 0 2 2,2,2
+24161: truth 6 0 2 1,2,2
+24161: not 12 1 0
+24161: and_star 7 2 0
+24161: xor 7 2 4 0,2
+24161: and 9 2 0
+24161: or 10 2 0
+24161: implies 14 2 0
+NO CLASH, using fixed ground order
+24162: Facts:
+24162: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+24162: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+24162: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+24162: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+24162: Id : 6, {_}:
+ or ?14 ?15 =<= implies (not ?14) ?15
+ [15, 14] by or_definition ?14 ?15
+24162: Id : 7, {_}:
+ or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
+ [19, 18, 17] by or_associativity ?17 ?18 ?19
+24162: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
+24162: Id : 9, {_}:
+ and ?24 ?25 =<= not (or (not ?24) (not ?25))
+ [25, 24] by and_definition ?24 ?25
+24162: Id : 10, {_}:
+ and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
+ [29, 28, 27] by and_associativity ?27 ?28 ?29
+24162: Id : 11, {_}:
+ and ?31 ?32 =?= and ?32 ?31
+ [32, 31] by and_commutativity ?31 ?32
+24162: Id : 12, {_}:
+ xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
+ [35, 34] by xor_definition ?34 ?35
+24162: Id : 13, {_}:
+ xor ?37 ?38 =?= xor ?38 ?37
+ [38, 37] by xor_commutativity ?37 ?38
+24162: Id : 14, {_}:
+ and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
+ [41, 40] by and_star_definition ?40 ?41
+24162: Id : 15, {_}:
+ and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45)
+ [45, 44, 43] by and_star_associativity ?43 ?44 ?45
+24162: Id : 16, {_}:
+ and_star ?47 ?48 =?= and_star ?48 ?47
+ [48, 47] by and_star_commutativity ?47 ?48
+24162: Id : 17, {_}: not truth =>= falsehood [] by false_definition
+24162: Goal:
+24162: Id : 1, {_}:
+ xor x (xor truth y) =<= xor (xor x truth) y
+ [] by prove_alternative_wajsberg_axiom
+24162: Order:
+24162: lpo
+24162: Leaf order:
+24162: falsehood 1 0 0
+24162: x 2 0 2 1,2
+24162: y 2 0 2 2,2,2
+24162: truth 6 0 2 1,2,2
+24162: not 12 1 0
+24162: and_star 7 2 0
+24162: xor 7 2 4 0,2
+24162: and 9 2 0
+24162: or 10 2 0
+24162: implies 14 2 0
+Statistics :
+Max weight : 32
+Found proof, 8.845379s
+% SZS status Unsatisfiable for LCL159-1.p
+% SZS output start CNFRefutation for LCL159-1.p
+Id : 11, {_}: and ?31 ?32 =?= and ?32 ?31 [32, 31] by and_commutativity ?31 ?32
+Id : 10, {_}: and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29) [29, 28, 27] by and_associativity ?27 ?28 ?29
+Id : 13, {_}: xor ?37 ?38 =?= xor ?38 ?37 [38, 37] by xor_commutativity ?37 ?38
+Id : 5, {_}: implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth [12, 11] by wajsberg_4 ?11 ?12
+Id : 7, {_}: or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19) [19, 18, 17] by or_associativity ?17 ?18 ?19
+Id : 39, {_}: implies (implies ?111 ?112) ?112 =?= implies (implies ?112 ?111) ?111 [112, 111] by wajsberg_3 ?111 ?112
+Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+Id : 3, {_}: implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) =>= truth [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+Id : 20, {_}: implies (implies ?55 ?56) (implies (implies ?56 ?57) (implies ?55 ?57)) =>= truth [57, 56, 55] by wajsberg_2 ?55 ?56 ?57
+Id : 17, {_}: not truth =>= falsehood [] by false_definition
+Id : 4, {_}: implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 [9, 8] by wajsberg_3 ?8 ?9
+Id : 6, {_}: or ?14 ?15 =<= implies (not ?14) ?15 [15, 14] by or_definition ?14 ?15
+Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
+Id : 9, {_}: and ?24 ?25 =<= not (or (not ?24) (not ?25)) [25, 24] by and_definition ?24 ?25
+Id : 14, {_}: and_star ?40 ?41 =<= not (or (not ?40) (not ?41)) [41, 40] by and_star_definition ?40 ?41
+Id : 12, {_}: xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35) [35, 34] by xor_definition ?34 ?35
+Id : 154, {_}: and_star ?40 ?41 =<= and ?40 ?41 [41, 40] by Demod 14 with 9 at 3
+Id : 162, {_}: xor ?34 ?35 =<= or (and_star ?34 (not ?35)) (and (not ?34) ?35) [35, 34] by Demod 12 with 154 at 1,3
+Id : 163, {_}: xor ?34 ?35 =<= or (and_star ?34 (not ?35)) (and_star (not ?34) ?35) [35, 34] by Demod 162 with 154 at 2,3
+Id : 173, {_}: or truth ?418 =<= implies falsehood ?418 [418] by Super 6 with 17 at 1,3
+Id : 183, {_}: implies (implies ?424 falsehood) falsehood =>= implies (or truth ?424) ?424 [424] by Super 4 with 173 at 1,3
+Id : 22, {_}: implies (implies (implies ?62 ?63) ?64) (implies (implies ?64 (implies (implies ?63 ?65) (implies ?62 ?65))) truth) =>= truth [65, 64, 63, 62] by Super 20 with 3 at 2,2,2
+Id : 437, {_}: implies (implies ?923 truth) (implies ?924 (implies ?923 ?924)) =>= truth [924, 923] by Super 20 with 2 at 1,2,2
+Id : 438, {_}: implies (implies truth truth) (implies ?926 ?926) =>= truth [926] by Super 437 with 2 at 2,2,2
+Id : 471, {_}: implies truth (implies ?926 ?926) =>= truth [926] by Demod 438 with 2 at 1,2
+Id : 472, {_}: implies ?926 ?926 =>= truth [926] by Demod 471 with 2 at 2
+Id : 501, {_}: implies (implies (implies ?1003 ?1003) ?1004) (implies (implies ?1004 truth) truth) =>= truth [1004, 1003] by Super 22 with 472 at 2,1,2,2
+Id : 529, {_}: implies (implies truth ?1004) (implies (implies ?1004 truth) truth) =>= truth [1004] by Demod 501 with 472 at 1,1,2
+Id : 40, {_}: implies (implies ?114 truth) truth =>= implies ?114 ?114 [114] by Super 39 with 2 at 1,3
+Id : 495, {_}: implies (implies ?114 truth) truth =>= truth [114] by Demod 40 with 472 at 3
+Id : 530, {_}: implies (implies truth ?1004) truth =>= truth [1004] by Demod 529 with 495 at 2,2
+Id : 531, {_}: implies ?1004 truth =>= truth [1004] by Demod 530 with 2 at 1,2
+Id : 567, {_}: or ?1050 truth =>= truth [1050] by Super 6 with 531 at 3
+Id : 621, {_}: or truth ?1090 =>= truth [1090] by Super 8 with 567 at 3
+Id : 637, {_}: implies (implies ?424 falsehood) falsehood =>= implies truth ?424 [424] by Demod 183 with 621 at 1,3
+Id : 638, {_}: implies (implies ?424 falsehood) falsehood =>= ?424 [424] by Demod 637 with 2 at 3
+Id : 157, {_}: and_star ?24 ?25 =<= not (or (not ?24) (not ?25)) [25, 24] by Demod 9 with 154 at 2
+Id : 327, {_}: and_star truth ?755 =<= not (or falsehood (not ?755)) [755] by Super 157 with 17 at 1,1,3
+Id : 328, {_}: and_star truth truth =<= not (or falsehood falsehood) [] by Super 327 with 17 at 2,1,3
+Id : 341, {_}: or (or falsehood falsehood) ?773 =<= implies (and_star truth truth) ?773 [773] by Super 6 with 328 at 1,3
+Id : 346, {_}: or falsehood (or falsehood ?773) =<= implies (and_star truth truth) ?773 [773] by Demod 341 with 7 at 2
+Id : 750, {_}: implies (or falsehood (or falsehood falsehood)) falsehood =>= and_star truth truth [] by Super 638 with 346 at 1,2
+Id : 69, {_}: implies (or ?11 (not ?12)) (implies ?12 ?11) =>= truth [12, 11] by Demod 5 with 6 at 1,2
+Id : 174, {_}: implies (or ?420 falsehood) (implies truth ?420) =>= truth [420] by Super 69 with 17 at 2,1,2
+Id : 177, {_}: implies (or ?420 falsehood) ?420 =>= truth [420] by Demod 174 with 2 at 2,2
+Id : 777, {_}: implies truth falsehood =>= or falsehood falsehood [] by Super 638 with 177 at 1,2
+Id : 799, {_}: falsehood =<= or falsehood falsehood [] by Demod 777 with 2 at 2
+Id : 805, {_}: and_star truth truth =>= not falsehood [] by Demod 328 with 799 at 1,3
+Id : 809, {_}: or falsehood (or falsehood ?773) =<= implies (not falsehood) ?773 [773] by Demod 346 with 805 at 1,3
+Id : 810, {_}: or falsehood (or falsehood ?773) =>= or falsehood ?773 [773] by Demod 809 with 6 at 3
+Id : 898, {_}: implies (or falsehood falsehood) falsehood =>= and_star truth truth [] by Demod 750 with 810 at 1,2
+Id : 899, {_}: implies (or falsehood falsehood) falsehood =>= not falsehood [] by Demod 898 with 805 at 3
+Id : 900, {_}: truth =<= not falsehood [] by Demod 899 with 177 at 2
+Id : 904, {_}: or falsehood ?1384 =<= implies truth ?1384 [1384] by Super 6 with 900 at 1,3
+Id : 919, {_}: or falsehood ?1384 =>= ?1384 [1384] by Demod 904 with 2 at 3
+Id : 1209, {_}: or ?1836 falsehood =>= ?1836 [1836] by Super 8 with 919 at 3
+Id : 908, {_}: and_star falsehood ?1392 =<= not (or truth (not ?1392)) [1392] by Super 157 with 900 at 1,1,3
+Id : 916, {_}: and_star falsehood ?1392 =>= not truth [1392] by Demod 908 with 621 at 1,3
+Id : 917, {_}: and_star falsehood ?1392 =>= falsehood [1392] by Demod 916 with 17 at 3
+Id : 1175, {_}: xor falsehood ?1822 =<= or falsehood (and_star (not falsehood) ?1822) [1822] by Super 163 with 917 at 1,3
+Id : 1182, {_}: xor falsehood ?1822 =<= or falsehood (and_star truth ?1822) [1822] by Demod 1175 with 900 at 1,2,3
+Id : 907, {_}: and_star ?1390 falsehood =<= not (or (not ?1390) truth) [1390] by Super 157 with 900 at 2,1,3
+Id : 913, {_}: and_star ?1390 falsehood =<= not (or truth (not ?1390)) [1390] by Demod 907 with 8 at 1,3
+Id : 914, {_}: and_star ?1390 falsehood =>= not truth [1390] by Demod 913 with 621 at 1,3
+Id : 915, {_}: and_star ?1390 falsehood =>= falsehood [1390] by Demod 914 with 17 at 3
+Id : 1144, {_}: xor ?1792 falsehood =<= or (and_star ?1792 (not falsehood)) falsehood [1792] by Super 163 with 915 at 2,3
+Id : 1161, {_}: xor ?1792 falsehood =<= or falsehood (and_star ?1792 (not falsehood)) [1792] by Demod 1144 with 8 at 3
+Id : 1162, {_}: xor ?1792 falsehood =<= or falsehood (and_star ?1792 truth) [1792] by Demod 1161 with 900 at 2,2,3
+Id : 1257, {_}: xor ?1792 falsehood =>= and_star ?1792 truth [1792] by Demod 1162 with 919 at 3
+Id : 1258, {_}: xor falsehood ?1880 =>= and_star ?1880 truth [1880] by Super 13 with 1257 at 3
+Id : 1283, {_}: and_star ?1822 truth =<= or falsehood (and_star truth ?1822) [1822] by Demod 1182 with 1258 at 2
+Id : 1284, {_}: and_star ?1822 truth =?= and_star truth ?1822 [1822] by Demod 1283 with 919 at 3
+Id : 170, {_}: and_star truth ?412 =<= not (or falsehood (not ?412)) [412] by Super 157 with 17 at 1,1,3
+Id : 1193, {_}: and_star truth ?412 =>= not (not ?412) [412] by Demod 170 with 919 at 1,3
+Id : 1285, {_}: and_star ?1822 truth =>= not (not ?1822) [1822] by Demod 1284 with 1193 at 3
+Id : 158, {_}: and_star (and ?27 ?28) ?29 =<= and ?27 (and ?28 ?29) [29, 28, 27] by Demod 10 with 154 at 2
+Id : 159, {_}: and_star (and ?27 ?28) ?29 =?= and_star ?27 (and ?28 ?29) [29, 28, 27] by Demod 158 with 154 at 3
+Id : 160, {_}: and_star (and_star ?27 ?28) ?29 =?= and_star ?27 (and ?28 ?29) [29, 28, 27] by Demod 159 with 154 at 1,2
+Id : 161, {_}: and_star (and_star ?27 ?28) ?29 =>= and_star ?27 (and_star ?28 ?29) [29, 28, 27] by Demod 160 with 154 at 2,3
+Id : 1290, {_}: and_star (not (not ?1909)) ?1910 =>= and_star ?1909 (and_star truth ?1910) [1910, 1909] by Super 161 with 1285 at 1,2
+Id : 1306, {_}: and_star (not (not ?1909)) ?1910 =>= and_star ?1909 (not (not ?1910)) [1910, 1909] by Demod 1290 with 1193 at 2,3
+Id : 1659, {_}: and_star ?2411 (not (not truth)) =>= not (not (not (not ?2411))) [2411] by Super 1285 with 1306 at 2
+Id : 1669, {_}: and_star ?2411 (not falsehood) =>= not (not (not (not ?2411))) [2411] by Demod 1659 with 17 at 1,2,2
+Id : 1670, {_}: and_star ?2411 truth =>= not (not (not (not ?2411))) [2411] by Demod 1669 with 900 at 2,2
+Id : 1671, {_}: not (not ?2411) =<= not (not (not (not ?2411))) [2411] by Demod 1670 with 1285 at 2
+Id : 1703, {_}: or (not (not (not ?2451))) ?2452 =<= implies (not (not ?2451)) ?2452 [2452, 2451] by Super 6 with 1671 at 1,3
+Id : 1722, {_}: or (not (not (not ?2451))) ?2452 =>= or (not ?2451) ?2452 [2452, 2451] by Demod 1703 with 6 at 3
+Id : 1999, {_}: or (not ?2759) falsehood =>= not (not (not ?2759)) [2759] by Super 1209 with 1722 at 2
+Id : 2014, {_}: or falsehood (not ?2759) =>= not (not (not ?2759)) [2759] by Demod 1999 with 8 at 2
+Id : 2015, {_}: not ?2759 =<= not (not (not ?2759)) [2759] by Demod 2014 with 919 at 2
+Id : 2063, {_}: or (not (not ?2816)) ?2817 =<= implies (not ?2816) ?2817 [2817, 2816] by Super 6 with 2015 at 1,3
+Id : 2088, {_}: or (not (not ?2816)) ?2817 =>= or ?2816 ?2817 [2817, 2816] by Demod 2063 with 6 at 3
+Id : 2169, {_}: or ?2929 falsehood =>= not (not ?2929) [2929] by Super 1209 with 2088 at 2
+Id : 2202, {_}: ?2929 =<= not (not ?2929) [2929] by Demod 2169 with 1209 at 2
+Id : 2232, {_}: and_star ?2997 (not ?2998) =<= not (or (not ?2997) ?2998) [2998, 2997] by Super 157 with 2202 at 2,1,3
+Id : 2716, {_}: or (not ?3623) ?3624 =>= not (and_star ?3623 (not ?3624)) [3624, 3623] by Super 2202 with 2232 at 1,3
+Id : 2722, {_}: or ?3642 ?3643 =>= not (and_star (not ?3642) (not ?3643)) [3643, 3642] by Super 2716 with 2202 at 1,2
+Id : 2787, {_}: xor ?34 ?35 =>= not (and_star (not (and_star ?34 (not ?35))) (not (and_star (not ?34) ?35))) [35, 34] by Demod 163 with 2722 at 3
+Id : 2819, {_}: not (and_star (not (and_star ?37 (not ?38))) (not (and_star (not ?37) ?38))) =<= xor ?38 ?37 [38, 37] by Demod 13 with 2787 at 2
+Id : 2820, {_}: not (and_star (not (and_star ?37 (not ?38))) (not (and_star (not ?37) ?38))) =?= not (and_star (not (and_star ?38 (not ?37))) (not (and_star (not ?38) ?37))) [38, 37] by Demod 2819 with 2787 at 3
+Id : 2785, {_}: not (and_star (not ?21) (not ?22)) =<= or ?22 ?21 [22, 21] by Demod 8 with 2722 at 2
+Id : 2786, {_}: not (and_star (not ?21) (not ?22)) =?= not (and_star (not ?22) (not ?21)) [22, 21] by Demod 2785 with 2722 at 3
+Id : 155, {_}: and_star ?31 ?32 =<= and ?32 ?31 [32, 31] by Demod 11 with 154 at 2
+Id : 156, {_}: and_star ?31 ?32 =?= and_star ?32 ?31 [32, 31] by Demod 155 with 154 at 3
+Id : 2226, {_}: and_star truth ?412 =>= ?412 [412] by Demod 1193 with 2202 at 3
+Id : 2228, {_}: and_star ?1822 truth =>= ?1822 [1822] by Demod 1285 with 2202 at 3
+Id : 2921, {_}: not (and_star (not (and_star x y)) (not (and_star (not x) (not y)))) === not (and_star (not (and_star x y)) (not (and_star (not x) (not y)))) [] by Demod 2920 with 156 at 1,1,1,3
+Id : 2920, {_}: not (and_star (not (and_star x y)) (not (and_star (not x) (not y)))) =<= not (and_star (not (and_star y x)) (not (and_star (not x) (not y)))) [] by Demod 2919 with 2786 at 2,1,3
+Id : 2919, {_}: not (and_star (not (and_star x y)) (not (and_star (not x) (not y)))) =<= not (and_star (not (and_star y x)) (not (and_star (not y) (not x)))) [] by Demod 2918 with 2228 at 2,1,1,1,3
+Id : 2918, {_}: not (and_star (not (and_star x y)) (not (and_star (not x) (not y)))) =<= not (and_star (not (and_star y (and_star x truth))) (not (and_star (not y) (not x)))) [] by Demod 2917 with 2228 at 1,2,1,2,1,3
+Id : 2917, {_}: not (and_star (not (and_star x y)) (not (and_star (not x) (not y)))) =<= not (and_star (not (and_star y (and_star x truth))) (not (and_star (not y) (not (and_star x truth))))) [] by Demod 2916 with 900 at 2,2,1,1,1,3
+Id : 2916, {_}: not (and_star (not (and_star x y)) (not (and_star (not x) (not y)))) =<= not (and_star (not (and_star y (and_star x (not falsehood)))) (not (and_star (not y) (not (and_star x truth))))) [] by Demod 2915 with 2228 at 1,2,1,2,1,2
+Id : 2915, {_}: not (and_star (not (and_star x y)) (not (and_star (not x) (not (and_star y truth))))) =<= not (and_star (not (and_star y (and_star x (not falsehood)))) (not (and_star (not y) (not (and_star x truth))))) [] by Demod 2914 with 2228 at 2,1,1,1,2
+Id : 2914, {_}: not (and_star (not (and_star x (and_star y truth))) (not (and_star (not x) (not (and_star y truth))))) =<= not (and_star (not (and_star y (and_star x (not falsehood)))) (not (and_star (not y) (not (and_star x truth))))) [] by Demod 2913 with 2786 at 3
+Id : 2913, {_}: not (and_star (not (and_star x (and_star y truth))) (not (and_star (not x) (not (and_star y truth))))) =<= not (and_star (not (and_star (not y) (not (and_star x truth)))) (not (and_star y (and_star x (not falsehood))))) [] by Demod 2912 with 900 at 2,1,2,1,2,1,2
+Id : 2912, {_}: not (and_star (not (and_star x (and_star y truth))) (not (and_star (not x) (not (and_star y (not falsehood)))))) =<= not (and_star (not (and_star (not y) (not (and_star x truth)))) (not (and_star y (and_star x (not falsehood))))) [] by Demod 2911 with 900 at 2,2,1,1,1,2
+Id : 2911, {_}: not (and_star (not (and_star x (and_star y (not falsehood)))) (not (and_star (not x) (not (and_star y (not falsehood)))))) =<= not (and_star (not (and_star (not y) (not (and_star x truth)))) (not (and_star y (and_star x (not falsehood))))) [] by Demod 2910 with 917 at 1,2,2,1,2,1,3
+Id : 2910, {_}: not (and_star (not (and_star x (and_star y (not falsehood)))) (not (and_star (not x) (not (and_star y (not falsehood)))))) =<= not (and_star (not (and_star (not y) (not (and_star x truth)))) (not (and_star y (and_star x (not (and_star falsehood x)))))) [] by Demod 2909 with 2202 at 1,2,1,2,1,3
+Id : 2909, {_}: not (and_star (not (and_star x (and_star y (not falsehood)))) (not (and_star (not x) (not (and_star y (not falsehood)))))) =<= not (and_star (not (and_star (not y) (not (and_star x truth)))) (not (and_star y (and_star (not (not x)) (not (and_star falsehood x)))))) [] by Demod 2908 with 900 at 2,1,2,1,1,1,3
+Id : 2908, {_}: not (and_star (not (and_star x (and_star y (not falsehood)))) (not (and_star (not x) (not (and_star y (not falsehood)))))) =<= not (and_star (not (and_star (not y) (not (and_star x (not falsehood))))) (not (and_star y (and_star (not (not x)) (not (and_star falsehood x)))))) [] by Demod 2907 with 917 at 1,2,1,2,1,2,1,2
+Id : 2907, {_}: not (and_star (not (and_star x (and_star y (not falsehood)))) (not (and_star (not x) (not (and_star y (not (and_star falsehood y))))))) =<= not (and_star (not (and_star (not y) (not (and_star x (not falsehood))))) (not (and_star y (and_star (not (not x)) (not (and_star falsehood x)))))) [] by Demod 2906 with 2202 at 1,1,2,1,2,1,2
+Id : 2906, {_}: not (and_star (not (and_star x (and_star y (not falsehood)))) (not (and_star (not x) (not (and_star (not (not y)) (not (and_star falsehood y))))))) =<= not (and_star (not (and_star (not y) (not (and_star x (not falsehood))))) (not (and_star y (and_star (not (not x)) (not (and_star falsehood x)))))) [] by Demod 2905 with 917 at 1,2,2,1,1,1,2
+Id : 2905, {_}: not (and_star (not (and_star x (and_star y (not (and_star falsehood y))))) (not (and_star (not x) (not (and_star (not (not y)) (not (and_star falsehood y))))))) =<= not (and_star (not (and_star (not y) (not (and_star x (not falsehood))))) (not (and_star y (and_star (not (not x)) (not (and_star falsehood x)))))) [] by Demod 2904 with 156 at 2,1,2,1,3
+Id : 2904, {_}: not (and_star (not (and_star x (and_star y (not (and_star falsehood y))))) (not (and_star (not x) (not (and_star (not (not y)) (not (and_star falsehood y))))))) =<= not (and_star (not (and_star (not y) (not (and_star x (not falsehood))))) (not (and_star y (and_star (not (and_star falsehood x)) (not (not x)))))) [] by Demod 2903 with 917 at 1,2,1,2,1,1,1,3
+Id : 2903, {_}: not (and_star (not (and_star x (and_star y (not (and_star falsehood y))))) (not (and_star (not x) (not (and_star (not (not y)) (not (and_star falsehood y))))))) =<= not (and_star (not (and_star (not y) (not (and_star x (not (and_star falsehood x)))))) (not (and_star y (and_star (not (and_star falsehood x)) (not (not x)))))) [] by Demod 2902 with 2202 at 1,1,2,1,1,1,3
+Id : 2902, {_}: not (and_star (not (and_star x (and_star y (not (and_star falsehood y))))) (not (and_star (not x) (not (and_star (not (not y)) (not (and_star falsehood y))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (not x)) (not (and_star falsehood x)))))) (not (and_star y (and_star (not (and_star falsehood x)) (not (not x)))))) [] by Demod 2901 with 2786 at 2,1,2,1,2
+Id : 2901, {_}: not (and_star (not (and_star x (and_star y (not (and_star falsehood y))))) (not (and_star (not x) (not (and_star (not (and_star falsehood y)) (not (not y))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (not x)) (not (and_star falsehood x)))))) (not (and_star y (and_star (not (and_star falsehood x)) (not (not x)))))) [] by Demod 2900 with 156 at 1,2,2,1,1,1,2
+Id : 2900, {_}: not (and_star (not (and_star x (and_star y (not (and_star y falsehood))))) (not (and_star (not x) (not (and_star (not (and_star falsehood y)) (not (not y))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (not x)) (not (and_star falsehood x)))))) (not (and_star y (and_star (not (and_star falsehood x)) (not (not x)))))) [] by Demod 2899 with 2226 at 1,2,2,1,2,1,3
+Id : 2899, {_}: not (and_star (not (and_star x (and_star y (not (and_star y falsehood))))) (not (and_star (not x) (not (and_star (not (and_star falsehood y)) (not (not y))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (not x)) (not (and_star falsehood x)))))) (not (and_star y (and_star (not (and_star falsehood x)) (not (and_star truth (not x))))))) [] by Demod 2898 with 156 at 1,1,2,1,2,1,3
+Id : 2898, {_}: not (and_star (not (and_star x (and_star y (not (and_star y falsehood))))) (not (and_star (not x) (not (and_star (not (and_star falsehood y)) (not (not y))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (not x)) (not (and_star falsehood x)))))) (not (and_star y (and_star (not (and_star x falsehood)) (not (and_star truth (not x))))))) [] by Demod 2897 with 2786 at 2,1,1,1,3
+Id : 2897, {_}: not (and_star (not (and_star x (and_star y (not (and_star y falsehood))))) (not (and_star (not x) (not (and_star (not (and_star falsehood y)) (not (not y))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star falsehood x)) (not (not x)))))) (not (and_star y (and_star (not (and_star x falsehood)) (not (and_star truth (not x))))))) [] by Demod 2896 with 2226 at 1,2,1,2,1,2,1,2
+Id : 2896, {_}: not (and_star (not (and_star x (and_star y (not (and_star y falsehood))))) (not (and_star (not x) (not (and_star (not (and_star falsehood y)) (not (and_star truth (not y)))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star falsehood x)) (not (not x)))))) (not (and_star y (and_star (not (and_star x falsehood)) (not (and_star truth (not x))))))) [] by Demod 2895 with 156 at 1,1,1,2,1,2,1,2
+Id : 2895, {_}: not (and_star (not (and_star x (and_star y (not (and_star y falsehood))))) (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y)))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star falsehood x)) (not (not x)))))) (not (and_star y (and_star (not (and_star x falsehood)) (not (and_star truth (not x))))))) [] by Demod 2894 with 17 at 2,1,2,2,1,1,1,2
+Id : 2894, {_}: not (and_star (not (and_star x (and_star y (not (and_star y (not truth)))))) (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y)))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star falsehood x)) (not (not x)))))) (not (and_star y (and_star (not (and_star x falsehood)) (not (and_star truth (not x))))))) [] by Demod 2893 with 2202 at 1,2,1,1,1,2
+Id : 2893, {_}: not (and_star (not (and_star x (and_star (not (not y)) (not (and_star y (not truth)))))) (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y)))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star falsehood x)) (not (not x)))))) (not (and_star y (and_star (not (and_star x falsehood)) (not (and_star truth (not x))))))) [] by Demod 2892 with 156 at 1,2,2,1,2,1,3
+Id : 2892, {_}: not (and_star (not (and_star x (and_star (not (not y)) (not (and_star y (not truth)))))) (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y)))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star falsehood x)) (not (not x)))))) (not (and_star y (and_star (not (and_star x falsehood)) (not (and_star (not x) truth)))))) [] by Demod 2891 with 17 at 2,1,1,2,1,2,1,3
+Id : 2891, {_}: not (and_star (not (and_star x (and_star (not (not y)) (not (and_star y (not truth)))))) (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y)))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star falsehood x)) (not (not x)))))) (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth)))))) [] by Demod 2890 with 2226 at 1,2,1,2,1,1,1,3
+Id : 2890, {_}: not (and_star (not (and_star x (and_star (not (not y)) (not (and_star y (not truth)))))) (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y)))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star falsehood x)) (not (and_star truth (not x))))))) (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth)))))) [] by Demod 2889 with 156 at 1,1,1,2,1,1,1,3
+Id : 2889, {_}: not (and_star (not (and_star x (and_star (not (not y)) (not (and_star y (not truth)))))) (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y)))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star x falsehood)) (not (and_star truth (not x))))))) (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth)))))) [] by Demod 2888 with 2786 at 2
+Id : 2888, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y))))))) (not (and_star x (and_star (not (not y)) (not (and_star y (not truth))))))) =>= not (and_star (not (and_star (not y) (not (and_star (not (and_star x falsehood)) (not (and_star truth (not x))))))) (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth)))))) [] by Demod 2887 with 2786 at 3
+Id : 2887, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y))))))) (not (and_star x (and_star (not (not y)) (not (and_star y (not truth))))))) =>= not (and_star (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))) (not (and_star (not y) (not (and_star (not (and_star x falsehood)) (not (and_star truth (not x)))))))) [] by Demod 2886 with 156 at 1,2,2,1,2,1,2
+Id : 2886, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y))))))) (not (and_star x (and_star (not (not y)) (not (and_star (not truth) y)))))) =>= not (and_star (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))) (not (and_star (not y) (not (and_star (not (and_star x falsehood)) (not (and_star truth (not x)))))))) [] by Demod 2885 with 2226 at 1,1,2,1,2,1,2
+Id : 2885, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y))))))) (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y)))))) =>= not (and_star (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))) (not (and_star (not y) (not (and_star (not (and_star x falsehood)) (not (and_star truth (not x)))))))) [] by Demod 2884 with 156 at 1,2,1,2,1,1,1,2
+Id : 2884, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star (not y) truth)))))) (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y)))))) =>= not (and_star (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))) (not (and_star (not y) (not (and_star (not (and_star x falsehood)) (not (and_star truth (not x)))))))) [] by Demod 2883 with 17 at 2,1,1,1,2,1,1,1,2
+Id : 2883, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y (not truth))) (not (and_star (not y) truth)))))) (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y)))))) =>= not (and_star (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))) (not (and_star (not y) (not (and_star (not (and_star x falsehood)) (not (and_star truth (not x)))))))) [] by Demod 2882 with 156 at 1,2,1,2,1,2,1,3
+Id : 2882, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y (not truth))) (not (and_star (not y) truth)))))) (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y)))))) =>= not (and_star (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))) (not (and_star (not y) (not (and_star (not (and_star x falsehood)) (not (and_star (not x) truth))))))) [] by Demod 2881 with 17 at 2,1,1,1,2,1,2,1,3
+Id : 2881, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y (not truth))) (not (and_star (not y) truth)))))) (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y)))))) =>= not (and_star (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))) (not (and_star (not y) (not (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))))) [] by Demod 2880 with 2202 at 2,1,1,1,3
+Id : 2880, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y (not truth))) (not (and_star (not y) truth)))))) (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y)))))) =>= not (and_star (not (and_star y (not (not (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))))) (not (and_star (not y) (not (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))))) [] by Demod 2879 with 2786 at 2
+Id : 2879, {_}: not (and_star (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))) (not (and_star (not x) (not (and_star (not (and_star y (not truth))) (not (and_star (not y) truth))))))) =>= not (and_star (not (and_star y (not (not (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))))) (not (and_star (not y) (not (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))))) [] by Demod 2878 with 2787 at 2,1,2,1,3
+Id : 2878, {_}: not (and_star (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))) (not (and_star (not x) (not (and_star (not (and_star y (not truth))) (not (and_star (not y) truth))))))) =<= not (and_star (not (and_star y (not (not (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))))) (not (and_star (not y) (xor x truth)))) [] by Demod 2877 with 2787 at 1,2,1,1,1,3
+Id : 2877, {_}: not (and_star (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))) (not (and_star (not x) (not (and_star (not (and_star y (not truth))) (not (and_star (not y) truth))))))) =<= not (and_star (not (and_star y (not (xor x truth)))) (not (and_star (not y) (xor x truth)))) [] by Demod 2876 with 2820 at 2,1,2,1,2
+Id : 2876, {_}: not (and_star (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))) (not (and_star (not x) (not (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))))) =<= not (and_star (not (and_star y (not (xor x truth)))) (not (and_star (not y) (xor x truth)))) [] by Demod 2875 with 2202 at 2,1,1,1,2
+Id : 2875, {_}: not (and_star (not (and_star x (not (not (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))))) (not (and_star (not x) (not (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))))) =<= not (and_star (not (and_star y (not (xor x truth)))) (not (and_star (not y) (xor x truth)))) [] by Demod 2874 with 2820 at 3
+Id : 2874, {_}: not (and_star (not (and_star x (not (not (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))))) (not (and_star (not x) (not (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))))) =<= not (and_star (not (and_star (xor x truth) (not y))) (not (and_star (not (xor x truth)) y))) [] by Demod 2873 with 2787 at 2,1,2,1,2
+Id : 2873, {_}: not (and_star (not (and_star x (not (not (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))))) (not (and_star (not x) (xor truth y)))) =>= not (and_star (not (and_star (xor x truth) (not y))) (not (and_star (not (xor x truth)) y))) [] by Demod 2872 with 2787 at 1,2,1,1,1,2
+Id : 2872, {_}: not (and_star (not (and_star x (not (xor truth y)))) (not (and_star (not x) (xor truth y)))) =>= not (and_star (not (and_star (xor x truth) (not y))) (not (and_star (not (xor x truth)) y))) [] by Demod 2871 with 2787 at 3
+Id : 2871, {_}: not (and_star (not (and_star x (not (xor truth y)))) (not (and_star (not x) (xor truth y)))) =<= xor (xor x truth) y [] by Demod 1 with 2787 at 2
+Id : 1, {_}: xor x (xor truth y) =<= xor (xor x truth) y [] by prove_alternative_wajsberg_axiom
+% SZS output end CNFRefutation for LCL159-1.p
+24162: solved LCL159-1.p in 4.49628 using lpo
+24162: status Unsatisfiable for LCL159-1.p
+NO CLASH, using fixed ground order
+24168: Facts:
+24168: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+24168: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+24168: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+24168: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+24168: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+24168: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+24168: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+24168: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+24168: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+24168: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+24168: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+24168: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+NO CLASH, using fixed ground order
+24169: Facts:
+24169: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+24169: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+24169: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+24169: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+24169: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+24169: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+24169: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+24169: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+24169: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+24169: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+24169: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+24169: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+24169: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+24169: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+24169: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+24169: Goal:
+24169: Id : 1, {_}:
+ associator x y (add u v)
+ =>=
+ add (associator x y u) (associator x y v)
+ [] by prove_linearised_form1
+24169: Order:
+24169: lpo
+24169: Leaf order:
+24169: u 2 0 2 1,3,2
+24169: v 2 0 2 2,3,2
+24169: x 3 0 3 1,2
+24169: y 3 0 3 2,2
+24169: additive_identity 8 0 0
+24169: additive_inverse 6 1 0
+24169: commutator 1 2 0
+24169: add 18 2 2 0,3,2
+24169: multiply 22 2 0
+24169: associator 4 3 3 0,2
+NO CLASH, using fixed ground order
+24167: Facts:
+24167: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+24167: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+24167: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+24167: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+24167: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+24167: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+24167: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+24167: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+24167: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+24167: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+24167: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+24167: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+24167: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+24167: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+24167: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+24167: Goal:
+24167: Id : 1, {_}:
+ associator x y (add u v)
+ =<=
+ add (associator x y u) (associator x y v)
+ [] by prove_linearised_form1
+24167: Order:
+24167: nrkbo
+24167: Leaf order:
+24167: u 2 0 2 1,3,2
+24167: v 2 0 2 2,3,2
+24167: x 3 0 3 1,2
+24167: y 3 0 3 2,2
+24167: additive_identity 8 0 0
+24167: additive_inverse 6 1 0
+24167: commutator 1 2 0
+24167: add 18 2 2 0,3,2
+24167: multiply 22 2 0
+24167: associator 4 3 3 0,2
+24168: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+24168: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+24168: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+24168: Goal:
+24168: Id : 1, {_}:
+ associator x y (add u v)
+ =<=
+ add (associator x y u) (associator x y v)
+ [] by prove_linearised_form1
+24168: Order:
+24168: kbo
+24168: Leaf order:
+24168: u 2 0 2 1,3,2
+24168: v 2 0 2 2,3,2
+24168: x 3 0 3 1,2
+24168: y 3 0 3 2,2
+24168: additive_identity 8 0 0
+24168: additive_inverse 6 1 0
+24168: commutator 1 2 0
+24168: add 18 2 2 0,3,2
+24168: multiply 22 2 0
+24168: associator 4 3 3 0,2
+% SZS status Timeout for RNG019-6.p
+NO CLASH, using fixed ground order
+24186: Facts:
+24186: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+24186: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+24186: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+24186: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+24186: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+24186: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+24186: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+24186: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+24186: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+24186: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+24186: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+24186: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+24186: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+24186: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+24186: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+24186: Goal:
+24186: Id : 1, {_}:
+ associator (add u v) x y
+ =<=
+ add (associator u x y) (associator v x y)
+ [] by prove_linearised_form3
+24186: Order:
+24186: kbo
+24186: Leaf order:
+24186: u 2 0 2 1,1,2
+24186: v 2 0 2 2,1,2
+24186: x 3 0 3 2,2
+24186: y 3 0 3 3,2
+24186: additive_identity 8 0 0
+24186: additive_inverse 6 1 0
+24186: commutator 1 2 0
+24186: add 18 2 2 0,1,2
+24186: multiply 22 2 0
+24186: associator 4 3 3 0,2
+NO CLASH, using fixed ground order
+24185: Facts:
+24185: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+24185: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+24185: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+24185: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+24185: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+24185: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+24185: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+24185: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+24185: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+24185: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+24185: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+24185: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+24185: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+24185: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+24185: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+24185: Goal:
+24185: Id : 1, {_}:
+ associator (add u v) x y
+ =<=
+ add (associator u x y) (associator v x y)
+ [] by prove_linearised_form3
+24185: Order:
+24185: nrkbo
+24185: Leaf order:
+24185: u 2 0 2 1,1,2
+24185: v 2 0 2 2,1,2
+24185: x 3 0 3 2,2
+24185: y 3 0 3 3,2
+24185: additive_identity 8 0 0
+24185: additive_inverse 6 1 0
+24185: commutator 1 2 0
+24185: add 18 2 2 0,1,2
+24185: multiply 22 2 0
+24185: associator 4 3 3 0,2
+NO CLASH, using fixed ground order
+24187: Facts:
+24187: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+24187: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+24187: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+24187: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+24187: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+24187: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+24187: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+24187: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+24187: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+24187: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+24187: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+24187: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+24187: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+24187: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+24187: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+24187: Goal:
+24187: Id : 1, {_}:
+ associator (add u v) x y
+ =>=
+ add (associator u x y) (associator v x y)
+ [] by prove_linearised_form3
+24187: Order:
+24187: lpo
+24187: Leaf order:
+24187: u 2 0 2 1,1,2
+24187: v 2 0 2 2,1,2
+24187: x 3 0 3 2,2
+24187: y 3 0 3 3,2
+24187: additive_identity 8 0 0
+24187: additive_inverse 6 1 0
+24187: commutator 1 2 0
+24187: add 18 2 2 0,1,2
+24187: multiply 22 2 0
+24187: associator 4 3 3 0,2
+% SZS status Timeout for RNG021-6.p
+NO CLASH, using fixed ground order
+24214: Facts:
+24214: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+24214: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+24214: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+24214: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+24214: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+24214: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+24214: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+24214: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+24214: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+24214: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+24214: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+24214: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+24214: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+24214: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+24214: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+24214: Goal:
+24214: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
+24214: Order:
+24214: nrkbo
+24214: Leaf order:
+24214: y 1 0 1 2,2
+24214: x 2 0 2 1,2
+24214: additive_identity 9 0 1 3
+24214: additive_inverse 6 1 0
+24214: commutator 1 2 0
+24214: add 16 2 0
+24214: multiply 22 2 0
+24214: associator 2 3 1 0,2
+NO CLASH, using fixed ground order
+24215: Facts:
+24215: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+24215: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+24215: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+24215: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+24215: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+24215: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+24215: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+24215: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+24215: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+24215: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+24215: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+24215: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+24215: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+24215: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+24215: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+24215: Goal:
+24215: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
+24215: Order:
+24215: kbo
+24215: Leaf order:
+24215: y 1 0 1 2,2
+24215: x 2 0 2 1,2
+24215: additive_identity 9 0 1 3
+24215: additive_inverse 6 1 0
+24215: commutator 1 2 0
+24215: add 16 2 0
+24215: multiply 22 2 0
+24215: associator 2 3 1 0,2
+NO CLASH, using fixed ground order
+24216: Facts:
+24216: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+24216: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+24216: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+24216: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+24216: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+24216: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+24216: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+24216: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+24216: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+24216: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+24216: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+24216: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+24216: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+24216: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+24216: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+24216: Goal:
+24216: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
+24216: Order:
+24216: lpo
+24216: Leaf order:
+24216: y 1 0 1 2,2
+24216: x 2 0 2 1,2
+24216: additive_identity 9 0 1 3
+24216: additive_inverse 6 1 0
+24216: commutator 1 2 0
+24216: add 16 2 0
+24216: multiply 22 2 0
+24216: associator 2 3 1 0,2
+% SZS status Timeout for RNG025-6.p
+NO CLASH, using fixed ground order
+24240: Facts:
+24240: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+24240: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+24240: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+24240: Id : 5, {_}: add c c =>= c [] by idempotence
+24240: Goal:
+24240: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+24240: Order:
+24240: kbo
+24240: Leaf order:
+24240: a 2 0 2 1,1,1,2
+24240: c 3 0 0
+24240: b 3 0 3 1,2,1,1,2
+24240: negate 9 1 5 0,1,2
+24240: add 13 2 3 0,2
+NO CLASH, using fixed ground order
+24239: Facts:
+24239: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+24239: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+24239: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+24239: Id : 5, {_}: add c c =>= c [] by idempotence
+24239: Goal:
+24239: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+24239: Order:
+24239: nrkbo
+24239: Leaf order:
+24239: a 2 0 2 1,1,1,2
+24239: c 3 0 0
+24239: b 3 0 3 1,2,1,1,2
+24239: negate 9 1 5 0,1,2
+24239: add 13 2 3 0,2
+NO CLASH, using fixed ground order
+24241: Facts:
+24241: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+24241: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+24241: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+24241: Id : 5, {_}: add c c =>= c [] by idempotence
+24241: Goal:
+24241: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+24241: Order:
+24241: lpo
+24241: Leaf order:
+24241: a 2 0 2 1,1,1,2
+24241: c 3 0 0
+24241: b 3 0 3 1,2,1,1,2
+24241: negate 9 1 5 0,1,2
+24241: add 13 2 3 0,2
+% SZS status Timeout for ROB005-1.p
+NO CLASH, using fixed ground order
+24337: Facts:
+24337: Id : 2, {_}:
+ multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
+ =>=
+ multiply ?2 ?3 (multiply ?4 ?5 ?6)
+ [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
+24337: Id : 3, {_}: multiply ?8 ?8 ?9 =>= ?8 [9, 8] by ternary_multiply_2 ?8 ?9
+24337: Id : 4, {_}:
+ multiply (inverse ?11) ?11 ?12 =>= ?12
+ [12, 11] by left_inverse ?11 ?12
+24337: Id : 5, {_}:
+ multiply ?14 ?15 (inverse ?15) =>= ?14
+ [15, 14] by right_inverse ?14 ?15
+24337: Goal:
+24337: Id : 1, {_}: multiply y x x =>= x [] by prove_ternary_multiply_1_independant
+24337: Order:
+24337: nrkbo
+24337: Leaf order:
+24337: y 1 0 1 1,2
+24337: x 3 0 3 2,2
+24337: inverse 2 1 0
+24337: multiply 9 3 1 0,2
+NO CLASH, using fixed ground order
+24338: Facts:
+24338: Id : 2, {_}:
+ multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
+ =>=
+ multiply ?2 ?3 (multiply ?4 ?5 ?6)
+ [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
+24338: Id : 3, {_}: multiply ?8 ?8 ?9 =>= ?8 [9, 8] by ternary_multiply_2 ?8 ?9
+24338: Id : 4, {_}:
+ multiply (inverse ?11) ?11 ?12 =>= ?12
+ [12, 11] by left_inverse ?11 ?12
+24338: Id : 5, {_}:
+ multiply ?14 ?15 (inverse ?15) =>= ?14
+ [15, 14] by right_inverse ?14 ?15
+24338: Goal:
+24338: Id : 1, {_}: multiply y x x =>= x [] by prove_ternary_multiply_1_independant
+24338: Order:
+24338: kbo
+24338: Leaf order:
+24338: y 1 0 1 1,2
+24338: x 3 0 3 2,2
+24338: inverse 2 1 0
+24338: multiply 9 3 1 0,2
+NO CLASH, using fixed ground order
+24339: Facts:
+24339: Id : 2, {_}:
+ multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
+ =>=
+ multiply ?2 ?3 (multiply ?4 ?5 ?6)
+ [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
+24339: Id : 3, {_}: multiply ?8 ?8 ?9 =>= ?8 [9, 8] by ternary_multiply_2 ?8 ?9
+24339: Id : 4, {_}:
+ multiply (inverse ?11) ?11 ?12 =>= ?12
+ [12, 11] by left_inverse ?11 ?12
+24339: Id : 5, {_}:
+ multiply ?14 ?15 (inverse ?15) =>= ?14
+ [15, 14] by right_inverse ?14 ?15
+24339: Goal:
+24339: Id : 1, {_}: multiply y x x =>= x [] by prove_ternary_multiply_1_independant
+24339: Order:
+24339: lpo
+24339: Leaf order:
+24339: y 1 0 1 1,2
+24339: x 3 0 3 2,2
+24339: inverse 2 1 0
+24339: multiply 9 3 1 0,2
+% SZS status Timeout for BOO019-1.p
+CLASH, statistics insufficient
+25312: Facts:
+25312: Id : 2, {_}:
+ add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
+ [4, 3, 2] by l1 ?2 ?3 ?4
+25312: Id : 3, {_}:
+ add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
+ [8, 7, 6] by l3 ?6 ?7 ?8
+25312: Id : 4, {_}:
+ multiply (add ?10 ?11) (add ?10 (inverse ?11)) =>= ?10
+ [11, 10] by b1 ?10 ?11
+25312: Id : 5, {_}:
+ multiply (add (multiply ?13 ?14) ?13) (add ?13 ?14) =>= ?13
+ [14, 13] by majority1 ?13 ?14
+25312: Id : 6, {_}:
+ multiply (add (multiply ?16 ?16) ?17) (add ?16 ?16) =>= ?16
+ [17, 16] by majority2 ?16 ?17
+25312: Id : 7, {_}:
+ multiply (add (multiply ?19 ?20) ?20) (add ?19 ?20) =>= ?20
+ [20, 19] by majority3 ?19 ?20
+25312: Goal:
+25312: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
+25312: Order:
+25312: nrkbo
+25312: Leaf order:
+25312: a 2 0 2 1,1,2
+25312: inverse 3 1 2 0,2
+25312: multiply 11 2 0
+25312: add 11 2 0
+CLASH, statistics insufficient
+25313: Facts:
+25313: Id : 2, {_}:
+ add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
+ [4, 3, 2] by l1 ?2 ?3 ?4
+25313: Id : 3, {_}:
+ add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
+ [8, 7, 6] by l3 ?6 ?7 ?8
+25313: Id : 4, {_}:
+ multiply (add ?10 ?11) (add ?10 (inverse ?11)) =>= ?10
+ [11, 10] by b1 ?10 ?11
+25313: Id : 5, {_}:
+ multiply (add (multiply ?13 ?14) ?13) (add ?13 ?14) =>= ?13
+ [14, 13] by majority1 ?13 ?14
+25313: Id : 6, {_}:
+ multiply (add (multiply ?16 ?16) ?17) (add ?16 ?16) =>= ?16
+ [17, 16] by majority2 ?16 ?17
+25313: Id : 7, {_}:
+ multiply (add (multiply ?19 ?20) ?20) (add ?19 ?20) =>= ?20
+ [20, 19] by majority3 ?19 ?20
+25313: Goal:
+25313: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
+25313: Order:
+25313: kbo
+25313: Leaf order:
+25313: a 2 0 2 1,1,2
+25313: inverse 3 1 2 0,2
+25313: multiply 11 2 0
+25313: add 11 2 0
+CLASH, statistics insufficient
+25314: Facts:
+25314: Id : 2, {_}:
+ add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
+ [4, 3, 2] by l1 ?2 ?3 ?4
+25314: Id : 3, {_}:
+ add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
+ [8, 7, 6] by l3 ?6 ?7 ?8
+25314: Id : 4, {_}:
+ multiply (add ?10 ?11) (add ?10 (inverse ?11)) =>= ?10
+ [11, 10] by b1 ?10 ?11
+25314: Id : 5, {_}:
+ multiply (add (multiply ?13 ?14) ?13) (add ?13 ?14) =>= ?13
+ [14, 13] by majority1 ?13 ?14
+25314: Id : 6, {_}:
+ multiply (add (multiply ?16 ?16) ?17) (add ?16 ?16) =>= ?16
+ [17, 16] by majority2 ?16 ?17
+25314: Id : 7, {_}:
+ multiply (add (multiply ?19 ?20) ?20) (add ?19 ?20) =>= ?20
+ [20, 19] by majority3 ?19 ?20
+25314: Goal:
+25314: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
+25314: Order:
+25314: lpo
+25314: Leaf order:
+25314: a 2 0 2 1,1,2
+25314: inverse 3 1 2 0,2
+25314: multiply 11 2 0
+25314: add 11 2 0
+% SZS status Timeout for BOO030-1.p
+CLASH, statistics insufficient
+25341: Facts:
+25341: Id : 2, {_}:
+ add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
+ [4, 3, 2] by l1 ?2 ?3 ?4
+25341: Id : 3, {_}:
+ add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
+ [8, 7, 6] by l3 ?6 ?7 ?8
+25341: Id : 4, {_}:
+ multiply (add ?10 (inverse ?10)) ?11 =>= ?11
+ [11, 10] by property3 ?10 ?11
+25341: Id : 5, {_}:
+ multiply ?13 (add ?14 (add ?13 ?15)) =>= ?13
+ [15, 14, 13] by l2 ?13 ?14 ?15
+25341: Id : 6, {_}:
+ multiply (multiply (add ?17 ?18) (add ?18 ?19)) ?18 =>= ?18
+ [19, 18, 17] by l4 ?17 ?18 ?19
+25341: Id : 7, {_}:
+ add (multiply ?21 (inverse ?21)) ?22 =>= ?22
+ [22, 21] by property3_dual ?21 ?22
+25341: Id : 8, {_}:
+ add (multiply (add ?24 ?25) ?24) (multiply ?24 ?25) =>= ?24
+ [25, 24] by majority1 ?24 ?25
+25341: Id : 9, {_}:
+ add (multiply (add ?27 ?27) ?28) (multiply ?27 ?27) =>= ?27
+ [28, 27] by majority2 ?27 ?28
+25341: Id : 10, {_}:
+ add (multiply (add ?30 ?31) ?31) (multiply ?30 ?31) =>= ?31
+ [31, 30] by majority3 ?30 ?31
+25341: Id : 11, {_}:
+ multiply (add (multiply ?33 ?34) ?33) (add ?33 ?34) =>= ?33
+ [34, 33] by majority1_dual ?33 ?34
+25341: Id : 12, {_}:
+ multiply (add (multiply ?36 ?36) ?37) (add ?36 ?36) =>= ?36
+ [37, 36] by majority2_dual ?36 ?37
+25341: Id : 13, {_}:
+ multiply (add (multiply ?39 ?40) ?40) (add ?39 ?40) =>= ?40
+ [40, 39] by majority3_dual ?39 ?40
+25341: Goal:
+25341: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
+25341: Order:
+25341: nrkbo
+25341: Leaf order:
+25341: a 2 0 2 1,1,2
+25341: inverse 4 1 2 0,2
+25341: multiply 21 2 0
+25341: add 21 2 0
+CLASH, statistics insufficient
+25342: Facts:
+25342: Id : 2, {_}:
+ add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
+ [4, 3, 2] by l1 ?2 ?3 ?4
+25342: Id : 3, {_}:
+ add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
+ [8, 7, 6] by l3 ?6 ?7 ?8
+25342: Id : 4, {_}:
+ multiply (add ?10 (inverse ?10)) ?11 =>= ?11
+ [11, 10] by property3 ?10 ?11
+25342: Id : 5, {_}:
+ multiply ?13 (add ?14 (add ?13 ?15)) =>= ?13
+ [15, 14, 13] by l2 ?13 ?14 ?15
+25342: Id : 6, {_}:
+ multiply (multiply (add ?17 ?18) (add ?18 ?19)) ?18 =>= ?18
+ [19, 18, 17] by l4 ?17 ?18 ?19
+25342: Id : 7, {_}:
+ add (multiply ?21 (inverse ?21)) ?22 =>= ?22
+ [22, 21] by property3_dual ?21 ?22
+25342: Id : 8, {_}:
+ add (multiply (add ?24 ?25) ?24) (multiply ?24 ?25) =>= ?24
+ [25, 24] by majority1 ?24 ?25
+25342: Id : 9, {_}:
+ add (multiply (add ?27 ?27) ?28) (multiply ?27 ?27) =>= ?27
+ [28, 27] by majority2 ?27 ?28
+25342: Id : 10, {_}:
+ add (multiply (add ?30 ?31) ?31) (multiply ?30 ?31) =>= ?31
+ [31, 30] by majority3 ?30 ?31
+25342: Id : 11, {_}:
+ multiply (add (multiply ?33 ?34) ?33) (add ?33 ?34) =>= ?33
+ [34, 33] by majority1_dual ?33 ?34
+25342: Id : 12, {_}:
+ multiply (add (multiply ?36 ?36) ?37) (add ?36 ?36) =>= ?36
+ [37, 36] by majority2_dual ?36 ?37
+25342: Id : 13, {_}:
+ multiply (add (multiply ?39 ?40) ?40) (add ?39 ?40) =>= ?40
+ [40, 39] by majority3_dual ?39 ?40
+25342: Goal:
+25342: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
+25342: Order:
+25342: kbo
+25342: Leaf order:
+25342: a 2 0 2 1,1,2
+25342: inverse 4 1 2 0,2
+25342: multiply 21 2 0
+25342: add 21 2 0
+CLASH, statistics insufficient
+25343: Facts:
+25343: Id : 2, {_}:
+ add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2
+ [4, 3, 2] by l1 ?2 ?3 ?4
+25343: Id : 3, {_}:
+ add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7
+ [8, 7, 6] by l3 ?6 ?7 ?8
+25343: Id : 4, {_}:
+ multiply (add ?10 (inverse ?10)) ?11 =>= ?11
+ [11, 10] by property3 ?10 ?11
+25343: Id : 5, {_}:
+ multiply ?13 (add ?14 (add ?13 ?15)) =>= ?13
+ [15, 14, 13] by l2 ?13 ?14 ?15
+25343: Id : 6, {_}:
+ multiply (multiply (add ?17 ?18) (add ?18 ?19)) ?18 =>= ?18
+ [19, 18, 17] by l4 ?17 ?18 ?19
+25343: Id : 7, {_}:
+ add (multiply ?21 (inverse ?21)) ?22 =>= ?22
+ [22, 21] by property3_dual ?21 ?22
+25343: Id : 8, {_}:
+ add (multiply (add ?24 ?25) ?24) (multiply ?24 ?25) =>= ?24
+ [25, 24] by majority1 ?24 ?25
+25343: Id : 9, {_}:
+ add (multiply (add ?27 ?27) ?28) (multiply ?27 ?27) =>= ?27
+ [28, 27] by majority2 ?27 ?28
+25343: Id : 10, {_}:
+ add (multiply (add ?30 ?31) ?31) (multiply ?30 ?31) =>= ?31
+ [31, 30] by majority3 ?30 ?31
+25343: Id : 11, {_}:
+ multiply (add (multiply ?33 ?34) ?33) (add ?33 ?34) =>= ?33
+ [34, 33] by majority1_dual ?33 ?34
+25343: Id : 12, {_}:
+ multiply (add (multiply ?36 ?36) ?37) (add ?36 ?36) =>= ?36
+ [37, 36] by majority2_dual ?36 ?37
+25343: Id : 13, {_}:
+ multiply (add (multiply ?39 ?40) ?40) (add ?39 ?40) =>= ?40
+ [40, 39] by majority3_dual ?39 ?40
+25343: Goal:
+25343: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
+25343: Order:
+25343: lpo
+25343: Leaf order:
+25343: a 2 0 2 1,1,2
+25343: inverse 4 1 2 0,2
+25343: multiply 21 2 0
+25343: add 21 2 0
+% SZS status Timeout for BOO032-1.p
+NO CLASH, using fixed ground order
+25370: Facts:
+25370: Id : 2, {_}:
+ add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
+ =<=
+ multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
+ [4, 3, 2] by distributivity ?2 ?3 ?4
+25370: Id : 3, {_}:
+ add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
+ [8, 7, 6] by l1 ?6 ?7 ?8
+25370: Id : 4, {_}:
+ add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
+ [12, 11, 10] by l3 ?10 ?11 ?12
+25370: Id : 5, {_}:
+ multiply (add ?14 (inverse ?14)) ?15 =>= ?15
+ [15, 14] by property3 ?14 ?15
+25370: Id : 6, {_}:
+ multiply (add (multiply ?17 ?18) ?17) (add ?17 ?18) =>= ?17
+ [18, 17] by majority1 ?17 ?18
+25370: Id : 7, {_}:
+ multiply (add (multiply ?20 ?20) ?21) (add ?20 ?20) =>= ?20
+ [21, 20] by majority2 ?20 ?21
+25370: Id : 8, {_}:
+ multiply (add (multiply ?23 ?24) ?24) (add ?23 ?24) =>= ?24
+ [24, 23] by majority3 ?23 ?24
+25370: Goal:
+25370: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
+25370: Order:
+25370: nrkbo
+25370: Leaf order:
+25370: a 2 0 2 1,1,2
+25370: inverse 3 1 2 0,2
+25370: add 15 2 0 multiply
+25370: multiply 16 2 0 add
+NO CLASH, using fixed ground order
+25371: Facts:
+25371: Id : 2, {_}:
+ add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
+ =<=
+ multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
+ [4, 3, 2] by distributivity ?2 ?3 ?4
+25371: Id : 3, {_}:
+ add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
+ [8, 7, 6] by l1 ?6 ?7 ?8
+25371: Id : 4, {_}:
+ add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
+ [12, 11, 10] by l3 ?10 ?11 ?12
+25371: Id : 5, {_}:
+ multiply (add ?14 (inverse ?14)) ?15 =>= ?15
+ [15, 14] by property3 ?14 ?15
+25371: Id : 6, {_}:
+ multiply (add (multiply ?17 ?18) ?17) (add ?17 ?18) =>= ?17
+ [18, 17] by majority1 ?17 ?18
+25371: Id : 7, {_}:
+ multiply (add (multiply ?20 ?20) ?21) (add ?20 ?20) =>= ?20
+ [21, 20] by majority2 ?20 ?21
+25371: Id : 8, {_}:
+ multiply (add (multiply ?23 ?24) ?24) (add ?23 ?24) =>= ?24
+ [24, 23] by majority3 ?23 ?24
+25371: Goal:
+25371: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
+25371: Order:
+25371: kbo
+25371: Leaf order:
+25371: a 2 0 2 1,1,2
+25371: inverse 3 1 2 0,2
+25371: add 15 2 0 multiply
+25371: multiply 16 2 0 add
+NO CLASH, using fixed ground order
+25372: Facts:
+25372: Id : 2, {_}:
+ add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2))
+ =<=
+ multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2))
+ [4, 3, 2] by distributivity ?2 ?3 ?4
+25372: Id : 3, {_}:
+ add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6
+ [8, 7, 6] by l1 ?6 ?7 ?8
+25372: Id : 4, {_}:
+ add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11
+ [12, 11, 10] by l3 ?10 ?11 ?12
+25372: Id : 5, {_}:
+ multiply (add ?14 (inverse ?14)) ?15 =>= ?15
+ [15, 14] by property3 ?14 ?15
+25372: Id : 6, {_}:
+ multiply (add (multiply ?17 ?18) ?17) (add ?17 ?18) =>= ?17
+ [18, 17] by majority1 ?17 ?18
+25372: Id : 7, {_}:
+ multiply (add (multiply ?20 ?20) ?21) (add ?20 ?20) =>= ?20
+ [21, 20] by majority2 ?20 ?21
+25372: Id : 8, {_}:
+ multiply (add (multiply ?23 ?24) ?24) (add ?23 ?24) =>= ?24
+ [24, 23] by majority3 ?23 ?24
+25372: Goal:
+25372: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution
+25372: Order:
+25372: lpo
+25372: Leaf order:
+25372: a 2 0 2 1,1,2
+25372: inverse 3 1 2 0,2
+25372: add 15 2 0 multiply
+25372: multiply 16 2 0 add
+% SZS status Timeout for BOO033-1.p
+NO CLASH, using fixed ground order
+25403: Facts:
+25403: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+25403: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+25403: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply (apply b (apply w w))
+ (apply (apply b (apply b w)) (apply (apply b b) b))
+ [] by strong_fixed_point
+25403: Goal:
+25403: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+25403: Order:
+25403: nrkbo
+25403: Leaf order:
+25403: strong_fixed_point 3 0 2 1,2
+25403: fixed_pt 3 0 3 2,2
+25403: w 4 0 0
+25403: b 7 0 0
+25403: apply 20 2 3 0,2
+NO CLASH, using fixed ground order
+25404: Facts:
+25404: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+25404: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+25404: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply (apply b (apply w w))
+ (apply (apply b (apply b w)) (apply (apply b b) b))
+ [] by strong_fixed_point
+25404: Goal:
+25404: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+25404: Order:
+25404: kbo
+25404: Leaf order:
+25404: strong_fixed_point 3 0 2 1,2
+25404: fixed_pt 3 0 3 2,2
+25404: w 4 0 0
+25404: b 7 0 0
+25404: apply 20 2 3 0,2
+NO CLASH, using fixed ground order
+25405: Facts:
+25405: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+25405: Id : 3, {_}:
+ apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7
+ [7, 6] by w_definition ?6 ?7
+25405: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply (apply b (apply w w))
+ (apply (apply b (apply b w)) (apply (apply b b) b))
+ [] by strong_fixed_point
+25405: Goal:
+25405: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+25405: Order:
+25405: lpo
+25405: Leaf order:
+25405: strong_fixed_point 3 0 2 1,2
+25405: fixed_pt 3 0 3 2,2
+25405: w 4 0 0
+25405: b 7 0 0
+25405: apply 20 2 3 0,2
+% SZS status Timeout for COL003-20.p
+NO CLASH, using fixed ground order
+25421: Facts:
+25421: Id : 2, {_}:
+ apply (apply (apply s ?2) ?3) ?4
+ =?=
+ apply (apply ?2 ?4) (apply ?3 ?4)
+ [4, 3, 2] by s_definition ?2 ?3 ?4
+25421: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+25421: Goal:
+25421: Id : 1, {_}:
+ apply
+ (apply
+ (apply (apply s (apply k (apply s (apply (apply s k) k))))
+ (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))
+ x) y
+ =>=
+ apply y (apply (apply x x) y)
+ [] by prove_u_combinator
+25421: Order:
+25421: nrkbo
+25421: Leaf order:
+25421: x 3 0 3 2,1,2
+25421: y 3 0 3 2,2
+25421: s 7 0 6 1,1,1,1,2
+25421: k 8 0 7 1,2,1,1,1,2
+25421: apply 25 2 17 0,2
+NO CLASH, using fixed ground order
+25422: Facts:
+25422: Id : 2, {_}:
+ apply (apply (apply s ?2) ?3) ?4
+ =?=
+ apply (apply ?2 ?4) (apply ?3 ?4)
+ [4, 3, 2] by s_definition ?2 ?3 ?4
+25422: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+25422: Goal:
+25422: Id : 1, {_}:
+ apply
+ (apply
+ (apply (apply s (apply k (apply s (apply (apply s k) k))))
+ (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))
+ x) y
+ =>=
+ apply y (apply (apply x x) y)
+ [] by prove_u_combinator
+25422: Order:
+25422: kbo
+25422: Leaf order:
+25422: x 3 0 3 2,1,2
+25422: y 3 0 3 2,2
+25422: s 7 0 6 1,1,1,1,2
+25422: k 8 0 7 1,2,1,1,1,2
+25422: apply 25 2 17 0,2
+NO CLASH, using fixed ground order
+25423: Facts:
+25423: Id : 2, {_}:
+ apply (apply (apply s ?2) ?3) ?4
+ =?=
+ apply (apply ?2 ?4) (apply ?3 ?4)
+ [4, 3, 2] by s_definition ?2 ?3 ?4
+25423: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+25423: Goal:
+25423: Id : 1, {_}:
+ apply
+ (apply
+ (apply (apply s (apply k (apply s (apply (apply s k) k))))
+ (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))
+ x) y
+ =>=
+ apply y (apply (apply x x) y)
+ [] by prove_u_combinator
+25423: Order:
+25423: lpo
+25423: Leaf order:
+25423: x 3 0 3 2,1,2
+25423: y 3 0 3 2,2
+25423: s 7 0 6 1,1,1,1,2
+25423: k 8 0 7 1,2,1,1,1,2
+25423: apply 25 2 17 0,2
+Statistics :
+Max weight : 29
+Found proof, 0.116079s
+% SZS status Unsatisfiable for COL004-3.p
+% SZS output start CNFRefutation for COL004-3.p
+Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+Id : 2, {_}: apply (apply (apply s ?2) ?3) ?4 =?= apply (apply ?2 ?4) (apply ?3 ?4) [4, 3, 2] by s_definition ?2 ?3 ?4
+Id : 35, {_}: apply y (apply (apply x x) y) === apply y (apply (apply x x) y) [] by Demod 34 with 3 at 1,2
+Id : 34, {_}: apply (apply (apply k y) (apply k y)) (apply (apply x x) y) =>= apply y (apply (apply x x) y) [] by Demod 33 with 2 at 1,2
+Id : 33, {_}: apply (apply (apply (apply s k) k) y) (apply (apply x x) y) =>= apply y (apply (apply x x) y) [] by Demod 32 with 2 at 2
+Id : 32, {_}: apply (apply (apply s (apply (apply s k) k)) (apply x x)) y =>= apply y (apply (apply x x) y) [] by Demod 31 with 3 at 2,2,1,2
+Id : 31, {_}: apply (apply (apply s (apply (apply s k) k)) (apply x (apply (apply k x) (apply k x)))) y =>= apply y (apply (apply x x) y) [] by Demod 30 with 3 at 1,2,1,2
+Id : 30, {_}: apply (apply (apply s (apply (apply s k) k)) (apply (apply (apply k x) (apply k x)) (apply (apply k x) (apply k x)))) y =>= apply y (apply (apply x x) y) [] by Demod 20 with 3 at 1,1,2
+Id : 20, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply k x) (apply k x)) (apply (apply k x) (apply k x)))) y =>= apply y (apply (apply x x) y) [] by Demod 19 with 2 at 2,2,1,2
+Id : 19, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply k x) (apply k x)) (apply (apply (apply s k) k) x))) y =>= apply y (apply (apply x x) y) [] by Demod 18 with 2 at 1,2,1,2
+Id : 18, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply (apply s k) k) x) (apply (apply (apply s k) k) x))) y =>= apply y (apply (apply x x) y) [] by Demod 17 with 2 at 2,1,2
+Id : 17, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)) x)) y =>= apply y (apply (apply x x) y) [] by Demod 1 with 2 at 1,2
+Id : 1, {_}: apply (apply (apply (apply s (apply k (apply s (apply (apply s k) k)))) (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))) x) y =>= apply y (apply (apply x x) y) [] by prove_u_combinator
+% SZS output end CNFRefutation for COL004-3.p
+25423: solved COL004-3.p in 0.020001 using lpo
+25423: status Unsatisfiable for COL004-3.p
+CLASH, statistics insufficient
+25428: Facts:
+25428: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+25428: Id : 3, {_}:
+ apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
+ [8, 7] by w_definition ?7 ?8
+25428: Goal:
+25428: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_model ?1
+25428: Order:
+25428: nrkbo
+25428: Leaf order:
+25428: s 1 0 0
+25428: w 1 0 0
+25428: combinator 1 0 1 1,3
+25428: apply 11 2 1 0,3
+CLASH, statistics insufficient
+25429: Facts:
+25429: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+25429: Id : 3, {_}:
+ apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
+ [8, 7] by w_definition ?7 ?8
+25429: Goal:
+25429: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_model ?1
+25429: Order:
+25429: kbo
+25429: Leaf order:
+25429: s 1 0 0
+25429: w 1 0 0
+25429: combinator 1 0 1 1,3
+25429: apply 11 2 1 0,3
+CLASH, statistics insufficient
+25430: Facts:
+25430: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+25430: Id : 3, {_}:
+ apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
+ [8, 7] by w_definition ?7 ?8
+25430: Goal:
+25430: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_model ?1
+25430: Order:
+25430: lpo
+25430: Leaf order:
+25430: s 1 0 0
+25430: w 1 0 0
+25430: combinator 1 0 1 1,3
+25430: apply 11 2 1 0,3
+% SZS status Timeout for COL005-1.p
+CLASH, statistics insufficient
+25470: Facts:
+25470: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+25470: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
+25470: Id : 4, {_}:
+ apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10
+ [11, 10, 9] by v_definition ?9 ?10 ?11
+25470: Goal:
+CLASH, statistics insufficient
+25471: Facts:
+25471: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+25471: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
+25471: Id : 4, {_}:
+ apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10
+ [11, 10, 9] by v_definition ?9 ?10 ?11
+25471: Goal:
+25471: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+25471: Order:
+25471: kbo
+25471: Leaf order:
+25471: b 1 0 0
+25471: m 1 0 0
+25471: v 1 0 0
+25471: f 3 1 3 0,2,2
+25471: apply 15 2 3 0,2
+25470: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+25470: Order:
+25470: nrkbo
+25470: Leaf order:
+25470: b 1 0 0
+25470: m 1 0 0
+25470: v 1 0 0
+25470: f 3 1 3 0,2,2
+25470: apply 15 2 3 0,2
+CLASH, statistics insufficient
+25472: Facts:
+25472: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+25472: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
+25472: Id : 4, {_}:
+ apply (apply (apply v ?9) ?10) ?11 =?= apply (apply ?11 ?9) ?10
+ [11, 10, 9] by v_definition ?9 ?10 ?11
+25472: Goal:
+25472: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+25472: Order:
+25472: lpo
+25472: Leaf order:
+25472: b 1 0 0
+25472: m 1 0 0
+25472: v 1 0 0
+25472: f 3 1 3 0,2,2
+25472: apply 15 2 3 0,2
+Goal subsumed
+Statistics :
+Max weight : 78
+Found proof, 6.291189s
+% SZS status Unsatisfiable for COL038-1.p
+% SZS output start CNFRefutation for COL038-1.p
+Id : 4, {_}: apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10 [11, 10, 9] by v_definition ?9 ?10 ?11
+Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7
+Id : 19, {_}: apply (apply (apply v ?47) ?48) ?49 =>= apply (apply ?49 ?47) ?48 [49, 48, 47] by v_definition ?47 ?48 ?49
+Id : 5, {_}: apply (apply (apply b ?13) ?14) ?15 =>= apply ?13 (apply ?14 ?15) [15, 14, 13] by b_definition ?13 ?14 ?15
+Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
+Id : 6, {_}: apply ?17 (apply ?18 ?19) =?= apply ?17 (apply ?18 ?19) [19, 18, 17] by Super 5 with 2 at 2
+Id : 1244, {_}: apply (apply m (apply v ?1596)) ?1597 =?= apply (apply ?1597 ?1596) (apply v ?1596) [1597, 1596] by Super 19 with 3 at 1,2
+Id : 18, {_}: apply m (apply (apply v ?44) ?45) =<= apply (apply (apply (apply v ?44) ?45) ?44) ?45 [45, 44] by Super 3 with 4 at 3
+Id : 224, {_}: apply m (apply (apply v ?485) ?486) =<= apply (apply (apply ?485 ?485) ?486) ?486 [486, 485] by Demod 18 with 4 at 1,3
+Id : 232, {_}: apply m (apply (apply v ?509) ?510) =<= apply (apply (apply m ?509) ?510) ?510 [510, 509] by Super 224 with 3 at 1,1,3
+Id : 7751, {_}: apply (apply m (apply v ?7787)) (apply (apply m ?7788) ?7787) =<= apply (apply m (apply (apply v ?7788) ?7787)) (apply v ?7787) [7788, 7787] by Super 1244 with 232 at 1,3
+Id : 9, {_}: apply (apply (apply m b) ?24) ?25 =>= apply b (apply ?24 ?25) [25, 24] by Super 2 with 3 at 1,1,2
+Id : 236, {_}: apply m (apply (apply v (apply v ?521)) ?522) =<= apply (apply (apply ?522 ?521) (apply v ?521)) ?522 [522, 521] by Super 224 with 4 at 1,3
+Id : 2866, {_}: apply m (apply (apply v (apply v b)) m) =>= apply b (apply (apply v b) m) [] by Super 9 with 236 at 2
+Id : 7790, {_}: apply (apply m (apply v m)) (apply (apply m (apply v b)) m) =>= apply (apply b (apply (apply v b) m)) (apply v m) [] by Super 7751 with 2866 at 1,3
+Id : 20, {_}: apply (apply m (apply v ?51)) ?52 =?= apply (apply ?52 ?51) (apply v ?51) [52, 51] by Super 19 with 3 at 1,2
+Id : 7860, {_}: apply (apply m (apply v m)) (apply (apply m b) (apply v b)) =>= apply (apply b (apply (apply v b) m)) (apply v m) [] by Demod 7790 with 20 at 2,2
+Id : 11, {_}: apply m (apply (apply b ?30) ?31) =<= apply ?30 (apply ?31 (apply (apply b ?30) ?31)) [31, 30] by Super 2 with 3 at 2
+Id : 9568, {_}: apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b)) (apply m (apply (apply b (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b))) m)) =?= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b)) (apply m (apply (apply b (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b))) m)) [] by Super 9567 with 11 at 2
+Id : 9567, {_}: apply m (apply (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) m) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply m (apply (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) m)) [8771] by Demod 9566 with 2 at 2,3
+Id : 9566, {_}: apply m (apply (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) m) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m) [8771] by Demod 9565 with 2 at 2
+Id : 9565, {_}: apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m) [8771] by Demod 9564 with 4 at 1,2,3
+Id : 9564, {_}: apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m) [8771] by Demod 9563 with 4 at 1,2
+Id : 9563, {_}: apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m) [8771] by Demod 9562 with 4 at 2,3
+Id : 9562, {_}: apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))))) [8771] by Demod 9561 with 4 at 2
+Id : 9561, {_}: apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))))) [8771] by Demod 9560 with 2 at 2,3
+Id : 9560, {_}: apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9559 with 2 at 2
+Id : 9559, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9558 with 7860 at 1,2,3
+Id : 9558, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9557 with 7860 at 2,1,1,1,3
+Id : 9557, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) =<= apply (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9556 with 7860 at 2,1,1,2,2,2
+Id : 9556, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771))) =<= apply (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9078 with 7860 at 1,2
+Id : 9078, {_}: apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771))) =<= apply (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Super 174 with 7860 at 2,1,1,2,2,2,3
+Id : 174, {_}: apply (apply ?379 ?380) (apply ?381 (f (apply (apply b (apply ?379 ?380)) ?381))) =<= apply (f (apply (apply b (apply ?379 ?380)) ?381)) (apply (apply ?379 ?380) (apply ?381 (f (apply (apply b (apply ?379 ?380)) ?381)))) [381, 380, 379] by Super 8 with 6 at 1,1,2,2,2,3
+Id : 8, {_}: apply ?21 (apply ?22 (f (apply (apply b ?21) ?22))) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Demod 7 with 2 at 2
+Id : 7, {_}: apply (apply (apply b ?21) ?22) (f (apply (apply b ?21) ?22)) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Super 1 with 2 at 2,3
+Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1
+% SZS output end CNFRefutation for COL038-1.p
+25471: solved COL038-1.p in 3.192199 using kbo
+25471: status Unsatisfiable for COL038-1.p
+CLASH, statistics insufficient
+25477: Facts:
+25477: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+25477: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+25477: Id : 4, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11
+25477: Goal:
+25477: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+25477: Order:
+25477: nrkbo
+25477: Leaf order:
+25477: s 1 0 0
+25477: b 1 0 0
+25477: m 1 0 0
+25477: f 3 1 3 0,2,2
+25477: apply 16 2 3 0,2
+CLASH, statistics insufficient
+25478: Facts:
+25478: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+25478: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+25478: Id : 4, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11
+25478: Goal:
+25478: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+25478: Order:
+25478: kbo
+25478: Leaf order:
+25478: s 1 0 0
+25478: b 1 0 0
+25478: m 1 0 0
+25478: f 3 1 3 0,2,2
+25478: apply 16 2 3 0,2
+CLASH, statistics insufficient
+25479: Facts:
+25479: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+25479: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+25479: Id : 4, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11
+25479: Goal:
+25479: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+25479: Order:
+25479: lpo
+25479: Leaf order:
+25479: s 1 0 0
+25479: b 1 0 0
+25479: m 1 0 0
+25479: f 3 1 3 0,2,2
+25479: apply 16 2 3 0,2
+% SZS status Timeout for COL046-1.p
+CLASH, statistics insufficient
+25500: Facts:
+25500: Id : 2, {_}:
+ apply (apply l ?3) ?4 =?= apply ?3 (apply ?4 ?4)
+ [4, 3] by l_definition ?3 ?4
+25500: Id : 3, {_}:
+ apply (apply (apply q ?6) ?7) ?8 =>= apply ?7 (apply ?6 ?8)
+ [8, 7, 6] by q_definition ?6 ?7 ?8
+25500: Goal:
+25500: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_model ?1
+25500: Order:
+25500: nrkbo
+25500: Leaf order:
+25500: l 1 0 0
+25500: q 1 0 0
+25500: f 3 1 3 0,2,2
+25500: apply 12 2 3 0,2
+CLASH, statistics insufficient
+25501: Facts:
+25501: Id : 2, {_}:
+ apply (apply l ?3) ?4 =?= apply ?3 (apply ?4 ?4)
+ [4, 3] by l_definition ?3 ?4
+25501: Id : 3, {_}:
+ apply (apply (apply q ?6) ?7) ?8 =>= apply ?7 (apply ?6 ?8)
+ [8, 7, 6] by q_definition ?6 ?7 ?8
+25501: Goal:
+25501: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_model ?1
+25501: Order:
+25501: kbo
+25501: Leaf order:
+25501: l 1 0 0
+25501: q 1 0 0
+25501: f 3 1 3 0,2,2
+25501: apply 12 2 3 0,2
+CLASH, statistics insufficient
+25502: Facts:
+25502: Id : 2, {_}:
+ apply (apply l ?3) ?4 =?= apply ?3 (apply ?4 ?4)
+ [4, 3] by l_definition ?3 ?4
+25502: Id : 3, {_}:
+ apply (apply (apply q ?6) ?7) ?8 =>= apply ?7 (apply ?6 ?8)
+ [8, 7, 6] by q_definition ?6 ?7 ?8
+25502: Goal:
+25502: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_model ?1
+25502: Order:
+25502: lpo
+25502: Leaf order:
+25502: l 1 0 0
+25502: q 1 0 0
+25502: f 3 1 3 0,2,2
+25502: apply 12 2 3 0,2
+% SZS status Timeout for COL047-1.p
+CLASH, statistics insufficient
+25526: Facts:
+25526: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+25526: Id : 3, {_}:
+ apply (apply t ?7) ?8 =>= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+25526: Goal:
+25526: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (g ?1) (apply (f ?1) (h ?1))
+ [1] by prove_q_combinator ?1
+25526: Order:
+25526: nrkbo
+25526: Leaf order:
+25526: b 1 0 0
+25526: t 1 0 0
+25526: f 2 1 2 0,2,1,1,2
+25526: g 2 1 2 0,2,1,2
+25526: h 2 1 2 0,2,2
+25526: apply 13 2 5 0,2
+CLASH, statistics insufficient
+25527: Facts:
+25527: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+25527: Id : 3, {_}:
+ apply (apply t ?7) ?8 =>= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+25527: Goal:
+25527: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (g ?1) (apply (f ?1) (h ?1))
+ [1] by prove_q_combinator ?1
+25527: Order:
+25527: kbo
+25527: Leaf order:
+25527: b 1 0 0
+25527: t 1 0 0
+25527: f 2 1 2 0,2,1,1,2
+25527: g 2 1 2 0,2,1,2
+25527: h 2 1 2 0,2,2
+25527: apply 13 2 5 0,2
+CLASH, statistics insufficient
+25528: Facts:
+25528: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+25528: Id : 3, {_}:
+ apply (apply t ?7) ?8 =?= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+25528: Goal:
+25528: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (g ?1) (apply (f ?1) (h ?1))
+ [1] by prove_q_combinator ?1
+25528: Order:
+25528: lpo
+25528: Leaf order:
+25528: b 1 0 0
+25528: t 1 0 0
+25528: f 2 1 2 0,2,1,1,2
+25528: g 2 1 2 0,2,1,2
+25528: h 2 1 2 0,2,2
+25528: apply 13 2 5 0,2
+Goal subsumed
+Statistics :
+Max weight : 76
+Found proof, 0.356753s
+% SZS status Unsatisfiable for COL060-1.p
+% SZS output start CNFRefutation for COL060-1.p
+Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
+Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
+Id : 447, {_}: apply (g (apply (apply b (apply t b)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t b)) (apply (apply b b) t))) (h (apply (apply b (apply t b)) (apply (apply b b) t)))) === apply (g (apply (apply b (apply t b)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t b)) (apply (apply b b) t))) (h (apply (apply b (apply t b)) (apply (apply b b) t)))) [] by Super 445 with 2 at 2
+Id : 445, {_}: apply (apply (apply ?1404 (g (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (f (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t))) =>= apply (g (apply (apply b (apply t ?1404)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t ?1404)) (apply (apply b b) t))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) [1404] by Super 277 with 3 at 1,2
+Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (apply (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) [901, 900] by Super 29 with 2 at 1,2
+Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (apply (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) [87, 86, 85] by Super 13 with 3 at 1,1,2
+Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (g (apply (apply b ?33) (apply (apply b ?34) ?35))) (apply (f (apply (apply b ?33) (apply (apply b ?34) ?35))) (h (apply (apply b ?33) (apply (apply b ?34) ?35)))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
+Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (g (apply (apply b ?18) ?19)) (apply (f (apply (apply b ?18) ?19)) (h (apply (apply b ?18) ?19))) [19, 18] by Super 1 with 2 at 1,1,2
+Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (g ?1) (apply (f ?1) (h ?1)) [1] by prove_q_combinator ?1
+% SZS output end CNFRefutation for COL060-1.p
+25526: solved COL060-1.p in 0.368022 using nrkbo
+25526: status Unsatisfiable for COL060-1.p
+CLASH, statistics insufficient
+25533: Facts:
+25533: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+25533: Id : 3, {_}:
+ apply (apply t ?7) ?8 =>= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+25533: Goal:
+25533: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (f ?1) (apply (h ?1) (g ?1))
+ [1] by prove_q1_combinator ?1
+25533: Order:
+25533: nrkbo
+25533: Leaf order:
+25533: b 1 0 0
+25533: t 1 0 0
+25533: f 2 1 2 0,2,1,1,2
+25533: g 2 1 2 0,2,1,2
+25533: h 2 1 2 0,2,2
+25533: apply 13 2 5 0,2
+CLASH, statistics insufficient
+25534: Facts:
+25534: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+25534: Id : 3, {_}:
+ apply (apply t ?7) ?8 =>= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+25534: Goal:
+25534: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (f ?1) (apply (h ?1) (g ?1))
+ [1] by prove_q1_combinator ?1
+25534: Order:
+25534: kbo
+25534: Leaf order:
+25534: b 1 0 0
+25534: t 1 0 0
+25534: f 2 1 2 0,2,1,1,2
+25534: g 2 1 2 0,2,1,2
+25534: h 2 1 2 0,2,2
+25534: apply 13 2 5 0,2
+CLASH, statistics insufficient
+25535: Facts:
+25535: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+25535: Id : 3, {_}:
+ apply (apply t ?7) ?8 =?= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+25535: Goal:
+25535: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (f ?1) (apply (h ?1) (g ?1))
+ [1] by prove_q1_combinator ?1
+25535: Order:
+25535: lpo
+25535: Leaf order:
+25535: b 1 0 0
+25535: t 1 0 0
+25535: f 2 1 2 0,2,1,1,2
+25535: g 2 1 2 0,2,1,2
+25535: h 2 1 2 0,2,2
+25535: apply 13 2 5 0,2
+Goal subsumed
+Statistics :
+Max weight : 76
+Found proof, 0.641348s
+% SZS status Unsatisfiable for COL061-1.p
+% SZS output start CNFRefutation for COL061-1.p
+Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
+Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
+Id : 447, {_}: apply (f (apply (apply b (apply t t)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) b))) (g (apply (apply b (apply t t)) (apply (apply b b) b)))) === apply (f (apply (apply b (apply t t)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) b))) (g (apply (apply b (apply t t)) (apply (apply b b) b)))) [] by Super 446 with 3 at 2,2
+Id : 446, {_}: apply (f (apply (apply b (apply t ?1406)) (apply (apply b b) b))) (apply (apply ?1406 (g (apply (apply b (apply t ?1406)) (apply (apply b b) b)))) (h (apply (apply b (apply t ?1406)) (apply (apply b b) b)))) =>= apply (f (apply (apply b (apply t ?1406)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t ?1406)) (apply (apply b b) b))) (g (apply (apply b (apply t ?1406)) (apply (apply b b) b)))) [1406] by Super 277 with 2 at 2
+Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (apply (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) [901, 900] by Super 29 with 2 at 1,2
+Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (apply (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) [87, 86, 85] by Super 13 with 3 at 1,1,2
+Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (f (apply (apply b ?33) (apply (apply b ?34) ?35))) (apply (h (apply (apply b ?33) (apply (apply b ?34) ?35))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
+Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (f (apply (apply b ?18) ?19)) (apply (h (apply (apply b ?18) ?19)) (g (apply (apply b ?18) ?19))) [19, 18] by Super 1 with 2 at 1,1,2
+Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (f ?1) (apply (h ?1) (g ?1)) [1] by prove_q1_combinator ?1
+% SZS output end CNFRefutation for COL061-1.p
+25533: solved COL061-1.p in 0.344021 using nrkbo
+25533: status Unsatisfiable for COL061-1.p
+CLASH, statistics insufficient
+25541: Facts:
+25541: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+25541: Id : 3, {_}:
+ apply (apply t ?7) ?8 =>= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+25541: Goal:
+25541: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (apply (f ?1) (h ?1)) (g ?1)
+ [1] by prove_c_combinator ?1
+25541: Order:
+25541: kbo
+25541: Leaf order:
+25541: b 1 0 0
+25541: t 1 0 0
+25541: f 2 1 2 0,2,1,1,2
+25541: g 2 1 2 0,2,1,2
+25541: h 2 1 2 0,2,2
+25541: apply 13 2 5 0,2
+CLASH, statistics insufficient
+25540: Facts:
+25540: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+25540: Id : 3, {_}:
+ apply (apply t ?7) ?8 =>= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+25540: Goal:
+25540: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (apply (f ?1) (h ?1)) (g ?1)
+ [1] by prove_c_combinator ?1
+25540: Order:
+25540: nrkbo
+25540: Leaf order:
+25540: b 1 0 0
+25540: t 1 0 0
+25540: f 2 1 2 0,2,1,1,2
+25540: g 2 1 2 0,2,1,2
+25540: h 2 1 2 0,2,2
+25540: apply 13 2 5 0,2
+CLASH, statistics insufficient
+25542: Facts:
+25542: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+25542: Id : 3, {_}:
+ apply (apply t ?7) ?8 =?= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+25542: Goal:
+25542: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (apply (f ?1) (h ?1)) (g ?1)
+ [1] by prove_c_combinator ?1
+25542: Order:
+25542: lpo
+25542: Leaf order:
+25542: b 1 0 0
+25542: t 1 0 0
+25542: f 2 1 2 0,2,1,1,2
+25542: g 2 1 2 0,2,1,2
+25542: h 2 1 2 0,2,2
+25542: apply 13 2 5 0,2
+Goal subsumed
+Statistics :
+Max weight : 100
+Found proof, 1.793493s
+% SZS status Unsatisfiable for COL062-1.p
+% SZS output start CNFRefutation for COL062-1.p
+Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
+Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
+Id : 1574, {_}: apply (apply (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) === apply (apply (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) [] by Super 1573 with 3 at 2
+Id : 1573, {_}: apply (apply ?5215 (g (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t)))) (apply (f (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t)))) =>= apply (apply (f (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t))) [5215] by Super 447 with 2 at 2
+Id : 447, {_}: apply (apply (apply ?1408 (apply ?1409 (g (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))))) (f (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t)))) (h (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))) =>= apply (apply (f (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))) [1409, 1408] by Super 445 with 2 at 1,1,2
+Id : 445, {_}: apply (apply (apply ?1404 (g (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (f (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t))) =>= apply (apply (f (apply (apply b (apply t ?1404)) (apply (apply b b) t))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (g (apply (apply b (apply t ?1404)) (apply (apply b b) t))) [1404] by Super 277 with 3 at 1,2
+Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (apply (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) [901, 900] by Super 29 with 2 at 1,2
+Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (apply (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) [87, 86, 85] by Super 13 with 3 at 1,1,2
+Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (apply (f (apply (apply b ?33) (apply (apply b ?34) ?35))) (h (apply (apply b ?33) (apply (apply b ?34) ?35)))) (g (apply (apply b ?33) (apply (apply b ?34) ?35))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
+Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (apply (f (apply (apply b ?18) ?19)) (h (apply (apply b ?18) ?19))) (g (apply (apply b ?18) ?19)) [19, 18] by Super 1 with 2 at 1,1,2
+Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (f ?1) (h ?1)) (g ?1) [1] by prove_c_combinator ?1
+% SZS output end CNFRefutation for COL062-1.p
+25540: solved COL062-1.p in 1.808112 using nrkbo
+25540: status Unsatisfiable for COL062-1.p
+CLASH, statistics insufficient
+25547: Facts:
+25547: Id : 2, {_}:
+ apply (apply (apply n ?3) ?4) ?5
+ =?=
+ apply (apply (apply ?3 ?5) ?4) ?5
+ [5, 4, 3] by n_definition ?3 ?4 ?5
+25547: Id : 3, {_}:
+ apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
+ [9, 8, 7] by q_definition ?7 ?8 ?9
+25547: Goal:
+25547: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+25547: Order:
+25547: nrkbo
+25547: Leaf order:
+25547: n 1 0 0
+25547: q 1 0 0
+25547: f 3 1 3 0,2,2
+25547: apply 14 2 3 0,2
+CLASH, statistics insufficient
+25548: Facts:
+25548: Id : 2, {_}:
+ apply (apply (apply n ?3) ?4) ?5
+ =?=
+ apply (apply (apply ?3 ?5) ?4) ?5
+ [5, 4, 3] by n_definition ?3 ?4 ?5
+25548: Id : 3, {_}:
+ apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
+ [9, 8, 7] by q_definition ?7 ?8 ?9
+25548: Goal:
+25548: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+25548: Order:
+25548: kbo
+25548: Leaf order:
+25548: n 1 0 0
+25548: q 1 0 0
+25548: f 3 1 3 0,2,2
+25548: apply 14 2 3 0,2
+CLASH, statistics insufficient
+25549: Facts:
+25549: Id : 2, {_}:
+ apply (apply (apply n ?3) ?4) ?5
+ =?=
+ apply (apply (apply ?3 ?5) ?4) ?5
+ [5, 4, 3] by n_definition ?3 ?4 ?5
+25549: Id : 3, {_}:
+ apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
+ [9, 8, 7] by q_definition ?7 ?8 ?9
+25549: Goal:
+25549: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+25549: Order:
+25549: lpo
+25549: Leaf order:
+25549: n 1 0 0
+25549: q 1 0 0
+25549: f 3 1 3 0,2,2
+25549: apply 14 2 3 0,2
+% SZS status Timeout for COL071-1.p
+CLASH, statistics insufficient
+25572: Facts:
+25572: Id : 2, {_}:
+ apply (apply (apply n1 ?3) ?4) ?5
+ =?=
+ apply (apply (apply ?3 ?4) ?4) ?5
+ [5, 4, 3] by n1_definition ?3 ?4 ?5
+25572: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+25572: Goal:
+25572: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_strong_fixed_point ?1
+25572: Order:
+25572: nrkbo
+25572: Leaf order:
+25572: n1 1 0 0
+25572: b 1 0 0
+25572: f 3 1 3 0,2,2
+25572: apply 14 2 3 0,2
+CLASH, statistics insufficient
+25573: Facts:
+25573: Id : 2, {_}:
+ apply (apply (apply n1 ?3) ?4) ?5
+ =?=
+ apply (apply (apply ?3 ?4) ?4) ?5
+ [5, 4, 3] by n1_definition ?3 ?4 ?5
+25573: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+25573: Goal:
+25573: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_strong_fixed_point ?1
+25573: Order:
+25573: kbo
+25573: Leaf order:
+25573: n1 1 0 0
+25573: b 1 0 0
+25573: f 3 1 3 0,2,2
+25573: apply 14 2 3 0,2
+CLASH, statistics insufficient
+25574: Facts:
+25574: Id : 2, {_}:
+ apply (apply (apply n1 ?3) ?4) ?5
+ =?=
+ apply (apply (apply ?3 ?4) ?4) ?5
+ [5, 4, 3] by n1_definition ?3 ?4 ?5
+25574: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+25574: Goal:
+25574: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_strong_fixed_point ?1
+25574: Order:
+25574: lpo
+25574: Leaf order:
+25574: n1 1 0 0
+25574: b 1 0 0
+25574: f 3 1 3 0,2,2
+25574: apply 14 2 3 0,2
+% SZS status Timeout for COL073-1.p
+NO CLASH, using fixed ground order
+25603: Facts:
+25603: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25603: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25603: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25603: Id : 5, {_}:
+ commutator ?10 ?11
+ =<=
+ multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11))
+ [11, 10] by name ?10 ?11
+25603: Id : 6, {_}:
+ commutator (commutator ?13 ?14) ?15
+ =?=
+ commutator ?13 (commutator ?14 ?15)
+ [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15
+25603: Goal:
+25603: Id : 1, {_}:
+ multiply a (commutator b c) =<= multiply (commutator b c) a
+ [] by prove_center
+25603: Order:
+25603: nrkbo
+25603: Leaf order:
+25603: identity 2 0 0
+25603: a 2 0 2 1,2
+25603: b 2 0 2 1,2,2
+25603: c 2 0 2 2,2,2
+25603: inverse 3 1 0
+25603: commutator 7 2 2 0,2,2
+25603: multiply 11 2 2 0,2
+NO CLASH, using fixed ground order
+25604: Facts:
+25604: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25604: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25604: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25604: Id : 5, {_}:
+ commutator ?10 ?11
+ =<=
+ multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11))
+ [11, 10] by name ?10 ?11
+25604: Id : 6, {_}:
+ commutator (commutator ?13 ?14) ?15
+ =>=
+ commutator ?13 (commutator ?14 ?15)
+ [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15
+25604: Goal:
+25604: Id : 1, {_}:
+ multiply a (commutator b c) =<= multiply (commutator b c) a
+ [] by prove_center
+25604: Order:
+25604: kbo
+25604: Leaf order:
+25604: identity 2 0 0
+25604: a 2 0 2 1,2
+25604: b 2 0 2 1,2,2
+25604: c 2 0 2 2,2,2
+25604: inverse 3 1 0
+25604: commutator 7 2 2 0,2,2
+25604: multiply 11 2 2 0,2
+NO CLASH, using fixed ground order
+25605: Facts:
+25605: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25605: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25605: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25605: Id : 5, {_}:
+ commutator ?10 ?11
+ =<=
+ multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11))
+ [11, 10] by name ?10 ?11
+25605: Id : 6, {_}:
+ commutator (commutator ?13 ?14) ?15
+ =>=
+ commutator ?13 (commutator ?14 ?15)
+ [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15
+25605: Goal:
+25605: Id : 1, {_}:
+ multiply a (commutator b c) =<= multiply (commutator b c) a
+ [] by prove_center
+25605: Order:
+25605: lpo
+25605: Leaf order:
+25605: identity 2 0 0
+25605: a 2 0 2 1,2
+25605: b 2 0 2 1,2,2
+25605: c 2 0 2 2,2,2
+25605: inverse 3 1 0
+25605: commutator 7 2 2 0,2,2
+25605: multiply 11 2 2 0,2
+% SZS status Timeout for GRP024-5.p
+CLASH, statistics insufficient
+25668: Facts:
+25668: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25668: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25668: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25668: Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity
+25668: Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
+25668: Id : 7, {_}:
+ inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13)
+ [14, 13] by inverse_product_lemma ?13 ?14
+25668: Id : 8, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16
+25668: Id : 9, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18
+25668: Id : 10, {_}:
+ intersection ?20 ?21 =?= intersection ?21 ?20
+ [21, 20] by intersection_commutative ?20 ?21
+25668: Id : 11, {_}:
+ union ?23 ?24 =?= union ?24 ?23
+ [24, 23] by union_commutative ?23 ?24
+25668: Id : 12, {_}:
+ intersection ?26 (intersection ?27 ?28)
+ =?=
+ intersection (intersection ?26 ?27) ?28
+ [28, 27, 26] by intersection_associative ?26 ?27 ?28
+25668: Id : 13, {_}:
+ union ?30 (union ?31 ?32) =?= union (union ?30 ?31) ?32
+ [32, 31, 30] by union_associative ?30 ?31 ?32
+25668: Id : 14, {_}:
+ union (intersection ?34 ?35) ?35 =>= ?35
+ [35, 34] by union_intersection_absorbtion ?34 ?35
+25668: Id : 15, {_}:
+ intersection (union ?37 ?38) ?38 =>= ?38
+ [38, 37] by intersection_union_absorbtion ?37 ?38
+25668: Id : 16, {_}:
+ multiply ?40 (union ?41 ?42)
+ =<=
+ union (multiply ?40 ?41) (multiply ?40 ?42)
+ [42, 41, 40] by multiply_union1 ?40 ?41 ?42
+25668: Id : 17, {_}:
+ multiply ?44 (intersection ?45 ?46)
+ =<=
+ intersection (multiply ?44 ?45) (multiply ?44 ?46)
+ [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
+25668: Id : 18, {_}:
+ multiply (union ?48 ?49) ?50
+ =<=
+ union (multiply ?48 ?50) (multiply ?49 ?50)
+ [50, 49, 48] by multiply_union2 ?48 ?49 ?50
+25668: Id : 19, {_}:
+ multiply (intersection ?52 ?53) ?54
+ =<=
+ intersection (multiply ?52 ?54) (multiply ?53 ?54)
+ [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54
+25668: Id : 20, {_}:
+ positive_part ?56 =<= union ?56 identity
+ [56] by positive_part ?56
+25668: Id : 21, {_}:
+ negative_part ?58 =<= intersection ?58 identity
+ [58] by negative_part ?58
+25668: Goal:
+25668: Id : 1, {_}:
+ multiply (positive_part a) (negative_part a) =>= a
+ [] by prove_product
+25668: Order:
+25668: nrkbo
+25668: Leaf order:
+25668: a 3 0 3 1,1,2
+25668: identity 6 0 0
+25668: positive_part 2 1 1 0,1,2
+25668: negative_part 2 1 1 0,2,2
+25668: inverse 7 1 0
+25668: intersection 14 2 0
+25668: union 14 2 0
+25668: multiply 21 2 1 0,2
+CLASH, statistics insufficient
+25669: Facts:
+25669: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25669: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25669: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25669: Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity
+25669: Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
+25669: Id : 7, {_}:
+ inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13)
+ [14, 13] by inverse_product_lemma ?13 ?14
+25669: Id : 8, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16
+CLASH, statistics insufficient
+25670: Facts:
+25670: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25670: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25670: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25670: Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity
+25670: Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
+25670: Id : 7, {_}:
+ inverse (multiply ?13 ?14) =?= multiply (inverse ?14) (inverse ?13)
+ [14, 13] by inverse_product_lemma ?13 ?14
+25670: Id : 8, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16
+25669: Id : 9, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18
+25669: Id : 10, {_}:
+ intersection ?20 ?21 =?= intersection ?21 ?20
+ [21, 20] by intersection_commutative ?20 ?21
+25669: Id : 11, {_}:
+ union ?23 ?24 =?= union ?24 ?23
+ [24, 23] by union_commutative ?23 ?24
+25669: Id : 12, {_}:
+ intersection ?26 (intersection ?27 ?28)
+ =<=
+ intersection (intersection ?26 ?27) ?28
+ [28, 27, 26] by intersection_associative ?26 ?27 ?28
+25669: Id : 13, {_}:
+ union ?30 (union ?31 ?32) =<= union (union ?30 ?31) ?32
+ [32, 31, 30] by union_associative ?30 ?31 ?32
+25669: Id : 14, {_}:
+ union (intersection ?34 ?35) ?35 =>= ?35
+ [35, 34] by union_intersection_absorbtion ?34 ?35
+25669: Id : 15, {_}:
+ intersection (union ?37 ?38) ?38 =>= ?38
+ [38, 37] by intersection_union_absorbtion ?37 ?38
+25669: Id : 16, {_}:
+ multiply ?40 (union ?41 ?42)
+ =<=
+ union (multiply ?40 ?41) (multiply ?40 ?42)
+ [42, 41, 40] by multiply_union1 ?40 ?41 ?42
+25669: Id : 17, {_}:
+ multiply ?44 (intersection ?45 ?46)
+ =<=
+ intersection (multiply ?44 ?45) (multiply ?44 ?46)
+ [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
+25669: Id : 18, {_}:
+ multiply (union ?48 ?49) ?50
+ =<=
+ union (multiply ?48 ?50) (multiply ?49 ?50)
+ [50, 49, 48] by multiply_union2 ?48 ?49 ?50
+25669: Id : 19, {_}:
+ multiply (intersection ?52 ?53) ?54
+ =<=
+ intersection (multiply ?52 ?54) (multiply ?53 ?54)
+ [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54
+25669: Id : 20, {_}:
+ positive_part ?56 =<= union ?56 identity
+ [56] by positive_part ?56
+25669: Id : 21, {_}:
+ negative_part ?58 =<= intersection ?58 identity
+ [58] by negative_part ?58
+25669: Goal:
+25669: Id : 1, {_}:
+ multiply (positive_part a) (negative_part a) =>= a
+ [] by prove_product
+25669: Order:
+25669: kbo
+25669: Leaf order:
+25669: a 3 0 3 1,1,2
+25669: identity 6 0 0
+25669: positive_part 2 1 1 0,1,2
+25669: negative_part 2 1 1 0,2,2
+25669: inverse 7 1 0
+25669: intersection 14 2 0
+25669: union 14 2 0
+25669: multiply 21 2 1 0,2
+25670: Id : 9, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18
+25670: Id : 10, {_}:
+ intersection ?20 ?21 =?= intersection ?21 ?20
+ [21, 20] by intersection_commutative ?20 ?21
+25670: Id : 11, {_}:
+ union ?23 ?24 =?= union ?24 ?23
+ [24, 23] by union_commutative ?23 ?24
+25670: Id : 12, {_}:
+ intersection ?26 (intersection ?27 ?28)
+ =<=
+ intersection (intersection ?26 ?27) ?28
+ [28, 27, 26] by intersection_associative ?26 ?27 ?28
+25670: Id : 13, {_}:
+ union ?30 (union ?31 ?32) =<= union (union ?30 ?31) ?32
+ [32, 31, 30] by union_associative ?30 ?31 ?32
+25670: Id : 14, {_}:
+ union (intersection ?34 ?35) ?35 =>= ?35
+ [35, 34] by union_intersection_absorbtion ?34 ?35
+25670: Id : 15, {_}:
+ intersection (union ?37 ?38) ?38 =>= ?38
+ [38, 37] by intersection_union_absorbtion ?37 ?38
+25670: Id : 16, {_}:
+ multiply ?40 (union ?41 ?42)
+ =>=
+ union (multiply ?40 ?41) (multiply ?40 ?42)
+ [42, 41, 40] by multiply_union1 ?40 ?41 ?42
+25670: Id : 17, {_}:
+ multiply ?44 (intersection ?45 ?46)
+ =>=
+ intersection (multiply ?44 ?45) (multiply ?44 ?46)
+ [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
+25670: Id : 18, {_}:
+ multiply (union ?48 ?49) ?50
+ =>=
+ union (multiply ?48 ?50) (multiply ?49 ?50)
+ [50, 49, 48] by multiply_union2 ?48 ?49 ?50
+25670: Id : 19, {_}:
+ multiply (intersection ?52 ?53) ?54
+ =>=
+ intersection (multiply ?52 ?54) (multiply ?53 ?54)
+ [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54
+25670: Id : 20, {_}:
+ positive_part ?56 =>= union ?56 identity
+ [56] by positive_part ?56
+25670: Id : 21, {_}:
+ negative_part ?58 =>= intersection ?58 identity
+ [58] by negative_part ?58
+25670: Goal:
+25670: Id : 1, {_}:
+ multiply (positive_part a) (negative_part a) =>= a
+ [] by prove_product
+25670: Order:
+25670: lpo
+25670: Leaf order:
+25670: a 3 0 3 1,1,2
+25670: identity 6 0 0
+25670: positive_part 2 1 1 0,1,2
+25670: negative_part 2 1 1 0,2,2
+25670: inverse 7 1 0
+25670: intersection 14 2 0
+25670: union 14 2 0
+25670: multiply 21 2 1 0,2
+Statistics :
+Max weight : 16
+Found proof, 7.917801s
+% SZS status Unsatisfiable for GRP114-1.p
+% SZS output start CNFRefutation for GRP114-1.p
+Id : 12, {_}: intersection ?26 (intersection ?27 ?28) =?= intersection (intersection ?26 ?27) ?28 [28, 27, 26] by intersection_associative ?26 ?27 ?28
+Id : 17, {_}: multiply ?44 (intersection ?45 ?46) =<= intersection (multiply ?44 ?45) (multiply ?44 ?46) [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46
+Id : 14, {_}: union (intersection ?34 ?35) ?35 =>= ?35 [35, 34] by union_intersection_absorbtion ?34 ?35
+Id : 16, {_}: multiply ?40 (union ?41 ?42) =<= union (multiply ?40 ?41) (multiply ?40 ?42) [42, 41, 40] by multiply_union1 ?40 ?41 ?42
+Id : 13, {_}: union ?30 (union ?31 ?32) =?= union (union ?30 ?31) ?32 [32, 31, 30] by union_associative ?30 ?31 ?32
+Id : 241, {_}: multiply (union ?684 ?685) ?686 =<= union (multiply ?684 ?686) (multiply ?685 ?686) [686, 685, 684] by multiply_union2 ?684 ?685 ?686
+Id : 20, {_}: positive_part ?56 =<= union ?56 identity [56] by positive_part ?56
+Id : 11, {_}: union ?23 ?24 =?= union ?24 ?23 [24, 23] by union_commutative ?23 ?24
+Id : 15, {_}: intersection (union ?37 ?38) ?38 =>= ?38 [38, 37] by intersection_union_absorbtion ?37 ?38
+Id : 205, {_}: multiply ?602 (intersection ?603 ?604) =<= intersection (multiply ?602 ?603) (multiply ?602 ?604) [604, 603, 602] by multiply_intersection1 ?602 ?603 ?604
+Id : 21, {_}: negative_part ?58 =<= intersection ?58 identity [58] by negative_part ?58
+Id : 10, {_}: intersection ?20 ?21 =?= intersection ?21 ?20 [21, 20] by intersection_commutative ?20 ?21
+Id : 276, {_}: multiply (intersection ?769 ?770) ?771 =<= intersection (multiply ?769 ?771) (multiply ?770 ?771) [771, 770, 769] by multiply_intersection2 ?769 ?770 ?771
+Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11
+Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity
+Id : 58, {_}: inverse (multiply ?149 ?150) =<= multiply (inverse ?150) (inverse ?149) [150, 149] by inverse_product_lemma ?149 ?150
+Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+Id : 26, {_}: multiply (multiply ?67 ?68) ?69 =?= multiply ?67 (multiply ?68 ?69) [69, 68, 67] by associativity ?67 ?68 ?69
+Id : 28, {_}: multiply (multiply ?74 (inverse ?75)) ?75 =>= multiply ?74 identity [75, 74] by Super 26 with 3 at 2,3
+Id : 59, {_}: inverse (multiply identity ?152) =<= multiply (inverse ?152) identity [152] by Super 58 with 5 at 2,3
+Id : 459, {_}: inverse ?1057 =<= multiply (inverse ?1057) identity [1057] by Demod 59 with 2 at 1,2
+Id : 461, {_}: inverse (inverse ?1060) =<= multiply ?1060 identity [1060] by Super 459 with 6 at 1,3
+Id : 475, {_}: ?1060 =<= multiply ?1060 identity [1060] by Demod 461 with 6 at 2
+Id : 570, {_}: multiply (multiply ?74 (inverse ?75)) ?75 =>= ?74 [75, 74] by Demod 28 with 475 at 3
+Id : 62, {_}: inverse (multiply ?159 (inverse ?160)) =>= multiply ?160 (inverse ?159) [160, 159] by Super 58 with 6 at 1,3
+Id : 283, {_}: multiply (intersection (inverse ?796) ?797) ?796 =>= intersection identity (multiply ?797 ?796) [797, 796] by Super 276 with 3 at 1,3
+Id : 329, {_}: intersection identity ?869 =>= negative_part ?869 [869] by Super 10 with 21 at 3
+Id : 16231, {_}: multiply (intersection (inverse ?20320) ?20321) ?20320 =>= negative_part (multiply ?20321 ?20320) [20321, 20320] by Demod 283 with 329 at 3
+Id : 16259, {_}: multiply (negative_part (inverse ?20413)) ?20413 =>= negative_part (multiply identity ?20413) [20413] by Super 16231 with 21 at 1,2
+Id : 16311, {_}: multiply (negative_part (inverse ?20413)) ?20413 =>= negative_part ?20413 [20413] by Demod 16259 with 2 at 1,3
+Id : 16342, {_}: inverse (negative_part (inverse ?20447)) =<= multiply ?20447 (inverse (negative_part (inverse (inverse ?20447)))) [20447] by Super 62 with 16311 at 1,2
+Id : 16414, {_}: inverse (negative_part (inverse ?20447)) =<= multiply ?20447 (inverse (negative_part ?20447)) [20447] by Demod 16342 with 6 at 1,1,2,3
+Id : 16644, {_}: multiply (inverse (negative_part (inverse ?20815))) (negative_part ?20815) =>= ?20815 [20815] by Super 570 with 16414 at 1,2
+Id : 60, {_}: inverse (multiply (inverse ?154) ?155) =>= multiply (inverse ?155) ?154 [155, 154] by Super 58 with 6 at 2,3
+Id : 207, {_}: multiply (inverse ?609) (intersection ?610 ?609) =>= intersection (multiply (inverse ?609) ?610) identity [610, 609] by Super 205 with 3 at 2,3
+Id : 228, {_}: multiply (inverse ?609) (intersection ?610 ?609) =>= intersection identity (multiply (inverse ?609) ?610) [610, 609] by Demod 207 with 10 at 3
+Id : 10379, {_}: multiply (inverse ?609) (intersection ?610 ?609) =>= negative_part (multiply (inverse ?609) ?610) [610, 609] by Demod 228 with 329 at 3
+Id : 10396, {_}: inverse (negative_part (multiply (inverse ?14999) ?15000)) =<= multiply (inverse (intersection ?15000 ?14999)) ?14999 [15000, 14999] by Super 60 with 10379 at 1,2
+Id : 309, {_}: union identity ?834 =>= positive_part ?834 [834] by Super 11 with 20 at 3
+Id : 360, {_}: intersection (positive_part ?914) ?914 =>= ?914 [914] by Super 15 with 309 at 1,2
+Id : 686, {_}: intersection ?1353 (positive_part ?1353) =>= ?1353 [1353] by Super 10 with 360 at 3
+Id : 248, {_}: multiply (union (inverse ?711) ?712) ?711 =>= union identity (multiply ?712 ?711) [712, 711] by Super 241 with 3 at 1,3
+Id : 10542, {_}: multiply (union (inverse ?15313) ?15314) ?15313 =>= positive_part (multiply ?15314 ?15313) [15314, 15313] by Demod 248 with 309 at 3
+Id : 359, {_}: union identity (union ?911 ?912) =>= union (positive_part ?911) ?912 [912, 911] by Super 13 with 309 at 1,3
+Id : 367, {_}: positive_part (union ?911 ?912) =>= union (positive_part ?911) ?912 [912, 911] by Demod 359 with 309 at 2
+Id : 312, {_}: union ?841 (union ?842 identity) =>= positive_part (union ?841 ?842) [842, 841] by Super 13 with 20 at 3
+Id : 324, {_}: union ?841 (positive_part ?842) =<= positive_part (union ?841 ?842) [842, 841] by Demod 312 with 20 at 2,2
+Id : 709, {_}: union ?911 (positive_part ?912) =?= union (positive_part ?911) ?912 [912, 911] by Demod 367 with 324 at 2
+Id : 487, {_}: multiply ?1085 (union ?1086 identity) =?= union (multiply ?1085 ?1086) ?1085 [1086, 1085] by Super 16 with 475 at 2,3
+Id : 2720, {_}: multiply ?5029 (positive_part ?5030) =<= union (multiply ?5029 ?5030) ?5029 [5030, 5029] by Demod 487 with 20 at 2,2
+Id : 2722, {_}: multiply (inverse ?5034) (positive_part ?5034) =>= union identity (inverse ?5034) [5034] by Super 2720 with 3 at 1,3
+Id : 2784, {_}: multiply (inverse ?5160) (positive_part ?5160) =>= positive_part (inverse ?5160) [5160] by Demod 2722 with 309 at 3
+Id : 307, {_}: positive_part (intersection ?831 identity) =>= identity [831] by Super 14 with 20 at 2
+Id : 514, {_}: positive_part (negative_part ?831) =>= identity [831] by Demod 307 with 21 at 1,2
+Id : 2786, {_}: multiply (inverse (negative_part ?5163)) identity =>= positive_part (inverse (negative_part ?5163)) [5163] by Super 2784 with 514 at 2,2
+Id : 2807, {_}: inverse (negative_part ?5163) =<= positive_part (inverse (negative_part ?5163)) [5163] by Demod 2786 with 475 at 2
+Id : 2823, {_}: union (inverse (negative_part ?5198)) (positive_part ?5199) =>= union (inverse (negative_part ?5198)) ?5199 [5199, 5198] by Super 709 with 2807 at 1,3
+Id : 10564, {_}: multiply (union (inverse (negative_part ?15386)) ?15387) (negative_part ?15386) =>= positive_part (multiply (positive_part ?15387) (negative_part ?15386)) [15387, 15386] by Super 10542 with 2823 at 1,2
+Id : 10509, {_}: multiply (union (inverse ?711) ?712) ?711 =>= positive_part (multiply ?712 ?711) [712, 711] by Demod 248 with 309 at 3
+Id : 10604, {_}: positive_part (multiply ?15387 (negative_part ?15386)) =<= positive_part (multiply (positive_part ?15387) (negative_part ?15386)) [15386, 15387] by Demod 10564 with 10509 at 2
+Id : 481, {_}: multiply ?1071 (intersection ?1072 identity) =?= intersection (multiply ?1071 ?1072) ?1071 [1072, 1071] by Super 17 with 475 at 2,3
+Id : 505, {_}: multiply ?1071 (negative_part ?1072) =<= intersection (multiply ?1071 ?1072) ?1071 [1072, 1071] by Demod 481 with 21 at 2,2
+Id : 10568, {_}: multiply (positive_part (inverse ?15398)) ?15398 =>= positive_part (multiply identity ?15398) [15398] by Super 10542 with 20 at 1,2
+Id : 10608, {_}: multiply (positive_part (inverse ?15398)) ?15398 =>= positive_part ?15398 [15398] by Demod 10568 with 2 at 1,3
+Id : 10645, {_}: multiply (positive_part (inverse ?15507)) (negative_part ?15507) =>= intersection (positive_part ?15507) (positive_part (inverse ?15507)) [15507] by Super 505 with 10608 at 1,3
+Id : 11493, {_}: positive_part (multiply (inverse ?16415) (negative_part ?16415)) =<= positive_part (intersection (positive_part ?16415) (positive_part (inverse ?16415))) [16415] by Super 10604 with 10645 at 1,3
+Id : 3426, {_}: multiply ?5989 (negative_part ?5990) =<= intersection (multiply ?5989 ?5990) ?5989 [5990, 5989] by Demod 481 with 21 at 2,2
+Id : 3428, {_}: multiply (inverse ?5994) (negative_part ?5994) =>= intersection identity (inverse ?5994) [5994] by Super 3426 with 3 at 1,3
+Id : 3468, {_}: multiply (inverse ?5994) (negative_part ?5994) =>= negative_part (inverse ?5994) [5994] by Demod 3428 with 329 at 3
+Id : 11531, {_}: positive_part (negative_part (inverse ?16415)) =<= positive_part (intersection (positive_part ?16415) (positive_part (inverse ?16415))) [16415] by Demod 11493 with 3468 at 1,2
+Id : 11532, {_}: identity =<= positive_part (intersection (positive_part ?16415) (positive_part (inverse ?16415))) [16415] by Demod 11531 with 514 at 2
+Id : 52635, {_}: intersection (intersection (positive_part ?60922) (positive_part (inverse ?60922))) identity =>= intersection (positive_part ?60922) (positive_part (inverse ?60922)) [60922] by Super 686 with 11532 at 2,2
+Id : 52914, {_}: intersection identity (intersection (positive_part ?60922) (positive_part (inverse ?60922))) =>= intersection (positive_part ?60922) (positive_part (inverse ?60922)) [60922] by Demod 52635 with 10 at 2
+Id : 52915, {_}: negative_part (intersection (positive_part ?60922) (positive_part (inverse ?60922))) =>= intersection (positive_part ?60922) (positive_part (inverse ?60922)) [60922] by Demod 52914 with 329 at 2
+Id : 332, {_}: intersection ?876 (intersection ?877 identity) =>= negative_part (intersection ?876 ?877) [877, 876] by Super 12 with 21 at 3
+Id : 344, {_}: intersection ?876 (negative_part ?877) =<= negative_part (intersection ?876 ?877) [877, 876] by Demod 332 with 21 at 2,2
+Id : 52916, {_}: intersection (positive_part ?60922) (negative_part (positive_part (inverse ?60922))) =>= intersection (positive_part ?60922) (positive_part (inverse ?60922)) [60922] by Demod 52915 with 344 at 2
+Id : 52917, {_}: intersection (negative_part (positive_part (inverse ?60922))) (positive_part ?60922) =>= intersection (positive_part ?60922) (positive_part (inverse ?60922)) [60922] by Demod 52916 with 10 at 2
+Id : 421, {_}: intersection identity (intersection ?1000 ?1001) =>= intersection (negative_part ?1000) ?1001 [1001, 1000] by Super 12 with 329 at 1,3
+Id : 435, {_}: negative_part (intersection ?1000 ?1001) =>= intersection (negative_part ?1000) ?1001 [1001, 1000] by Demod 421 with 329 at 2
+Id : 903, {_}: intersection ?1965 (negative_part ?1966) =?= intersection (negative_part ?1965) ?1966 [1966, 1965] by Demod 435 with 344 at 2
+Id : 327, {_}: negative_part (union ?866 identity) =>= identity [866] by Super 15 with 21 at 2
+Id : 346, {_}: negative_part (positive_part ?866) =>= identity [866] by Demod 327 with 20 at 1,2
+Id : 914, {_}: intersection (positive_part ?1997) (negative_part ?1998) =>= intersection identity ?1998 [1998, 1997] by Super 903 with 346 at 1,2
+Id : 945, {_}: intersection (negative_part ?1998) (positive_part ?1997) =>= intersection identity ?1998 [1997, 1998] by Demod 914 with 10 at 2
+Id : 946, {_}: intersection (negative_part ?1998) (positive_part ?1997) =>= negative_part ?1998 [1997, 1998] by Demod 945 with 329 at 3
+Id : 52918, {_}: negative_part (positive_part (inverse ?60922)) =<= intersection (positive_part ?60922) (positive_part (inverse ?60922)) [60922] by Demod 52917 with 946 at 2
+Id : 52919, {_}: identity =<= intersection (positive_part ?60922) (positive_part (inverse ?60922)) [60922] by Demod 52918 with 346 at 2
+Id : 53306, {_}: inverse (negative_part (multiply (inverse (positive_part (inverse ?61296))) (positive_part ?61296))) =>= multiply (inverse identity) (positive_part (inverse ?61296)) [61296] by Super 10396 with 52919 at 1,1,3
+Id : 10642, {_}: inverse (positive_part (inverse ?15501)) =<= multiply ?15501 (inverse (positive_part (inverse (inverse ?15501)))) [15501] by Super 62 with 10608 at 1,2
+Id : 10686, {_}: inverse (positive_part (inverse ?15501)) =<= multiply ?15501 (inverse (positive_part ?15501)) [15501] by Demod 10642 with 6 at 1,1,2,3
+Id : 10895, {_}: multiply (inverse (positive_part (inverse ?15767))) (positive_part ?15767) =>= ?15767 [15767] by Super 570 with 10686 at 1,2
+Id : 53366, {_}: inverse (negative_part ?61296) =<= multiply (inverse identity) (positive_part (inverse ?61296)) [61296] by Demod 53306 with 10895 at 1,1,2
+Id : 53367, {_}: inverse (negative_part ?61296) =<= multiply identity (positive_part (inverse ?61296)) [61296] by Demod 53366 with 5 at 1,3
+Id : 53816, {_}: inverse (negative_part ?61700) =<= positive_part (inverse ?61700) [61700] by Demod 53367 with 2 at 3
+Id : 53819, {_}: inverse (negative_part (multiply (inverse ?61705) ?61706)) =>= positive_part (multiply (inverse ?61706) ?61705) [61706, 61705] by Super 53816 with 60 at 1,3
+Id : 62826, {_}: inverse (positive_part (multiply (inverse ?68982) ?68983)) =>= negative_part (multiply (inverse ?68983) ?68982) [68983, 68982] by Super 6 with 53819 at 1,2
+Id : 62827, {_}: inverse (positive_part (multiply identity ?68985)) =<= negative_part (multiply (inverse ?68985) identity) [68985] by Super 62826 with 5 at 1,1,1,2
+Id : 63051, {_}: inverse (positive_part ?68985) =<= negative_part (multiply (inverse ?68985) identity) [68985] by Demod 62827 with 2 at 1,1,2
+Id : 63052, {_}: inverse (positive_part ?68985) =<= negative_part (inverse ?68985) [68985] by Demod 63051 with 475 at 1,3
+Id : 66930, {_}: multiply (inverse (inverse (positive_part ?20815))) (negative_part ?20815) =>= ?20815 [20815] by Demod 16644 with 63052 at 1,1,2
+Id : 66931, {_}: multiply (positive_part ?20815) (negative_part ?20815) =>= ?20815 [20815] by Demod 66930 with 6 at 1,2
+Id : 67152, {_}: a === a [] by Demod 1 with 66931 at 2
+Id : 1, {_}: multiply (positive_part a) (negative_part a) =>= a [] by prove_product
+% SZS output end CNFRefutation for GRP114-1.p
+25668: solved GRP114-1.p in 7.932495 using nrkbo
+25668: status Unsatisfiable for GRP114-1.p
+NO CLASH, using fixed ground order
+25676: Facts:
+25676: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25676: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25676: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25676: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25676: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25676: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25676: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25676: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25676: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25676: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25676: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25676: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25676: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25676: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25676: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25676: Id : 17, {_}: inverse identity =>= identity [] by p19_1
+25676: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p19_2 ?51
+25676: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p19_3 ?53 ?54
+25676: Goal:
+25676: Id : 1, {_}:
+ a
+ =<=
+ multiply (least_upper_bound a identity)
+ (greatest_lower_bound a identity)
+ [] by prove_p19
+25676: Order:
+25676: kbo
+25676: Leaf order:
+25676: a 3 0 3 2
+25676: identity 6 0 2 2,1,3
+25676: inverse 7 1 0
+25676: least_upper_bound 14 2 1 0,1,3
+25676: greatest_lower_bound 14 2 1 0,2,3
+25676: multiply 21 2 1 0,3
+NO CLASH, using fixed ground order
+25675: Facts:
+25675: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25675: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25675: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25675: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25675: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25675: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25675: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25675: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25675: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25675: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25675: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25675: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25675: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25675: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25675: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25675: Id : 17, {_}: inverse identity =>= identity [] by p19_1
+25675: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p19_2 ?51
+25675: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p19_3 ?53 ?54
+25675: Goal:
+25675: Id : 1, {_}:
+ a
+ =<=
+ multiply (least_upper_bound a identity)
+ (greatest_lower_bound a identity)
+ [] by prove_p19
+25675: Order:
+25675: nrkbo
+25675: Leaf order:
+25675: a 3 0 3 2
+25675: identity 6 0 2 2,1,3
+25675: inverse 7 1 0
+25675: least_upper_bound 14 2 1 0,1,3
+25675: greatest_lower_bound 14 2 1 0,2,3
+25675: multiply 21 2 1 0,3
+NO CLASH, using fixed ground order
+25677: Facts:
+25677: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25677: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25677: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25677: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25677: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25677: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25677: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25677: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25677: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25677: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25677: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25677: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25677: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25677: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25677: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25677: Id : 17, {_}: inverse identity =>= identity [] by p19_1
+25677: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p19_2 ?51
+25677: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p19_3 ?53 ?54
+25677: Goal:
+25677: Id : 1, {_}:
+ a
+ =<=
+ multiply (least_upper_bound a identity)
+ (greatest_lower_bound a identity)
+ [] by prove_p19
+25677: Order:
+25677: lpo
+25677: Leaf order:
+25677: a 3 0 3 2
+25677: identity 6 0 2 2,1,3
+25677: inverse 7 1 0
+25677: least_upper_bound 14 2 1 0,1,3
+25677: greatest_lower_bound 14 2 1 0,2,3
+25677: multiply 21 2 1 0,3
+% SZS status Timeout for GRP167-4.p
+NO CLASH, using fixed ground order
+25699: Facts:
+25699: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25699: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25699: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25699: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25699: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25699: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25699: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25699: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25699: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25699: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25699: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25699: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25699: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25699: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25699: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25699: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p08b_1
+25699: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p08b_2
+25699: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p08b_3
+25699: Goal:
+25699: Id : 1, {_}:
+ greatest_lower_bound (greatest_lower_bound a (multiply b c))
+ (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
+ =>=
+ greatest_lower_bound a (multiply b c)
+ [] by prove_p08b
+25699: Order:
+25699: nrkbo
+25699: Leaf order:
+25699: b 4 0 3 1,2,1,2
+25699: c 4 0 3 2,2,1,2
+25699: a 5 0 4 1,1,2
+25699: identity 8 0 0
+25699: inverse 1 1 0
+25699: least_upper_bound 13 2 0
+25699: multiply 21 2 3 0,2,1,2
+25699: greatest_lower_bound 21 2 5 0,2
+NO CLASH, using fixed ground order
+25700: Facts:
+25700: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25700: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25700: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25700: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25700: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25700: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25700: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25700: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25700: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25700: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25700: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25700: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25700: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25700: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25700: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25700: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p08b_1
+25700: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p08b_2
+25700: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p08b_3
+25700: Goal:
+25700: Id : 1, {_}:
+ greatest_lower_bound (greatest_lower_bound a (multiply b c))
+ (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
+ =>=
+ greatest_lower_bound a (multiply b c)
+ [] by prove_p08b
+25700: Order:
+25700: kbo
+25700: Leaf order:
+25700: b 4 0 3 1,2,1,2
+25700: c 4 0 3 2,2,1,2
+25700: a 5 0 4 1,1,2
+25700: identity 8 0 0
+25700: inverse 1 1 0
+25700: least_upper_bound 13 2 0
+25700: multiply 21 2 3 0,2,1,2
+25700: greatest_lower_bound 21 2 5 0,2
+NO CLASH, using fixed ground order
+25701: Facts:
+25701: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25701: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25701: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25701: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25701: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25701: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25701: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25701: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25701: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25701: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25701: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25701: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25701: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25701: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25701: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25701: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p08b_1
+25701: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p08b_2
+25701: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p08b_3
+25701: Goal:
+25701: Id : 1, {_}:
+ greatest_lower_bound (greatest_lower_bound a (multiply b c))
+ (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
+ =>=
+ greatest_lower_bound a (multiply b c)
+ [] by prove_p08b
+25701: Order:
+25701: lpo
+25701: Leaf order:
+25701: b 4 0 3 1,2,1,2
+25701: c 4 0 3 2,2,1,2
+25701: a 5 0 4 1,1,2
+25701: identity 8 0 0
+25701: inverse 1 1 0
+25701: least_upper_bound 13 2 0
+25701: multiply 21 2 3 0,2,1,2
+25701: greatest_lower_bound 21 2 5 0,2
+% SZS status Timeout for GRP177-2.p
+NO CLASH, using fixed ground order
+25723: Facts:
+NO CLASH, using fixed ground order
+25724: Facts:
+25724: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25724: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25724: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25724: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25724: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25724: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25724: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25724: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+NO CLASH, using fixed ground order
+25725: Facts:
+25725: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25725: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25725: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25725: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25725: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25725: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25725: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25725: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25725: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25725: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25723: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25725: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25723: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25725: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25725: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25725: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25723: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25723: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25725: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25723: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25725: Id : 17, {_}: inverse identity =>= identity [] by p18_1
+25725: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p18_2 ?51
+25723: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25725: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p18_3 ?53 ?54
+25725: Goal:
+25725: Id : 1, {_}:
+ least_upper_bound (inverse a) identity
+ =>=
+ inverse (greatest_lower_bound a identity)
+ [] by prove_p18
+25725: Order:
+25725: lpo
+25725: Leaf order:
+25725: a 2 0 2 1,1,2
+25725: identity 6 0 2 2,2
+25725: inverse 9 1 2 0,1,2
+25725: greatest_lower_bound 14 2 1 0,1,3
+25725: least_upper_bound 14 2 1 0,2
+25723: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25723: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25723: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25723: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25723: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25723: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25723: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25723: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25723: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25723: Id : 17, {_}: inverse identity =>= identity [] by p18_1
+25723: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p18_2 ?51
+25723: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p18_3 ?53 ?54
+25723: Goal:
+25723: Id : 1, {_}:
+ least_upper_bound (inverse a) identity
+ =>=
+ inverse (greatest_lower_bound a identity)
+ [] by prove_p18
+25723: Order:
+25723: nrkbo
+25723: Leaf order:
+25723: a 2 0 2 1,1,2
+25723: identity 6 0 2 2,2
+25723: inverse 9 1 2 0,1,2
+25723: greatest_lower_bound 14 2 1 0,1,3
+25723: least_upper_bound 14 2 1 0,2
+25723: multiply 20 2 0
+25724: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25725: multiply 20 2 0
+25724: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25724: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25724: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25724: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25724: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25724: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25724: Id : 17, {_}: inverse identity =>= identity [] by p18_1
+25724: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p18_2 ?51
+25724: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p18_3 ?53 ?54
+25724: Goal:
+25724: Id : 1, {_}:
+ least_upper_bound (inverse a) identity
+ =>=
+ inverse (greatest_lower_bound a identity)
+ [] by prove_p18
+25724: Order:
+25724: kbo
+25724: Leaf order:
+25724: a 2 0 2 1,1,2
+25724: identity 6 0 2 2,2
+25724: inverse 9 1 2 0,1,2
+25724: greatest_lower_bound 14 2 1 0,1,3
+25724: least_upper_bound 14 2 1 0,2
+25724: multiply 20 2 0
+% SZS status Timeout for GRP179-3.p
+NO CLASH, using fixed ground order
+25752: Facts:
+25752: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25752: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25752: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25752: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25752: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25752: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25752: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25752: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25752: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25752: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25752: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25752: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25752: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25752: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25752: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25752: Id : 17, {_}: inverse identity =>= identity [] by p11_1
+25752: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p11_2 ?51
+25752: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p11_3 ?53 ?54
+25752: Goal:
+25752: Id : 1, {_}:
+ multiply a (multiply (inverse (greatest_lower_bound a b)) b)
+ =>=
+ least_upper_bound a b
+ [] by prove_p11
+25752: Order:
+25752: nrkbo
+25752: Leaf order:
+25752: a 3 0 3 1,2
+25752: b 3 0 3 2,1,1,2,2
+25752: identity 4 0 0
+25752: inverse 8 1 1 0,1,2,2
+25752: greatest_lower_bound 14 2 1 0,1,1,2,2
+25752: least_upper_bound 14 2 1 0,3
+25752: multiply 22 2 2 0,2
+NO CLASH, using fixed ground order
+25753: Facts:
+25753: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25753: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25753: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25753: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25753: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25753: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25753: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25753: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25753: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25753: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25753: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25753: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25753: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25753: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25753: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25753: Id : 17, {_}: inverse identity =>= identity [] by p11_1
+25753: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p11_2 ?51
+25753: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p11_3 ?53 ?54
+25753: Goal:
+25753: Id : 1, {_}:
+ multiply a (multiply (inverse (greatest_lower_bound a b)) b)
+ =>=
+ least_upper_bound a b
+ [] by prove_p11
+25753: Order:
+25753: kbo
+25753: Leaf order:
+25753: a 3 0 3 1,2
+25753: b 3 0 3 2,1,1,2,2
+25753: identity 4 0 0
+25753: inverse 8 1 1 0,1,2,2
+25753: greatest_lower_bound 14 2 1 0,1,1,2,2
+25753: least_upper_bound 14 2 1 0,3
+25753: multiply 22 2 2 0,2
+NO CLASH, using fixed ground order
+25754: Facts:
+25754: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25754: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25754: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25754: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25754: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25754: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25754: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25754: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25754: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25754: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25754: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25754: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25754: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25754: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25754: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25754: Id : 17, {_}: inverse identity =>= identity [] by p11_1
+25754: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p11_2 ?51
+25754: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p11_3 ?53 ?54
+25754: Goal:
+25754: Id : 1, {_}:
+ multiply a (multiply (inverse (greatest_lower_bound a b)) b)
+ =>=
+ least_upper_bound a b
+ [] by prove_p11
+25754: Order:
+25754: lpo
+25754: Leaf order:
+25754: a 3 0 3 1,2
+25754: b 3 0 3 2,1,1,2,2
+25754: identity 4 0 0
+25754: inverse 8 1 1 0,1,2,2
+25754: greatest_lower_bound 14 2 1 0,1,1,2,2
+25754: least_upper_bound 14 2 1 0,3
+25754: multiply 22 2 2 0,2
+% SZS status Timeout for GRP180-2.p
+CLASH, statistics insufficient
+25775: Facts:
+25775: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25775: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25775: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25775: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25775: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25775: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25775: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25775: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25775: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25775: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25775: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25775: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25775: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25775: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25775: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25775: Id : 17, {_}: inverse identity =>= identity [] by p12x_1
+25775: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
+25775: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p12x_3 ?53 ?54
+25775: Id : 20, {_}:
+ greatest_lower_bound a c =>= greatest_lower_bound b c
+ [] by p12x_4
+25775: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
+25775: Id : 22, {_}:
+ inverse (greatest_lower_bound ?58 ?59)
+ =<=
+ least_upper_bound (inverse ?58) (inverse ?59)
+ [59, 58] by p12x_6 ?58 ?59
+25775: Id : 23, {_}:
+ inverse (least_upper_bound ?61 ?62)
+ =<=
+ greatest_lower_bound (inverse ?61) (inverse ?62)
+ [62, 61] by p12x_7 ?61 ?62
+25775: Goal:
+25775: Id : 1, {_}: a =>= b [] by prove_p12x
+25775: Order:
+25775: nrkbo
+25775: Leaf order:
+25775: a 3 0 1 2
+25775: b 3 0 1 3
+25775: identity 4 0 0
+25775: c 4 0 0
+25775: inverse 13 1 0
+25775: greatest_lower_bound 17 2 0
+25775: least_upper_bound 17 2 0
+25775: multiply 20 2 0
+CLASH, statistics insufficient
+25776: Facts:
+25776: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25776: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25776: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25776: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25776: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25776: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25776: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25776: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25776: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25776: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25776: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25776: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25776: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25776: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25776: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25776: Id : 17, {_}: inverse identity =>= identity [] by p12x_1
+25776: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
+25776: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p12x_3 ?53 ?54
+25776: Id : 20, {_}:
+ greatest_lower_bound a c =>= greatest_lower_bound b c
+ [] by p12x_4
+25776: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
+25776: Id : 22, {_}:
+ inverse (greatest_lower_bound ?58 ?59)
+ =<=
+ least_upper_bound (inverse ?58) (inverse ?59)
+ [59, 58] by p12x_6 ?58 ?59
+25776: Id : 23, {_}:
+ inverse (least_upper_bound ?61 ?62)
+ =<=
+ greatest_lower_bound (inverse ?61) (inverse ?62)
+ [62, 61] by p12x_7 ?61 ?62
+25776: Goal:
+25776: Id : 1, {_}: a =>= b [] by prove_p12x
+25776: Order:
+25776: kbo
+25776: Leaf order:
+25776: a 3 0 1 2
+25776: b 3 0 1 3
+25776: identity 4 0 0
+25776: c 4 0 0
+25776: inverse 13 1 0
+25776: greatest_lower_bound 17 2 0
+25776: least_upper_bound 17 2 0
+25776: multiply 20 2 0
+CLASH, statistics insufficient
+25777: Facts:
+25777: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25777: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25777: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25777: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25777: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25777: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25777: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25777: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25777: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25777: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25777: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25777: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25777: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25777: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25777: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25777: Id : 17, {_}: inverse identity =>= identity [] by p12x_1
+25777: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
+25777: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p12x_3 ?53 ?54
+25777: Id : 20, {_}:
+ greatest_lower_bound a c =>= greatest_lower_bound b c
+ [] by p12x_4
+25777: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
+25777: Id : 22, {_}:
+ inverse (greatest_lower_bound ?58 ?59)
+ =>=
+ least_upper_bound (inverse ?58) (inverse ?59)
+ [59, 58] by p12x_6 ?58 ?59
+25777: Id : 23, {_}:
+ inverse (least_upper_bound ?61 ?62)
+ =>=
+ greatest_lower_bound (inverse ?61) (inverse ?62)
+ [62, 61] by p12x_7 ?61 ?62
+25777: Goal:
+25777: Id : 1, {_}: a =>= b [] by prove_p12x
+25777: Order:
+25777: lpo
+25777: Leaf order:
+25777: a 3 0 1 2
+25777: b 3 0 1 3
+25777: identity 4 0 0
+25777: c 4 0 0
+25777: inverse 13 1 0
+25777: greatest_lower_bound 17 2 0
+25777: least_upper_bound 17 2 0
+25777: multiply 20 2 0
+Statistics :
+Max weight : 16
+Found proof, 8.150042s
+% SZS status Unsatisfiable for GRP181-4.p
+% SZS output start CNFRefutation for GRP181-4.p
+Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
+Id : 20, {_}: greatest_lower_bound a c =>= greatest_lower_bound b c [] by p12x_4
+Id : 188, {_}: multiply ?586 (greatest_lower_bound ?587 ?588) =<= greatest_lower_bound (multiply ?586 ?587) (multiply ?586 ?588) [588, 587, 586] by monotony_glb1 ?586 ?587 ?588
+Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5
+Id : 364, {_}: inverse (least_upper_bound ?929 ?930) =<= greatest_lower_bound (inverse ?929) (inverse ?930) [930, 929] by p12x_7 ?929 ?930
+Id : 342, {_}: inverse (greatest_lower_bound ?890 ?891) =<= least_upper_bound (inverse ?890) (inverse ?891) [891, 890] by p12x_6 ?890 ?891
+Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
+Id : 158, {_}: multiply ?515 (least_upper_bound ?516 ?517) =<= least_upper_bound (multiply ?515 ?516) (multiply ?515 ?517) [517, 516, 515] by monotony_lub1 ?515 ?516 ?517
+Id : 4, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
+Id : 19, {_}: inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) [54, 53] by p12x_3 ?53 ?54
+Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+Id : 17, {_}: inverse identity =>= identity [] by p12x_1
+Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+Id : 28, {_}: multiply (multiply ?71 ?72) ?73 =?= multiply ?71 (multiply ?72 ?73) [73, 72, 71] by associativity ?71 ?72 ?73
+Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51
+Id : 302, {_}: inverse (multiply ?845 ?846) =<= multiply (inverse ?846) (inverse ?845) [846, 845] by p12x_3 ?845 ?846
+Id : 803, {_}: inverse (multiply ?1561 (inverse ?1562)) =>= multiply ?1562 (inverse ?1561) [1562, 1561] by Super 302 with 18 at 1,3
+Id : 30, {_}: multiply (multiply ?78 (inverse ?79)) ?79 =>= multiply ?78 identity [79, 78] by Super 28 with 3 at 2,3
+Id : 303, {_}: inverse (multiply identity ?848) =<= multiply (inverse ?848) identity [848] by Super 302 with 17 at 2,3
+Id : 394, {_}: inverse ?984 =<= multiply (inverse ?984) identity [984] by Demod 303 with 2 at 1,2
+Id : 396, {_}: inverse (inverse ?987) =<= multiply ?987 identity [987] by Super 394 with 18 at 1,3
+Id : 406, {_}: ?987 =<= multiply ?987 identity [987] by Demod 396 with 18 at 2
+Id : 638, {_}: multiply (multiply ?78 (inverse ?79)) ?79 =>= ?78 [79, 78] by Demod 30 with 406 at 3
+Id : 816, {_}: inverse ?1599 =<= multiply ?1600 (inverse (multiply ?1599 (inverse (inverse ?1600)))) [1600, 1599] by Super 803 with 638 at 1,2
+Id : 306, {_}: inverse (multiply ?855 (inverse ?856)) =>= multiply ?856 (inverse ?855) [856, 855] by Super 302 with 18 at 1,3
+Id : 837, {_}: inverse ?1599 =<= multiply ?1600 (multiply (inverse ?1600) (inverse ?1599)) [1600, 1599] by Demod 816 with 306 at 2,3
+Id : 838, {_}: inverse ?1599 =<= multiply ?1600 (inverse (multiply ?1599 ?1600)) [1600, 1599] by Demod 837 with 19 at 2,3
+Id : 285, {_}: multiply ?794 (inverse ?794) =>= identity [794] by Super 3 with 18 at 1,2
+Id : 607, {_}: multiply (multiply ?1261 ?1262) (inverse ?1262) =>= multiply ?1261 identity [1262, 1261] by Super 4 with 285 at 2,3
+Id : 19344, {_}: multiply (multiply ?27523 ?27524) (inverse ?27524) =>= ?27523 [27524, 27523] by Demod 607 with 406 at 3
+Id : 160, {_}: multiply (inverse ?522) (least_upper_bound ?523 ?522) =>= least_upper_bound (multiply (inverse ?522) ?523) identity [523, 522] by Super 158 with 3 at 2,3
+Id : 177, {_}: multiply (inverse ?522) (least_upper_bound ?523 ?522) =>= least_upper_bound identity (multiply (inverse ?522) ?523) [523, 522] by Demod 160 with 6 at 3
+Id : 345, {_}: inverse (greatest_lower_bound identity ?898) =>= least_upper_bound identity (inverse ?898) [898] by Super 342 with 17 at 1,3
+Id : 487, {_}: inverse (multiply (greatest_lower_bound identity ?1114) ?1115) =<= multiply (inverse ?1115) (least_upper_bound identity (inverse ?1114)) [1115, 1114] by Super 19 with 345 at 2,3
+Id : 11534, {_}: inverse (multiply (greatest_lower_bound identity ?15482) (inverse ?15482)) =>= least_upper_bound identity (multiply (inverse (inverse ?15482)) identity) [15482] by Super 177 with 487 at 2
+Id : 11607, {_}: multiply ?15482 (inverse (greatest_lower_bound identity ?15482)) =?= least_upper_bound identity (multiply (inverse (inverse ?15482)) identity) [15482] by Demod 11534 with 306 at 2
+Id : 11608, {_}: multiply ?15482 (inverse (greatest_lower_bound identity ?15482)) =>= least_upper_bound identity (inverse (inverse ?15482)) [15482] by Demod 11607 with 406 at 2,3
+Id : 11609, {_}: multiply ?15482 (least_upper_bound identity (inverse ?15482)) =>= least_upper_bound identity (inverse (inverse ?15482)) [15482] by Demod 11608 with 345 at 2,2
+Id : 11610, {_}: multiply ?15482 (least_upper_bound identity (inverse ?15482)) =>= least_upper_bound identity ?15482 [15482] by Demod 11609 with 18 at 2,3
+Id : 19409, {_}: multiply (least_upper_bound identity ?27743) (inverse (least_upper_bound identity (inverse ?27743))) =>= ?27743 [27743] by Super 19344 with 11610 at 1,2
+Id : 366, {_}: inverse (least_upper_bound ?934 (inverse ?935)) =>= greatest_lower_bound (inverse ?934) ?935 [935, 934] by Super 364 with 18 at 2,3
+Id : 19451, {_}: multiply (least_upper_bound identity ?27743) (greatest_lower_bound (inverse identity) ?27743) =>= ?27743 [27743] by Demod 19409 with 366 at 2,2
+Id : 44019, {_}: multiply (least_upper_bound identity ?52011) (greatest_lower_bound identity ?52011) =>= ?52011 [52011] by Demod 19451 with 17 at 1,2,2
+Id : 367, {_}: inverse (least_upper_bound identity ?937) =>= greatest_lower_bound identity (inverse ?937) [937] by Super 364 with 17 at 1,3
+Id : 8913, {_}: multiply (inverse ?11632) (least_upper_bound ?11632 ?11633) =>= least_upper_bound identity (multiply (inverse ?11632) ?11633) [11633, 11632] by Super 158 with 3 at 1,3
+Id : 326, {_}: least_upper_bound c a =<= least_upper_bound b c [] by Demod 21 with 6 at 2
+Id : 327, {_}: least_upper_bound c a =>= least_upper_bound c b [] by Demod 326 with 6 at 3
+Id : 8921, {_}: multiply (inverse c) (least_upper_bound c b) =>= least_upper_bound identity (multiply (inverse c) a) [] by Super 8913 with 327 at 2,2
+Id : 164, {_}: multiply (inverse ?538) (least_upper_bound ?538 ?539) =>= least_upper_bound identity (multiply (inverse ?538) ?539) [539, 538] by Super 158 with 3 at 1,3
+Id : 9001, {_}: least_upper_bound identity (multiply (inverse c) b) =<= least_upper_bound identity (multiply (inverse c) a) [] by Demod 8921 with 164 at 2
+Id : 9081, {_}: inverse (least_upper_bound identity (multiply (inverse c) b)) =>= greatest_lower_bound identity (inverse (multiply (inverse c) a)) [] by Super 367 with 9001 at 1,2
+Id : 9110, {_}: greatest_lower_bound identity (inverse (multiply (inverse c) b)) =<= greatest_lower_bound identity (inverse (multiply (inverse c) a)) [] by Demod 9081 with 367 at 2
+Id : 304, {_}: inverse (multiply (inverse ?850) ?851) =>= multiply (inverse ?851) ?850 [851, 850] by Super 302 with 18 at 2,3
+Id : 9111, {_}: greatest_lower_bound identity (inverse (multiply (inverse c) b)) =>= greatest_lower_bound identity (multiply (inverse a) c) [] by Demod 9110 with 304 at 2,3
+Id : 9112, {_}: greatest_lower_bound identity (multiply (inverse b) c) =<= greatest_lower_bound identity (multiply (inverse a) c) [] by Demod 9111 with 304 at 2,2
+Id : 44043, {_}: multiply (least_upper_bound identity (multiply (inverse a) c)) (greatest_lower_bound identity (multiply (inverse b) c)) =>= multiply (inverse a) c [] by Super 44019 with 9112 at 2,2
+Id : 10178, {_}: multiply (inverse ?13641) (greatest_lower_bound ?13641 ?13642) =>= greatest_lower_bound identity (multiply (inverse ?13641) ?13642) [13642, 13641] by Super 188 with 3 at 1,3
+Id : 315, {_}: greatest_lower_bound c a =<= greatest_lower_bound b c [] by Demod 20 with 5 at 2
+Id : 316, {_}: greatest_lower_bound c a =>= greatest_lower_bound c b [] by Demod 315 with 5 at 3
+Id : 10190, {_}: multiply (inverse c) (greatest_lower_bound c b) =>= greatest_lower_bound identity (multiply (inverse c) a) [] by Super 10178 with 316 at 2,2
+Id : 194, {_}: multiply (inverse ?609) (greatest_lower_bound ?609 ?610) =>= greatest_lower_bound identity (multiply (inverse ?609) ?610) [610, 609] by Super 188 with 3 at 1,3
+Id : 10270, {_}: greatest_lower_bound identity (multiply (inverse c) b) =<= greatest_lower_bound identity (multiply (inverse c) a) [] by Demod 10190 with 194 at 2
+Id : 10361, {_}: inverse (greatest_lower_bound identity (multiply (inverse c) b)) =>= least_upper_bound identity (inverse (multiply (inverse c) a)) [] by Super 345 with 10270 at 1,2
+Id : 10393, {_}: least_upper_bound identity (inverse (multiply (inverse c) b)) =<= least_upper_bound identity (inverse (multiply (inverse c) a)) [] by Demod 10361 with 345 at 2
+Id : 10394, {_}: least_upper_bound identity (inverse (multiply (inverse c) b)) =>= least_upper_bound identity (multiply (inverse a) c) [] by Demod 10393 with 304 at 2,3
+Id : 10395, {_}: least_upper_bound identity (multiply (inverse b) c) =<= least_upper_bound identity (multiply (inverse a) c) [] by Demod 10394 with 304 at 2,2
+Id : 44130, {_}: multiply (least_upper_bound identity (multiply (inverse b) c)) (greatest_lower_bound identity (multiply (inverse b) c)) =>= multiply (inverse a) c [] by Demod 44043 with 10395 at 1,2
+Id : 19452, {_}: multiply (least_upper_bound identity ?27743) (greatest_lower_bound identity ?27743) =>= ?27743 [27743] by Demod 19451 with 17 at 1,2,2
+Id : 44131, {_}: multiply (inverse b) c =<= multiply (inverse a) c [] by Demod 44130 with 19452 at 2
+Id : 44165, {_}: inverse (inverse a) =<= multiply c (inverse (multiply (inverse b) c)) [] by Super 838 with 44131 at 1,2,3
+Id : 44200, {_}: a =<= multiply c (inverse (multiply (inverse b) c)) [] by Demod 44165 with 18 at 2
+Id : 44201, {_}: a =<= inverse (inverse b) [] by Demod 44200 with 838 at 3
+Id : 44202, {_}: a =>= b [] by Demod 44201 with 18 at 3
+Id : 44399, {_}: b === b [] by Demod 1 with 44202 at 2
+Id : 1, {_}: a =>= b [] by prove_p12x
+% SZS output end CNFRefutation for GRP181-4.p
+25775: solved GRP181-4.p in 8.112506 using nrkbo
+25775: status Unsatisfiable for GRP181-4.p
+NO CLASH, using fixed ground order
+25788: Facts:
+25788: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25788: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25788: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25788: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25788: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25788: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25788: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25788: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25788: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25788: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25788: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25788: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25788: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25788: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25788: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25788: Goal:
+25788: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =>=
+ identity
+ [] by prove_p20
+25788: Order:
+25788: nrkbo
+25788: Leaf order:
+25788: a 2 0 2 1,1,2
+25788: identity 5 0 3 2,1,2
+25788: inverse 2 1 1 0,2,2
+25788: least_upper_bound 14 2 1 0,1,2
+25788: greatest_lower_bound 15 2 2 0,2
+25788: multiply 18 2 0
+NO CLASH, using fixed ground order
+25789: Facts:
+25789: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25789: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25789: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25789: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25789: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25789: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25789: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25789: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25789: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25789: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25789: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25789: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+NO CLASH, using fixed ground order
+25790: Facts:
+25790: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25790: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25790: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25790: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25790: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25790: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25790: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25790: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25790: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25790: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25790: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25790: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25790: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25790: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25790: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25790: Goal:
+25790: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =>=
+ identity
+ [] by prove_p20
+25790: Order:
+25790: lpo
+25790: Leaf order:
+25790: a 2 0 2 1,1,2
+25790: identity 5 0 3 2,1,2
+25790: inverse 2 1 1 0,2,2
+25790: least_upper_bound 14 2 1 0,1,2
+25790: greatest_lower_bound 15 2 2 0,2
+25790: multiply 18 2 0
+25789: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25789: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25789: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25789: Goal:
+25789: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =>=
+ identity
+ [] by prove_p20
+25789: Order:
+25789: kbo
+25789: Leaf order:
+25789: a 2 0 2 1,1,2
+25789: identity 5 0 3 2,1,2
+25789: inverse 2 1 1 0,2,2
+25789: least_upper_bound 14 2 1 0,1,2
+25789: greatest_lower_bound 15 2 2 0,2
+25789: multiply 18 2 0
+% SZS status Timeout for GRP183-1.p
+NO CLASH, using fixed ground order
+25806: Facts:
+25806: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25806: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25806: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25806: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25806: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25806: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25806: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25806: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25806: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25806: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25806: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25806: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25806: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25806: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25806: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25806: Goal:
+25806: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound a identity)
+ (least_upper_bound (inverse a) identity)
+ =>=
+ identity
+ [] by prove_20x
+25806: Order:
+25806: nrkbo
+25806: Leaf order:
+25806: a 2 0 2 1,1,2
+25806: identity 5 0 3 2,1,2
+25806: inverse 2 1 1 0,1,2,2
+25806: greatest_lower_bound 14 2 1 0,2
+25806: least_upper_bound 15 2 2 0,1,2
+25806: multiply 18 2 0
+NO CLASH, using fixed ground order
+25807: Facts:
+25807: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25807: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25807: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25807: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25807: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25807: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25807: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25807: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25807: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25807: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25807: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25807: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25807: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25807: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25807: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25807: Goal:
+25807: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound a identity)
+ (least_upper_bound (inverse a) identity)
+ =>=
+ identity
+ [] by prove_20x
+25807: Order:
+25807: kbo
+25807: Leaf order:
+25807: a 2 0 2 1,1,2
+25807: identity 5 0 3 2,1,2
+25807: inverse 2 1 1 0,1,2,2
+25807: greatest_lower_bound 14 2 1 0,2
+25807: least_upper_bound 15 2 2 0,1,2
+25807: multiply 18 2 0
+NO CLASH, using fixed ground order
+25808: Facts:
+25808: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25808: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25808: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25808: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25808: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25808: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25808: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25808: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25808: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25808: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25808: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25808: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25808: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25808: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25808: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25808: Goal:
+25808: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound a identity)
+ (least_upper_bound (inverse a) identity)
+ =>=
+ identity
+ [] by prove_20x
+25808: Order:
+25808: lpo
+25808: Leaf order:
+25808: a 2 0 2 1,1,2
+25808: identity 5 0 3 2,1,2
+25808: inverse 2 1 1 0,1,2,2
+25808: greatest_lower_bound 14 2 1 0,2
+25808: least_upper_bound 15 2 2 0,1,2
+25808: multiply 18 2 0
+% SZS status Timeout for GRP183-3.p
+NO CLASH, using fixed ground order
+25839: Facts:
+25839: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25839: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25839: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25839: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25839: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25839: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25839: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25839: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25839: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25839: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25839: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25839: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25839: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25839: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25839: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25839: Id : 17, {_}: inverse identity =>= identity [] by p20x_1
+25839: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51
+25839: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p20x_3 ?53 ?54
+25839: Goal:
+25839: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound a identity)
+ (least_upper_bound (inverse a) identity)
+ =>=
+ identity
+ [] by prove_20x
+25839: Order:
+25839: nrkbo
+25839: Leaf order:
+25839: a 2 0 2 1,1,2
+25839: identity 7 0 3 2,1,2
+25839: inverse 8 1 1 0,1,2,2
+25839: greatest_lower_bound 14 2 1 0,2
+25839: least_upper_bound 15 2 2 0,1,2
+25839: multiply 20 2 0
+NO CLASH, using fixed ground order
+25840: Facts:
+25840: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25840: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25840: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25840: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+NO CLASH, using fixed ground order
+25841: Facts:
+25841: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25841: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25841: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25841: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25841: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25841: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25841: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25841: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25841: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25841: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25841: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25841: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25841: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25841: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25841: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25841: Id : 17, {_}: inverse identity =>= identity [] by p20x_1
+25841: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51
+25841: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p20x_3 ?53 ?54
+25841: Goal:
+25841: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound a identity)
+ (least_upper_bound (inverse a) identity)
+ =>=
+ identity
+ [] by prove_20x
+25841: Order:
+25841: lpo
+25841: Leaf order:
+25841: a 2 0 2 1,1,2
+25841: identity 7 0 3 2,1,2
+25841: inverse 8 1 1 0,1,2,2
+25841: greatest_lower_bound 14 2 1 0,2
+25841: least_upper_bound 15 2 2 0,1,2
+25841: multiply 20 2 0
+25840: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25840: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25840: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25840: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25840: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25840: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25840: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25840: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25840: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25840: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25840: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25840: Id : 17, {_}: inverse identity =>= identity [] by p20x_1
+25840: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51
+25840: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p20x_3 ?53 ?54
+25840: Goal:
+25840: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound a identity)
+ (least_upper_bound (inverse a) identity)
+ =>=
+ identity
+ [] by prove_20x
+25840: Order:
+25840: kbo
+25840: Leaf order:
+25840: a 2 0 2 1,1,2
+25840: identity 7 0 3 2,1,2
+25840: inverse 8 1 1 0,1,2,2
+25840: greatest_lower_bound 14 2 1 0,2
+25840: least_upper_bound 15 2 2 0,1,2
+25840: multiply 20 2 0
+% SZS status Timeout for GRP183-4.p
+NO CLASH, using fixed ground order
+25861: Facts:
+25861: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25861: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25861: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25861: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25861: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25861: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25861: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25861: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25861: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25861: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25861: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25861: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25861: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25861: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25861: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25861: Goal:
+25861: Id : 1, {_}:
+ multiply (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =>=
+ multiply (inverse (greatest_lower_bound a identity))
+ (least_upper_bound a identity)
+ [] by prove_p21
+25861: Order:
+25861: nrkbo
+25861: Leaf order:
+25861: a 4 0 4 1,1,2
+25861: identity 6 0 4 2,1,2
+25861: inverse 3 1 2 0,2,2
+25861: least_upper_bound 15 2 2 0,1,2
+25861: greatest_lower_bound 15 2 2 0,1,2,2
+25861: multiply 20 2 2 0,2
+NO CLASH, using fixed ground order
+25862: Facts:
+25862: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25862: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25862: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25862: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25862: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25862: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25862: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25862: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25862: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25862: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25862: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25862: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25862: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25862: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25862: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25862: Goal:
+25862: Id : 1, {_}:
+ multiply (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =<=
+ multiply (inverse (greatest_lower_bound a identity))
+ (least_upper_bound a identity)
+ [] by prove_p21
+25862: Order:
+25862: kbo
+25862: Leaf order:
+25862: a 4 0 4 1,1,2
+25862: identity 6 0 4 2,1,2
+25862: inverse 3 1 2 0,2,2
+25862: least_upper_bound 15 2 2 0,1,2
+25862: greatest_lower_bound 15 2 2 0,1,2,2
+25862: multiply 20 2 2 0,2
+NO CLASH, using fixed ground order
+25863: Facts:
+25863: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25863: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25863: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25863: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25863: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25863: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25863: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25863: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25863: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25863: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25863: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25863: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25863: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25863: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25863: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25863: Goal:
+25863: Id : 1, {_}:
+ multiply (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =<=
+ multiply (inverse (greatest_lower_bound a identity))
+ (least_upper_bound a identity)
+ [] by prove_p21
+25863: Order:
+25863: lpo
+25863: Leaf order:
+25863: a 4 0 4 1,1,2
+25863: identity 6 0 4 2,1,2
+25863: inverse 3 1 2 0,2,2
+25863: least_upper_bound 15 2 2 0,1,2
+25863: greatest_lower_bound 15 2 2 0,1,2,2
+25863: multiply 20 2 2 0,2
+% SZS status Timeout for GRP184-1.p
+NO CLASH, using fixed ground order
+25898: Facts:
+25898: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25898: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25898: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25898: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25898: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25898: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25898: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25898: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25898: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25898: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25898: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25898: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25898: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25898: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25898: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25898: Goal:
+25898: Id : 1, {_}:
+ multiply (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =>=
+ multiply (inverse (greatest_lower_bound a identity))
+ (least_upper_bound a identity)
+ [] by prove_p21x
+25898: Order:
+25898: nrkbo
+25898: Leaf order:
+25898: a 4 0 4 1,1,2
+25898: identity 6 0 4 2,1,2
+25898: inverse 3 1 2 0,2,2
+25898: least_upper_bound 15 2 2 0,1,2
+25898: greatest_lower_bound 15 2 2 0,1,2,2
+25898: multiply 20 2 2 0,2
+NO CLASH, using fixed ground order
+25899: Facts:
+25899: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25899: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25899: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25899: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25899: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25899: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25899: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25899: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25899: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25899: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25899: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25899: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25899: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25899: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25899: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25899: Goal:
+25899: Id : 1, {_}:
+ multiply (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =<=
+ multiply (inverse (greatest_lower_bound a identity))
+ (least_upper_bound a identity)
+ [] by prove_p21x
+25899: Order:
+25899: kbo
+25899: Leaf order:
+25899: a 4 0 4 1,1,2
+25899: identity 6 0 4 2,1,2
+25899: inverse 3 1 2 0,2,2
+25899: least_upper_bound 15 2 2 0,1,2
+25899: greatest_lower_bound 15 2 2 0,1,2,2
+25899: multiply 20 2 2 0,2
+NO CLASH, using fixed ground order
+25900: Facts:
+25900: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25900: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25900: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25900: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25900: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25900: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25900: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25900: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25900: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25900: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25900: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25900: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25900: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25900: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25900: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25900: Goal:
+25900: Id : 1, {_}:
+ multiply (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =<=
+ multiply (inverse (greatest_lower_bound a identity))
+ (least_upper_bound a identity)
+ [] by prove_p21x
+25900: Order:
+25900: lpo
+25900: Leaf order:
+25900: a 4 0 4 1,1,2
+25900: identity 6 0 4 2,1,2
+25900: inverse 3 1 2 0,2,2
+25900: least_upper_bound 15 2 2 0,1,2
+25900: greatest_lower_bound 15 2 2 0,1,2,2
+25900: multiply 20 2 2 0,2
+% SZS status Timeout for GRP184-3.p
+NO CLASH, using fixed ground order
+25933: Facts:
+25933: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25933: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25933: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25933: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25933: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25933: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25933: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25933: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25933: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25933: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25933: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25933: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25933: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+NO CLASH, using fixed ground order
+25934: Facts:
+25934: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25934: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25934: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25934: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25934: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25934: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25934: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25934: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25934: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25934: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25934: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25934: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25934: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25934: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25934: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25934: Goal:
+25934: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound (multiply a b) identity)
+ (multiply (least_upper_bound a identity)
+ (least_upper_bound b identity))
+ =>=
+ least_upper_bound (multiply a b) identity
+ [] by prove_p22b
+25934: Order:
+25934: lpo
+25934: Leaf order:
+25934: a 3 0 3 1,1,1,2
+25934: b 3 0 3 2,1,1,2
+25934: identity 6 0 4 2,1,2
+25934: inverse 1 1 0
+25934: greatest_lower_bound 14 2 1 0,2
+25934: least_upper_bound 17 2 4 0,1,2
+25934: multiply 21 2 3 0,1,1,2
+NO CLASH, using fixed ground order
+25932: Facts:
+25932: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25932: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25932: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25932: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25932: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25932: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25932: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25932: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25932: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25932: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25932: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25932: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25932: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25932: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25932: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25932: Goal:
+25932: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound (multiply a b) identity)
+ (multiply (least_upper_bound a identity)
+ (least_upper_bound b identity))
+ =>=
+ least_upper_bound (multiply a b) identity
+ [] by prove_p22b
+25932: Order:
+25932: nrkbo
+25932: Leaf order:
+25932: a 3 0 3 1,1,1,2
+25932: b 3 0 3 2,1,1,2
+25932: identity 6 0 4 2,1,2
+25932: inverse 1 1 0
+25932: greatest_lower_bound 14 2 1 0,2
+25932: least_upper_bound 17 2 4 0,1,2
+25932: multiply 21 2 3 0,1,1,2
+25933: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25933: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25933: Goal:
+25933: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound (multiply a b) identity)
+ (multiply (least_upper_bound a identity)
+ (least_upper_bound b identity))
+ =>=
+ least_upper_bound (multiply a b) identity
+ [] by prove_p22b
+25933: Order:
+25933: kbo
+25933: Leaf order:
+25933: a 3 0 3 1,1,1,2
+25933: b 3 0 3 2,1,1,2
+25933: identity 6 0 4 2,1,2
+25933: inverse 1 1 0
+25933: greatest_lower_bound 14 2 1 0,2
+25933: least_upper_bound 17 2 4 0,1,2
+25933: multiply 21 2 3 0,1,1,2
+Statistics :
+Max weight : 21
+Found proof, 1.351481s
+% SZS status Unsatisfiable for GRP185-3.p
+% SZS output start CNFRefutation for GRP185-3.p
+Id : 108, {_}: greatest_lower_bound ?251 (least_upper_bound ?251 ?252) =>= ?251 [252, 251] by glb_absorbtion ?251 ?252
+Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+Id : 21, {_}: multiply (multiply ?57 ?58) ?59 =>= multiply ?57 (multiply ?58 ?59) [59, 58, 57] by associativity ?57 ?58 ?59
+Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
+Id : 23, {_}: multiply identity ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Super 21 with 3 at 1,2
+Id : 392, {_}: ?594 =<= multiply (inverse ?595) (multiply ?595 ?594) [595, 594] by Demod 23 with 2 at 2
+Id : 394, {_}: ?599 =<= multiply (inverse (inverse ?599)) identity [599] by Super 392 with 3 at 2,3
+Id : 27, {_}: ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Demod 23 with 2 at 2
+Id : 400, {_}: multiply ?621 ?622 =<= multiply (inverse (inverse ?621)) ?622 [622, 621] by Super 392 with 27 at 2,3
+Id : 525, {_}: ?599 =<= multiply ?599 identity [599] by Demod 394 with 400 at 3
+Id : 815, {_}: greatest_lower_bound ?1092 (least_upper_bound ?1093 ?1092) =>= ?1092 [1093, 1092] by Super 108 with 6 at 2,2
+Id : 822, {_}: greatest_lower_bound ?1112 (least_upper_bound ?1113 (least_upper_bound ?1114 ?1112)) =>= ?1112 [1114, 1113, 1112] by Super 815 with 8 at 2,2
+Id : 2353, {_}: least_upper_bound identity (multiply a b) === least_upper_bound identity (multiply a b) [] by Demod 2352 with 822 at 2
+Id : 2352, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2351 with 8 at 2,2,2
+Id : 2351, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound b (least_upper_bound (least_upper_bound a identity) (multiply a b))) =>= least_upper_bound identity (multiply a b) [] by Demod 2350 with 8 at 2,2
+Id : 2350, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound b (least_upper_bound a identity)) (multiply a b)) =>= least_upper_bound identity (multiply a b) [] by Demod 2349 with 6 at 2,2
+Id : 2349, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a identity))) =>= least_upper_bound identity (multiply a b) [] by Demod 2348 with 2 at 2,2,2,2,2
+Id : 2348, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a (multiply identity identity)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2347 with 525 at 1,2,2,2,2
+Id : 2347, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2346 with 2 at 1,2,2,2
+Id : 2346, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2345 with 8 at 2,2
+Id : 2345, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity))) =>= least_upper_bound identity (multiply a b) [] by Demod 2344 with 15 at 2,2,2
+Id : 2344, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound identity (multiply a b) [] by Demod 2343 with 15 at 1,2,2
+Id : 2343, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound identity (multiply a b) [] by Demod 2342 with 6 at 3
+Id : 2342, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 2341 with 13 at 2,2
+Id : 2341, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 1 with 6 at 1,2
+Id : 1, {_}: greatest_lower_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by prove_p22b
+% SZS output end CNFRefutation for GRP185-3.p
+25934: solved GRP185-3.p in 0.66004 using lpo
+25934: status Unsatisfiable for GRP185-3.p
+NO CLASH, using fixed ground order
+25939: Facts:
+25939: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25939: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25939: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25939: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25939: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25939: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25939: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25939: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25939: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25939: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25939: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25939: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25939: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25939: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25939: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25939: Id : 17, {_}: inverse identity =>= identity [] by p22b_1
+25939: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51
+25939: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p22b_3 ?53 ?54
+25939: Goal:
+25939: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound (multiply a b) identity)
+ (multiply (least_upper_bound a identity)
+ (least_upper_bound b identity))
+ =>=
+ least_upper_bound (multiply a b) identity
+ [] by prove_p22b
+25939: Order:
+25939: nrkbo
+25939: Leaf order:
+25939: a 3 0 3 1,1,1,2
+25939: b 3 0 3 2,1,1,2
+25939: identity 8 0 4 2,1,2
+25939: inverse 7 1 0
+25939: greatest_lower_bound 14 2 1 0,2
+25939: least_upper_bound 17 2 4 0,1,2
+25939: multiply 23 2 3 0,1,1,2
+NO CLASH, using fixed ground order
+25940: Facts:
+25940: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25940: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25940: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25940: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25940: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25940: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25940: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25940: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25940: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25940: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25940: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25940: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25940: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25940: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25940: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25940: Id : 17, {_}: inverse identity =>= identity [] by p22b_1
+25940: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51
+25940: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p22b_3 ?53 ?54
+25940: Goal:
+25940: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound (multiply a b) identity)
+ (multiply (least_upper_bound a identity)
+ (least_upper_bound b identity))
+ =>=
+ least_upper_bound (multiply a b) identity
+ [] by prove_p22b
+25940: Order:
+25940: kbo
+25940: Leaf order:
+25940: a 3 0 3 1,1,1,2
+25940: b 3 0 3 2,1,1,2
+25940: identity 8 0 4 2,1,2
+25940: inverse 7 1 0
+25940: greatest_lower_bound 14 2 1 0,2
+25940: least_upper_bound 17 2 4 0,1,2
+25940: multiply 23 2 3 0,1,1,2
+NO CLASH, using fixed ground order
+25941: Facts:
+25941: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25941: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25941: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25941: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25941: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25941: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25941: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25941: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25941: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25941: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25941: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25941: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25941: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25941: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25941: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25941: Id : 17, {_}: inverse identity =>= identity [] by p22b_1
+25941: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51
+25941: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p22b_3 ?53 ?54
+25941: Goal:
+25941: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound (multiply a b) identity)
+ (multiply (least_upper_bound a identity)
+ (least_upper_bound b identity))
+ =>=
+ least_upper_bound (multiply a b) identity
+ [] by prove_p22b
+25941: Order:
+25941: lpo
+25941: Leaf order:
+25941: a 3 0 3 1,1,1,2
+25941: b 3 0 3 2,1,1,2
+25941: identity 8 0 4 2,1,2
+25941: inverse 7 1 0
+25941: greatest_lower_bound 14 2 1 0,2
+25941: least_upper_bound 17 2 4 0,1,2
+25941: multiply 23 2 3 0,1,1,2
+Statistics :
+Max weight : 21
+Found proof, 0.930082s
+% SZS status Unsatisfiable for GRP185-4.p
+% SZS output start CNFRefutation for GRP185-4.p
+Id : 111, {_}: greatest_lower_bound ?257 (least_upper_bound ?257 ?258) =>= ?257 [258, 257] by glb_absorbtion ?257 ?258
+Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51
+Id : 17, {_}: inverse identity =>= identity [] by p22b_1
+Id : 338, {_}: inverse (multiply ?520 ?521) =?= multiply (inverse ?521) (inverse ?520) [521, 520] by p22b_3 ?520 ?521
+Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
+Id : 339, {_}: inverse (multiply identity ?523) =<= multiply (inverse ?523) identity [523] by Super 338 with 17 at 2,3
+Id : 372, {_}: inverse ?569 =<= multiply (inverse ?569) identity [569] by Demod 339 with 2 at 1,2
+Id : 374, {_}: inverse (inverse ?572) =<= multiply ?572 identity [572] by Super 372 with 18 at 1,3
+Id : 382, {_}: ?572 =<= multiply ?572 identity [572] by Demod 374 with 18 at 2
+Id : 704, {_}: greatest_lower_bound ?881 (least_upper_bound ?882 ?881) =>= ?881 [882, 881] by Super 111 with 6 at 2,2
+Id : 711, {_}: greatest_lower_bound ?901 (least_upper_bound ?902 (least_upper_bound ?903 ?901)) =>= ?901 [903, 902, 901] by Super 704 with 8 at 2,2
+Id : 1908, {_}: least_upper_bound identity (multiply a b) === least_upper_bound identity (multiply a b) [] by Demod 1907 with 711 at 2
+Id : 1907, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 1906 with 8 at 2,2,2
+Id : 1906, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound b (least_upper_bound (least_upper_bound a identity) (multiply a b))) =>= least_upper_bound identity (multiply a b) [] by Demod 1905 with 8 at 2,2
+Id : 1905, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound b (least_upper_bound a identity)) (multiply a b)) =>= least_upper_bound identity (multiply a b) [] by Demod 1904 with 6 at 2,2
+Id : 1904, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a identity))) =>= least_upper_bound identity (multiply a b) [] by Demod 1903 with 2 at 2,2,2,2,2
+Id : 1903, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a (multiply identity identity)))) =>= least_upper_bound identity (multiply a b) [] by Demod 1902 with 382 at 1,2,2,2,2
+Id : 1902, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound identity (multiply a b) [] by Demod 1901 with 2 at 1,2,2,2
+Id : 1901, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound identity (multiply a b) [] by Demod 1900 with 8 at 2,2
+Id : 1900, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity))) =>= least_upper_bound identity (multiply a b) [] by Demod 1899 with 15 at 2,2,2
+Id : 1899, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound identity (multiply a b) [] by Demod 1898 with 15 at 1,2,2
+Id : 1898, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound identity (multiply a b) [] by Demod 1897 with 6 at 3
+Id : 1897, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 1896 with 13 at 2,2
+Id : 1896, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 1 with 6 at 1,2
+Id : 1, {_}: greatest_lower_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by prove_p22b
+% SZS output end CNFRefutation for GRP185-4.p
+25941: solved GRP185-4.p in 0.432027 using lpo
+25941: status Unsatisfiable for GRP185-4.p
+NO CLASH, using fixed ground order
+25948: Facts:
+25948: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25948: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25948: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25948: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25948: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25948: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25948: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25948: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25948: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25948: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25948: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25948: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25948: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25948: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25948: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25948: Id : 17, {_}: inverse identity =>= identity [] by p23_1
+25948: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51
+25948: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p23_3 ?53 ?54
+25948: Goal:
+25948: Id : 1, {_}:
+ least_upper_bound (multiply a b) identity
+ =<=
+ multiply a (inverse (greatest_lower_bound a (inverse b)))
+ [] by prove_p23
+25948: Order:
+25948: nrkbo
+25948: Leaf order:
+25948: b 2 0 2 2,1,2
+25948: a 3 0 3 1,1,2
+25948: identity 5 0 1 2,2
+25948: inverse 9 1 2 0,2,3
+25948: greatest_lower_bound 14 2 1 0,1,2,3
+25948: least_upper_bound 14 2 1 0,2
+25948: multiply 22 2 2 0,1,2
+NO CLASH, using fixed ground order
+25950: Facts:
+25950: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25950: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25950: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25950: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25950: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25950: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25950: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25950: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25950: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25950: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25950: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25950: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25950: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25950: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25950: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25950: Id : 17, {_}: inverse identity =>= identity [] by p23_1
+25950: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51
+25950: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p23_3 ?53 ?54
+25950: Goal:
+25950: Id : 1, {_}:
+ least_upper_bound (multiply a b) identity
+ =<=
+ multiply a (inverse (greatest_lower_bound a (inverse b)))
+ [] by prove_p23
+25950: Order:
+25950: lpo
+25950: Leaf order:
+25950: b 2 0 2 2,1,2
+25950: a 3 0 3 1,1,2
+25950: identity 5 0 1 2,2
+25950: inverse 9 1 2 0,2,3
+25950: greatest_lower_bound 14 2 1 0,1,2,3
+25950: least_upper_bound 14 2 1 0,2
+25950: multiply 22 2 2 0,1,2
+NO CLASH, using fixed ground order
+25949: Facts:
+25949: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25949: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25949: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25949: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25949: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25949: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25949: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25949: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25949: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25949: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25949: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25949: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25949: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25949: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25949: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25949: Id : 17, {_}: inverse identity =>= identity [] by p23_1
+25949: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51
+25949: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p23_3 ?53 ?54
+25949: Goal:
+25949: Id : 1, {_}:
+ least_upper_bound (multiply a b) identity
+ =<=
+ multiply a (inverse (greatest_lower_bound a (inverse b)))
+ [] by prove_p23
+25949: Order:
+25949: kbo
+25949: Leaf order:
+25949: b 2 0 2 2,1,2
+25949: a 3 0 3 1,1,2
+25949: identity 5 0 1 2,2
+25949: inverse 9 1 2 0,2,3
+25949: greatest_lower_bound 14 2 1 0,1,2,3
+25949: least_upper_bound 14 2 1 0,2
+25949: multiply 22 2 2 0,1,2
+% SZS status Timeout for GRP186-2.p
+NO CLASH, using fixed ground order
+26073: Facts:
+26073: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+26073: Id : 3, {_}:
+ multiply (left_inverse ?4) ?4 =>= identity
+ [4] by left_inverse ?4
+26073: Id : 4, {_}:
+ multiply (multiply ?6 (multiply ?7 ?8)) ?6
+ =?=
+ multiply (multiply ?6 ?7) (multiply ?8 ?6)
+ [8, 7, 6] by moufang1 ?6 ?7 ?8
+26073: Goal:
+26073: Id : 1, {_}:
+ multiply (multiply (multiply a b) c) b
+ =>=
+ multiply a (multiply b (multiply c b))
+ [] by prove_moufang2
+26073: Order:
+26073: nrkbo
+26073: Leaf order:
+26073: identity 2 0 0
+26073: a 2 0 2 1,1,1,2
+26073: c 2 0 2 2,1,2
+26073: b 4 0 4 2,1,1,2
+26073: left_inverse 1 1 0
+26073: multiply 14 2 6 0,2
+NO CLASH, using fixed ground order
+26074: Facts:
+26074: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+26074: Id : 3, {_}:
+ multiply (left_inverse ?4) ?4 =>= identity
+ [4] by left_inverse ?4
+26074: Id : 4, {_}:
+ multiply (multiply ?6 (multiply ?7 ?8)) ?6
+ =>=
+ multiply (multiply ?6 ?7) (multiply ?8 ?6)
+ [8, 7, 6] by moufang1 ?6 ?7 ?8
+26074: Goal:
+26074: Id : 1, {_}:
+ multiply (multiply (multiply a b) c) b
+ =>=
+ multiply a (multiply b (multiply c b))
+ [] by prove_moufang2
+26074: Order:
+26074: kbo
+26074: Leaf order:
+26074: identity 2 0 0
+26074: a 2 0 2 1,1,1,2
+26074: c 2 0 2 2,1,2
+26074: b 4 0 4 2,1,1,2
+26074: left_inverse 1 1 0
+26074: multiply 14 2 6 0,2
+NO CLASH, using fixed ground order
+26075: Facts:
+26075: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+26075: Id : 3, {_}:
+ multiply (left_inverse ?4) ?4 =>= identity
+ [4] by left_inverse ?4
+26075: Id : 4, {_}:
+ multiply (multiply ?6 (multiply ?7 ?8)) ?6
+ =>=
+ multiply (multiply ?6 ?7) (multiply ?8 ?6)
+ [8, 7, 6] by moufang1 ?6 ?7 ?8
+26075: Goal:
+26075: Id : 1, {_}:
+ multiply (multiply (multiply a b) c) b
+ =>=
+ multiply a (multiply b (multiply c b))
+ [] by prove_moufang2
+26075: Order:
+26075: lpo
+26075: Leaf order:
+26075: identity 2 0 0
+26075: a 2 0 2 1,1,1,2
+26075: c 2 0 2 2,1,2
+26075: b 4 0 4 2,1,1,2
+26075: left_inverse 1 1 0
+26075: multiply 14 2 6 0,2
+% SZS status Timeout for GRP204-1.p
+CLASH, statistics insufficient
+26204: Facts:
+26204: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+26204: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+26204: Id : 4, {_}:
+ multiply ?6 (left_division ?6 ?7) =>= ?7
+ [7, 6] by multiply_left_division ?6 ?7
+26204: Id : 5, {_}:
+ left_division ?9 (multiply ?9 ?10) =>= ?10
+ [10, 9] by left_division_multiply ?9 ?10
+26204: Id : 6, {_}:
+ multiply (right_division ?12 ?13) ?13 =>= ?12
+ [13, 12] by multiply_right_division ?12 ?13
+26204: Id : 7, {_}:
+ right_division (multiply ?15 ?16) ?16 =>= ?15
+ [16, 15] by right_division_multiply ?15 ?16
+26204: Id : 8, {_}:
+ multiply ?18 (right_inverse ?18) =>= identity
+ [18] by right_inverse ?18
+26204: Id : 9, {_}:
+ multiply (left_inverse ?20) ?20 =>= identity
+ [20] by left_inverse ?20
+26204: Id : 10, {_}:
+ multiply (multiply (multiply ?22 ?23) ?22) ?24
+ =?=
+ multiply ?22 (multiply ?23 (multiply ?22 ?24))
+ [24, 23, 22] by moufang3 ?22 ?23 ?24
+26204: Goal:
+26204: Id : 1, {_}:
+ multiply x (multiply (multiply y z) x)
+ =<=
+ multiply (multiply x y) (multiply z x)
+ [] by prove_moufang4
+26204: Order:
+26204: nrkbo
+26204: Leaf order:
+26204: y 2 0 2 1,1,2,2
+26204: z 2 0 2 2,1,2,2
+26204: identity 4 0 0
+26204: x 4 0 4 1,2
+26204: right_inverse 1 1 0
+26204: left_inverse 1 1 0
+26204: left_division 2 2 0
+26204: right_division 2 2 0
+26204: multiply 20 2 6 0,2
+CLASH, statistics insufficient
+26205: Facts:
+26205: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+26205: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+26205: Id : 4, {_}:
+ multiply ?6 (left_division ?6 ?7) =>= ?7
+ [7, 6] by multiply_left_division ?6 ?7
+26205: Id : 5, {_}:
+ left_division ?9 (multiply ?9 ?10) =>= ?10
+ [10, 9] by left_division_multiply ?9 ?10
+26205: Id : 6, {_}:
+ multiply (right_division ?12 ?13) ?13 =>= ?12
+ [13, 12] by multiply_right_division ?12 ?13
+26205: Id : 7, {_}:
+ right_division (multiply ?15 ?16) ?16 =>= ?15
+ [16, 15] by right_division_multiply ?15 ?16
+26205: Id : 8, {_}:
+ multiply ?18 (right_inverse ?18) =>= identity
+ [18] by right_inverse ?18
+26205: Id : 9, {_}:
+ multiply (left_inverse ?20) ?20 =>= identity
+ [20] by left_inverse ?20
+26205: Id : 10, {_}:
+ multiply (multiply (multiply ?22 ?23) ?22) ?24
+ =>=
+ multiply ?22 (multiply ?23 (multiply ?22 ?24))
+ [24, 23, 22] by moufang3 ?22 ?23 ?24
+26205: Goal:
+26205: Id : 1, {_}:
+ multiply x (multiply (multiply y z) x)
+ =<=
+ multiply (multiply x y) (multiply z x)
+ [] by prove_moufang4
+26205: Order:
+26205: kbo
+26205: Leaf order:
+26205: y 2 0 2 1,1,2,2
+26205: z 2 0 2 2,1,2,2
+26205: identity 4 0 0
+26205: x 4 0 4 1,2
+26205: right_inverse 1 1 0
+26205: left_inverse 1 1 0
+26205: left_division 2 2 0
+26205: right_division 2 2 0
+26205: multiply 20 2 6 0,2
+CLASH, statistics insufficient
+26206: Facts:
+26206: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+26206: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+26206: Id : 4, {_}:
+ multiply ?6 (left_division ?6 ?7) =>= ?7
+ [7, 6] by multiply_left_division ?6 ?7
+26206: Id : 5, {_}:
+ left_division ?9 (multiply ?9 ?10) =>= ?10
+ [10, 9] by left_division_multiply ?9 ?10
+26206: Id : 6, {_}:
+ multiply (right_division ?12 ?13) ?13 =>= ?12
+ [13, 12] by multiply_right_division ?12 ?13
+26206: Id : 7, {_}:
+ right_division (multiply ?15 ?16) ?16 =>= ?15
+ [16, 15] by right_division_multiply ?15 ?16
+26206: Id : 8, {_}:
+ multiply ?18 (right_inverse ?18) =>= identity
+ [18] by right_inverse ?18
+26206: Id : 9, {_}:
+ multiply (left_inverse ?20) ?20 =>= identity
+ [20] by left_inverse ?20
+26206: Id : 10, {_}:
+ multiply (multiply (multiply ?22 ?23) ?22) ?24
+ =>=
+ multiply ?22 (multiply ?23 (multiply ?22 ?24))
+ [24, 23, 22] by moufang3 ?22 ?23 ?24
+26206: Goal:
+26206: Id : 1, {_}:
+ multiply x (multiply (multiply y z) x)
+ =<=
+ multiply (multiply x y) (multiply z x)
+ [] by prove_moufang4
+26206: Order:
+26206: lpo
+26206: Leaf order:
+26206: y 2 0 2 1,1,2,2
+26206: z 2 0 2 2,1,2,2
+26206: identity 4 0 0
+26206: x 4 0 4 1,2
+26206: right_inverse 1 1 0
+26206: left_inverse 1 1 0
+26206: left_division 2 2 0
+26206: right_division 2 2 0
+26206: multiply 20 2 6 0,2
+Statistics :
+Max weight : 20
+Found proof, 29.317631s
+% SZS status Unsatisfiable for GRP205-1.p
+% SZS output start CNFRefutation for GRP205-1.p
+Id : 56, {_}: multiply (multiply (multiply ?126 ?127) ?126) ?128 =>= multiply ?126 (multiply ?127 (multiply ?126 ?128)) [128, 127, 126] by moufang3 ?126 ?127 ?128
+Id : 4, {_}: multiply ?6 (left_division ?6 ?7) =>= ?7 [7, 6] by multiply_left_division ?6 ?7
+Id : 9, {_}: multiply (left_inverse ?20) ?20 =>= identity [20] by left_inverse ?20
+Id : 22, {_}: left_division ?48 (multiply ?48 ?49) =>= ?49 [49, 48] by left_division_multiply ?48 ?49
+Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+Id : 5, {_}: left_division ?9 (multiply ?9 ?10) =>= ?10 [10, 9] by left_division_multiply ?9 ?10
+Id : 8, {_}: multiply ?18 (right_inverse ?18) =>= identity [18] by right_inverse ?18
+Id : 6, {_}: multiply (right_division ?12 ?13) ?13 =>= ?12 [13, 12] by multiply_right_division ?12 ?13
+Id : 10, {_}: multiply (multiply (multiply ?22 ?23) ?22) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by moufang3 ?22 ?23 ?24
+Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4
+Id : 7, {_}: right_division (multiply ?15 ?16) ?16 =>= ?15 [16, 15] by right_division_multiply ?15 ?16
+Id : 53, {_}: multiply ?115 (multiply ?116 (multiply ?115 identity)) =>= multiply (multiply ?115 ?116) ?115 [116, 115] by Super 3 with 10 at 2
+Id : 70, {_}: multiply ?115 (multiply ?116 ?115) =<= multiply (multiply ?115 ?116) ?115 [116, 115] by Demod 53 with 3 at 2,2,2
+Id : 889, {_}: right_division (multiply ?1099 (multiply ?1100 ?1099)) ?1099 =>= multiply ?1099 ?1100 [1100, 1099] by Super 7 with 70 at 1,2
+Id : 895, {_}: right_division (multiply ?1115 ?1116) ?1115 =<= multiply ?1115 (right_division ?1116 ?1115) [1116, 1115] by Super 889 with 6 at 2,1,2
+Id : 55, {_}: right_division (multiply ?122 (multiply ?123 (multiply ?122 ?124))) ?124 =>= multiply (multiply ?122 ?123) ?122 [124, 123, 122] by Super 7 with 10 at 1,2
+Id : 2553, {_}: right_division (multiply ?3478 (multiply ?3479 (multiply ?3478 ?3480))) ?3480 =>= multiply ?3478 (multiply ?3479 ?3478) [3480, 3479, 3478] by Demod 55 with 70 at 3
+Id : 647, {_}: multiply ?831 (multiply ?832 ?831) =<= multiply (multiply ?831 ?832) ?831 [832, 831] by Demod 53 with 3 at 2,2,2
+Id : 654, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= multiply identity ?850 [850] by Super 647 with 8 at 1,3
+Id : 677, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= ?850 [850] by Demod 654 with 2 at 3
+Id : 763, {_}: left_division ?991 ?991 =<= multiply (right_inverse ?991) ?991 [991] by Super 5 with 677 at 2,2
+Id : 24, {_}: left_division ?53 ?53 =>= identity [53] by Super 22 with 3 at 2,2
+Id : 789, {_}: identity =<= multiply (right_inverse ?991) ?991 [991] by Demod 763 with 24 at 2
+Id : 816, {_}: right_division identity ?1047 =>= right_inverse ?1047 [1047] by Super 7 with 789 at 1,2
+Id : 45, {_}: right_division identity ?99 =>= left_inverse ?99 [99] by Super 7 with 9 at 1,2
+Id : 843, {_}: left_inverse ?1047 =<= right_inverse ?1047 [1047] by Demod 816 with 45 at 2
+Id : 857, {_}: multiply ?18 (left_inverse ?18) =>= identity [18] by Demod 8 with 843 at 2,2
+Id : 2562, {_}: right_division (multiply ?3513 (multiply ?3514 identity)) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Super 2553 with 857 at 2,2,1,2
+Id : 2621, {_}: right_division (multiply ?3513 ?3514) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Demod 2562 with 3 at 2,1,2
+Id : 2806, {_}: right_division (multiply (left_inverse ?3781) (multiply ?3781 ?3782)) (left_inverse ?3781) =>= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Super 895 with 2621 at 2,3
+Id : 52, {_}: multiply ?111 (multiply ?112 (multiply ?111 (left_division (multiply (multiply ?111 ?112) ?111) ?113))) =>= ?113 [113, 112, 111] by Super 4 with 10 at 2
+Id : 963, {_}: multiply ?1216 (multiply ?1217 (multiply ?1216 (left_division (multiply ?1216 (multiply ?1217 ?1216)) ?1218))) =>= ?1218 [1218, 1217, 1216] by Demod 52 with 70 at 1,2,2,2,2
+Id : 970, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division (multiply ?1242 identity) ?1243))) =>= ?1243 [1243, 1242] by Super 963 with 9 at 2,1,2,2,2,2
+Id : 1030, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division ?1242 ?1243))) =>= ?1243 [1243, 1242] by Demod 970 with 3 at 1,2,2,2,2
+Id : 1031, {_}: multiply ?1242 (multiply (left_inverse ?1242) ?1243) =>= ?1243 [1243, 1242] by Demod 1030 with 4 at 2,2,2
+Id : 1164, {_}: left_division ?1548 ?1549 =<= multiply (left_inverse ?1548) ?1549 [1549, 1548] by Super 5 with 1031 at 2,2
+Id : 2852, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =<= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2806 with 1164 at 1,2
+Id : 2853, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =>= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2852 with 1164 at 3
+Id : 2854, {_}: right_division ?3782 (left_inverse ?3781) =<= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3781, 3782] by Demod 2853 with 5 at 1,2
+Id : 2855, {_}: right_division ?3782 (left_inverse ?3781) =>= multiply ?3782 ?3781 [3781, 3782] by Demod 2854 with 5 at 3
+Id : 1378, {_}: right_division (left_division ?1827 ?1828) ?1828 =>= left_inverse ?1827 [1828, 1827] by Super 7 with 1164 at 1,2
+Id : 28, {_}: left_division (right_division ?62 ?63) ?62 =>= ?63 [63, 62] by Super 5 with 6 at 2,2
+Id : 1384, {_}: right_division ?1844 ?1845 =<= left_inverse (right_division ?1845 ?1844) [1845, 1844] by Super 1378 with 28 at 1,2
+Id : 3643, {_}: multiply (multiply ?4879 ?4880) ?4881 =<= multiply ?4880 (multiply (left_division ?4880 ?4879) (multiply ?4880 ?4881)) [4881, 4880, 4879] by Super 56 with 4 at 1,1,2
+Id : 3648, {_}: multiply (multiply ?4897 ?4898) (left_division ?4898 ?4899) =>= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Super 3643 with 4 at 2,2,3
+Id : 2922, {_}: right_division (left_inverse ?3910) ?3911 =>= left_inverse (multiply ?3911 ?3910) [3911, 3910] by Super 1384 with 2855 at 1,3
+Id : 3008, {_}: left_inverse (multiply (left_inverse ?4021) ?4022) =>= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Super 2855 with 2922 at 2
+Id : 3027, {_}: left_inverse (left_division ?4021 ?4022) =<= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Demod 3008 with 1164 at 1,2
+Id : 3028, {_}: left_inverse (left_division ?4021 ?4022) =>= left_division ?4022 ?4021 [4022, 4021] by Demod 3027 with 1164 at 3
+Id : 3191, {_}: right_division ?4224 (left_division ?4225 ?4226) =<= multiply ?4224 (left_division ?4226 ?4225) [4226, 4225, 4224] by Super 2855 with 3028 at 2,2
+Id : 8019, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Demod 3648 with 3191 at 2
+Id : 3187, {_}: left_division (left_division ?4210 ?4211) ?4212 =<= multiply (left_division ?4211 ?4210) ?4212 [4212, 4211, 4210] by Super 1164 with 3028 at 1,3
+Id : 8020, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (left_division (left_division ?4897 ?4898) ?4899) [4899, 4898, 4897] by Demod 8019 with 3187 at 2,3
+Id : 8021, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =>= right_division ?4898 (left_division ?4899 (left_division ?4897 ?4898)) [4899, 4898, 4897] by Demod 8020 with 3191 at 3
+Id : 8034, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= left_inverse (right_division ?9767 (left_division ?9766 (left_division ?9768 ?9767))) [9768, 9767, 9766] by Super 1384 with 8021 at 1,3
+Id : 8099, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= right_division (left_division ?9766 (left_division ?9768 ?9767)) ?9767 [9768, 9767, 9766] by Demod 8034 with 1384 at 3
+Id : 23672, {_}: right_division (left_division ?25246 (left_inverse ?25247)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25247, 25246] by Super 2855 with 8099 at 2
+Id : 2932, {_}: right_division ?3937 (left_inverse ?3938) =>= multiply ?3937 ?3938 [3938, 3937] by Demod 2854 with 5 at 3
+Id : 46, {_}: left_division (left_inverse ?101) identity =>= ?101 [101] by Super 5 with 9 at 2,2
+Id : 40, {_}: left_division ?91 identity =>= right_inverse ?91 [91] by Super 5 with 8 at 2,2
+Id : 426, {_}: right_inverse (left_inverse ?101) =>= ?101 [101] by Demod 46 with 40 at 2
+Id : 860, {_}: left_inverse (left_inverse ?101) =>= ?101 [101] by Demod 426 with 843 at 2
+Id : 2936, {_}: right_division ?3949 ?3950 =<= multiply ?3949 (left_inverse ?3950) [3950, 3949] by Super 2932 with 860 at 2,2
+Id : 3077, {_}: left_division ?4125 (left_inverse ?4126) =>= right_division (left_inverse ?4125) ?4126 [4126, 4125] by Super 1164 with 2936 at 3
+Id : 3115, {_}: left_division ?4125 (left_inverse ?4126) =>= left_inverse (multiply ?4126 ?4125) [4126, 4125] by Demod 3077 with 2922 at 3
+Id : 23819, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23672 with 3115 at 1,2
+Id : 23820, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23819 with 2936 at 2,2
+Id : 23821, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25248, 25246, 25247] by Demod 23820 with 3187 at 3
+Id : 23822, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23821 with 2922 at 2
+Id : 23823, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23822 with 3115 at 1,1,3
+Id : 1167, {_}: multiply ?1556 (multiply (left_inverse ?1556) ?1557) =>= ?1557 [1557, 1556] by Demod 1030 with 4 at 2,2,2
+Id : 1177, {_}: multiply ?1584 ?1585 =<= left_division (left_inverse ?1584) ?1585 [1585, 1584] by Super 1167 with 4 at 2,2
+Id : 1414, {_}: multiply (right_division ?1873 ?1874) ?1875 =>= left_division (right_division ?1874 ?1873) ?1875 [1875, 1874, 1873] by Super 1177 with 1384 at 1,3
+Id : 23824, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25248, 25247] by Demod 23823 with 1414 at 1,2
+Id : 23825, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =>= left_division (multiply (multiply ?25247 ?25248) ?25246) ?25247 [25246, 25248, 25247] by Demod 23824 with 1177 at 1,3
+Id : 37248, {_}: left_division (multiply ?37773 ?37774) (right_division ?37773 ?37775) =<= left_division (multiply (multiply ?37773 ?37775) ?37774) ?37773 [37775, 37774, 37773] by Demod 23825 with 3028 at 2
+Id : 37265, {_}: left_division (multiply ?37844 ?37845) (right_division ?37844 (left_inverse ?37846)) =>= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Super 37248 with 2936 at 1,1,3
+Id : 37472, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Demod 37265 with 2855 at 2,2
+Id : 37473, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (left_division (right_division ?37846 ?37844) ?37845) ?37844 [37846, 37845, 37844] by Demod 37472 with 1414 at 1,3
+Id : 8041, {_}: right_division (multiply ?9794 ?9795) (left_division ?9796 ?9795) =>= right_division ?9795 (left_division ?9796 (left_division ?9794 ?9795)) [9796, 9795, 9794] by Demod 8020 with 3191 at 3
+Id : 8054, {_}: right_division (multiply ?9845 (left_inverse ?9846)) (left_inverse (multiply ?9846 ?9847)) =>= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Super 8041 with 3115 at 2,2
+Id : 8126, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Demod 8054 with 2855 at 2
+Id : 8127, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8126 with 2922 at 3
+Id : 8128, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8127 with 2936 at 1,2
+Id : 8129, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9846, 9845] by Demod 8128 with 3187 at 1,3
+Id : 8130, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9845, 9846] by Demod 8129 with 1414 at 2
+Id : 8131, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) [9847, 9845, 9846] by Demod 8130 with 3028 at 3
+Id : 8132, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_inverse (multiply ?9846 ?9845)) ?9847) [9847, 9845, 9846] by Demod 8131 with 3115 at 1,2,3
+Id : 24031, {_}: left_division (right_division ?25824 ?25825) (multiply ?25824 ?25826) =>= left_division ?25824 (multiply (multiply ?25824 ?25825) ?25826) [25826, 25825, 25824] by Demod 8132 with 1177 at 2,3
+Id : 24068, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =<= left_division ?25977 (multiply (multiply ?25977 (left_inverse ?25978)) ?25979) [25979, 25978, 25977] by Super 24031 with 2855 at 1,2
+Id : 24287, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (multiply (right_division ?25977 ?25978) ?25979) [25979, 25978, 25977] by Demod 24068 with 2936 at 1,2,3
+Id : 24288, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (left_division (right_division ?25978 ?25977) ?25979) [25979, 25978, 25977] by Demod 24287 with 1414 at 2,3
+Id : 47819, {_}: left_division ?49234 (left_division (right_division ?49235 ?49234) ?49236) =<= left_division (left_division (right_division ?49236 ?49234) ?49235) ?49234 [49236, 49235, 49234] by Demod 37473 with 24288 at 2
+Id : 1246, {_}: multiply (left_inverse ?1641) (multiply ?1642 (left_inverse ?1641)) =>= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Super 70 with 1164 at 1,3
+Id : 1310, {_}: left_division ?1641 (multiply ?1642 (left_inverse ?1641)) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1246 with 1164 at 2
+Id : 3056, {_}: left_division ?1641 (right_division ?1642 ?1641) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1310 with 2936 at 2,2
+Id : 3057, {_}: left_division ?1641 (right_division ?1642 ?1641) =>= right_division (left_division ?1641 ?1642) ?1641 [1642, 1641] by Demod 3056 with 2936 at 3
+Id : 47887, {_}: left_division ?49524 (left_division (right_division (right_division ?49525 (right_division ?49526 ?49524)) ?49524) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Super 47819 with 3057 at 1,3
+Id : 59, {_}: multiply (multiply ?136 ?137) ?138 =<= multiply ?137 (multiply (left_division ?137 ?136) (multiply ?137 ?138)) [138, 137, 136] by Super 56 with 4 at 1,1,2
+Id : 3632, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= multiply (left_division ?4830 ?4831) (multiply ?4830 ?4832) [4832, 4831, 4830] by Super 5 with 59 at 2,2
+Id : 7833, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= left_division (left_division ?4831 ?4830) (multiply ?4830 ?4832) [4832, 4831, 4830] by Demod 3632 with 3187 at 3
+Id : 7841, {_}: left_inverse (left_division ?9488 (multiply (multiply ?9489 ?9488) ?9490)) =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9489, 9488] by Super 3028 with 7833 at 1,2
+Id : 7910, {_}: left_division (multiply (multiply ?9489 ?9488) ?9490) ?9488 =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9488, 9489] by Demod 7841 with 3028 at 2
+Id : 22545, {_}: left_division (multiply (left_inverse ?23598) ?23599) (left_division ?23600 (left_inverse ?23598)) =>= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Super 3115 with 7910 at 2
+Id : 22628, {_}: left_division (left_division ?23598 ?23599) (left_division ?23600 (left_inverse ?23598)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22545 with 1164 at 1,2
+Id : 22629, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22628 with 3115 at 2,2
+Id : 22630, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23600, 23599, 23598] by Demod 22629 with 2936 at 1,2,1,3
+Id : 22631, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23599, 23600, 23598] by Demod 22630 with 3115 at 2
+Id : 22632, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22631 with 1414 at 2,1,3
+Id : 22633, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =<= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22632 with 3191 at 1,2
+Id : 22634, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =>= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23599, 23600, 23598] by Demod 22633 with 3191 at 1,3
+Id : 22635, {_}: right_division (left_division ?23599 ?23598) (multiply ?23598 ?23600) =<= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23600, 23598, 23599] by Demod 22634 with 1384 at 2
+Id : 33282, {_}: right_division (left_division ?33402 ?33403) (multiply ?33403 ?33404) =<= right_division (left_division ?33402 (right_division ?33403 ?33404)) ?33403 [33404, 33403, 33402] by Demod 22635 with 1384 at 3
+Id : 33363, {_}: right_division (left_division (left_inverse ?33737) ?33738) (multiply ?33738 ?33739) =>= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Super 33282 with 1177 at 1,3
+Id : 33649, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Demod 33363 with 1177 at 1,2
+Id : 2939, {_}: right_division ?3957 (right_division ?3958 ?3959) =<= multiply ?3957 (right_division ?3959 ?3958) [3959, 3958, 3957] by Super 2932 with 1384 at 2,2
+Id : 33650, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (right_division ?33737 (right_division ?33739 ?33738)) ?33738 [33739, 33738, 33737] by Demod 33649 with 2939 at 1,3
+Id : 48257, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Demod 47887 with 33650 at 1,2,2
+Id : 640, {_}: multiply (multiply ?22 (multiply ?23 ?22)) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by Demod 10 with 70 at 1,2
+Id : 1251, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =<= multiply ?1655 (multiply (left_inverse ?1656) (multiply ?1655 ?1657)) [1657, 1656, 1655] by Super 640 with 1164 at 2,1,2
+Id : 1306, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1251 with 1164 at 2,3
+Id : 5008, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1306 with 3191 at 1,2
+Id : 5009, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5008 with 3191 at 3
+Id : 5010, {_}: left_division (right_division (left_division ?1655 ?1656) ?1655) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5009 with 1414 at 2
+Id : 48258, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49526, 49525, 49524] by Demod 48257 with 5010 at 3
+Id : 3070, {_}: multiply (multiply (left_inverse ?4103) (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Super 640 with 2936 at 2,1,2
+Id : 3126, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3070 with 1164 at 1,2
+Id : 3127, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3126 with 1164 at 3
+Id : 3128, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3127 with 3057 at 1,2
+Id : 3129, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3128 with 1164 at 2,2,3
+Id : 3130, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3129 with 1414 at 2
+Id : 7047, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (right_division ?4104 (left_division ?4105 ?4103)) [4105, 4104, 4103] by Demod 3130 with 3191 at 2,3
+Id : 7063, {_}: left_division ?8435 (right_division ?8436 (left_division (left_inverse ?8437) ?8435)) =>= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Super 3115 with 7047 at 2
+Id : 7165, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Demod 7063 with 1177 at 2,2,2
+Id : 7166, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (right_division ?8437 (right_division (left_division ?8435 ?8436) ?8435)) [8437, 8436, 8435] by Demod 7165 with 2939 at 1,3
+Id : 7167, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =>= right_division (right_division (left_division ?8435 ?8436) ?8435) ?8437 [8437, 8436, 8435] by Demod 7166 with 1384 at 3
+Id : 21426, {_}: left_inverse (right_division (right_division (left_division ?22100 ?22101) ?22100) ?22102) =>= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22102, 22101, 22100] by Super 3028 with 7167 at 1,2
+Id : 21547, {_}: right_division ?22102 (right_division (left_division ?22100 ?22101) ?22100) =<= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22101, 22100, 22102] by Demod 21426 with 1384 at 2
+Id : 48259, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49525, 49526, 49524] by Demod 48258 with 21547 at 2,2
+Id : 48260, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49525, 49526, 49524] by Demod 48259 with 1414 at 1,2,3
+Id : 3073, {_}: left_division ?4114 (right_division ?4114 ?4115) =>= left_inverse ?4115 [4115, 4114] by Super 5 with 2936 at 2,2
+Id : 48261, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =<= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49524, 49525, 49526] by Demod 48260 with 3073 at 2
+Id : 48262, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48261 with 28 at 1,2,3
+Id : 48263, {_}: right_division ?49526 (left_division ?49526 (multiply ?49525 ?49524)) =<= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48262 with 1384 at 2
+Id : 52424, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= left_inverse (right_division ?54688 (left_division ?54688 (multiply ?54689 ?54690))) [54690, 54689, 54688] by Super 1384 with 48263 at 1,3
+Id : 52654, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= right_division (left_division ?54688 (multiply ?54689 ?54690)) ?54688 [54690, 54689, 54688] by Demod 52424 with 1384 at 3
+Id : 54963, {_}: right_division (left_division (left_inverse ?57654) ?57655) (right_division (left_inverse ?57654) ?57656) =>= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Super 2855 with 52654 at 2
+Id : 55156, {_}: right_division (multiply ?57654 ?57655) (right_division (left_inverse ?57654) ?57656) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 54963 with 1177 at 1,2
+Id : 55157, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55156 with 2922 at 2,2
+Id : 55158, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55157 with 3187 at 3
+Id : 55159, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55158 with 2855 at 2
+Id : 55160, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_inverse (multiply ?57654 (multiply ?57655 ?57656))) ?57654 [57656, 57655, 57654] by Demod 55159 with 3115 at 1,3
+Id : 55161, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= multiply (multiply ?57654 (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55160 with 1177 at 3
+Id : 55162, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =>= multiply ?57654 (multiply (multiply ?57655 ?57656) ?57654) [57656, 57655, 57654] by Demod 55161 with 70 at 3
+Id : 56911, {_}: multiply x (multiply (multiply y z) x) =?= multiply x (multiply (multiply y z) x) [] by Demod 1 with 55162 at 3
+Id : 1, {_}: multiply x (multiply (multiply y z) x) =<= multiply (multiply x y) (multiply z x) [] by prove_moufang4
+% SZS output end CNFRefutation for GRP205-1.p
+26205: solved GRP205-1.p in 14.680917 using kbo
+26205: status Unsatisfiable for GRP205-1.p
+NO CLASH, using fixed ground order
+26244: Facts:
+26244: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply ?3
+ (multiply
+ (multiply (multiply ?4 (inverse ?4))
+ (inverse (multiply ?2 ?3))) ?2)))
+ =>=
+ ?2
+ [4, 3, 2] by single_non_axiom ?2 ?3 ?4
+26244: Goal:
+26244: Id : 1, {_}:
+ multiply x
+ (inverse
+ (multiply y
+ (multiply
+ (multiply (multiply z (inverse z)) (inverse (multiply u y)))
+ x)))
+ =>=
+ u
+ [] by try_prove_this_axiom
+26244: Order:
+26244: nrkbo
+26244: Leaf order:
+26244: z 2 0 2 1,1,1,2,1,2,2
+26244: u 2 0 2 1,1,2,1,2,1,2,2
+26244: y 2 0 2 1,1,2,2
+26244: x 2 0 2 1,2
+26244: inverse 6 1 3 0,2,2
+26244: multiply 12 2 6 0,2
+NO CLASH, using fixed ground order
+26245: Facts:
+26245: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply ?3
+ (multiply
+ (multiply (multiply ?4 (inverse ?4))
+ (inverse (multiply ?2 ?3))) ?2)))
+ =>=
+ ?2
+ [4, 3, 2] by single_non_axiom ?2 ?3 ?4
+26245: Goal:
+26245: Id : 1, {_}:
+ multiply x
+ (inverse
+ (multiply y
+ (multiply
+ (multiply (multiply z (inverse z)) (inverse (multiply u y)))
+ x)))
+ =>=
+ u
+ [] by try_prove_this_axiom
+26245: Order:
+26245: kbo
+26245: Leaf order:
+26245: z 2 0 2 1,1,1,2,1,2,2
+26245: u 2 0 2 1,1,2,1,2,1,2,2
+26245: y 2 0 2 1,1,2,2
+26245: x 2 0 2 1,2
+26245: inverse 6 1 3 0,2,2
+26245: multiply 12 2 6 0,2
+NO CLASH, using fixed ground order
+26246: Facts:
+26246: Id : 2, {_}:
+ multiply ?2
+ (inverse
+ (multiply ?3
+ (multiply
+ (multiply (multiply ?4 (inverse ?4))
+ (inverse (multiply ?2 ?3))) ?2)))
+ =>=
+ ?2
+ [4, 3, 2] by single_non_axiom ?2 ?3 ?4
+26246: Goal:
+26246: Id : 1, {_}:
+ multiply x
+ (inverse
+ (multiply y
+ (multiply
+ (multiply (multiply z (inverse z)) (inverse (multiply u y)))
+ x)))
+ =>=
+ u
+ [] by try_prove_this_axiom
+26246: Order:
+26246: lpo
+26246: Leaf order:
+26246: z 2 0 2 1,1,1,2,1,2,2
+26246: u 2 0 2 1,1,2,1,2,1,2,2
+26246: y 2 0 2 1,1,2,2
+26246: x 2 0 2 1,2
+26246: inverse 6 1 3 0,2,2
+26246: multiply 12 2 6 0,2
+% SZS status Timeout for GRP207-1.p
+Fatal error: exception Assert_failure("matitaprover.ml", 269, 46)
+NO CLASH, using fixed ground order
+26289: Facts:
+26289: Id : 2, {_}:
+ inverse
+ (multiply
+ (inverse
+ (multiply ?2
+ (inverse
+ (multiply (inverse ?3)
+ (inverse
+ (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
+ (multiply ?2 ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+26289: Goal:
+26289: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+26289: Order:
+26289: nrkbo
+26289: Leaf order:
+26289: a3 2 0 2 1,1,2
+26289: b3 2 0 2 2,1,2
+26289: c3 2 0 2 2,2
+26289: inverse 7 1 0
+26289: multiply 10 2 4 0,2
+NO CLASH, using fixed ground order
+26290: Facts:
+26290: Id : 2, {_}:
+ inverse
+ (multiply
+ (inverse
+ (multiply ?2
+ (inverse
+ (multiply (inverse ?3)
+ (inverse
+ (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
+ (multiply ?2 ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+26290: Goal:
+26290: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+26290: Order:
+26290: kbo
+26290: Leaf order:
+26290: a3 2 0 2 1,1,2
+26290: b3 2 0 2 2,1,2
+26290: c3 2 0 2 2,2
+26290: inverse 7 1 0
+26290: multiply 10 2 4 0,2
+NO CLASH, using fixed ground order
+26291: Facts:
+26291: Id : 2, {_}:
+ inverse
+ (multiply
+ (inverse
+ (multiply ?2
+ (inverse
+ (multiply (inverse ?3)
+ (inverse
+ (multiply ?4 (inverse (multiply (inverse ?4) ?4))))))))
+ (multiply ?2 ?4))
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+26291: Goal:
+26291: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+26291: Order:
+26291: lpo
+26291: Leaf order:
+26291: a3 2 0 2 1,1,2
+26291: b3 2 0 2 2,1,2
+26291: c3 2 0 2 2,2
+26291: inverse 7 1 0
+26291: multiply 10 2 4 0,2
+% SZS status Timeout for GRP420-1.p
+NO CLASH, using fixed ground order
+26320: Facts:
+26320: Id : 2, {_}:
+ divide
+ (divide (divide ?2 ?2)
+ (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
+ ?4
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+26320: Id : 3, {_}:
+ multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
+ [8, 7, 6] by multiply ?6 ?7 ?8
+26320: Id : 4, {_}:
+ inverse ?10 =<= divide (divide ?11 ?11) ?10
+ [11, 10] by inverse ?10 ?11
+26320: Goal:
+26320: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+26320: Order:
+26320: nrkbo
+26320: Leaf order:
+26320: a3 2 0 2 1,1,2
+26320: b3 2 0 2 2,1,2
+26320: c3 2 0 2 2,2
+26320: inverse 1 1 0
+26320: multiply 5 2 4 0,2
+26320: divide 13 2 0
+NO CLASH, using fixed ground order
+26321: Facts:
+26321: Id : 2, {_}:
+ divide
+ (divide (divide ?2 ?2)
+ (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
+ ?4
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+26321: Id : 3, {_}:
+ multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
+ [8, 7, 6] by multiply ?6 ?7 ?8
+26321: Id : 4, {_}:
+ inverse ?10 =<= divide (divide ?11 ?11) ?10
+ [11, 10] by inverse ?10 ?11
+26321: Goal:
+26321: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+26321: Order:
+26321: kbo
+26321: Leaf order:
+26321: a3 2 0 2 1,1,2
+26321: b3 2 0 2 2,1,2
+26321: c3 2 0 2 2,2
+26321: inverse 1 1 0
+26321: multiply 5 2 4 0,2
+26321: divide 13 2 0
+NO CLASH, using fixed ground order
+26322: Facts:
+26322: Id : 2, {_}:
+ divide
+ (divide (divide ?2 ?2)
+ (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4))))
+ ?4
+ =>=
+ ?3
+ [4, 3, 2] by single_axiom ?2 ?3 ?4
+26322: Id : 3, {_}:
+ multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7)
+ [8, 7, 6] by multiply ?6 ?7 ?8
+26322: Id : 4, {_}:
+ inverse ?10 =<= divide (divide ?11 ?11) ?10
+ [11, 10] by inverse ?10 ?11
+26322: Goal:
+26322: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+26322: Order:
+26322: lpo
+26322: Leaf order:
+26322: a3 2 0 2 1,1,2
+26322: b3 2 0 2 2,1,2
+26322: c3 2 0 2 2,2
+26322: inverse 1 1 0
+26322: multiply 5 2 4 0,2
+26322: divide 13 2 0
+Statistics :
+Max weight : 38
+Found proof, 2.679419s
+% SZS status Unsatisfiable for GRP453-1.p
+% SZS output start CNFRefutation for GRP453-1.p
+Id : 35, {_}: inverse ?90 =<= divide (divide ?91 ?91) ?90 [91, 90] by inverse ?90 ?91
+Id : 2, {_}: divide (divide (divide ?2 ?2) (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4
+Id : 5, {_}: divide (divide (divide ?13 ?13) (divide ?13 (divide ?14 (divide (divide (divide ?13 ?13) ?13) ?15)))) ?15 =>= ?14 [15, 14, 13] by single_axiom ?13 ?14 ?15
+Id : 4, {_}: inverse ?10 =<= divide (divide ?11 ?11) ?10 [11, 10] by inverse ?10 ?11
+Id : 3, {_}: multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) [8, 7, 6] by multiply ?6 ?7 ?8
+Id : 29, {_}: multiply ?6 ?7 =<= divide ?6 (inverse ?7) [7, 6] by Demod 3 with 4 at 2,3
+Id : 6, {_}: divide (divide (divide ?17 ?17) (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Super 5 with 2 at 2,2,1,2
+Id : 142, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 6 with 4 at 1,2
+Id : 143, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 142 with 4 at 3
+Id : 144, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 143 with 4 at 1,2,2,1,3
+Id : 145, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (inverse ?17) ?19)))) [20, 19, 18, 17] by Demod 144 with 4 at 1,2,2,2,1,3
+Id : 36, {_}: inverse ?93 =<= divide (inverse (divide ?94 ?94)) ?93 [94, 93] by Super 35 with 4 at 1,3
+Id : 226, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (divide (divide ?529 ?529) (divide ?527 (inverse (divide (inverse ?526) ?528)))) [529, 528, 527, 526] by Super 145 with 36 at 2,2,1,3
+Id : 249, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (inverse (divide ?527 (inverse (divide (inverse ?526) ?528)))) [528, 527, 526] by Demod 226 with 4 at 1,3
+Id : 250, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (inverse (multiply ?527 (divide (inverse ?526) ?528))) [528, 527, 526] by Demod 249 with 29 at 1,1,3
+Id : 13, {_}: divide (multiply (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50))) ?50 =>= ?49 [50, 49, 48] by Super 2 with 3 at 1,2
+Id : 32, {_}: multiply (divide ?79 ?79) ?80 =>= inverse (inverse ?80) [80, 79] by Super 29 with 4 at 3
+Id : 479, {_}: divide (inverse (inverse (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 13 with 32 at 1,2
+Id : 480, {_}: divide (inverse (inverse (divide ?49 (divide (inverse (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 479 with 4 at 1,2,1,1,1,2
+Id : 481, {_}: divide (inverse (inverse (divide ?49 (inverse ?50)))) ?50 =>= ?49 [50, 49] by Demod 480 with 36 at 2,1,1,1,2
+Id : 482, {_}: divide (inverse (inverse (multiply ?49 ?50))) ?50 =>= ?49 [50, 49] by Demod 481 with 29 at 1,1,1,2
+Id : 888, {_}: divide (inverse (divide ?1873 ?1874)) ?1875 =<= inverse (inverse (multiply ?1874 (divide (inverse ?1873) ?1875))) [1875, 1874, 1873] by Demod 249 with 29 at 1,1,3
+Id : 903, {_}: divide (inverse (divide (divide ?1940 ?1940) ?1941)) ?1942 =>= inverse (inverse (multiply ?1941 (inverse ?1942))) [1942, 1941, 1940] by Super 888 with 36 at 2,1,1,3
+Id : 936, {_}: divide (inverse (inverse ?1941)) ?1942 =<= inverse (inverse (multiply ?1941 (inverse ?1942))) [1942, 1941] by Demod 903 with 4 at 1,1,2
+Id : 969, {_}: divide (inverse (inverse ?2088)) ?2089 =<= inverse (inverse (multiply ?2088 (inverse ?2089))) [2089, 2088] by Demod 903 with 4 at 1,1,2
+Id : 980, {_}: divide (inverse (inverse (divide ?2127 ?2127))) ?2128 =>= inverse (inverse (inverse (inverse (inverse ?2128)))) [2128, 2127] by Super 969 with 32 at 1,1,3
+Id : 223, {_}: inverse ?515 =<= divide (inverse (inverse (divide ?516 ?516))) ?515 [516, 515] by Super 4 with 36 at 1,3
+Id : 1009, {_}: inverse ?2128 =<= inverse (inverse (inverse (inverse (inverse ?2128)))) [2128] by Demod 980 with 223 at 2
+Id : 1026, {_}: multiply ?2199 (inverse (inverse (inverse (inverse ?2200)))) =>= divide ?2199 (inverse ?2200) [2200, 2199] by Super 29 with 1009 at 2,3
+Id : 1064, {_}: multiply ?2199 (inverse (inverse (inverse (inverse ?2200)))) =>= multiply ?2199 ?2200 [2200, 2199] by Demod 1026 with 29 at 3
+Id : 1096, {_}: divide (inverse (inverse ?2287)) (inverse (inverse (inverse ?2288))) =>= inverse (inverse (multiply ?2287 ?2288)) [2288, 2287] by Super 936 with 1064 at 1,1,3
+Id : 1169, {_}: multiply (inverse (inverse ?2287)) (inverse (inverse ?2288)) =>= inverse (inverse (multiply ?2287 ?2288)) [2288, 2287] by Demod 1096 with 29 at 2
+Id : 1211, {_}: divide (inverse (inverse (inverse (inverse ?2471)))) (inverse ?2472) =>= inverse (inverse (inverse (inverse (multiply ?2471 ?2472)))) [2472, 2471] by Super 936 with 1169 at 1,1,3
+Id : 1253, {_}: multiply (inverse (inverse (inverse (inverse ?2471)))) ?2472 =>= inverse (inverse (inverse (inverse (multiply ?2471 ?2472)))) [2472, 2471] by Demod 1211 with 29 at 2
+Id : 1506, {_}: divide (inverse (inverse (inverse (inverse (inverse (inverse (multiply ?3181 ?3182))))))) ?3182 =>= inverse (inverse (inverse (inverse ?3181))) [3182, 3181] by Super 482 with 1253 at 1,1,1,2
+Id : 1558, {_}: divide (inverse (inverse (multiply ?3181 ?3182))) ?3182 =>= inverse (inverse (inverse (inverse ?3181))) [3182, 3181] by Demod 1506 with 1009 at 1,2
+Id : 1559, {_}: ?3181 =<= inverse (inverse (inverse (inverse ?3181))) [3181] by Demod 1558 with 482 at 2
+Id : 1611, {_}: multiply ?3343 (inverse (inverse (inverse ?3344))) =>= divide ?3343 ?3344 [3344, 3343] by Super 29 with 1559 at 2,3
+Id : 1683, {_}: divide (inverse (inverse ?3483)) (inverse (inverse ?3484)) =>= inverse (inverse (divide ?3483 ?3484)) [3484, 3483] by Super 936 with 1611 at 1,1,3
+Id : 1717, {_}: multiply (inverse (inverse ?3483)) (inverse ?3484) =>= inverse (inverse (divide ?3483 ?3484)) [3484, 3483] by Demod 1683 with 29 at 2
+Id : 1782, {_}: divide (inverse (inverse (inverse (inverse (divide ?3605 ?3606))))) (inverse ?3606) =>= inverse (inverse ?3605) [3606, 3605] by Super 482 with 1717 at 1,1,1,2
+Id : 1824, {_}: multiply (inverse (inverse (inverse (inverse (divide ?3605 ?3606))))) ?3606 =>= inverse (inverse ?3605) [3606, 3605] by Demod 1782 with 29 at 2
+Id : 1825, {_}: multiply (divide ?3605 ?3606) ?3606 =>= inverse (inverse ?3605) [3606, 3605] by Demod 1824 with 1559 at 1,2
+Id : 1854, {_}: inverse (inverse ?3731) =<= divide (divide ?3731 (inverse (inverse (inverse ?3732)))) ?3732 [3732, 3731] by Super 1611 with 1825 at 2
+Id : 2675, {_}: inverse (inverse ?6008) =<= divide (multiply ?6008 (inverse (inverse ?6009))) ?6009 [6009, 6008] by Demod 1854 with 29 at 1,3
+Id : 224, {_}: multiply (inverse (inverse (divide ?518 ?518))) ?519 =>= inverse (inverse ?519) [519, 518] by Super 32 with 36 at 1,2
+Id : 2701, {_}: inverse (inverse (inverse (inverse (divide ?6099 ?6099)))) =?= divide (inverse (inverse (inverse (inverse ?6100)))) ?6100 [6100, 6099] by Super 2675 with 224 at 1,3
+Id : 2754, {_}: divide ?6099 ?6099 =?= divide (inverse (inverse (inverse (inverse ?6100)))) ?6100 [6100, 6099] by Demod 2701 with 1559 at 2
+Id : 2755, {_}: divide ?6099 ?6099 =?= divide ?6100 ?6100 [6100, 6099] by Demod 2754 with 1559 at 1,3
+Id : 2822, {_}: divide (inverse (divide ?6299 (divide (inverse ?6300) (divide (inverse ?6299) ?6301)))) ?6301 =?= inverse (divide ?6300 (divide ?6302 ?6302)) [6302, 6301, 6300, 6299] by Super 145 with 2755 at 2,1,3
+Id : 30, {_}: divide (inverse (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 2 with 4 at 1,2
+Id : 31, {_}: divide (inverse (divide ?2 (divide ?3 (divide (inverse ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 30 with 4 at 1,2,2,1,1,2
+Id : 2899, {_}: inverse ?6300 =<= inverse (divide ?6300 (divide ?6302 ?6302)) [6302, 6300] by Demod 2822 with 31 at 2
+Id : 2957, {_}: divide ?6663 (divide ?6664 ?6664) =>= inverse (inverse (inverse (inverse ?6663))) [6664, 6663] by Super 1559 with 2899 at 1,1,1,3
+Id : 3011, {_}: divide ?6663 (divide ?6664 ?6664) =>= ?6663 [6664, 6663] by Demod 2957 with 1559 at 3
+Id : 3087, {_}: divide (inverse (divide ?6934 ?6935)) (divide ?6936 ?6936) =>= inverse (inverse (multiply ?6935 (inverse ?6934))) [6936, 6935, 6934] by Super 250 with 3011 at 2,1,1,3
+Id : 3149, {_}: inverse (divide ?6934 ?6935) =<= inverse (inverse (multiply ?6935 (inverse ?6934))) [6935, 6934] by Demod 3087 with 3011 at 2
+Id : 3445, {_}: inverse (divide ?7675 ?7676) =<= divide (inverse (inverse ?7676)) ?7675 [7676, 7675] by Demod 3149 with 936 at 3
+Id : 1622, {_}: ?3381 =<= inverse (inverse (inverse (inverse ?3381))) [3381] by Demod 1558 with 482 at 2
+Id : 1636, {_}: multiply ?3417 (inverse ?3418) =<= inverse (inverse (divide (inverse (inverse ?3417)) ?3418)) [3418, 3417] by Super 1622 with 936 at 1,1,3
+Id : 3150, {_}: inverse (divide ?6934 ?6935) =<= divide (inverse (inverse ?6935)) ?6934 [6935, 6934] by Demod 3149 with 936 at 3
+Id : 3402, {_}: multiply ?3417 (inverse ?3418) =<= inverse (inverse (inverse (divide ?3418 ?3417))) [3418, 3417] by Demod 1636 with 3150 at 1,1,3
+Id : 3466, {_}: inverse (divide ?7752 (inverse (divide ?7753 ?7754))) =>= divide (multiply ?7754 (inverse ?7753)) ?7752 [7754, 7753, 7752] by Super 3445 with 3402 at 1,3
+Id : 3559, {_}: inverse (multiply ?7752 (divide ?7753 ?7754)) =<= divide (multiply ?7754 (inverse ?7753)) ?7752 [7754, 7753, 7752] by Demod 3466 with 29 at 1,2
+Id : 229, {_}: inverse ?541 =<= divide (inverse (divide ?542 ?542)) ?541 [542, 541] by Super 35 with 4 at 1,3
+Id : 236, {_}: inverse ?562 =<= divide (inverse (inverse (inverse (divide ?563 ?563)))) ?562 [563, 562] by Super 229 with 36 at 1,1,3
+Id : 3400, {_}: inverse ?562 =<= inverse (divide ?562 (inverse (divide ?563 ?563))) [563, 562] by Demod 236 with 3150 at 3
+Id : 3405, {_}: inverse ?562 =<= inverse (multiply ?562 (divide ?563 ?563)) [563, 562] by Demod 3400 with 29 at 1,3
+Id : 3088, {_}: multiply ?6938 (divide ?6939 ?6939) =>= inverse (inverse ?6938) [6939, 6938] by Super 1825 with 3011 at 1,2
+Id : 3773, {_}: inverse ?562 =<= inverse (inverse (inverse ?562)) [562] by Demod 3405 with 3088 at 1,3
+Id : 3776, {_}: multiply ?3343 (inverse ?3344) =>= divide ?3343 ?3344 [3344, 3343] by Demod 1611 with 3773 at 2,2
+Id : 4266, {_}: inverse (multiply ?8883 (divide ?8884 ?8885)) =>= divide (divide ?8885 ?8884) ?8883 [8885, 8884, 8883] by Demod 3559 with 3776 at 1,3
+Id : 3463, {_}: inverse (divide ?7741 (inverse (inverse ?7742))) =>= divide ?7742 ?7741 [7742, 7741] by Super 3445 with 1559 at 1,3
+Id : 3558, {_}: inverse (multiply ?7741 (inverse ?7742)) =>= divide ?7742 ?7741 [7742, 7741] by Demod 3463 with 29 at 1,2
+Id : 3777, {_}: inverse (divide ?7741 ?7742) =>= divide ?7742 ?7741 [7742, 7741] by Demod 3558 with 3776 at 1,2
+Id : 3787, {_}: divide (divide ?527 ?526) ?528 =<= inverse (inverse (multiply ?527 (divide (inverse ?526) ?528))) [528, 526, 527] by Demod 250 with 3777 at 1,2
+Id : 3399, {_}: inverse (divide ?50 (multiply ?49 ?50)) =>= ?49 [49, 50] by Demod 482 with 3150 at 2
+Id : 3783, {_}: divide (multiply ?49 ?50) ?50 =>= ?49 [50, 49] by Demod 3399 with 3777 at 2
+Id : 1860, {_}: multiply (divide ?3752 ?3753) ?3753 =>= inverse (inverse ?3752) [3753, 3752] by Demod 1824 with 1559 at 1,2
+Id : 1869, {_}: multiply (multiply ?3781 ?3782) (inverse ?3782) =>= inverse (inverse ?3781) [3782, 3781] by Super 1860 with 29 at 1,2
+Id : 3779, {_}: divide (multiply ?3781 ?3782) ?3782 =>= inverse (inverse ?3781) [3782, 3781] by Demod 1869 with 3776 at 2
+Id : 3799, {_}: inverse (inverse ?49) =>= ?49 [49] by Demod 3783 with 3779 at 2
+Id : 3800, {_}: divide (divide ?527 ?526) ?528 =<= multiply ?527 (divide (inverse ?526) ?528) [528, 526, 527] by Demod 3787 with 3799 at 3
+Id : 4296, {_}: inverse (divide (divide ?9013 ?9014) ?9015) =<= divide (divide ?9015 (inverse ?9014)) ?9013 [9015, 9014, 9013] by Super 4266 with 3800 at 1,2
+Id : 4346, {_}: divide ?9015 (divide ?9013 ?9014) =<= divide (divide ?9015 (inverse ?9014)) ?9013 [9014, 9013, 9015] by Demod 4296 with 3777 at 2
+Id : 4347, {_}: divide ?9015 (divide ?9013 ?9014) =<= divide (multiply ?9015 ?9014) ?9013 [9014, 9013, 9015] by Demod 4346 with 29 at 1,3
+Id : 4244, {_}: inverse (multiply ?7752 (divide ?7753 ?7754)) =>= divide (divide ?7754 ?7753) ?7752 [7754, 7753, 7752] by Demod 3559 with 3776 at 1,3
+Id : 4262, {_}: inverse (divide (divide ?8865 ?8866) ?8867) =>= multiply ?8867 (divide ?8866 ?8865) [8867, 8866, 8865] by Super 3799 with 4244 at 1,2
+Id : 4303, {_}: divide ?8867 (divide ?8865 ?8866) =>= multiply ?8867 (divide ?8866 ?8865) [8866, 8865, 8867] by Demod 4262 with 3777 at 2
+Id : 4889, {_}: multiply ?9015 (divide ?9014 ?9013) =<= divide (multiply ?9015 ?9014) ?9013 [9013, 9014, 9015] by Demod 4347 with 4303 at 2
+Id : 4905, {_}: multiply (multiply ?10384 ?10385) ?10386 =<= multiply ?10384 (divide ?10385 (inverse ?10386)) [10386, 10385, 10384] by Super 29 with 4889 at 3
+Id : 4955, {_}: multiply (multiply ?10384 ?10385) ?10386 =>= multiply ?10384 (multiply ?10385 ?10386) [10386, 10385, 10384] by Demod 4905 with 29 at 2,3
+Id : 5096, {_}: multiply a3 (multiply b3 c3) =?= multiply a3 (multiply b3 c3) [] by Demod 1 with 4955 at 2
+Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3
+% SZS output end CNFRefutation for GRP453-1.p
+26321: solved GRP453-1.p in 1.372085 using kbo
+26321: status Unsatisfiable for GRP453-1.p
+Fatal error: exception Assert_failure("matitaprover.ml", 269, 46)
+NO CLASH, using fixed ground order
+26331: Facts:
+26331: Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3
+26331: Id : 3, {_}:
+ meet ?5 (join ?6 ?7) =<= join (meet ?7 ?5) (meet ?6 ?5)
+ [7, 6, 5] by distribution ?5 ?6 ?7
+26331: Goal:
+26331: Id : 1, {_}:
+ join (join a b) c =>= join a (join b c)
+ [] by prove_associativity_of_join
+26331: Order:
+26331: nrkbo
+26331: Leaf order:
+26331: a 2 0 2 1,1,2
+26331: b 2 0 2 2,1,2
+26331: c 2 0 2 2,2
+26331: meet 4 2 0
+26331: join 7 2 4 0,2
+NO CLASH, using fixed ground order
+26332: Facts:
+26332: Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3
+26332: Id : 3, {_}:
+ meet ?5 (join ?6 ?7) =<= join (meet ?7 ?5) (meet ?6 ?5)
+ [7, 6, 5] by distribution ?5 ?6 ?7
+26332: Goal:
+26332: Id : 1, {_}:
+ join (join a b) c =>= join a (join b c)
+ [] by prove_associativity_of_join
+26332: Order:
+26332: kbo
+26332: Leaf order:
+26332: a 2 0 2 1,1,2
+26332: b 2 0 2 2,1,2
+26332: c 2 0 2 2,2
+26332: meet 4 2 0
+26332: join 7 2 4 0,2
+NO CLASH, using fixed ground order
+26333: Facts:
+26333: Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3
+26333: Id : 3, {_}:
+ meet ?5 (join ?6 ?7) =?= join (meet ?7 ?5) (meet ?6 ?5)
+ [7, 6, 5] by distribution ?5 ?6 ?7
+26333: Goal:
+26333: Id : 1, {_}:
+ join (join a b) c =>= join a (join b c)
+ [] by prove_associativity_of_join
+26333: Order:
+26333: lpo
+26333: Leaf order:
+26333: a 2 0 2 1,1,2
+26333: b 2 0 2 2,1,2
+26333: c 2 0 2 2,2
+26333: meet 4 2 0
+26333: join 7 2 4 0,2
+Statistics :
+Max weight : 31
+Found proof, 28.344880s
+% SZS status Unsatisfiable for LAT007-1.p
+% SZS output start CNFRefutation for LAT007-1.p
+Id : 3, {_}: meet ?5 (join ?6 ?7) =<= join (meet ?7 ?5) (meet ?6 ?5) [7, 6, 5] by distribution ?5 ?6 ?7
+Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3
+Id : 7, {_}: meet ?18 (join ?19 ?20) =<= join (meet ?20 ?18) (meet ?19 ?18) [20, 19, 18] by distribution ?18 ?19 ?20
+Id : 8, {_}: meet (join ?22 ?23) (join ?22 ?24) =<= join (meet ?24 (join ?22 ?23)) ?22 [24, 23, 22] by Super 7 with 2 at 2,3
+Id : 13, {_}: meet (meet ?44 ?45) (meet ?45 (join ?46 ?44)) =>= meet ?44 ?45 [46, 45, 44] by Super 2 with 3 at 2,2
+Id : 15, {_}: meet (meet ?53 ?54) ?54 =>= meet ?53 ?54 [54, 53] by Super 13 with 2 at 2,2
+Id : 21, {_}: meet ?68 (join (meet ?69 ?68) ?70) =<= join (meet ?70 ?68) (meet ?69 ?68) [70, 69, 68] by Super 3 with 15 at 2,3
+Id : 69, {_}: meet ?209 (join (meet ?210 ?209) ?211) =>= meet ?209 (join ?210 ?211) [211, 210, 209] by Demod 21 with 3 at 3
+Id : 74, {_}: meet ?231 (meet ?231 (join ?232 ?233)) =<= meet ?231 (join ?233 (meet ?232 ?231)) [233, 232, 231] by Super 69 with 3 at 2,2
+Id : 22, {_}: meet ?72 (join ?73 (meet ?74 ?72)) =<= join (meet ?74 ?72) (meet ?73 ?72) [74, 73, 72] by Super 3 with 15 at 1,3
+Id : 33, {_}: meet ?72 (join ?73 (meet ?74 ?72)) =>= meet ?72 (join ?73 ?74) [74, 73, 72] by Demod 22 with 3 at 3
+Id : 219, {_}: meet ?572 (meet ?572 (join ?573 ?574)) =>= meet ?572 (join ?574 ?573) [574, 573, 572] by Demod 74 with 33 at 3
+Id : 224, {_}: meet ?597 ?597 =<= meet ?597 (join ?598 ?597) [598, 597] by Super 219 with 2 at 2,2
+Id : 244, {_}: meet (join ?635 ?636) (join ?635 ?636) =>= join (meet ?636 ?636) ?635 [636, 635] by Super 8 with 224 at 1,3
+Id : 247, {_}: meet ?644 ?644 =>= ?644 [644] by Super 2 with 224 at 2
+Id : 1803, {_}: join ?635 ?636 =<= join (meet ?636 ?636) ?635 [636, 635] by Demod 244 with 247 at 2
+Id : 1804, {_}: join ?635 ?636 =?= join ?636 ?635 [636, 635] by Demod 1803 with 247 at 1,3
+Id : 9, {_}: meet (join ?26 ?27) (join ?28 ?26) =<= join ?26 (meet ?28 (join ?26 ?27)) [28, 27, 26] by Super 7 with 2 at 1,3
+Id : 6, {_}: meet (meet ?14 ?15) (meet ?15 (join ?16 ?14)) =>= meet ?14 ?15 [16, 15, 14] by Super 2 with 3 at 2,2
+Id : 11, {_}: meet (meet ?34 (join ?35 ?36)) (join (meet ?36 ?34) ?37) =<= join (meet ?37 (meet ?34 (join ?35 ?36))) (meet ?36 ?34) [37, 36, 35, 34] by Super 3 with 6 at 2,3
+Id : 364, {_}: meet (meet ?919 (join ?920 ?919)) (join (meet ?919 ?919) ?921) =>= join (meet ?921 (meet ?919 (join ?920 ?919))) ?919 [921, 920, 919] by Super 11 with 247 at 2,3
+Id : 349, {_}: ?597 =<= meet ?597 (join ?598 ?597) [598, 597] by Demod 224 with 247 at 2
+Id : 370, {_}: meet ?919 (join (meet ?919 ?919) ?921) =<= join (meet ?921 (meet ?919 (join ?920 ?919))) ?919 [920, 921, 919] by Demod 364 with 349 at 1,2
+Id : 371, {_}: meet ?919 (join ?919 ?921) =<= join (meet ?921 (meet ?919 (join ?920 ?919))) ?919 [920, 921, 919] by Demod 370 with 247 at 1,2,2
+Id : 372, {_}: meet ?919 (join ?919 ?921) =<= join (meet ?921 ?919) ?919 [921, 919] by Demod 371 with 349 at 2,1,3
+Id : 411, {_}: ?977 =<= join (meet ?978 ?977) ?977 [978, 977] by Demod 372 with 2 at 2
+Id : 420, {_}: join ?1006 ?1007 =<= join ?1007 (join ?1006 ?1007) [1007, 1006] by Super 411 with 349 at 1,3
+Id : 703, {_}: meet (join ?1582 (join ?1583 ?1582)) (join ?1584 ?1582) =>= join ?1582 (meet ?1584 (join ?1583 ?1582)) [1584, 1583, 1582] by Super 9 with 420 at 2,2,3
+Id : 2541, {_}: meet (join ?5116 ?5117) (join ?5118 ?5117) =<= join ?5117 (meet ?5118 (join ?5116 ?5117)) [5118, 5117, 5116] by Demod 703 with 420 at 1,2
+Id : 419, {_}: ?1004 =<= join ?1004 ?1004 [1004] by Super 411 with 247 at 1,3
+Id : 446, {_}: meet ?1028 (join ?1029 ?1029) =>= meet ?1029 ?1028 [1029, 1028] by Super 3 with 419 at 3
+Id : 462, {_}: meet ?1028 ?1029 =?= meet ?1029 ?1028 [1029, 1028] by Demod 446 with 419 at 2,2
+Id : 2566, {_}: meet (join ?5222 ?5223) (join ?5224 ?5223) =<= join ?5223 (meet (join ?5222 ?5223) ?5224) [5224, 5223, 5222] by Super 2541 with 462 at 2,3
+Id : 1841, {_}: meet (join ?3986 ?3987) (join ?3988 ?3986) =<= join ?3986 (meet ?3988 (join ?3987 ?3986)) [3988, 3987, 3986] by Super 9 with 1804 at 2,2,3
+Id : 731, {_}: meet (join ?1583 ?1582) (join ?1584 ?1582) =<= join ?1582 (meet ?1584 (join ?1583 ?1582)) [1584, 1582, 1583] by Demod 703 with 420 at 1,2
+Id : 6413, {_}: meet (join ?3986 ?3987) (join ?3988 ?3986) =?= meet (join ?3987 ?3986) (join ?3988 ?3986) [3988, 3987, 3986] by Demod 1841 with 731 at 3
+Id : 210, {_}: meet ?231 (meet ?231 (join ?232 ?233)) =>= meet ?231 (join ?233 ?232) [233, 232, 231] by Demod 74 with 33 at 3
+Id : 449, {_}: meet ?1037 (meet ?1037 ?1038) =?= meet ?1037 (join ?1038 ?1038) [1038, 1037] by Super 210 with 419 at 2,2,2
+Id : 457, {_}: meet ?1037 (meet ?1037 ?1038) =>= meet ?1037 ?1038 [1038, 1037] by Demod 449 with 419 at 2,3
+Id : 754, {_}: meet ?231 (join ?232 ?233) =?= meet ?231 (join ?233 ?232) [233, 232, 231] by Demod 210 with 457 at 2
+Id : 32, {_}: meet ?68 (join (meet ?69 ?68) ?70) =>= meet ?68 (join ?69 ?70) [70, 69, 68] by Demod 21 with 3 at 3
+Id : 763, {_}: meet (meet ?1697 ?1698) (join (meet ?1697 ?1698) ?1699) =>= meet (meet ?1697 ?1698) (join ?1697 ?1699) [1699, 1698, 1697] by Super 32 with 457 at 1,2,2
+Id : 793, {_}: meet ?1697 ?1698 =<= meet (meet ?1697 ?1698) (join ?1697 ?1699) [1699, 1698, 1697] by Demod 763 with 2 at 2
+Id : 2682, {_}: meet (join ?5359 ?5360) (join ?5361 (meet ?5359 ?5362)) =<= join (meet ?5359 ?5362) (meet ?5361 (join ?5359 ?5360)) [5362, 5361, 5360, 5359] by Super 3 with 793 at 1,3
+Id : 1421, {_}: meet ?2943 (join ?2944 (meet ?2943 ?2945)) =>= meet ?2943 (join ?2944 ?2945) [2945, 2944, 2943] by Super 33 with 462 at 2,2,2
+Id : 4338, {_}: meet (join ?8616 (meet ?8617 ?8618)) (join ?8616 ?8617) =>= join (meet ?8617 (join ?8616 ?8618)) ?8616 [8618, 8617, 8616] by Super 8 with 1421 at 1,3
+Id : 4448, {_}: meet (join ?8616 (meet ?8617 ?8618)) (join ?8616 ?8617) =>= meet (join ?8616 ?8618) (join ?8616 ?8617) [8618, 8617, 8616] by Demod 4338 with 8 at 3
+Id : 62692, {_}: meet (join ?135834 ?135835) (join (join ?135834 (meet ?135835 ?135836)) (meet ?135834 ?135837)) =>= join (meet ?135834 ?135837) (meet (join ?135834 ?135836) (join ?135834 ?135835)) [135837, 135836, 135835, 135834] by Super 2682 with 4448 at 2,3
+Id : 62942, {_}: meet (join ?135834 ?135835) (join (meet ?135834 ?135837) (join ?135834 (meet ?135835 ?135836))) =>= join (meet ?135834 ?135837) (meet (join ?135834 ?135836) (join ?135834 ?135835)) [135836, 135837, 135835, 135834] by Demod 62692 with 754 at 2
+Id : 62943, {_}: meet (join ?135834 ?135835) (join (meet ?135834 ?135837) (join ?135834 (meet ?135835 ?135836))) =>= meet (join ?135834 ?135835) (join (join ?135834 ?135836) (meet ?135834 ?135837)) [135836, 135837, 135835, 135834] by Demod 62942 with 2682 at 3
+Id : 373, {_}: ?919 =<= join (meet ?921 ?919) ?919 [921, 919] by Demod 372 with 2 at 2
+Id : 2674, {_}: join ?5321 ?5322 =<= join (meet ?5321 ?5323) (join ?5321 ?5322) [5323, 5322, 5321] by Super 373 with 793 at 1,3
+Id : 62944, {_}: meet (join ?135834 ?135835) (join ?135834 (meet ?135835 ?135836)) =?= meet (join ?135834 ?135835) (join (join ?135834 ?135836) (meet ?135834 ?135837)) [135837, 135836, 135835, 135834] by Demod 62943 with 2674 at 2,2
+Id : 62945, {_}: meet (join ?135834 ?135835) (join ?135834 (meet ?135835 ?135836)) =?= meet (join ?135834 ?135835) (join (meet ?135834 ?135837) (join ?135834 ?135836)) [135837, 135836, 135835, 135834] by Demod 62944 with 754 at 3
+Id : 762, {_}: meet (meet ?1693 ?1694) (meet (meet ?1693 ?1694) (join ?1695 ?1693)) =>= meet ?1693 (meet ?1693 ?1694) [1695, 1694, 1693] by Super 6 with 457 at 1,2
+Id : 794, {_}: meet (meet ?1693 ?1694) (join ?1695 ?1693) =>= meet ?1693 (meet ?1693 ?1694) [1695, 1694, 1693] by Demod 762 with 457 at 2
+Id : 795, {_}: meet (meet ?1693 ?1694) (join ?1695 ?1693) =>= meet ?1693 ?1694 [1695, 1694, 1693] by Demod 794 with 457 at 3
+Id : 2860, {_}: meet (join ?5717 ?5718) (join ?5717 (meet ?5718 ?5719)) =>= join (meet ?5718 ?5719) ?5717 [5719, 5718, 5717] by Super 8 with 795 at 1,3
+Id : 62946, {_}: join (meet ?135835 ?135836) ?135834 =<= meet (join ?135834 ?135835) (join (meet ?135834 ?135837) (join ?135834 ?135836)) [135837, 135834, 135836, 135835] by Demod 62945 with 2860 at 2
+Id : 62947, {_}: join (meet ?135835 ?135836) ?135834 =<= meet (join ?135834 ?135835) (join ?135834 ?135836) [135834, 135836, 135835] by Demod 62946 with 2674 at 2,3
+Id : 63610, {_}: meet (join ?137323 ?137324) (join ?137325 ?137323) =>= join (meet ?137324 ?137325) ?137323 [137325, 137324, 137323] by Super 754 with 62947 at 3
+Id : 64209, {_}: join (meet ?3987 ?3988) ?3986 =<= meet (join ?3987 ?3986) (join ?3988 ?3986) [3986, 3988, 3987] by Demod 6413 with 63610 at 2
+Id : 64222, {_}: join (meet ?5222 ?5224) ?5223 =<= join ?5223 (meet (join ?5222 ?5223) ?5224) [5223, 5224, 5222] by Demod 2566 with 64209 at 2
+Id : 64386, {_}: join (meet ?139191 (join ?139192 ?139191)) ?139193 =?= join ?139193 (join (meet ?139193 ?139192) ?139191) [139193, 139192, 139191] by Super 64222 with 63610 at 2,3
+Id : 66054, {_}: join ?143110 ?143111 =<= join ?143111 (join (meet ?143111 ?143112) ?143110) [143112, 143111, 143110] by Demod 64386 with 349 at 1,2
+Id : 36, {_}: meet (join ?109 ?110) (join ?109 ?111) =<= join (meet ?111 (join ?109 ?110)) ?109 [111, 110, 109] by Super 7 with 2 at 2,3
+Id : 39, {_}: meet (join ?123 ?124) (join ?123 ?123) =>= join ?123 ?123 [124, 123] by Super 36 with 2 at 1,3
+Id : 438, {_}: meet (join ?123 ?124) ?123 =>= join ?123 ?123 [124, 123] by Demod 39 with 419 at 2,2
+Id : 439, {_}: meet (join ?123 ?124) ?123 =>= ?123 [124, 123] by Demod 438 with 419 at 3
+Id : 66061, {_}: join ?143140 (join ?143141 ?143142) =<= join (join ?143141 ?143142) (join ?143141 ?143140) [143142, 143141, 143140] by Super 66054 with 439 at 1,2,3
+Id : 706, {_}: meet (join ?1593 (join ?1594 ?1593)) (join ?1593 ?1595) =>= join (meet ?1595 (join ?1594 ?1593)) ?1593 [1595, 1594, 1593] by Super 8 with 420 at 2,1,3
+Id : 2402, {_}: meet (join ?4835 ?4836) (join ?4836 ?4837) =<= join (meet ?4837 (join ?4835 ?4836)) ?4836 [4837, 4836, 4835] by Demod 706 with 420 at 1,2
+Id : 2426, {_}: meet (join ?4936 ?4937) (join ?4937 ?4938) =<= join (meet (join ?4936 ?4937) ?4938) ?4937 [4938, 4937, 4936] by Super 2402 with 462 at 1,3
+Id : 1831, {_}: meet (join ?3948 ?3949) (join ?3948 ?3950) =<= join (meet ?3950 (join ?3949 ?3948)) ?3948 [3950, 3949, 3948] by Super 8 with 1804 at 2,1,3
+Id : 729, {_}: meet (join ?1594 ?1593) (join ?1593 ?1595) =<= join (meet ?1595 (join ?1594 ?1593)) ?1593 [1595, 1593, 1594] by Demod 706 with 420 at 1,2
+Id : 5899, {_}: meet (join ?3948 ?3949) (join ?3948 ?3950) =?= meet (join ?3949 ?3948) (join ?3948 ?3950) [3950, 3949, 3948] by Demod 1831 with 729 at 3
+Id : 63510, {_}: join (meet ?3949 ?3950) ?3948 =<= meet (join ?3949 ?3948) (join ?3948 ?3950) [3948, 3950, 3949] by Demod 5899 with 62947 at 2
+Id : 63518, {_}: join (meet ?4936 ?4938) ?4937 =<= join (meet (join ?4936 ?4937) ?4938) ?4937 [4937, 4938, 4936] by Demod 2426 with 63510 at 2
+Id : 63690, {_}: join (meet ?137703 (join ?137703 ?137704)) ?137705 =?= join (join (meet ?137705 ?137704) ?137703) ?137705 [137705, 137704, 137703] by Super 63518 with 62947 at 1,3
+Id : 65015, {_}: join ?140539 ?140540 =<= join (join (meet ?140540 ?140541) ?140539) ?140540 [140541, 140540, 140539] by Demod 63690 with 2 at 1,2
+Id : 65022, {_}: join ?140569 (join ?140570 ?140571) =<= join (join ?140570 ?140569) (join ?140570 ?140571) [140571, 140570, 140569] by Super 65015 with 439 at 1,1,3
+Id : 71034, {_}: join ?143140 (join ?143141 ?143142) =?= join ?143142 (join ?143141 ?143140) [143142, 143141, 143140] by Demod 66061 with 65022 at 3
+Id : 709, {_}: meet (join ?1606 ?1607) ?1607 =>= ?1607 [1607, 1606] by Super 439 with 420 at 1,2
+Id : 1049, {_}: meet ?2275 (join ?2275 ?2276) =<= meet ?2275 (join (join ?2277 ?2275) ?2276) [2277, 2276, 2275] by Super 32 with 709 at 1,2,2
+Id : 1082, {_}: ?2275 =<= meet ?2275 (join (join ?2277 ?2275) ?2276) [2276, 2277, 2275] by Demod 1049 with 2 at 2
+Id : 10434, {_}: join (join ?21238 ?21239) ?21240 =<= join ?21239 (join (join ?21238 ?21239) ?21240) [21240, 21239, 21238] by Super 373 with 1082 at 1,3
+Id : 10435, {_}: join (join ?21242 ?21243) ?21244 =<= join ?21243 (join (join ?21243 ?21242) ?21244) [21244, 21243, 21242] by Super 10434 with 1804 at 1,2,3
+Id : 7878, {_}: join ?15712 ?15713 =<= join (meet ?15712 ?15714) (join ?15712 ?15713) [15714, 15713, 15712] by Super 373 with 793 at 1,3
+Id : 7917, {_}: join (join ?15885 ?15886) ?15887 =<= join ?15885 (join (join ?15885 ?15886) ?15887) [15887, 15886, 15885] by Super 7878 with 439 at 1,3
+Id : 21540, {_}: join (join ?21242 ?21243) ?21244 =?= join (join ?21243 ?21242) ?21244 [21244, 21243, 21242] by Demod 10435 with 7917 at 3
+Id : 63854, {_}: join ?137703 ?137705 =<= join (join (meet ?137705 ?137704) ?137703) ?137705 [137704, 137705, 137703] by Demod 63690 with 2 at 1,2
+Id : 67172, {_}: join (join ?145721 (meet ?145722 ?145723)) ?145722 =>= join ?145721 ?145722 [145723, 145722, 145721] by Super 21540 with 63854 at 3
+Id : 67179, {_}: join (join ?145751 ?145752) (join ?145752 ?145753) =>= join ?145751 (join ?145752 ?145753) [145753, 145752, 145751] by Super 67172 with 439 at 2,1,2
+Id : 66065, {_}: join ?143156 (join ?143157 ?143158) =<= join (join ?143157 ?143158) (join ?143158 ?143156) [143158, 143157, 143156] by Super 66054 with 709 at 1,2,3
+Id : 73159, {_}: join ?145753 (join ?145751 ?145752) =?= join ?145751 (join ?145752 ?145753) [145752, 145751, 145753] by Demod 67179 with 66065 at 2
+Id : 359, {_}: meet ?904 (join ?905 ?904) =<= join ?904 (meet ?905 ?904) [905, 904] by Super 3 with 247 at 1,3
+Id : 386, {_}: ?904 =<= join ?904 (meet ?905 ?904) [905, 904] by Demod 359 with 349 at 2
+Id : 1047, {_}: meet ?2267 (meet ?2267 (join ?2268 (join ?2269 ?2267))) =>= meet (join ?2269 ?2267) ?2267 [2269, 2268, 2267] by Super 6 with 709 at 1,2
+Id : 1084, {_}: meet ?2267 (join ?2268 (join ?2269 ?2267)) =>= meet (join ?2269 ?2267) ?2267 [2269, 2268, 2267] by Demod 1047 with 457 at 2
+Id : 1085, {_}: meet ?2267 (join ?2268 (join ?2269 ?2267)) =>= ?2267 [2269, 2268, 2267] by Demod 1084 with 709 at 3
+Id : 11489, {_}: join ?23526 (join ?23527 ?23528) =<= join (join ?23526 (join ?23527 ?23528)) ?23528 [23528, 23527, 23526] by Super 386 with 1085 at 2,3
+Id : 11490, {_}: join ?23530 (join ?23531 ?23532) =<= join (join ?23530 (join ?23532 ?23531)) ?23532 [23532, 23531, 23530] by Super 11489 with 1804 at 2,1,3
+Id : 2878, {_}: meet (meet ?5800 ?5801) (join ?5802 ?5800) =>= meet ?5800 ?5801 [5802, 5801, 5800] by Demod 794 with 457 at 3
+Id : 2907, {_}: meet ?5929 (join ?5930 (join ?5929 ?5931)) =>= meet (join ?5929 ?5931) ?5929 [5931, 5930, 5929] by Super 2878 with 439 at 1,2
+Id : 3014, {_}: meet ?5929 (join ?5930 (join ?5929 ?5931)) =>= ?5929 [5931, 5930, 5929] by Demod 2907 with 439 at 3
+Id : 10163, {_}: join ?20474 (join ?20475 ?20476) =<= join (join ?20474 (join ?20475 ?20476)) ?20475 [20476, 20475, 20474] by Super 386 with 3014 at 2,3
+Id : 22205, {_}: join ?23530 (join ?23531 ?23532) =?= join ?23530 (join ?23532 ?23531) [23532, 23531, 23530] by Demod 11490 with 10163 at 3
+Id : 73995, {_}: join a (join b c) === join a (join b c) [] by Demod 73994 with 22205 at 2
+Id : 73994, {_}: join a (join c b) =>= join a (join b c) [] by Demod 73993 with 73159 at 2
+Id : 73993, {_}: join b (join a c) =>= join a (join b c) [] by Demod 73992 with 71034 at 2
+Id : 73992, {_}: join c (join a b) =>= join a (join b c) [] by Demod 1 with 1804 at 2
+Id : 1, {_}: join (join a b) c =>= join a (join b c) [] by prove_associativity_of_join
+% SZS output end CNFRefutation for LAT007-1.p
+26331: solved LAT007-1.p in 28.241764 using nrkbo
+26331: status Unsatisfiable for LAT007-1.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+26339: Facts:
+26339: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
+26339: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
+26339: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
+26339: Id : 5, {_}:
+ meet ?9 ?10 =?= meet ?10 ?9
+ [10, 9] by commutativity_of_meet ?9 ?10
+26339: Id : 6, {_}:
+ join ?12 ?13 =?= join ?13 ?12
+ [13, 12] by commutativity_of_join ?12 ?13
+26339: Id : 7, {_}:
+ meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
+ [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
+26339: Id : 8, {_}:
+ join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
+ [21, 20, 19] by associativity_of_join ?19 ?20 ?21
+26339: Id : 9, {_}:
+ complement (complement ?23) =>= ?23
+ [23] by complement_involution ?23
+26339: Id : 10, {_}:
+ join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
+ [26, 25] by join_complement ?25 ?26
+26339: Id : 11, {_}:
+ meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
+ [29, 28] by meet_complement ?28 ?29
+26339: Goal:
+NO CLASH, using fixed ground order
+26340: Facts:
+26340: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
+26340: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
+26340: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
+26340: Id : 5, {_}:
+ meet ?9 ?10 =?= meet ?10 ?9
+ [10, 9] by commutativity_of_meet ?9 ?10
+26340: Id : 6, {_}:
+ join ?12 ?13 =?= join ?13 ?12
+ [13, 12] by commutativity_of_join ?12 ?13
+26340: Id : 7, {_}:
+ meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
+ [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
+26340: Id : 8, {_}:
+ join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
+ [21, 20, 19] by associativity_of_join ?19 ?20 ?21
+26340: Id : 9, {_}:
+ complement (complement ?23) =>= ?23
+ [23] by complement_involution ?23
+26340: Id : 10, {_}:
+ join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
+ [26, 25] by join_complement ?25 ?26
+26340: Id : 11, {_}:
+ meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
+ [29, 28] by meet_complement ?28 ?29
+26340: Goal:
+26338: Facts:
+26340: Id : 1, {_}:
+ join (complement (join (meet a (complement b)) (complement a)))
+ (join (meet a (complement b))
+ (join
+ (meet (complement a) (meet (join a (complement b)) (join a b)))
+ (meet (complement a)
+ (complement (meet (join a (complement b)) (join a b))))))
+ =>=
+ n1
+ [] by prove_e1
+26340: Order:
+26340: lpo
+26340: Leaf order:
+26340: n0 1 0 0
+26340: n1 2 0 1 3
+26340: b 6 0 6 1,2,1,1,1,2
+26340: a 9 0 9 1,1,1,1,2
+26340: complement 18 1 9 0,1,2
+26340: meet 15 2 6 0,1,1,1,2
+26340: join 20 2 8 0,2
+26339: Id : 1, {_}:
+ join (complement (join (meet a (complement b)) (complement a)))
+ (join (meet a (complement b))
+ (join
+ (meet (complement a) (meet (join a (complement b)) (join a b)))
+ (meet (complement a)
+ (complement (meet (join a (complement b)) (join a b))))))
+ =>=
+ n1
+ [] by prove_e1
+26339: Order:
+26339: kbo
+26339: Leaf order:
+26339: n0 1 0 0
+26339: n1 2 0 1 3
+26339: b 6 0 6 1,2,1,1,1,2
+26339: a 9 0 9 1,1,1,1,2
+26339: complement 18 1 9 0,1,2
+26339: meet 15 2 6 0,1,1,1,2
+26339: join 20 2 8 0,2
+26338: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
+26338: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
+26338: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
+26338: Id : 5, {_}:
+ meet ?9 ?10 =?= meet ?10 ?9
+ [10, 9] by commutativity_of_meet ?9 ?10
+26338: Id : 6, {_}:
+ join ?12 ?13 =?= join ?13 ?12
+ [13, 12] by commutativity_of_join ?12 ?13
+26338: Id : 7, {_}:
+ meet (meet ?15 ?16) ?17 =?= meet ?15 (meet ?16 ?17)
+ [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
+26338: Id : 8, {_}:
+ join (join ?19 ?20) ?21 =?= join ?19 (join ?20 ?21)
+ [21, 20, 19] by associativity_of_join ?19 ?20 ?21
+26338: Id : 9, {_}:
+ complement (complement ?23) =>= ?23
+ [23] by complement_involution ?23
+26338: Id : 10, {_}:
+ join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
+ [26, 25] by join_complement ?25 ?26
+26338: Id : 11, {_}:
+ meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
+ [29, 28] by meet_complement ?28 ?29
+26338: Goal:
+26338: Id : 1, {_}:
+ join (complement (join (meet a (complement b)) (complement a)))
+ (join (meet a (complement b))
+ (join
+ (meet (complement a) (meet (join a (complement b)) (join a b)))
+ (meet (complement a)
+ (complement (meet (join a (complement b)) (join a b))))))
+ =>=
+ n1
+ [] by prove_e1
+26338: Order:
+26338: nrkbo
+26338: Leaf order:
+26338: n0 1 0 0
+26338: n1 2 0 1 3
+26338: b 6 0 6 1,2,1,1,1,2
+26338: a 9 0 9 1,1,1,1,2
+26338: complement 18 1 9 0,1,2
+26338: meet 15 2 6 0,1,1,1,2
+26338: join 20 2 8 0,2
+% SZS status Timeout for LAT016-1.p
+NO CLASH, using fixed ground order
+26368: Facts:
+26368: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26368: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26368: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
+26368: Id : 5, {_}:
+ join ?9 ?10 =?= join ?10 ?9
+ [10, 9] by commutativity_of_join ?9 ?10
+26368: Id : 6, {_}:
+ meet (meet ?12 ?13) ?14 =?= meet ?12 (meet ?13 ?14)
+ [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
+26368: Id : 7, {_}:
+ join (join ?16 ?17) ?18 =?= join ?16 (join ?17 ?18)
+ [18, 17, 16] by associativity_of_join ?16 ?17 ?18
+26368: Id : 8, {_}:
+ join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
+ =>=
+ meet ?20 (join ?21 ?22)
+ [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
+26368: Id : 9, {_}:
+ meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
+ =>=
+ join ?24 (meet ?25 ?26)
+ [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
+26368: Id : 10, {_}: meet2 ?28 ?28 =>= ?28 [28] by idempotence_of_meet2 ?28
+26368: Id : 11, {_}:
+ meet2 ?30 ?31 =?= meet2 ?31 ?30
+ [31, 30] by commutativity_of_meet2 ?30 ?31
+26368: Id : 12, {_}:
+ meet2 (meet2 ?33 ?34) ?35 =?= meet2 ?33 (meet2 ?34 ?35)
+ [35, 34, 33] by associativity_of_meet2 ?33 ?34 ?35
+26368: Id : 13, {_}:
+ join (meet2 ?37 (join ?38 ?39)) (meet2 ?37 ?38)
+ =>=
+ meet2 ?37 (join ?38 ?39)
+ [39, 38, 37] by quasi_lattice1_2 ?37 ?38 ?39
+26368: Id : 14, {_}:
+ meet2 (join ?41 (meet2 ?42 ?43)) (join ?41 ?42)
+ =>=
+ join ?41 (meet2 ?42 ?43)
+ [43, 42, 41] by quasi_lattice2_2 ?41 ?42 ?43
+26368: Goal:
+26368: Id : 1, {_}: meet a b =<= meet2 a b [] by prove_meets_equal
+26368: Order:
+26368: nrkbo
+26368: Leaf order:
+26368: a 2 0 2 1,2
+26368: b 2 0 2 2,2
+26368: meet 14 2 1 0,2
+26368: meet2 14 2 1 0,3
+26368: join 19 2 0
+NO CLASH, using fixed ground order
+26369: Facts:
+26369: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26369: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26369: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
+26369: Id : 5, {_}:
+ join ?9 ?10 =?= join ?10 ?9
+ [10, 9] by commutativity_of_join ?9 ?10
+26369: Id : 6, {_}:
+ meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14)
+ [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
+26369: Id : 7, {_}:
+ join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18)
+ [18, 17, 16] by associativity_of_join ?16 ?17 ?18
+26369: Id : 8, {_}:
+ join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
+ =>=
+ meet ?20 (join ?21 ?22)
+ [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
+26369: Id : 9, {_}:
+ meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
+ =>=
+ join ?24 (meet ?25 ?26)
+ [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
+26369: Id : 10, {_}: meet2 ?28 ?28 =>= ?28 [28] by idempotence_of_meet2 ?28
+26369: Id : 11, {_}:
+ meet2 ?30 ?31 =?= meet2 ?31 ?30
+ [31, 30] by commutativity_of_meet2 ?30 ?31
+26369: Id : 12, {_}:
+ meet2 (meet2 ?33 ?34) ?35 =>= meet2 ?33 (meet2 ?34 ?35)
+ [35, 34, 33] by associativity_of_meet2 ?33 ?34 ?35
+26369: Id : 13, {_}:
+ join (meet2 ?37 (join ?38 ?39)) (meet2 ?37 ?38)
+ =>=
+ meet2 ?37 (join ?38 ?39)
+ [39, 38, 37] by quasi_lattice1_2 ?37 ?38 ?39
+26369: Id : 14, {_}:
+ meet2 (join ?41 (meet2 ?42 ?43)) (join ?41 ?42)
+ =>=
+ join ?41 (meet2 ?42 ?43)
+ [43, 42, 41] by quasi_lattice2_2 ?41 ?42 ?43
+26369: Goal:
+26369: Id : 1, {_}: meet a b =<= meet2 a b [] by prove_meets_equal
+26369: Order:
+26369: kbo
+26369: Leaf order:
+26369: a 2 0 2 1,2
+26369: b 2 0 2 2,2
+26369: meet 14 2 1 0,2
+26369: meet2 14 2 1 0,3
+26369: join 19 2 0
+NO CLASH, using fixed ground order
+26370: Facts:
+26370: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26370: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26370: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
+26370: Id : 5, {_}:
+ join ?9 ?10 =?= join ?10 ?9
+ [10, 9] by commutativity_of_join ?9 ?10
+26370: Id : 6, {_}:
+ meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14)
+ [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
+26370: Id : 7, {_}:
+ join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18)
+ [18, 17, 16] by associativity_of_join ?16 ?17 ?18
+26370: Id : 8, {_}:
+ join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
+ =>=
+ meet ?20 (join ?21 ?22)
+ [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
+26370: Id : 9, {_}:
+ meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
+ =>=
+ join ?24 (meet ?25 ?26)
+ [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
+26370: Id : 10, {_}: meet2 ?28 ?28 =>= ?28 [28] by idempotence_of_meet2 ?28
+26370: Id : 11, {_}:
+ meet2 ?30 ?31 =?= meet2 ?31 ?30
+ [31, 30] by commutativity_of_meet2 ?30 ?31
+26370: Id : 12, {_}:
+ meet2 (meet2 ?33 ?34) ?35 =>= meet2 ?33 (meet2 ?34 ?35)
+ [35, 34, 33] by associativity_of_meet2 ?33 ?34 ?35
+26370: Id : 13, {_}:
+ join (meet2 ?37 (join ?38 ?39)) (meet2 ?37 ?38)
+ =>=
+ meet2 ?37 (join ?38 ?39)
+ [39, 38, 37] by quasi_lattice1_2 ?37 ?38 ?39
+26370: Id : 14, {_}:
+ meet2 (join ?41 (meet2 ?42 ?43)) (join ?41 ?42)
+ =>=
+ join ?41 (meet2 ?42 ?43)
+ [43, 42, 41] by quasi_lattice2_2 ?41 ?42 ?43
+26370: Goal:
+26370: Id : 1, {_}: meet a b =<= meet2 a b [] by prove_meets_equal
+26370: Order:
+26370: lpo
+26370: Leaf order:
+26370: a 2 0 2 1,2
+26370: b 2 0 2 2,2
+26370: meet 14 2 1 0,2
+26370: meet2 14 2 1 0,3
+26370: join 19 2 0
+% SZS status Timeout for LAT024-1.p
+NO CLASH, using fixed ground order
+26386: Facts:
+26386: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26386: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26386: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26386: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26386: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26386: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26386: Id : 8, {_}:
+ join ?18 (meet ?19 (meet ?18 ?20)) =>= ?18
+ [20, 19, 18] by tnl_1 ?18 ?19 ?20
+26386: Id : 9, {_}:
+ meet ?22 (join ?23 (join ?22 ?24)) =>= ?22
+ [24, 23, 22] by tnl_2 ?22 ?23 ?24
+26386: Id : 10, {_}: meet2 ?26 ?26 =>= ?26 [26] by idempotence_of_meet2 ?26
+26386: Id : 11, {_}:
+ meet2 ?28 (join ?28 ?29) =>= ?28
+ [29, 28] by absorption1_2 ?28 ?29
+26386: Id : 12, {_}:
+ join ?31 (meet2 ?31 ?32) =>= ?31
+ [32, 31] by absorption2_2 ?31 ?32
+26386: Id : 13, {_}:
+ meet2 ?34 ?35 =?= meet2 ?35 ?34
+ [35, 34] by commutativity_of_meet2 ?34 ?35
+26386: Id : 14, {_}:
+ join ?37 (meet2 ?38 (meet2 ?37 ?39)) =>= ?37
+ [39, 38, 37] by tnl_1_2 ?37 ?38 ?39
+26386: Id : 15, {_}:
+ meet2 ?41 (join ?42 (join ?41 ?43)) =>= ?41
+ [43, 42, 41] by tnl_2_2 ?41 ?42 ?43
+26386: Goal:
+26386: Id : 1, {_}: meet a b =<= meet2 a b [] by prove_meets_equal
+26386: Order:
+26386: nrkbo
+26386: Leaf order:
+26386: a 2 0 2 1,2
+26386: b 2 0 2 2,2
+26386: meet 9 2 1 0,2
+26386: meet2 9 2 1 0,3
+26386: join 13 2 0
+NO CLASH, using fixed ground order
+26387: Facts:
+26387: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26387: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26387: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26387: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26387: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26387: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26387: Id : 8, {_}:
+ join ?18 (meet ?19 (meet ?18 ?20)) =>= ?18
+ [20, 19, 18] by tnl_1 ?18 ?19 ?20
+26387: Id : 9, {_}:
+ meet ?22 (join ?23 (join ?22 ?24)) =>= ?22
+ [24, 23, 22] by tnl_2 ?22 ?23 ?24
+26387: Id : 10, {_}: meet2 ?26 ?26 =>= ?26 [26] by idempotence_of_meet2 ?26
+26387: Id : 11, {_}:
+ meet2 ?28 (join ?28 ?29) =>= ?28
+ [29, 28] by absorption1_2 ?28 ?29
+26387: Id : 12, {_}:
+ join ?31 (meet2 ?31 ?32) =>= ?31
+ [32, 31] by absorption2_2 ?31 ?32
+26387: Id : 13, {_}:
+ meet2 ?34 ?35 =?= meet2 ?35 ?34
+ [35, 34] by commutativity_of_meet2 ?34 ?35
+26387: Id : 14, {_}:
+ join ?37 (meet2 ?38 (meet2 ?37 ?39)) =>= ?37
+ [39, 38, 37] by tnl_1_2 ?37 ?38 ?39
+NO CLASH, using fixed ground order
+26388: Facts:
+26388: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26388: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26388: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26388: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26388: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26388: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26388: Id : 8, {_}:
+ join ?18 (meet ?19 (meet ?18 ?20)) =>= ?18
+ [20, 19, 18] by tnl_1 ?18 ?19 ?20
+26388: Id : 9, {_}:
+ meet ?22 (join ?23 (join ?22 ?24)) =>= ?22
+ [24, 23, 22] by tnl_2 ?22 ?23 ?24
+26388: Id : 10, {_}: meet2 ?26 ?26 =>= ?26 [26] by idempotence_of_meet2 ?26
+26388: Id : 11, {_}:
+ meet2 ?28 (join ?28 ?29) =>= ?28
+ [29, 28] by absorption1_2 ?28 ?29
+26388: Id : 12, {_}:
+ join ?31 (meet2 ?31 ?32) =>= ?31
+ [32, 31] by absorption2_2 ?31 ?32
+26388: Id : 13, {_}:
+ meet2 ?34 ?35 =?= meet2 ?35 ?34
+ [35, 34] by commutativity_of_meet2 ?34 ?35
+26388: Id : 14, {_}:
+ join ?37 (meet2 ?38 (meet2 ?37 ?39)) =>= ?37
+ [39, 38, 37] by tnl_1_2 ?37 ?38 ?39
+26388: Id : 15, {_}:
+ meet2 ?41 (join ?42 (join ?41 ?43)) =>= ?41
+ [43, 42, 41] by tnl_2_2 ?41 ?42 ?43
+26388: Goal:
+26388: Id : 1, {_}: meet a b =<= meet2 a b [] by prove_meets_equal
+26388: Order:
+26388: lpo
+26388: Leaf order:
+26388: a 2 0 2 1,2
+26388: b 2 0 2 2,2
+26388: meet 9 2 1 0,2
+26388: meet2 9 2 1 0,3
+26388: join 13 2 0
+26387: Id : 15, {_}:
+ meet2 ?41 (join ?42 (join ?41 ?43)) =>= ?41
+ [43, 42, 41] by tnl_2_2 ?41 ?42 ?43
+26387: Goal:
+26387: Id : 1, {_}: meet a b =<= meet2 a b [] by prove_meets_equal
+26387: Order:
+26387: kbo
+26387: Leaf order:
+26387: a 2 0 2 1,2
+26387: b 2 0 2 2,2
+26387: meet 9 2 1 0,2
+26387: meet2 9 2 1 0,3
+26387: join 13 2 0
+% SZS status Timeout for LAT025-1.p
+CLASH, statistics insufficient
+26417: Facts:
+26417: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26417: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26417: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26417: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26417: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26417: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26417: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26417: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26417: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+26417: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+26417: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+26417: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+26417: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+26417: Id : 15, {_}:
+ join ?38 (meet ?39 (join ?38 ?40))
+ =>=
+ meet (join ?38 ?39) (join ?38 ?40)
+ [40, 39, 38] by modular_law ?38 ?39 ?40
+26417: Goal:
+26417: Id : 1, {_}:
+ meet a (join b c) =<= join (meet a b) (meet a c)
+ [] by prove_distributivity
+26417: Order:
+26417: nrkbo
+26417: Leaf order:
+26417: n1 1 0 0
+26417: n0 1 0 0
+26417: b 2 0 2 1,2,2
+26417: c 2 0 2 2,2,2
+26417: a 3 0 3 1,2
+26417: complement 10 1 0
+26417: meet 17 2 3 0,2
+26417: join 18 2 2 0,2,2
+CLASH, statistics insufficient
+26418: Facts:
+26418: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26418: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26418: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26418: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26418: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26418: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26418: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26418: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26418: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+26418: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+26418: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+26418: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+26418: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+26418: Id : 15, {_}:
+ join ?38 (meet ?39 (join ?38 ?40))
+ =>=
+ meet (join ?38 ?39) (join ?38 ?40)
+ [40, 39, 38] by modular_law ?38 ?39 ?40
+26418: Goal:
+26418: Id : 1, {_}:
+ meet a (join b c) =<= join (meet a b) (meet a c)
+ [] by prove_distributivity
+26418: Order:
+26418: kbo
+26418: Leaf order:
+26418: n1 1 0 0
+26418: n0 1 0 0
+26418: b 2 0 2 1,2,2
+26418: c 2 0 2 2,2,2
+26418: a 3 0 3 1,2
+26418: complement 10 1 0
+26418: meet 17 2 3 0,2
+26418: join 18 2 2 0,2,2
+CLASH, statistics insufficient
+26419: Facts:
+26419: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26419: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26419: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26419: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26419: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26419: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26419: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26419: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26419: Id : 10, {_}:
+ complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+26419: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+26419: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+26419: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+26419: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+26419: Id : 15, {_}:
+ join ?38 (meet ?39 (join ?38 ?40))
+ =>=
+ meet (join ?38 ?39) (join ?38 ?40)
+ [40, 39, 38] by modular_law ?38 ?39 ?40
+26419: Goal:
+26419: Id : 1, {_}:
+ meet a (join b c) =<= join (meet a b) (meet a c)
+ [] by prove_distributivity
+26419: Order:
+26419: lpo
+26419: Leaf order:
+26419: n1 1 0 0
+26419: n0 1 0 0
+26419: b 2 0 2 1,2,2
+26419: c 2 0 2 2,2,2
+26419: a 3 0 3 1,2
+26419: complement 10 1 0
+26419: meet 17 2 3 0,2
+26419: join 18 2 2 0,2,2
+% SZS status Timeout for LAT046-1.p
+NO CLASH, using fixed ground order
+26436: Facts:
+26436: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26436: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26436: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26436: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26436: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26436: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26436: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26436: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26436: Goal:
+26436: Id : 1, {_}:
+ join a (meet b (join a c)) =>= meet (join a b) (join a c)
+ [] by prove_modularity
+26436: Order:
+26436: nrkbo
+26436: Leaf order:
+26436: b 2 0 2 1,2,2
+26436: c 2 0 2 2,2,2,2
+26436: a 4 0 4 1,2
+26436: meet 11 2 2 0,2,2
+26436: join 13 2 4 0,2
+NO CLASH, using fixed ground order
+26437: Facts:
+26437: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26437: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26437: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26437: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26437: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26437: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26437: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26437: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26437: Goal:
+26437: Id : 1, {_}:
+ join a (meet b (join a c)) =>= meet (join a b) (join a c)
+ [] by prove_modularity
+26437: Order:
+26437: kbo
+26437: Leaf order:
+26437: b 2 0 2 1,2,2
+26437: c 2 0 2 2,2,2,2
+26437: a 4 0 4 1,2
+26437: meet 11 2 2 0,2,2
+26437: join 13 2 4 0,2
+NO CLASH, using fixed ground order
+26438: Facts:
+26438: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26438: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26438: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26438: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26438: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26438: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26438: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26438: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26438: Goal:
+26438: Id : 1, {_}:
+ join a (meet b (join a c)) =>= meet (join a b) (join a c)
+ [] by prove_modularity
+26438: Order:
+26438: lpo
+26438: Leaf order:
+26438: b 2 0 2 1,2,2
+26438: c 2 0 2 2,2,2,2
+26438: a 4 0 4 1,2
+26438: meet 11 2 2 0,2,2
+26438: join 13 2 4 0,2
+% SZS status Timeout for LAT047-1.p
+NO CLASH, using fixed ground order
+26479: Facts:
+26479: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26479: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26479: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26479: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26479: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26479: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26479: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26479: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26479: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+26479: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+26479: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+26479: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+26479: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+26479: Id : 15, {_}:
+ join (meet (complement ?38) (join ?38 ?39))
+ (join (complement ?39) (meet ?38 ?39))
+ =>=
+ n1
+ [39, 38] by weak_orthomodular_law ?38 ?39
+26479: Goal:
+26479: Id : 1, {_}:
+ join a (meet (complement a) (join a b)) =>= join a b
+ [] by prove_orthomodular_law
+26479: Order:
+26479: nrkbo
+26479: Leaf order:
+26479: n0 1 0 0
+26479: n1 2 0 0
+26479: b 2 0 2 2,2,2,2
+26479: a 4 0 4 1,2
+26479: complement 13 1 1 0,1,2,2
+26479: meet 15 2 1 0,2,2
+26479: join 18 2 3 0,2
+NO CLASH, using fixed ground order
+26480: Facts:
+26480: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26480: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26480: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26480: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26480: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26480: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26480: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26480: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26480: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+26480: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+26480: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+26480: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+26480: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+NO CLASH, using fixed ground order
+26481: Facts:
+26481: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26481: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26481: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26481: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26481: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26481: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26481: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26481: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26481: Id : 10, {_}:
+ complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+26481: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+26481: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+26481: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+26481: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+26481: Id : 15, {_}:
+ join (meet (complement ?38) (join ?38 ?39))
+ (join (complement ?39) (meet ?38 ?39))
+ =>=
+ n1
+ [39, 38] by weak_orthomodular_law ?38 ?39
+26481: Goal:
+26481: Id : 1, {_}:
+ join a (meet (complement a) (join a b)) =>= join a b
+ [] by prove_orthomodular_law
+26481: Order:
+26481: lpo
+26481: Leaf order:
+26481: n0 1 0 0
+26481: n1 2 0 0
+26481: b 2 0 2 2,2,2,2
+26481: a 4 0 4 1,2
+26481: complement 13 1 1 0,1,2,2
+26481: meet 15 2 1 0,2,2
+26481: join 18 2 3 0,2
+26480: Id : 15, {_}:
+ join (meet (complement ?38) (join ?38 ?39))
+ (join (complement ?39) (meet ?38 ?39))
+ =>=
+ n1
+ [39, 38] by weak_orthomodular_law ?38 ?39
+26480: Goal:
+26480: Id : 1, {_}:
+ join a (meet (complement a) (join a b)) =>= join a b
+ [] by prove_orthomodular_law
+26480: Order:
+26480: kbo
+26480: Leaf order:
+26480: n0 1 0 0
+26480: n1 2 0 0
+26480: b 2 0 2 2,2,2,2
+26480: a 4 0 4 1,2
+26480: complement 13 1 1 0,1,2,2
+26480: meet 15 2 1 0,2,2
+26480: join 18 2 3 0,2
+% SZS status Timeout for LAT048-1.p
+NO CLASH, using fixed ground order
+26500: Facts:
+26500: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26500: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26500: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26500: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26500: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26500: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26500: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26500: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26500: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+26500: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+26500: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+26500: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+26500: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+26500: Goal:
+26500: Id : 1, {_}:
+ join (meet (complement a) (join a b))
+ (join (complement b) (meet a b))
+ =>=
+ n1
+ [] by prove_weak_orthomodular_law
+26500: Order:
+26500: nrkbo
+26500: Leaf order:
+26500: n0 1 0 0
+26500: n1 2 0 1 3
+26500: a 3 0 3 1,1,1,2
+26500: b 3 0 3 2,2,1,2
+26500: complement 12 1 2 0,1,1,2
+26500: meet 14 2 2 0,1,2
+26500: join 15 2 3 0,2
+NO CLASH, using fixed ground order
+26501: Facts:
+26501: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26501: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26501: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26501: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26501: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26501: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26501: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26501: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26501: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+26501: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+26501: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+26501: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+26501: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+26501: Goal:
+26501: Id : 1, {_}:
+ join (meet (complement a) (join a b))
+ (join (complement b) (meet a b))
+ =>=
+ n1
+ [] by prove_weak_orthomodular_law
+26501: Order:
+26501: kbo
+26501: Leaf order:
+26501: n0 1 0 0
+26501: n1 2 0 1 3
+26501: a 3 0 3 1,1,1,2
+26501: b 3 0 3 2,2,1,2
+26501: complement 12 1 2 0,1,1,2
+26501: meet 14 2 2 0,1,2
+26501: join 15 2 3 0,2
+NO CLASH, using fixed ground order
+26502: Facts:
+26502: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26502: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26502: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26502: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26502: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26502: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26502: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26502: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26502: Id : 10, {_}:
+ complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+26502: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+26502: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+26502: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+26502: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+26502: Goal:
+26502: Id : 1, {_}:
+ join (meet (complement a) (join a b))
+ (join (complement b) (meet a b))
+ =>=
+ n1
+ [] by prove_weak_orthomodular_law
+26502: Order:
+26502: lpo
+26502: Leaf order:
+26502: n0 1 0 0
+26502: n1 2 0 1 3
+26502: a 3 0 3 1,1,1,2
+26502: b 3 0 3 2,2,1,2
+26502: complement 12 1 2 0,1,1,2
+26502: meet 14 2 2 0,1,2
+26502: join 15 2 3 0,2
+% SZS status Timeout for LAT049-1.p
+CLASH, statistics insufficient
+26530: Facts:
+26530: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26530: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26530: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26530: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26530: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26530: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26530: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26530: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26530: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+26530: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+26530: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+26530: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+26530: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+26530: Id : 15, {_}:
+ join ?38 (meet (complement ?38) (join ?38 ?39)) =>= join ?38 ?39
+ [39, 38] by orthomodular_law ?38 ?39
+26530: Goal:
+26530: Id : 1, {_}:
+ join a (meet b (join a c)) =>= meet (join a b) (join a c)
+ [] by prove_modular_law
+26530: Order:
+26530: nrkbo
+26530: Leaf order:
+26530: n1 1 0 0
+26530: n0 1 0 0
+26530: b 2 0 2 1,2,2
+26530: c 2 0 2 2,2,2,2
+26530: a 4 0 4 1,2
+26530: complement 11 1 0
+26530: meet 15 2 2 0,2,2
+26530: join 19 2 4 0,2
+CLASH, statistics insufficient
+26531: Facts:
+26531: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26531: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26531: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26531: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26531: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26531: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26531: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26531: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26531: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+26531: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+26531: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+26531: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+26531: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+26531: Id : 15, {_}:
+ join ?38 (meet (complement ?38) (join ?38 ?39)) =>= join ?38 ?39
+ [39, 38] by orthomodular_law ?38 ?39
+26531: Goal:
+26531: Id : 1, {_}:
+ join a (meet b (join a c)) =>= meet (join a b) (join a c)
+ [] by prove_modular_law
+26531: Order:
+26531: kbo
+26531: Leaf order:
+26531: n1 1 0 0
+26531: n0 1 0 0
+26531: b 2 0 2 1,2,2
+26531: c 2 0 2 2,2,2,2
+26531: a 4 0 4 1,2
+26531: complement 11 1 0
+26531: meet 15 2 2 0,2,2
+26531: join 19 2 4 0,2
+CLASH, statistics insufficient
+26532: Facts:
+26532: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26532: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26532: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26532: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26532: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26532: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26532: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26532: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26532: Id : 10, {_}:
+ complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+26532: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+26532: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+26532: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+26532: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+26532: Id : 15, {_}:
+ join ?38 (meet (complement ?38) (join ?38 ?39)) =>= join ?38 ?39
+ [39, 38] by orthomodular_law ?38 ?39
+26532: Goal:
+26532: Id : 1, {_}:
+ join a (meet b (join a c)) =>= meet (join a b) (join a c)
+ [] by prove_modular_law
+26532: Order:
+26532: lpo
+26532: Leaf order:
+26532: n1 1 0 0
+26532: n0 1 0 0
+26532: b 2 0 2 1,2,2
+26532: c 2 0 2 2,2,2,2
+26532: a 4 0 4 1,2
+26532: complement 11 1 0
+26532: meet 15 2 2 0,2,2
+26532: join 19 2 4 0,2
+% SZS status Timeout for LAT050-1.p
+CLASH, statistics insufficient
+26548: Facts:
+26548: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26548: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26548: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26548: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26548: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26548: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26548: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26548: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26548: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
+26548: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
+26548: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
+26548: Goal:
+26548: Id : 1, {_}:
+ complement (join a b) =<= meet (complement a) (complement b)
+ [] by prove_compatibility_law
+26548: Order:
+26548: nrkbo
+26548: Leaf order:
+26548: n1 1 0 0
+26548: n0 1 0 0
+26548: a 2 0 2 1,1,2
+26548: b 2 0 2 2,1,2
+26548: complement 7 1 3 0,2
+26548: join 11 2 1 0,1,2
+26548: meet 11 2 1 0,3
+CLASH, statistics insufficient
+26549: Facts:
+26549: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26549: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26549: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26549: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26549: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26549: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26549: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26549: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26549: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
+26549: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
+26549: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
+26549: Goal:
+26549: Id : 1, {_}:
+ complement (join a b) =<= meet (complement a) (complement b)
+ [] by prove_compatibility_law
+26549: Order:
+26549: kbo
+26549: Leaf order:
+26549: n1 1 0 0
+26549: n0 1 0 0
+26549: a 2 0 2 1,1,2
+26549: b 2 0 2 2,1,2
+26549: complement 7 1 3 0,2
+26549: join 11 2 1 0,1,2
+26549: meet 11 2 1 0,3
+CLASH, statistics insufficient
+26550: Facts:
+26550: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26550: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26550: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26550: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26550: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26550: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26550: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26550: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26550: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
+26550: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
+26550: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
+26550: Goal:
+26550: Id : 1, {_}:
+ complement (join a b) =>= meet (complement a) (complement b)
+ [] by prove_compatibility_law
+26550: Order:
+26550: lpo
+26550: Leaf order:
+26550: n1 1 0 0
+26550: n0 1 0 0
+26550: a 2 0 2 1,1,2
+26550: b 2 0 2 2,1,2
+26550: complement 7 1 3 0,2
+26550: join 11 2 1 0,1,2
+26550: meet 11 2 1 0,3
+% SZS status Timeout for LAT051-1.p
+CLASH, statistics insufficient
+26611: Facts:
+26611: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26611: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26611: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26611: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26611: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26611: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26611: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26611: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26611: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
+26611: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
+26611: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
+26611: Id : 13, {_}:
+ join ?32 (meet ?33 (join ?32 ?34))
+ =>=
+ meet (join ?32 ?33) (join ?32 ?34)
+ [34, 33, 32] by modular_law ?32 ?33 ?34
+26611: Goal:
+26611: Id : 1, {_}:
+ complement (join a b) =<= meet (complement a) (complement b)
+ [] by prove_compatibility_law
+26611: Order:
+26611: kbo
+26611: Leaf order:
+26611: n1 1 0 0
+26611: n0 1 0 0
+26611: a 2 0 2 1,1,2
+26611: b 2 0 2 2,1,2
+26611: complement 7 1 3 0,2
+26611: meet 13 2 1 0,3
+26611: join 15 2 1 0,1,2
+CLASH, statistics insufficient
+26612: Facts:
+26612: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26612: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26612: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26612: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26612: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26612: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26612: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26612: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26612: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
+26612: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
+26612: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
+26612: Id : 13, {_}:
+ join ?32 (meet ?33 (join ?32 ?34))
+ =>=
+ meet (join ?32 ?33) (join ?32 ?34)
+ [34, 33, 32] by modular_law ?32 ?33 ?34
+26612: Goal:
+26612: Id : 1, {_}:
+ complement (join a b) =>= meet (complement a) (complement b)
+ [] by prove_compatibility_law
+26612: Order:
+26612: lpo
+26612: Leaf order:
+26612: n1 1 0 0
+26612: n0 1 0 0
+26612: a 2 0 2 1,1,2
+26612: b 2 0 2 2,1,2
+26612: complement 7 1 3 0,2
+26612: meet 13 2 1 0,3
+26612: join 15 2 1 0,1,2
+CLASH, statistics insufficient
+26610: Facts:
+26610: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26610: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26610: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26610: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26610: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26610: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26610: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26610: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26610: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26
+26610: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28
+26610: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30
+26610: Id : 13, {_}:
+ join ?32 (meet ?33 (join ?32 ?34))
+ =>=
+ meet (join ?32 ?33) (join ?32 ?34)
+ [34, 33, 32] by modular_law ?32 ?33 ?34
+26610: Goal:
+26610: Id : 1, {_}:
+ complement (join a b) =<= meet (complement a) (complement b)
+ [] by prove_compatibility_law
+26610: Order:
+26610: nrkbo
+26610: Leaf order:
+26610: n1 1 0 0
+26610: n0 1 0 0
+26610: a 2 0 2 1,1,2
+26610: b 2 0 2 2,1,2
+26610: complement 7 1 3 0,2
+26610: meet 13 2 1 0,3
+26610: join 15 2 1 0,1,2
+% SZS status Timeout for LAT052-1.p
+CLASH, statistics insufficient
+26628: Facts:
+26628: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26628: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26628: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26628: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26628: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26628: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26628: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26628: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26628: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+26628: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+26628: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+26628: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+26628: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+26628: Goal:
+26628: Id : 1, {_}:
+ join a
+ (meet (complement b)
+ (join (complement a)
+ (meet (complement b)
+ (join a (meet (complement b) (complement a))))))
+ =<=
+ join a
+ (meet (complement b)
+ (join (complement a)
+ (meet (complement b)
+ (join a
+ (meet (complement b)
+ (join (complement a) (meet (complement b) a)))))))
+ [] by prove_this
+26628: Order:
+26628: nrkbo
+26628: Leaf order:
+26628: n1 1 0 0
+26628: n0 1 0 0
+26628: b 7 0 7 1,1,2,2
+26628: a 9 0 9 1,2
+26628: complement 21 1 11 0,1,2,2
+26628: join 19 2 7 0,2
+26628: meet 19 2 7 0,2,2
+CLASH, statistics insufficient
+26629: Facts:
+26629: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26629: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26629: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26629: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26629: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26629: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26629: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26629: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26629: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+26629: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+26629: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+26629: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+26629: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+26629: Goal:
+26629: Id : 1, {_}:
+ join a
+ (meet (complement b)
+ (join (complement a)
+ (meet (complement b)
+ (join a (meet (complement b) (complement a))))))
+ =<=
+ join a
+ (meet (complement b)
+ (join (complement a)
+ (meet (complement b)
+ (join a
+ (meet (complement b)
+ (join (complement a) (meet (complement b) a)))))))
+ [] by prove_this
+26629: Order:
+26629: kbo
+26629: Leaf order:
+26629: n1 1 0 0
+26629: n0 1 0 0
+26629: b 7 0 7 1,1,2,2
+26629: a 9 0 9 1,2
+26629: complement 21 1 11 0,1,2,2
+26629: join 19 2 7 0,2
+26629: meet 19 2 7 0,2,2
+CLASH, statistics insufficient
+26630: Facts:
+26630: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26630: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26630: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26630: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26630: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26630: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26630: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26630: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26630: Id : 10, {_}:
+ complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+26630: Id : 11, {_}:
+ complement (meet ?29 ?30) =>= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+26630: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+26630: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+26630: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+26630: Goal:
+26630: Id : 1, {_}:
+ join a
+ (meet (complement b)
+ (join (complement a)
+ (meet (complement b)
+ (join a (meet (complement b) (complement a))))))
+ =<=
+ join a
+ (meet (complement b)
+ (join (complement a)
+ (meet (complement b)
+ (join a
+ (meet (complement b)
+ (join (complement a) (meet (complement b) a)))))))
+ [] by prove_this
+26630: Order:
+26630: lpo
+26630: Leaf order:
+26630: n1 1 0 0
+26630: n0 1 0 0
+26630: b 7 0 7 1,1,2,2
+26630: a 9 0 9 1,2
+26630: complement 21 1 11 0,1,2,2
+26630: join 19 2 7 0,2
+26630: meet 19 2 7 0,2,2
+% SZS status Timeout for LAT054-1.p
+CLASH, statistics insufficient
+26659: Facts:
+26659: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26659: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26659: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26659: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26659: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26659: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26659: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26659: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26659: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
+26659: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
+26659: Id : 12, {_}:
+ meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
+ [31, 30] by compatibility ?30 ?31
+26659: Goal:
+26659: Id : 1, {_}:
+ meet (join a (complement b))
+ (join (join (meet a b) (meet (complement a) b))
+ (meet (complement a) (complement b)))
+ =>=
+ join (meet a b) (meet (complement a) (complement b))
+ [] by prove_e51
+26659: Order:
+26659: nrkbo
+26659: Leaf order:
+26659: n1 1 0 0
+26659: n0 1 0 0
+26659: a 6 0 6 1,1,2
+26659: b 6 0 6 1,2,1,2
+26659: complement 11 1 6 0,2,1,2
+26659: join 15 2 4 0,1,2
+26659: meet 17 2 6 0,2
+CLASH, statistics insufficient
+26660: Facts:
+26660: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26660: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26660: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26660: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26660: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26660: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26660: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26660: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26660: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
+26660: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
+26660: Id : 12, {_}:
+ meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
+ [31, 30] by compatibility ?30 ?31
+26660: Goal:
+26660: Id : 1, {_}:
+ meet (join a (complement b))
+ (join (join (meet a b) (meet (complement a) b))
+ (meet (complement a) (complement b)))
+ =>=
+ join (meet a b) (meet (complement a) (complement b))
+ [] by prove_e51
+26660: Order:
+26660: kbo
+26660: Leaf order:
+26660: n1 1 0 0
+26660: n0 1 0 0
+26660: a 6 0 6 1,1,2
+26660: b 6 0 6 1,2,1,2
+26660: complement 11 1 6 0,2,1,2
+26660: join 15 2 4 0,1,2
+26660: meet 17 2 6 0,2
+CLASH, statistics insufficient
+26661: Facts:
+26661: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26661: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26661: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26661: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26661: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26661: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26661: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26661: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26661: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
+26661: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
+26661: Id : 12, {_}:
+ meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
+ [31, 30] by compatibility ?30 ?31
+26661: Goal:
+26661: Id : 1, {_}:
+ meet (join a (complement b))
+ (join (join (meet a b) (meet (complement a) b))
+ (meet (complement a) (complement b)))
+ =>=
+ join (meet a b) (meet (complement a) (complement b))
+ [] by prove_e51
+26661: Order:
+26661: lpo
+26661: Leaf order:
+26661: n1 1 0 0
+26661: n0 1 0 0
+26661: a 6 0 6 1,1,2
+26661: b 6 0 6 1,2,1,2
+26661: complement 11 1 6 0,2,1,2
+26661: join 15 2 4 0,1,2
+26661: meet 17 2 6 0,2
+% SZS status Timeout for LAT062-1.p
+CLASH, statistics insufficient
+26678: Facts:
+26678: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26678: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26678: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26678: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26678: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26678: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26678: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26678: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26678: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
+26678: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
+26678: Id : 12, {_}:
+ meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
+ [31, 30] by compatibility ?30 ?31
+26678: Goal:
+26678: Id : 1, {_}:
+ meet a (join b (meet a (join (complement a) (meet a b))))
+ =>=
+ meet a (join (complement a) (meet a b))
+ [] by prove_e62
+26678: Order:
+26678: nrkbo
+26678: Leaf order:
+26678: n1 1 0 0
+26678: n0 1 0 0
+26678: b 3 0 3 1,2,2
+26678: a 7 0 7 1,2
+26678: complement 7 1 2 0,1,2,2,2,2
+26678: join 14 2 3 0,2,2
+26678: meet 16 2 5 0,2
+CLASH, statistics insufficient
+26679: Facts:
+26679: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26679: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26679: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26679: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26679: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26679: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26679: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26679: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26679: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
+26679: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
+26679: Id : 12, {_}:
+ meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
+ [31, 30] by compatibility ?30 ?31
+26679: Goal:
+26679: Id : 1, {_}:
+ meet a (join b (meet a (join (complement a) (meet a b))))
+ =>=
+ meet a (join (complement a) (meet a b))
+ [] by prove_e62
+26679: Order:
+26679: kbo
+26679: Leaf order:
+26679: n1 1 0 0
+26679: n0 1 0 0
+26679: b 3 0 3 1,2,2
+26679: a 7 0 7 1,2
+26679: complement 7 1 2 0,1,2,2,2,2
+26679: join 14 2 3 0,2,2
+26679: meet 16 2 5 0,2
+CLASH, statistics insufficient
+26680: Facts:
+26680: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26680: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26680: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26680: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26680: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26680: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26680: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26680: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26680: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26
+26680: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28
+26680: Id : 12, {_}:
+ meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31))
+ [31, 30] by compatibility ?30 ?31
+26680: Goal:
+26680: Id : 1, {_}:
+ meet a (join b (meet a (join (complement a) (meet a b))))
+ =>=
+ meet a (join (complement a) (meet a b))
+ [] by prove_e62
+26680: Order:
+26680: lpo
+26680: Leaf order:
+26680: n1 1 0 0
+26680: n0 1 0 0
+26680: b 3 0 3 1,2,2
+26680: a 7 0 7 1,2
+26680: complement 7 1 2 0,1,2,2,2,2
+26680: join 14 2 3 0,2,2
+26680: meet 16 2 5 0,2
+% SZS status Timeout for LAT063-1.p
+NO CLASH, using fixed ground order
+26708: Facts:
+26708: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26708: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26708: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26708: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26708: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26708: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26708: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26708: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26708: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?28 (join (meet ?26 (join ?27 ?28)) (meet ?27 ?28))))
+ [28, 27, 26] by equation_H2 ?26 ?27 ?28
+26708: Goal:
+26708: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+26708: Order:
+26708: nrkbo
+26708: Leaf order:
+26708: c 3 0 3 2,2,2,2
+26708: b 4 0 4 1,2,2
+26708: a 5 0 5 1,2
+26708: join 17 2 4 0,2,2
+26708: meet 21 2 6 0,2
+NO CLASH, using fixed ground order
+26709: Facts:
+26709: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26709: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26709: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26709: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26709: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26709: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26709: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26709: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26709: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?28 (join (meet ?26 (join ?27 ?28)) (meet ?27 ?28))))
+ [28, 27, 26] by equation_H2 ?26 ?27 ?28
+26709: Goal:
+26709: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+26709: Order:
+26709: kbo
+26709: Leaf order:
+26709: c 3 0 3 2,2,2,2
+26709: b 4 0 4 1,2,2
+26709: a 5 0 5 1,2
+26709: join 17 2 4 0,2,2
+26709: meet 21 2 6 0,2
+NO CLASH, using fixed ground order
+26710: Facts:
+26710: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26710: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26710: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26710: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26710: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26710: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26710: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26710: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26710: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?28 (join (meet ?26 (join ?27 ?28)) (meet ?27 ?28))))
+ [28, 27, 26] by equation_H2 ?26 ?27 ?28
+26710: Goal:
+26710: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+26710: Order:
+26710: lpo
+26710: Leaf order:
+26710: c 3 0 3 2,2,2,2
+26710: b 4 0 4 1,2,2
+26710: a 5 0 5 1,2
+26710: join 17 2 4 0,2,2
+26710: meet 21 2 6 0,2
+% SZS status Timeout for LAT098-1.p
+NO CLASH, using fixed ground order
+26734: Facts:
+26734: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26734: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26734: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26734: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26734: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26734: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26734: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26734: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26734: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join (meet ?26 (join ?27 (meet ?26 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H6 ?26 ?27 ?28
+26734: Goal:
+26734: Id : 1, {_}:
+ meet a (join b (meet a (join c d)))
+ =<=
+ meet a (join b (meet (join a (meet b d)) (join c d)))
+ [] by prove_H4
+26734: Order:
+26734: nrkbo
+26734: Leaf order:
+26734: c 2 0 2 1,2,2,2,2
+26734: b 3 0 3 1,2,2
+26734: d 3 0 3 2,2,2,2,2
+26734: a 4 0 4 1,2
+26734: join 18 2 5 0,2,2
+26734: meet 20 2 5 0,2
+NO CLASH, using fixed ground order
+26735: Facts:
+26735: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26735: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26735: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26735: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26735: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26735: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26735: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26735: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26735: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join (meet ?26 (join ?27 (meet ?26 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H6 ?26 ?27 ?28
+26735: Goal:
+26735: Id : 1, {_}:
+ meet a (join b (meet a (join c d)))
+ =<=
+ meet a (join b (meet (join a (meet b d)) (join c d)))
+ [] by prove_H4
+26735: Order:
+26735: kbo
+26735: Leaf order:
+26735: c 2 0 2 1,2,2,2,2
+26735: b 3 0 3 1,2,2
+26735: d 3 0 3 2,2,2,2,2
+26735: a 4 0 4 1,2
+26735: join 18 2 5 0,2,2
+26735: meet 20 2 5 0,2
+NO CLASH, using fixed ground order
+26736: Facts:
+26736: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26736: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26736: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26736: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26736: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26736: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26736: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26736: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26736: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join (meet ?26 (join ?27 (meet ?26 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H6 ?26 ?27 ?28
+26736: Goal:
+26736: Id : 1, {_}:
+ meet a (join b (meet a (join c d)))
+ =<=
+ meet a (join b (meet (join a (meet b d)) (join c d)))
+ [] by prove_H4
+26736: Order:
+26736: lpo
+26736: Leaf order:
+26736: c 2 0 2 1,2,2,2,2
+26736: b 3 0 3 1,2,2
+26736: d 3 0 3 2,2,2,2,2
+26736: a 4 0 4 1,2
+26736: join 18 2 5 0,2,2
+26736: meet 20 2 5 0,2
+% SZS status Timeout for LAT100-1.p
+NO CLASH, using fixed ground order
+26775: Facts:
+26775: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26775: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26775: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26775: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26775: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26775: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26775: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26775: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26775: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join (meet ?26 (join ?27 (meet ?26 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H6 ?26 ?27 ?28
+26775: Goal:
+26775: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join a (meet b c))))
+ [] by prove_H10
+26775: Order:
+26775: nrkbo
+26775: Leaf order:
+26775: b 3 0 3 1,2,2
+26775: c 3 0 3 2,2,2,2
+26775: a 4 0 4 1,2
+26775: join 16 2 3 0,2,2
+26775: meet 20 2 5 0,2
+NO CLASH, using fixed ground order
+26776: Facts:
+26776: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26776: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26776: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26776: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26776: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26776: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26776: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26776: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26776: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join (meet ?26 (join ?27 (meet ?26 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H6 ?26 ?27 ?28
+26776: Goal:
+26776: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join a (meet b c))))
+ [] by prove_H10
+26776: Order:
+26776: kbo
+26776: Leaf order:
+26776: b 3 0 3 1,2,2
+26776: c 3 0 3 2,2,2,2
+26776: a 4 0 4 1,2
+26776: join 16 2 3 0,2,2
+26776: meet 20 2 5 0,2
+NO CLASH, using fixed ground order
+26777: Facts:
+26777: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26777: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26777: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26777: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26777: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26777: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26777: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26777: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26777: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join (meet ?26 (join ?27 (meet ?26 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H6 ?26 ?27 ?28
+26777: Goal:
+26777: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =>=
+ meet a (join b (meet c (join a (meet b c))))
+ [] by prove_H10
+26777: Order:
+26777: lpo
+26777: Leaf order:
+26777: b 3 0 3 1,2,2
+26777: c 3 0 3 2,2,2,2
+26777: a 4 0 4 1,2
+26777: join 16 2 3 0,2,2
+26777: meet 20 2 5 0,2
+% SZS status Timeout for LAT101-1.p
+NO CLASH, using fixed ground order
+26819: Facts:
+26819: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26819: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26819: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26819: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26819: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26819: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26819: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26819: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26819: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
+ [28, 27, 26] by equation_H7 ?26 ?27 ?28
+26819: Goal:
+26819: Id : 1, {_}:
+ meet a (join b (meet a (join c d)))
+ =<=
+ meet a (join b (meet (join a (meet b d)) (join c d)))
+ [] by prove_H4
+26819: Order:
+26819: nrkbo
+26819: Leaf order:
+26819: c 2 0 2 1,2,2,2,2
+26819: b 3 0 3 1,2,2
+26819: d 3 0 3 2,2,2,2,2
+26819: a 4 0 4 1,2
+26819: join 18 2 5 0,2,2
+26819: meet 20 2 5 0,2
+NO CLASH, using fixed ground order
+26820: Facts:
+26820: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26820: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26820: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26820: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26820: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26820: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26820: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26820: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26820: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
+ [28, 27, 26] by equation_H7 ?26 ?27 ?28
+26820: Goal:
+26820: Id : 1, {_}:
+ meet a (join b (meet a (join c d)))
+ =<=
+ meet a (join b (meet (join a (meet b d)) (join c d)))
+ [] by prove_H4
+26820: Order:
+26820: kbo
+26820: Leaf order:
+26820: c 2 0 2 1,2,2,2,2
+26820: b 3 0 3 1,2,2
+26820: d 3 0 3 2,2,2,2,2
+26820: a 4 0 4 1,2
+26820: join 18 2 5 0,2,2
+26820: meet 20 2 5 0,2
+NO CLASH, using fixed ground order
+26821: Facts:
+26821: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26821: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26821: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26821: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26821: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26821: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26821: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26821: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26821: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
+ [28, 27, 26] by equation_H7 ?26 ?27 ?28
+26821: Goal:
+26821: Id : 1, {_}:
+ meet a (join b (meet a (join c d)))
+ =<=
+ meet a (join b (meet (join a (meet b d)) (join c d)))
+ [] by prove_H4
+26821: Order:
+26821: lpo
+26821: Leaf order:
+26821: c 2 0 2 1,2,2,2,2
+26821: b 3 0 3 1,2,2
+26821: d 3 0 3 2,2,2,2,2
+26821: a 4 0 4 1,2
+26821: join 18 2 5 0,2,2
+26821: meet 20 2 5 0,2
+% SZS status Timeout for LAT102-1.p
+NO CLASH, using fixed ground order
+26896: Facts:
+26896: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26896: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26896: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26896: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26896: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26896: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26896: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26896: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26896: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?27 ?28))))
+ [28, 27, 26] by equation_H10 ?26 ?27 ?28
+26896: Goal:
+26896: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+26896: Order:
+26896: nrkbo
+26896: Leaf order:
+26896: b 3 0 3 1,2,2
+26896: c 3 0 3 2,2,2,2
+26896: a 6 0 6 1,2
+26896: join 16 2 4 0,2,2
+26896: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+26897: Facts:
+26897: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26897: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26897: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26897: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26897: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26897: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26897: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26897: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26897: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?27 ?28))))
+ [28, 27, 26] by equation_H10 ?26 ?27 ?28
+26897: Goal:
+26897: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+26897: Order:
+26897: kbo
+26897: Leaf order:
+26897: b 3 0 3 1,2,2
+26897: c 3 0 3 2,2,2,2
+26897: a 6 0 6 1,2
+26897: join 16 2 4 0,2,2
+26897: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+26898: Facts:
+26898: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26898: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26898: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26898: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26898: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26898: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26898: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26898: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26898: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?27 ?28))))
+ [28, 27, 26] by equation_H10 ?26 ?27 ?28
+26898: Goal:
+26898: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+26898: Order:
+26898: lpo
+26898: Leaf order:
+26898: b 3 0 3 1,2,2
+26898: c 3 0 3 2,2,2,2
+26898: a 6 0 6 1,2
+26898: join 16 2 4 0,2,2
+26898: meet 20 2 6 0,2
+% SZS status Timeout for LAT103-1.p
+NO CLASH, using fixed ground order
+26925: Facts:
+26925: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26925: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26925: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26925: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26925: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26925: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26925: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26925: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26925: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?26 (meet ?27 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H21 ?26 ?27 ?28
+26925: Goal:
+26925: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+26925: Order:
+26925: nrkbo
+26925: Leaf order:
+26925: c 3 0 3 2,2,2,2
+26925: b 4 0 4 1,2,2
+26925: a 5 0 5 1,2
+26925: join 17 2 4 0,2,2
+26925: meet 21 2 6 0,2
+NO CLASH, using fixed ground order
+26926: Facts:
+26926: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26926: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26926: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26926: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26926: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26926: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26926: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26926: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26926: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?26 (meet ?27 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H21 ?26 ?27 ?28
+26926: Goal:
+26926: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+26926: Order:
+26926: kbo
+26926: Leaf order:
+26926: c 3 0 3 2,2,2,2
+26926: b 4 0 4 1,2,2
+26926: a 5 0 5 1,2
+26926: join 17 2 4 0,2,2
+26926: meet 21 2 6 0,2
+NO CLASH, using fixed ground order
+26927: Facts:
+26927: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26927: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26927: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26927: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26927: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26927: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26927: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26927: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26927: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?26 (meet ?27 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H21 ?26 ?27 ?28
+26927: Goal:
+26927: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+26927: Order:
+26927: lpo
+26927: Leaf order:
+26927: c 3 0 3 2,2,2,2
+26927: b 4 0 4 1,2,2
+26927: a 5 0 5 1,2
+26927: join 17 2 4 0,2,2
+26927: meet 21 2 6 0,2
+% SZS status Timeout for LAT104-1.p
+NO CLASH, using fixed ground order
+26956: Facts:
+26956: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26956: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26956: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26956: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26956: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26956: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26956: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26956: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26956: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?26 (meet ?27 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H21 ?26 ?27 ?28
+26956: Goal:
+26956: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join a (meet b c))))
+ [] by prove_H10
+26956: Order:
+26956: nrkbo
+26956: Leaf order:
+26956: b 3 0 3 1,2,2
+26956: c 3 0 3 2,2,2,2
+26956: a 4 0 4 1,2
+26956: join 16 2 3 0,2,2
+26956: meet 20 2 5 0,2
+NO CLASH, using fixed ground order
+26957: Facts:
+26957: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26957: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26957: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26957: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26957: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26957: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26957: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26957: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26957: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?26 (meet ?27 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H21 ?26 ?27 ?28
+26957: Goal:
+26957: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join a (meet b c))))
+ [] by prove_H10
+26957: Order:
+26957: kbo
+26957: Leaf order:
+26957: b 3 0 3 1,2,2
+26957: c 3 0 3 2,2,2,2
+26957: a 4 0 4 1,2
+26957: join 16 2 3 0,2,2
+26957: meet 20 2 5 0,2
+NO CLASH, using fixed ground order
+26958: Facts:
+26958: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+26958: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+26958: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+26958: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+26958: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+26958: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+26958: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+26958: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+26958: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?26 (meet ?27 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H21 ?26 ?27 ?28
+26958: Goal:
+26958: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =>=
+ meet a (join b (meet c (join a (meet b c))))
+ [] by prove_H10
+26958: Order:
+26958: lpo
+26958: Leaf order:
+26958: b 3 0 3 1,2,2
+26958: c 3 0 3 2,2,2,2
+26958: a 4 0 4 1,2
+26958: join 16 2 3 0,2,2
+26958: meet 20 2 5 0,2
+% SZS status Timeout for LAT105-1.p
+NO CLASH, using fixed ground order
+27035: Facts:
+27035: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27035: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27035: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27035: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27035: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27035: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27035: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27035: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27035: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?28 (meet ?26 ?27)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H22 ?26 ?27 ?28
+27035: Goal:
+27035: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+27035: Order:
+27035: nrkbo
+27035: Leaf order:
+27035: c 3 0 3 2,2,2,2
+27035: b 4 0 4 1,2,2
+27035: a 5 0 5 1,2
+27035: join 17 2 4 0,2,2
+27035: meet 21 2 6 0,2
+NO CLASH, using fixed ground order
+27036: Facts:
+27036: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27036: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27036: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27036: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27036: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27036: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27036: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27036: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27036: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?28 (meet ?26 ?27)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H22 ?26 ?27 ?28
+27036: Goal:
+27036: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+27036: Order:
+27036: kbo
+27036: Leaf order:
+27036: c 3 0 3 2,2,2,2
+27036: b 4 0 4 1,2,2
+27036: a 5 0 5 1,2
+27036: join 17 2 4 0,2,2
+27036: meet 21 2 6 0,2
+NO CLASH, using fixed ground order
+27037: Facts:
+27037: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27037: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27037: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27037: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27037: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27037: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27037: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27037: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27037: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?28 (meet ?26 ?27)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H22 ?26 ?27 ?28
+27037: Goal:
+27037: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+27037: Order:
+27037: lpo
+27037: Leaf order:
+27037: c 3 0 3 2,2,2,2
+27037: b 4 0 4 1,2,2
+27037: a 5 0 5 1,2
+27037: join 17 2 4 0,2,2
+27037: meet 21 2 6 0,2
+% SZS status Timeout for LAT106-1.p
+NO CLASH, using fixed ground order
+27073: Facts:
+27073: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27073: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27073: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27073: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27073: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27073: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27073: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27073: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27073: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?28 (meet ?26 ?27)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H22 ?26 ?27 ?28
+27073: Goal:
+27073: Id : 1, {_}:
+ meet a (join (meet a b) (meet a c))
+ =<=
+ meet a (join (meet b (join a (meet b c))) (meet c (join a b)))
+ [] by prove_H17
+27073: Order:
+27073: nrkbo
+27073: Leaf order:
+27073: c 3 0 3 2,2,2,2
+27073: b 4 0 4 2,1,2,2
+27073: a 6 0 6 1,2
+27073: join 17 2 4 0,2,2
+27073: meet 22 2 7 0,2
+NO CLASH, using fixed ground order
+27074: Facts:
+27074: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27074: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27074: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27074: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27074: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27074: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27074: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27074: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27074: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?28 (meet ?26 ?27)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H22 ?26 ?27 ?28
+27074: Goal:
+27074: Id : 1, {_}:
+ meet a (join (meet a b) (meet a c))
+ =<=
+ meet a (join (meet b (join a (meet b c))) (meet c (join a b)))
+ [] by prove_H17
+27074: Order:
+27074: kbo
+27074: Leaf order:
+27074: c 3 0 3 2,2,2,2
+27074: b 4 0 4 2,1,2,2
+27074: a 6 0 6 1,2
+27074: join 17 2 4 0,2,2
+27074: meet 22 2 7 0,2
+NO CLASH, using fixed ground order
+27075: Facts:
+27075: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27075: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27075: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27075: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27075: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27075: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27075: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27075: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27075: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?28 (meet ?26 ?27)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H22 ?26 ?27 ?28
+27075: Goal:
+27075: Id : 1, {_}:
+ meet a (join (meet a b) (meet a c))
+ =>=
+ meet a (join (meet b (join a (meet b c))) (meet c (join a b)))
+ [] by prove_H17
+27075: Order:
+27075: lpo
+27075: Leaf order:
+27075: c 3 0 3 2,2,2,2
+27075: b 4 0 4 2,1,2,2
+27075: a 6 0 6 1,2
+27075: join 17 2 4 0,2,2
+27075: meet 22 2 7 0,2
+% SZS status Timeout for LAT107-1.p
+NO CLASH, using fixed ground order
+27091: Facts:
+27091: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27091: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27091: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27091: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27091: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27091: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27091: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27091: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27091: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
+ [29, 28, 27, 26] by equation_H31 ?26 ?27 ?28 ?29
+27091: Goal:
+27091: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+27091: Order:
+27091: nrkbo
+27091: Leaf order:
+27091: d 2 0 2 2,2,2,2,2
+27091: b 3 0 3 1,2,2
+27091: c 3 0 3 1,2,2,2
+27091: a 4 0 4 1,2
+27091: join 17 2 5 0,2,2
+27091: meet 21 2 5 0,2
+NO CLASH, using fixed ground order
+27092: Facts:
+27092: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27092: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27092: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27092: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27092: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27092: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27092: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27092: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27092: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
+ [29, 28, 27, 26] by equation_H31 ?26 ?27 ?28 ?29
+27092: Goal:
+27092: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+27092: Order:
+27092: kbo
+27092: Leaf order:
+27092: d 2 0 2 2,2,2,2,2
+27092: b 3 0 3 1,2,2
+27092: c 3 0 3 1,2,2,2
+27092: a 4 0 4 1,2
+27092: join 17 2 5 0,2,2
+27092: meet 21 2 5 0,2
+NO CLASH, using fixed ground order
+27093: Facts:
+27093: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27093: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27093: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27093: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27093: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27093: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27093: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27093: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27093: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
+ [29, 28, 27, 26] by equation_H31 ?26 ?27 ?28 ?29
+27093: Goal:
+27093: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+27093: Order:
+27093: lpo
+27093: Leaf order:
+27093: d 2 0 2 2,2,2,2,2
+27093: b 3 0 3 1,2,2
+27093: c 3 0 3 1,2,2,2
+27093: a 4 0 4 1,2
+27093: join 17 2 5 0,2,2
+27093: meet 21 2 5 0,2
+% SZS status Timeout for LAT108-1.p
+NO CLASH, using fixed ground order
+27126: Facts:
+27126: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27126: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27126: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27126: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27126: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27126: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27126: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27126: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27126: Id : 10, {_}:
+ meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
+27126: Goal:
+27126: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+27126: Order:
+27126: nrkbo
+27126: Leaf order:
+27126: d 2 0 2 2,2,2,2,2
+27126: b 3 0 3 1,2,2
+27126: c 3 0 3 1,2,2,2
+27126: a 4 0 4 1,2
+27126: meet 19 2 5 0,2
+27126: join 19 2 5 0,2,2
+NO CLASH, using fixed ground order
+27127: Facts:
+27127: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27127: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27127: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27127: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27127: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27127: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27127: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27127: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27127: Id : 10, {_}:
+ meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
+27127: Goal:
+27127: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+27127: Order:
+27127: kbo
+27127: Leaf order:
+27127: d 2 0 2 2,2,2,2,2
+27127: b 3 0 3 1,2,2
+27127: c 3 0 3 1,2,2,2
+27127: a 4 0 4 1,2
+27127: meet 19 2 5 0,2
+27127: join 19 2 5 0,2,2
+NO CLASH, using fixed ground order
+27128: Facts:
+27128: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27128: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27128: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27128: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27128: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27128: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27128: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27128: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27128: Id : 10, {_}:
+ meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
+ =?=
+ meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
+27128: Goal:
+27128: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+27128: Order:
+27128: lpo
+27128: Leaf order:
+27128: d 2 0 2 2,2,2,2,2
+27128: b 3 0 3 1,2,2
+27128: c 3 0 3 1,2,2,2
+27128: a 4 0 4 1,2
+27128: meet 19 2 5 0,2
+27128: join 19 2 5 0,2,2
+% SZS status Timeout for LAT109-1.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+27146: Facts:
+NO CLASH, using fixed ground order
+27146: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27146: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27146: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27146: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27146: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27146: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27146: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27146: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27146: Id : 10, {_}:
+ meet ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =?=
+ meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H45 ?26 ?27 ?28 ?29
+27146: Goal:
+27146: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+27146: Order:
+27146: lpo
+27146: Leaf order:
+27146: d 2 0 2 2,2,2,2,2
+27146: b 3 0 3 1,2,2
+27146: c 3 0 3 1,2,2,2
+27146: a 4 0 4 1,2
+27146: join 17 2 5 0,2,2
+27146: meet 21 2 5 0,2
+27144: Facts:
+27144: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27144: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27144: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27144: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27144: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27144: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27144: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27144: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27144: Id : 10, {_}:
+ meet ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H45 ?26 ?27 ?28 ?29
+27144: Goal:
+27144: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+27144: Order:
+27144: nrkbo
+27144: Leaf order:
+27144: d 2 0 2 2,2,2,2,2
+27144: b 3 0 3 1,2,2
+27144: c 3 0 3 1,2,2,2
+27144: a 4 0 4 1,2
+27144: join 17 2 5 0,2,2
+27144: meet 21 2 5 0,2
+27145: Facts:
+27145: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27145: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27145: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27145: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27145: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27145: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27145: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27145: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27145: Id : 10, {_}:
+ meet ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H45 ?26 ?27 ?28 ?29
+27145: Goal:
+27145: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+27145: Order:
+27145: kbo
+27145: Leaf order:
+27145: d 2 0 2 2,2,2,2,2
+27145: b 3 0 3 1,2,2
+27145: c 3 0 3 1,2,2,2
+27145: a 4 0 4 1,2
+27145: join 17 2 5 0,2,2
+27145: meet 21 2 5 0,2
+% SZS status Timeout for LAT111-1.p
+NO CLASH, using fixed ground order
+27177: Facts:
+27177: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27177: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27177: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27177: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27177: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27177: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27177: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27177: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27177: Id : 10, {_}:
+ meet ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
+ =<=
+ meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
+ [29, 28, 27, 26] by equation_H47 ?26 ?27 ?28 ?29
+27177: Goal:
+27177: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+27177: Order:
+27177: nrkbo
+27177: Leaf order:
+27177: d 2 0 2 2,2,2,2,2
+27177: b 3 0 3 1,2,2
+27177: c 3 0 3 1,2,2,2
+27177: a 4 0 4 1,2
+27177: join 17 2 5 0,2,2
+27177: meet 21 2 5 0,2
+NO CLASH, using fixed ground order
+27178: Facts:
+27178: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27178: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27178: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27178: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27178: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27178: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27178: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27178: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27178: Id : 10, {_}:
+ meet ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
+ =<=
+ meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
+ [29, 28, 27, 26] by equation_H47 ?26 ?27 ?28 ?29
+27178: Goal:
+27178: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+27178: Order:
+27178: kbo
+27178: Leaf order:
+27178: d 2 0 2 2,2,2,2,2
+27178: b 3 0 3 1,2,2
+27178: c 3 0 3 1,2,2,2
+27178: a 4 0 4 1,2
+27178: join 17 2 5 0,2,2
+27178: meet 21 2 5 0,2
+NO CLASH, using fixed ground order
+27179: Facts:
+27179: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27179: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27179: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27179: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27179: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27179: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27179: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27179: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27179: Id : 10, {_}:
+ meet ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
+ =?=
+ meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?27 (meet ?26 ?28)))))
+ [29, 28, 27, 26] by equation_H47 ?26 ?27 ?28 ?29
+27179: Goal:
+27179: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+27179: Order:
+27179: lpo
+27179: Leaf order:
+27179: d 2 0 2 2,2,2,2,2
+27179: b 3 0 3 1,2,2
+27179: c 3 0 3 1,2,2,2
+27179: a 4 0 4 1,2
+27179: join 17 2 5 0,2,2
+27179: meet 21 2 5 0,2
+% SZS status Timeout for LAT112-1.p
+NO CLASH, using fixed ground order
+27203: Facts:
+27203: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27203: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27203: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27203: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27203: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27203: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27203: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27203: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27203: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
+ [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
+27203: Goal:
+27203: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+27203: Order:
+27203: nrkbo
+27203: Leaf order:
+27203: d 2 0 2 2,2,2,2,2
+27203: b 3 0 3 1,2,2
+27203: c 3 0 3 1,2,2,2
+27203: a 4 0 4 1,2
+27203: meet 19 2 5 0,2
+27203: join 19 2 5 0,2,2
+NO CLASH, using fixed ground order
+27204: Facts:
+27204: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27204: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27204: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27204: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27204: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27204: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27204: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27204: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27204: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
+ [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
+27204: Goal:
+27204: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+27204: Order:
+27204: kbo
+27204: Leaf order:
+27204: d 2 0 2 2,2,2,2,2
+27204: b 3 0 3 1,2,2
+27204: c 3 0 3 1,2,2,2
+27204: a 4 0 4 1,2
+27204: meet 19 2 5 0,2
+27204: join 19 2 5 0,2,2
+NO CLASH, using fixed ground order
+27205: Facts:
+27205: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27205: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27205: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27205: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27205: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27205: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27205: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27205: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27205: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
+ [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
+27205: Goal:
+27205: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+27205: Order:
+27205: lpo
+27205: Leaf order:
+27205: d 2 0 2 2,2,2,2,2
+27205: b 3 0 3 1,2,2
+27205: c 3 0 3 1,2,2,2
+27205: a 4 0 4 1,2
+27205: meet 19 2 5 0,2
+27205: join 19 2 5 0,2,2
+% SZS status Timeout for LAT113-1.p
+NO CLASH, using fixed ground order
+27406: Facts:
+27406: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27406: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27406: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27406: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27406: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27406: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27406: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27406: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27406: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
+ [28, 27, 26] by equation_H55 ?26 ?27 ?28
+27406: Goal:
+27406: Id : 1, {_}:
+ join (meet a b) (meet a (join b c))
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H56
+27406: Order:
+27406: nrkbo
+27406: Leaf order:
+27406: c 2 0 2 2,2,2,2
+27406: a 5 0 5 1,1,2
+27406: b 5 0 5 2,1,2
+27406: meet 17 2 5 0,1,2
+27406: join 19 2 5 0,2
+NO CLASH, using fixed ground order
+27407: Facts:
+27407: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27407: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27407: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27407: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27407: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27407: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27407: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27407: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27407: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
+ [28, 27, 26] by equation_H55 ?26 ?27 ?28
+27407: Goal:
+27407: Id : 1, {_}:
+ join (meet a b) (meet a (join b c))
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H56
+27407: Order:
+27407: kbo
+27407: Leaf order:
+27407: c 2 0 2 2,2,2,2
+27407: a 5 0 5 1,1,2
+27407: b 5 0 5 2,1,2
+27407: meet 17 2 5 0,1,2
+27407: join 19 2 5 0,2
+NO CLASH, using fixed ground order
+27408: Facts:
+27408: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27408: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27408: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27408: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27408: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27408: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27408: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27408: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27408: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =?=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
+ [28, 27, 26] by equation_H55 ?26 ?27 ?28
+27408: Goal:
+27408: Id : 1, {_}:
+ join (meet a b) (meet a (join b c))
+ =>=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H56
+27408: Order:
+27408: lpo
+27408: Leaf order:
+27408: c 2 0 2 2,2,2,2
+27408: a 5 0 5 1,1,2
+27408: b 5 0 5 2,1,2
+27408: meet 17 2 5 0,1,2
+27408: join 19 2 5 0,2
+% SZS status Timeout for LAT114-1.p
+NO CLASH, using fixed ground order
+27552: Facts:
+27552: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27552: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27552: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27552: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27552: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27552: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27552: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27552: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27552: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
+ [28, 27, 26] by equation_H55 ?26 ?27 ?28
+27552: Goal:
+27552: Id : 1, {_}:
+ meet a (meet (join b c) (join b d))
+ =<=
+ meet a (join b (meet (join b d) (join c (meet a b))))
+ [] by prove_H59
+27552: Order:
+27552: nrkbo
+27552: Leaf order:
+27552: c 2 0 2 2,1,2,2
+27552: d 2 0 2 2,2,2,2
+27552: a 3 0 3 1,2
+27552: b 5 0 5 1,1,2,2
+27552: meet 17 2 5 0,2
+27552: join 19 2 5 0,1,2,2
+NO CLASH, using fixed ground order
+27553: Facts:
+27553: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27553: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27553: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27553: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27553: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27553: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27553: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27553: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27553: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
+ [28, 27, 26] by equation_H55 ?26 ?27 ?28
+27553: Goal:
+27553: Id : 1, {_}:
+ meet a (meet (join b c) (join b d))
+ =<=
+ meet a (join b (meet (join b d) (join c (meet a b))))
+ [] by prove_H59
+27553: Order:
+27553: kbo
+27553: Leaf order:
+27553: c 2 0 2 2,1,2,2
+27553: d 2 0 2 2,2,2,2
+27553: a 3 0 3 1,2
+27553: b 5 0 5 1,1,2,2
+27553: meet 17 2 5 0,2
+27553: join 19 2 5 0,1,2,2
+NO CLASH, using fixed ground order
+27554: Facts:
+27554: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27554: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27554: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27554: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27554: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27554: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27554: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27554: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27554: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =?=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
+ [28, 27, 26] by equation_H55 ?26 ?27 ?28
+27554: Goal:
+27554: Id : 1, {_}:
+ meet a (meet (join b c) (join b d))
+ =<=
+ meet a (join b (meet (join b d) (join c (meet a b))))
+ [] by prove_H59
+27554: Order:
+27554: lpo
+27554: Leaf order:
+27554: c 2 0 2 2,1,2,2
+27554: d 2 0 2 2,2,2,2
+27554: a 3 0 3 1,2
+27554: b 5 0 5 1,1,2,2
+27554: meet 17 2 5 0,2
+27554: join 19 2 5 0,1,2,2
+% SZS status Timeout for LAT115-1.p
+NO CLASH, using fixed ground order
+27591: Facts:
+27591: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27591: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27591: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27591: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27591: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27591: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27591: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27591: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27591: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
+ [28, 27, 26] by equation_H55 ?26 ?27 ?28
+27591: Goal:
+27591: Id : 1, {_}:
+ meet a (meet (join b c) (join b d))
+ =<=
+ meet a (join b (meet (join b c) (join d (meet a b))))
+ [] by prove_H60
+27591: Order:
+27591: nrkbo
+27591: Leaf order:
+27591: c 2 0 2 2,1,2,2
+27591: d 2 0 2 2,2,2,2
+27591: a 3 0 3 1,2
+27591: b 5 0 5 1,1,2,2
+27591: meet 17 2 5 0,2
+27591: join 19 2 5 0,1,2,2
+NO CLASH, using fixed ground order
+27592: Facts:
+27592: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27592: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27592: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27592: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27592: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27592: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27592: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27592: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27592: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
+ [28, 27, 26] by equation_H55 ?26 ?27 ?28
+27592: Goal:
+27592: Id : 1, {_}:
+ meet a (meet (join b c) (join b d))
+ =<=
+ meet a (join b (meet (join b c) (join d (meet a b))))
+ [] by prove_H60
+27592: Order:
+27592: kbo
+27592: Leaf order:
+27592: c 2 0 2 2,1,2,2
+27592: d 2 0 2 2,2,2,2
+27592: a 3 0 3 1,2
+27592: b 5 0 5 1,1,2,2
+27592: meet 17 2 5 0,2
+27592: join 19 2 5 0,1,2,2
+NO CLASH, using fixed ground order
+27593: Facts:
+27593: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27593: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27593: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27593: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27593: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27593: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27593: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27593: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27593: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =?=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
+ [28, 27, 26] by equation_H55 ?26 ?27 ?28
+27593: Goal:
+27593: Id : 1, {_}:
+ meet a (meet (join b c) (join b d))
+ =<=
+ meet a (join b (meet (join b c) (join d (meet a b))))
+ [] by prove_H60
+27593: Order:
+27593: lpo
+27593: Leaf order:
+27593: c 2 0 2 2,1,2,2
+27593: d 2 0 2 2,2,2,2
+27593: a 3 0 3 1,2
+27593: b 5 0 5 1,1,2,2
+27593: meet 17 2 5 0,2
+27593: join 19 2 5 0,1,2,2
+% SZS status Timeout for LAT116-1.p
+NO CLASH, using fixed ground order
+27609: Facts:
+27609: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27609: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27609: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27609: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27609: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27609: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27609: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27609: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27609: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 ?29))
+ =<=
+ meet ?26 (join ?27 (meet ?26 (join (meet ?26 ?27) (meet ?28 ?29))))
+ [29, 28, 27, 26] by equation_H65 ?26 ?27 ?28 ?29
+27609: Goal:
+27609: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+27609: Order:
+27609: nrkbo
+27609: Leaf order:
+27609: b 3 0 3 1,2,2
+27609: c 3 0 3 2,2,2
+27609: a 5 0 5 1,2
+27609: join 16 2 4 0,2,2
+27609: meet 20 2 5 0,2
+NO CLASH, using fixed ground order
+27610: Facts:
+27610: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27610: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27610: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27610: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27610: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27610: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27610: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27610: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27610: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 ?29))
+ =<=
+ meet ?26 (join ?27 (meet ?26 (join (meet ?26 ?27) (meet ?28 ?29))))
+ [29, 28, 27, 26] by equation_H65 ?26 ?27 ?28 ?29
+27610: Goal:
+27610: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+27610: Order:
+27610: kbo
+27610: Leaf order:
+27610: b 3 0 3 1,2,2
+27610: c 3 0 3 2,2,2
+27610: a 5 0 5 1,2
+27610: join 16 2 4 0,2,2
+27610: meet 20 2 5 0,2
+NO CLASH, using fixed ground order
+27611: Facts:
+27611: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+27611: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+27611: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+27611: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+27611: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+27611: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+27611: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+27611: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+27611: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 ?29))
+ =<=
+ meet ?26 (join ?27 (meet ?26 (join (meet ?26 ?27) (meet ?28 ?29))))
+ [29, 28, 27, 26] by equation_H65 ?26 ?27 ?28 ?29
+27611: Goal:
+27611: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+27611: Order:
+27611: lpo
+27611: Leaf order:
+27611: b 3 0 3 1,2,2
+27611: c 3 0 3 2,2,2
+27611: a 5 0 5 1,2
+27611: join 16 2 4 0,2,2
+27611: meet 20 2 5 0,2
+% SZS status Timeout for LAT117-1.p
+NO CLASH, using fixed ground order
+28243: Facts:
+28243: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28243: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28243: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28243: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28243: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28243: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28243: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28243: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28243: Id : 10, {_}:
+ meet ?26 (join (meet ?27 (join ?26 ?28)) (meet ?28 (join ?26 ?27)))
+ =>=
+ join (meet ?26 ?27) (meet ?26 ?28)
+ [28, 27, 26] by equation_H82 ?26 ?27 ?28
+28243: Goal:
+28243: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+28243: Order:
+28243: nrkbo
+28243: Leaf order:
+28243: c 3 0 3 2,2,2,2
+28243: b 4 0 4 1,2,2
+28243: a 5 0 5 1,2
+28243: join 17 2 4 0,2,2
+28243: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+28244: Facts:
+28244: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28244: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28244: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28244: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28244: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28244: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28244: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28244: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28244: Id : 10, {_}:
+ meet ?26 (join (meet ?27 (join ?26 ?28)) (meet ?28 (join ?26 ?27)))
+ =>=
+ join (meet ?26 ?27) (meet ?26 ?28)
+ [28, 27, 26] by equation_H82 ?26 ?27 ?28
+28244: Goal:
+28244: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+28244: Order:
+28244: kbo
+28244: Leaf order:
+28244: c 3 0 3 2,2,2,2
+28244: b 4 0 4 1,2,2
+28244: a 5 0 5 1,2
+28244: join 17 2 4 0,2,2
+28244: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+28246: Facts:
+28246: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28246: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28246: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28246: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28246: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28246: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28246: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28246: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28246: Id : 10, {_}:
+ meet ?26 (join (meet ?27 (join ?26 ?28)) (meet ?28 (join ?26 ?27)))
+ =>=
+ join (meet ?26 ?27) (meet ?26 ?28)
+ [28, 27, 26] by equation_H82 ?26 ?27 ?28
+28246: Goal:
+28246: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+28246: Order:
+28246: lpo
+28246: Leaf order:
+28246: c 3 0 3 2,2,2,2
+28246: b 4 0 4 1,2,2
+28246: a 5 0 5 1,2
+28246: join 17 2 4 0,2,2
+28246: meet 20 2 6 0,2
+% SZS status Timeout for LAT119-1.p
+NO CLASH, using fixed ground order
+28653: Facts:
+28653: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28653: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28653: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28653: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28653: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28653: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28653: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28653: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28653: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?27 ?28))))
+ [28, 27, 26] by equation_H10_dual ?26 ?27 ?28
+28653: Goal:
+28653: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H58
+28653: Order:
+28653: nrkbo
+28653: Leaf order:
+28653: c 2 0 2 2,2,2
+28653: a 4 0 4 1,2
+28653: b 4 0 4 1,2,2
+28653: meet 16 2 4 0,2
+28653: join 18 2 4 0,2,2
+NO CLASH, using fixed ground order
+28654: Facts:
+28654: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28654: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28654: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28654: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28654: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28654: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28654: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28654: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28654: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?27 ?28))))
+ [28, 27, 26] by equation_H10_dual ?26 ?27 ?28
+28654: Goal:
+28654: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H58
+28654: Order:
+28654: kbo
+28654: Leaf order:
+28654: c 2 0 2 2,2,2
+28654: a 4 0 4 1,2
+28654: b 4 0 4 1,2,2
+28654: meet 16 2 4 0,2
+28654: join 18 2 4 0,2,2
+NO CLASH, using fixed ground order
+28655: Facts:
+28655: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28655: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28655: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28655: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28655: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28655: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28655: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28655: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28655: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =?=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?27 ?28))))
+ [28, 27, 26] by equation_H10_dual ?26 ?27 ?28
+28655: Goal:
+28655: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H58
+28655: Order:
+28655: lpo
+28655: Leaf order:
+28655: c 2 0 2 2,2,2
+28655: a 4 0 4 1,2
+28655: b 4 0 4 1,2,2
+28655: meet 16 2 4 0,2
+28655: join 18 2 4 0,2,2
+% SZS status Timeout for LAT120-1.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+28691: Facts:
+28691: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28691: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28691: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28691: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28691: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28691: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28691: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28691: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28691: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?26 ?27)
+ (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
+ [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
+28691: Goal:
+28691: Id : 1, {_}:
+ join a (meet b (join a c))
+ =<=
+ join a (meet b (join c (meet a (join c b))))
+ [] by prove_H55
+28691: Order:
+28691: kbo
+28691: Leaf order:
+28691: b 3 0 3 1,2,2
+28691: c 3 0 3 2,2,2,2
+28691: a 4 0 4 1,2
+28691: meet 16 2 3 0,2,2
+28691: join 20 2 5 0,2
+28690: Facts:
+28690: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28690: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28690: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28690: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28690: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28690: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28690: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28690: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28690: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?26 ?27)
+ (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
+ [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
+28690: Goal:
+28690: Id : 1, {_}:
+ join a (meet b (join a c))
+ =<=
+ join a (meet b (join c (meet a (join c b))))
+ [] by prove_H55
+28690: Order:
+28690: nrkbo
+28690: Leaf order:
+28690: b 3 0 3 1,2,2
+28690: c 3 0 3 2,2,2,2
+28690: a 4 0 4 1,2
+28690: meet 16 2 3 0,2,2
+28690: join 20 2 5 0,2
+NO CLASH, using fixed ground order
+28692: Facts:
+28692: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28692: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28692: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28692: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28692: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28692: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28692: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28692: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28692: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?26 ?27)
+ (meet (join ?26 ?28) (join ?27 (meet ?26 ?28))))
+ [28, 27, 26] by equation_H18_dual ?26 ?27 ?28
+28692: Goal:
+28692: Id : 1, {_}:
+ join a (meet b (join a c))
+ =>=
+ join a (meet b (join c (meet a (join c b))))
+ [] by prove_H55
+28692: Order:
+28692: lpo
+28692: Leaf order:
+28692: b 3 0 3 1,2,2
+28692: c 3 0 3 2,2,2,2
+28692: a 4 0 4 1,2
+28692: meet 16 2 3 0,2,2
+28692: join 20 2 5 0,2
+% SZS status Timeout for LAT121-1.p
+NO CLASH, using fixed ground order
+28708: Facts:
+28708: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28708: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28708: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28708: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28708: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28708: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28708: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28708: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28708: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?27 (meet ?26 (join ?27 ?28)))
+ (join ?28 (meet ?26 ?27)))
+ [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
+28708: Goal:
+28708: Id : 1, {_}:
+ join a (meet b (join a c))
+ =<=
+ join a (meet b (join c (meet a (join c b))))
+ [] by prove_H55
+28708: Order:
+28708: nrkbo
+28708: Leaf order:
+28708: b 3 0 3 1,2,2
+28708: c 3 0 3 2,2,2,2
+28708: a 4 0 4 1,2
+28708: meet 16 2 3 0,2,2
+28708: join 20 2 5 0,2
+NO CLASH, using fixed ground order
+28709: Facts:
+28709: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28709: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28709: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28709: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28709: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28709: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28709: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28709: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28709: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?27 (meet ?26 (join ?27 ?28)))
+ (join ?28 (meet ?26 ?27)))
+ [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
+28709: Goal:
+28709: Id : 1, {_}:
+ join a (meet b (join a c))
+ =<=
+ join a (meet b (join c (meet a (join c b))))
+ [] by prove_H55
+28709: Order:
+28709: kbo
+28709: Leaf order:
+28709: b 3 0 3 1,2,2
+28709: c 3 0 3 2,2,2,2
+28709: a 4 0 4 1,2
+28709: meet 16 2 3 0,2,2
+28709: join 20 2 5 0,2
+NO CLASH, using fixed ground order
+28710: Facts:
+28710: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28710: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28710: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28710: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28710: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28710: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28710: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28710: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28710: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?27 (meet ?26 (join ?27 ?28)))
+ (join ?28 (meet ?26 ?27)))
+ [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
+28710: Goal:
+28710: Id : 1, {_}:
+ join a (meet b (join a c))
+ =>=
+ join a (meet b (join c (meet a (join c b))))
+ [] by prove_H55
+28710: Order:
+28710: lpo
+28710: Leaf order:
+28710: b 3 0 3 1,2,2
+28710: c 3 0 3 2,2,2,2
+28710: a 4 0 4 1,2
+28710: meet 16 2 3 0,2,2
+28710: join 20 2 5 0,2
+% SZS status Timeout for LAT122-1.p
+NO CLASH, using fixed ground order
+28742: Facts:
+28742: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28742: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28742: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28742: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28742: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28742: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28742: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28742: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28742: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?27 (meet ?28 (join ?26 ?27)))
+ (join ?28 (meet ?26 ?27)))
+ [28, 27, 26] by equation_H22_dual ?26 ?27 ?28
+28742: Goal:
+28742: Id : 1, {_}:
+ join a (meet b (join a c))
+ =<=
+ join a (meet b (join c (meet a (join c b))))
+ [] by prove_H55
+28742: Order:
+28742: nrkbo
+28742: Leaf order:
+28742: b 3 0 3 1,2,2
+28742: c 3 0 3 2,2,2,2
+28742: a 4 0 4 1,2
+28742: meet 16 2 3 0,2,2
+28742: join 20 2 5 0,2
+NO CLASH, using fixed ground order
+28743: Facts:
+28743: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28743: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28743: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28743: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28743: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28743: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28743: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28743: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28743: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?27 (meet ?28 (join ?26 ?27)))
+ (join ?28 (meet ?26 ?27)))
+ [28, 27, 26] by equation_H22_dual ?26 ?27 ?28
+28743: Goal:
+28743: Id : 1, {_}:
+ join a (meet b (join a c))
+ =<=
+ join a (meet b (join c (meet a (join c b))))
+ [] by prove_H55
+28743: Order:
+28743: kbo
+28743: Leaf order:
+28743: b 3 0 3 1,2,2
+28743: c 3 0 3 2,2,2,2
+28743: a 4 0 4 1,2
+28743: meet 16 2 3 0,2,2
+28743: join 20 2 5 0,2
+NO CLASH, using fixed ground order
+28744: Facts:
+28744: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28744: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28744: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28744: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28744: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28744: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28744: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28744: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28744: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?27 (meet ?28 (join ?26 ?27)))
+ (join ?28 (meet ?26 ?27)))
+ [28, 27, 26] by equation_H22_dual ?26 ?27 ?28
+28744: Goal:
+28744: Id : 1, {_}:
+ join a (meet b (join a c))
+ =>=
+ join a (meet b (join c (meet a (join c b))))
+ [] by prove_H55
+28744: Order:
+28744: lpo
+28744: Leaf order:
+28744: b 3 0 3 1,2,2
+28744: c 3 0 3 2,2,2,2
+28744: a 4 0 4 1,2
+28744: meet 16 2 3 0,2,2
+28744: join 20 2 5 0,2
+% SZS status Timeout for LAT123-1.p
+NO CLASH, using fixed ground order
+28780: Facts:
+28780: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28780: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28780: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28780: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28780: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28780: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28780: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28780: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28780: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 (join ?28 ?29)))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet (join ?26 ?29) (join ?27 ?29))))
+ [29, 28, 27, 26] by equation_H32_dual ?26 ?27 ?28 ?29
+28780: Goal:
+28780: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+28780: Order:
+28780: nrkbo
+28780: Leaf order:
+28780: b 3 0 3 1,2,2
+28780: c 3 0 3 2,2,2
+28780: a 5 0 5 1,2
+28780: meet 17 2 5 0,2
+28780: join 20 2 4 0,2,2
+NO CLASH, using fixed ground order
+28781: Facts:
+28781: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28781: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28781: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28781: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28781: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28781: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28781: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28781: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28781: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 (join ?28 ?29)))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet (join ?26 ?29) (join ?27 ?29))))
+ [29, 28, 27, 26] by equation_H32_dual ?26 ?27 ?28 ?29
+28781: Goal:
+28781: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+28781: Order:
+28781: kbo
+28781: Leaf order:
+28781: b 3 0 3 1,2,2
+28781: c 3 0 3 2,2,2
+28781: a 5 0 5 1,2
+28781: meet 17 2 5 0,2
+28781: join 20 2 4 0,2,2
+NO CLASH, using fixed ground order
+28782: Facts:
+28782: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28782: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28782: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28782: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28782: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28782: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28782: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28782: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28782: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 (join ?28 ?29)))
+ =?=
+ join ?26 (meet ?27 (join ?28 (meet (join ?26 ?29) (join ?27 ?29))))
+ [29, 28, 27, 26] by equation_H32_dual ?26 ?27 ?28 ?29
+28782: Goal:
+28782: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+28782: Order:
+28782: lpo
+28782: Leaf order:
+28782: b 3 0 3 1,2,2
+28782: c 3 0 3 2,2,2
+28782: a 5 0 5 1,2
+28782: meet 17 2 5 0,2
+28782: join 20 2 4 0,2,2
+% SZS status Timeout for LAT124-1.p
+NO CLASH, using fixed ground order
+28810: Facts:
+28810: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28810: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28810: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28810: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28810: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28810: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28810: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28810: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28810: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 ?29))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?27 (join ?29 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H34_dual ?26 ?27 ?28 ?29
+28810: Goal:
+28810: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+28810: Order:
+28810: nrkbo
+28810: Leaf order:
+28810: b 3 0 3 1,2,2
+28810: c 3 0 3 2,2,2
+28810: a 5 0 5 1,2
+28810: join 18 2 4 0,2,2
+28810: meet 18 2 5 0,2
+NO CLASH, using fixed ground order
+28811: Facts:
+28811: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28811: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28811: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28811: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28811: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28811: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28811: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28811: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28811: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 ?29))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?27 (join ?29 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H34_dual ?26 ?27 ?28 ?29
+28811: Goal:
+28811: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+28811: Order:
+28811: kbo
+28811: Leaf order:
+28811: b 3 0 3 1,2,2
+28811: c 3 0 3 2,2,2
+NO CLASH, using fixed ground order
+28812: Facts:
+28812: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28812: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28812: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28812: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28812: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28812: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28812: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28812: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28811: a 5 0 5 1,2
+28811: join 18 2 4 0,2,2
+28811: meet 18 2 5 0,2
+28812: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 ?29))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?27 (join ?29 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H34_dual ?26 ?27 ?28 ?29
+28812: Goal:
+28812: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+28812: Order:
+28812: lpo
+28812: Leaf order:
+28812: b 3 0 3 1,2,2
+28812: c 3 0 3 2,2,2
+28812: a 5 0 5 1,2
+28812: join 18 2 4 0,2,2
+28812: meet 18 2 5 0,2
+% SZS status Timeout for LAT125-1.p
+NO CLASH, using fixed ground order
+28829: Facts:
+28829: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28829: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28829: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28829: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28829: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28829: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28829: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28829: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28829: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?28))))
+ [29, 28, 27, 26] by equation_H39_dual ?26 ?27 ?28 ?29
+28829: Goal:
+28829: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+28829: Order:
+28829: kbo
+28829: Leaf order:
+28829: b 3 0 3 1,2,2
+28829: c 3 0 3 2,2,2
+28829: a 5 0 5 1,2
+28829: join 18 2 4 0,2,2
+28829: meet 18 2 5 0,2
+NO CLASH, using fixed ground order
+28828: Facts:
+28828: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28828: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28828: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28828: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28828: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28828: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28828: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28828: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28828: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?28))))
+ [29, 28, 27, 26] by equation_H39_dual ?26 ?27 ?28 ?29
+28828: Goal:
+28828: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+28828: Order:
+28828: nrkbo
+28828: Leaf order:
+28828: b 3 0 3 1,2,2
+28828: c 3 0 3 2,2,2
+28828: a 5 0 5 1,2
+28828: join 18 2 4 0,2,2
+28828: meet 18 2 5 0,2
+NO CLASH, using fixed ground order
+28830: Facts:
+28830: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28830: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28830: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28830: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28830: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28830: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28830: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28830: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28830: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =?=
+ join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?28))))
+ [29, 28, 27, 26] by equation_H39_dual ?26 ?27 ?28 ?29
+28830: Goal:
+28830: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+28830: Order:
+28830: lpo
+28830: Leaf order:
+28830: b 3 0 3 1,2,2
+28830: c 3 0 3 2,2,2
+28830: a 5 0 5 1,2
+28830: join 18 2 4 0,2,2
+28830: meet 18 2 5 0,2
+% SZS status Timeout for LAT126-1.p
+NO CLASH, using fixed ground order
+28859: Facts:
+28859: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28859: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28859: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28859: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28859: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28859: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28859: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28859: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28859: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 ?27))))
+ [28, 27, 26] by equation_H55_dual ?26 ?27 ?28
+28859: Goal:
+28859: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+28859: Order:
+28859: nrkbo
+28859: Leaf order:
+28859: b 3 0 3 1,2,2
+28859: c 3 0 3 2,2,2,2
+28859: a 6 0 6 1,2
+28859: join 16 2 4 0,2,2
+28859: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+28860: Facts:
+28860: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28860: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28860: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28860: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28860: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28860: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28860: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28860: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28860: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 ?27))))
+ [28, 27, 26] by equation_H55_dual ?26 ?27 ?28
+28860: Goal:
+28860: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+28860: Order:
+28860: kbo
+28860: Leaf order:
+28860: b 3 0 3 1,2,2
+28860: c 3 0 3 2,2,2,2
+28860: a 6 0 6 1,2
+28860: join 16 2 4 0,2,2
+28860: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+28861: Facts:
+28861: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28861: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28861: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28861: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28861: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28861: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28861: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28861: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28861: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 ?27))))
+ [28, 27, 26] by equation_H55_dual ?26 ?27 ?28
+28861: Goal:
+28861: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+28861: Order:
+28861: lpo
+28861: Leaf order:
+28861: b 3 0 3 1,2,2
+28861: c 3 0 3 2,2,2,2
+28861: a 6 0 6 1,2
+28861: join 16 2 4 0,2,2
+28861: meet 20 2 6 0,2
+% SZS status Timeout for LAT127-1.p
+NO CLASH, using fixed ground order
+28878: Facts:
+28878: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28878: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28878: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28878: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28878: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28878: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28878: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28878: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28878: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
+ [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
+28878: Goal:
+28878: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+28878: Order:
+28878: nrkbo
+28878: Leaf order:
+28878: c 3 0 3 2,2,2,2
+28878: b 4 0 4 1,2,2
+28878: a 5 0 5 1,2
+28878: join 17 2 4 0,2,2
+28878: meet 19 2 6 0,2
+NO CLASH, using fixed ground order
+28879: Facts:
+28879: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28879: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28879: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28879: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28879: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28879: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28879: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28879: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28879: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
+ [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
+28879: Goal:
+28879: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+28879: Order:
+28879: kbo
+28879: Leaf order:
+28879: c 3 0 3 2,2,2,2
+28879: b 4 0 4 1,2,2
+NO CLASH, using fixed ground order
+28880: Facts:
+28880: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28880: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28880: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28880: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28880: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28880: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28880: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28880: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28880: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
+ [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
+28880: Goal:
+28880: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join b (meet a (join c (meet a b))))))
+ [] by prove_H3
+28880: Order:
+28880: lpo
+28880: Leaf order:
+28880: c 3 0 3 2,2,2,2
+28880: b 4 0 4 1,2,2
+28880: a 5 0 5 1,2
+28880: join 17 2 4 0,2,2
+28880: meet 19 2 6 0,2
+28879: a 5 0 5 1,2
+28879: join 17 2 4 0,2,2
+28879: meet 19 2 6 0,2
+% SZS status Timeout for LAT128-1.p
+NO CLASH, using fixed ground order
+28929: Facts:
+28929: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28929: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28929: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28929: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28929: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28929: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28929: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28929: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28929: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
+ [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
+28929: Goal:
+28929: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join a (meet b c))))
+ [] by prove_H10
+28929: Order:
+28929: nrkbo
+28929: Leaf order:
+28929: b 3 0 3 1,2,2
+28929: c 3 0 3 2,2,2,2
+28929: a 4 0 4 1,2
+28929: join 16 2 3 0,2,2
+28929: meet 18 2 5 0,2
+NO CLASH, using fixed ground order
+28930: Facts:
+28930: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28930: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28930: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28930: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28930: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28930: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28930: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28930: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28930: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
+ [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
+28930: Goal:
+28930: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join a (meet b c))))
+ [] by prove_H10
+28930: Order:
+28930: kbo
+28930: Leaf order:
+28930: b 3 0 3 1,2,2
+28930: c 3 0 3 2,2,2,2
+28930: a 4 0 4 1,2
+28930: join 16 2 3 0,2,2
+28930: meet 18 2 5 0,2
+NO CLASH, using fixed ground order
+28931: Facts:
+28931: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28931: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28931: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28931: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28931: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28931: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28931: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28931: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28931: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))
+ [28, 27, 26] by equation_H58_dual ?26 ?27 ?28
+28931: Goal:
+28931: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =>=
+ meet a (join b (meet c (join a (meet b c))))
+ [] by prove_H10
+28931: Order:
+28931: lpo
+28931: Leaf order:
+28931: b 3 0 3 1,2,2
+28931: c 3 0 3 2,2,2,2
+28931: a 4 0 4 1,2
+28931: join 16 2 3 0,2,2
+28931: meet 18 2 5 0,2
+% SZS status Timeout for LAT129-1.p
+NO CLASH, using fixed ground order
+28978: Facts:
+28978: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28978: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28978: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28978: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28978: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28978: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28978: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28978: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28978: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
+ [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
+28978: Goal:
+28978: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet a c))))
+ [] by prove_H39
+28978: Order:
+28978: nrkbo
+28978: Leaf order:
+28978: b 2 0 2 1,2,2
+28978: d 2 0 2 2,2,2,2,2
+28978: c 3 0 3 1,2,2,2
+28978: a 4 0 4 1,2
+28978: join 17 2 4 0,2,2
+28978: meet 17 2 5 0,2
+NO CLASH, using fixed ground order
+28979: Facts:
+28979: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28979: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28979: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28979: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28979: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28979: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28979: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28979: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28979: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
+ [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
+28979: Goal:
+28979: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet a c))))
+ [] by prove_H39
+28979: Order:
+28979: kbo
+28979: Leaf order:
+28979: b 2 0 2 1,2,2
+28979: d 2 0 2 2,2,2,2,2
+28979: c 3 0 3 1,2,2,2
+28979: a 4 0 4 1,2
+28979: join 17 2 4 0,2,2
+28979: meet 17 2 5 0,2
+NO CLASH, using fixed ground order
+28980: Facts:
+28980: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+28980: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+28980: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+28980: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+28980: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+28980: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+28980: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+28980: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+28980: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
+ [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
+28980: Goal:
+28980: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet a c))))
+ [] by prove_H39
+28980: Order:
+28980: lpo
+28980: Leaf order:
+28980: b 2 0 2 1,2,2
+28980: d 2 0 2 2,2,2,2,2
+28980: c 3 0 3 1,2,2,2
+28980: a 4 0 4 1,2
+28980: join 17 2 4 0,2,2
+28980: meet 17 2 5 0,2
+% SZS status Timeout for LAT130-1.p
+NO CLASH, using fixed ground order
+29013: Facts:
+29013: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29013: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29013: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29013: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29013: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29013: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29013: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29013: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29013: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
+ [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
+29013: Goal:
+29013: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+29013: Order:
+29013: nrkbo
+29013: Leaf order:
+29013: d 2 0 2 2,2,2,2,2
+29013: b 3 0 3 1,2,2
+29013: c 3 0 3 1,2,2,2
+29013: a 4 0 4 1,2
+29013: meet 17 2 5 0,2
+29013: join 18 2 5 0,2,2
+NO CLASH, using fixed ground order
+29014: Facts:
+29014: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29014: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29014: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29014: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29014: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29014: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29014: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29014: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29014: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
+ [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
+29014: Goal:
+29014: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+29014: Order:
+29014: kbo
+29014: Leaf order:
+29014: d 2 0 2 2,2,2,2,2
+29014: b 3 0 3 1,2,2
+29014: c 3 0 3 1,2,2,2
+29014: a 4 0 4 1,2
+29014: meet 17 2 5 0,2
+29014: join 18 2 5 0,2,2
+NO CLASH, using fixed ground order
+29015: Facts:
+29015: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29015: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29015: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29015: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29015: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29015: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29015: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29015: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29015: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27))))
+ [28, 27, 26] by equation_H68_dual ?26 ?27 ?28
+29015: Goal:
+29015: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =>=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+29015: Order:
+29015: lpo
+29015: Leaf order:
+29015: d 2 0 2 2,2,2,2,2
+29015: b 3 0 3 1,2,2
+29015: c 3 0 3 1,2,2,2
+29015: a 4 0 4 1,2
+29015: meet 17 2 5 0,2
+29015: join 18 2 5 0,2,2
+% SZS status Timeout for LAT131-1.p
+NO CLASH, using fixed ground order
+29032: Facts:
+29032: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29032: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29032: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29032: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29032: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29032: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29032: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29032: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29032: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ meet (join ?26 (meet ?28 (join ?26 ?27)))
+ (join ?26 (meet ?27 (join ?26 ?28)))
+ [28, 27, 26] by equation_H69_dual ?26 ?27 ?28
+29032: Goal:
+29032: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+29032: Order:
+29032: nrkbo
+29032: Leaf order:
+29032: d 2 0 2 2,2,2,2,2
+29032: b 3 0 3 1,2,2
+29032: c 3 0 3 1,2,2,2
+29032: a 4 0 4 1,2
+29032: meet 18 2 5 0,2
+29032: join 19 2 5 0,2,2
+NO CLASH, using fixed ground order
+29033: Facts:
+29033: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29033: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29033: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29033: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29033: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29033: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29033: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29033: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29033: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ meet (join ?26 (meet ?28 (join ?26 ?27)))
+ (join ?26 (meet ?27 (join ?26 ?28)))
+ [28, 27, 26] by equation_H69_dual ?26 ?27 ?28
+29033: Goal:
+29033: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+29033: Order:
+29033: kbo
+29033: Leaf order:
+29033: d 2 0 2 2,2,2,2,2
+29033: b 3 0 3 1,2,2
+29033: c 3 0 3 1,2,2,2
+29033: a 4 0 4 1,2
+29033: meet 18 2 5 0,2
+29033: join 19 2 5 0,2,2
+NO CLASH, using fixed ground order
+29034: Facts:
+29034: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29034: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29034: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29034: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29034: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29034: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29034: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29034: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29034: Id : 10, {_}:
+ join ?26 (meet ?27 ?28)
+ =<=
+ meet (join ?26 (meet ?28 (join ?26 ?27)))
+ (join ?26 (meet ?27 (join ?26 ?28)))
+ [28, 27, 26] by equation_H69_dual ?26 ?27 ?28
+29034: Goal:
+29034: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =>=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+29034: Order:
+29034: lpo
+29034: Leaf order:
+29034: d 2 0 2 2,2,2,2,2
+29034: b 3 0 3 1,2,2
+29034: c 3 0 3 1,2,2,2
+29034: a 4 0 4 1,2
+29034: meet 18 2 5 0,2
+29034: join 19 2 5 0,2,2
+% SZS status Timeout for LAT132-1.p
+NO CLASH, using fixed ground order
+29065: Facts:
+29065: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29065: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29065: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29065: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29065: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29065: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29065: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29065: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29065: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
+ [28, 27, 26] by equation_H55 ?26 ?27 ?28
+29065: Goal:
+29065: Id : 1, {_}:
+ join a (meet b (join a c))
+ =<=
+ join a (meet (join a (meet b (join a c))) (join c (meet a b)))
+ [] by prove_H6_dual
+29065: Order:
+29065: nrkbo
+29065: Leaf order:
+29065: b 3 0 3 1,2,2
+29065: c 3 0 3 2,2,2,2
+29065: a 6 0 6 1,2
+29065: meet 16 2 4 0,2,2
+29065: join 20 2 6 0,2
+NO CLASH, using fixed ground order
+29066: Facts:
+29066: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29066: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29066: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29066: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29066: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29066: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29066: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29066: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29066: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
+ [28, 27, 26] by equation_H55 ?26 ?27 ?28
+29066: Goal:
+29066: Id : 1, {_}:
+ join a (meet b (join a c))
+ =<=
+ join a (meet (join a (meet b (join a c))) (join c (meet a b)))
+ [] by prove_H6_dual
+29066: Order:
+29066: kbo
+29066: Leaf order:
+29066: b 3 0 3 1,2,2
+29066: c 3 0 3 2,2,2,2
+29066: a 6 0 6 1,2
+29066: meet 16 2 4 0,2,2
+29066: join 20 2 6 0,2
+NO CLASH, using fixed ground order
+29067: Facts:
+29067: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29067: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29067: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29067: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29067: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29067: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29067: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29067: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29067: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?26 ?28))
+ =?=
+ join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27))))
+ [28, 27, 26] by equation_H55 ?26 ?27 ?28
+29067: Goal:
+29067: Id : 1, {_}:
+ join a (meet b (join a c))
+ =<=
+ join a (meet (join a (meet b (join a c))) (join c (meet a b)))
+ [] by prove_H6_dual
+29067: Order:
+29067: lpo
+29067: Leaf order:
+29067: b 3 0 3 1,2,2
+29067: c 3 0 3 2,2,2,2
+29067: a 6 0 6 1,2
+29067: meet 16 2 4 0,2,2
+29067: join 20 2 6 0,2
+% SZS status Timeout for LAT133-1.p
+NO CLASH, using fixed ground order
+29084: Facts:
+29084: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29084: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29084: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29084: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29084: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29084: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29084: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29084: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29084: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26 (meet (join ?26 ?27) (join (meet ?26 ?27) ?28))
+ [28, 27, 26] by equation_H61 ?26 ?27 ?28
+29084: Goal:
+29084: Id : 1, {_}:
+ meet (join a b) (join a c)
+ =<=
+ join a (meet (join b (meet c (join a b))) (join c (meet a b)))
+ [] by prove_H22_dual
+29084: Order:
+29084: nrkbo
+29084: Leaf order:
+29084: c 3 0 3 2,2,2
+29084: b 4 0 4 2,1,2
+29084: a 5 0 5 1,1,2
+29084: meet 16 2 4 0,2
+29084: join 20 2 6 0,1,2
+NO CLASH, using fixed ground order
+29085: Facts:
+29085: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29085: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29085: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29085: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29085: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29085: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29085: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29085: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29085: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26 (meet (join ?26 ?27) (join (meet ?26 ?27) ?28))
+ [28, 27, 26] by equation_H61 ?26 ?27 ?28
+29085: Goal:
+29085: Id : 1, {_}:
+ meet (join a b) (join a c)
+ =<=
+ join a (meet (join b (meet c (join a b))) (join c (meet a b)))
+ [] by prove_H22_dual
+29085: Order:
+29085: kbo
+29085: Leaf order:
+29085: c 3 0 3 2,2,2
+29085: b 4 0 4 2,1,2
+29085: a 5 0 5 1,1,2
+29085: meet 16 2 4 0,2
+29085: join 20 2 6 0,1,2
+NO CLASH, using fixed ground order
+29086: Facts:
+29086: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29086: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29086: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29086: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29086: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29086: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29086: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29086: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29086: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26 (meet (join ?26 ?27) (join (meet ?26 ?27) ?28))
+ [28, 27, 26] by equation_H61 ?26 ?27 ?28
+29086: Goal:
+29086: Id : 1, {_}:
+ meet (join a b) (join a c)
+ =<=
+ join a (meet (join b (meet c (join a b))) (join c (meet a b)))
+ [] by prove_H22_dual
+29086: Order:
+29086: lpo
+29086: Leaf order:
+29086: c 3 0 3 2,2,2
+29086: b 4 0 4 2,1,2
+29086: a 5 0 5 1,1,2
+29086: meet 16 2 4 0,2
+29086: join 20 2 6 0,1,2
+% SZS status Timeout for LAT134-1.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+29118: Facts:
+29118: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29118: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29118: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29118: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29118: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29118: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29118: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29118: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29118: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
+ [28, 27, 26] by equation_H68 ?26 ?27 ?28
+29118: Goal:
+29118: Id : 1, {_}:
+ join a (meet b (join c (meet a d)))
+ =<=
+ join a (meet b (join c (meet d (join a c))))
+ [] by prove_H39_dual
+29118: Order:
+29118: kbo
+29118: Leaf order:
+29118: b 2 0 2 1,2,2
+29118: d 2 0 2 2,2,2,2,2
+29118: c 3 0 3 1,2,2,2
+29118: a 4 0 4 1,2
+29118: meet 17 2 4 0,2,2
+29118: join 17 2 5 0,2
+29117: Facts:
+29117: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29117: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29117: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29117: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29117: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29117: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29117: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29117: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29117: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
+ [28, 27, 26] by equation_H68 ?26 ?27 ?28
+29117: Goal:
+29117: Id : 1, {_}:
+ join a (meet b (join c (meet a d)))
+ =<=
+ join a (meet b (join c (meet d (join a c))))
+ [] by prove_H39_dual
+29117: Order:
+29117: nrkbo
+29117: Leaf order:
+29117: b 2 0 2 1,2,2
+29117: d 2 0 2 2,2,2,2,2
+29117: c 3 0 3 1,2,2,2
+29117: a 4 0 4 1,2
+29117: meet 17 2 4 0,2,2
+29117: join 17 2 5 0,2
+NO CLASH, using fixed ground order
+29119: Facts:
+29119: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29119: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29119: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29119: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29119: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29119: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29119: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29119: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29119: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
+ [28, 27, 26] by equation_H68 ?26 ?27 ?28
+29119: Goal:
+29119: Id : 1, {_}:
+ join a (meet b (join c (meet a d)))
+ =<=
+ join a (meet b (join c (meet d (join a c))))
+ [] by prove_H39_dual
+29119: Order:
+29119: lpo
+29119: Leaf order:
+29119: b 2 0 2 1,2,2
+29119: d 2 0 2 2,2,2,2,2
+29119: c 3 0 3 1,2,2,2
+29119: a 4 0 4 1,2
+29119: meet 17 2 4 0,2,2
+29119: join 17 2 5 0,2
+% SZS status Timeout for LAT135-1.p
+NO CLASH, using fixed ground order
+29145: Facts:
+29145: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29145: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29145: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29145: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29145: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29145: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29145: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29145: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29145: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ join (meet ?26 (join ?28 (meet ?26 ?27)))
+ (meet ?26 (join ?27 (meet ?26 ?28)))
+ [28, 27, 26] by equation_H69 ?26 ?27 ?28
+29145: Goal:
+29145: Id : 1, {_}:
+ join a (meet b (join c (meet a d)))
+ =<=
+ join a (meet b (join c (meet d (join a c))))
+ [] by prove_H39_dual
+29145: Order:
+29145: nrkbo
+29145: Leaf order:
+29145: b 2 0 2 1,2,2
+29145: d 2 0 2 2,2,2,2,2
+29145: c 3 0 3 1,2,2,2
+29145: a 4 0 4 1,2
+29145: meet 18 2 4 0,2,2
+29145: join 18 2 5 0,2
+NO CLASH, using fixed ground order
+29146: Facts:
+29146: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29146: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29146: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29146: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29146: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29146: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29146: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29146: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29146: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ join (meet ?26 (join ?28 (meet ?26 ?27)))
+ (meet ?26 (join ?27 (meet ?26 ?28)))
+ [28, 27, 26] by equation_H69 ?26 ?27 ?28
+29146: Goal:
+29146: Id : 1, {_}:
+ join a (meet b (join c (meet a d)))
+ =<=
+ join a (meet b (join c (meet d (join a c))))
+ [] by prove_H39_dual
+29146: Order:
+29146: kbo
+29146: Leaf order:
+29146: b 2 0 2 1,2,2
+29146: d 2 0 2 2,2,2,2,2
+29146: c 3 0 3 1,2,2,2
+29146: a 4 0 4 1,2
+29146: meet 18 2 4 0,2,2
+29146: join 18 2 5 0,2
+NO CLASH, using fixed ground order
+29147: Facts:
+29147: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29147: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29147: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29147: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29147: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29147: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29147: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29147: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29147: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ join (meet ?26 (join ?28 (meet ?26 ?27)))
+ (meet ?26 (join ?27 (meet ?26 ?28)))
+ [28, 27, 26] by equation_H69 ?26 ?27 ?28
+29147: Goal:
+29147: Id : 1, {_}:
+ join a (meet b (join c (meet a d)))
+ =<=
+ join a (meet b (join c (meet d (join a c))))
+ [] by prove_H39_dual
+29147: Order:
+29147: lpo
+29147: Leaf order:
+29147: b 2 0 2 1,2,2
+29147: d 2 0 2 2,2,2,2,2
+29147: c 3 0 3 1,2,2,2
+29147: a 4 0 4 1,2
+29147: meet 18 2 4 0,2,2
+29147: join 18 2 5 0,2
+% SZS status Timeout for LAT136-1.p
+NO CLASH, using fixed ground order
+29176: Facts:
+29176: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29176: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29176: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29176: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29176: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29176: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29176: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29176: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29176: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ join (meet ?26 (join ?28 (meet ?26 ?27)))
+ (meet ?26 (join ?27 (meet ?26 ?28)))
+ [28, 27, 26] by equation_H69 ?26 ?27 ?28
+29176: Goal:
+29176: Id : 1, {_}:
+ join a (meet b (join c (meet a d)))
+ =<=
+ join a (meet b (join c (meet d (join c (meet a b)))))
+ [] by prove_H40_dual
+29176: Order:
+29176: nrkbo
+29176: Leaf order:
+29176: d 2 0 2 2,2,2,2,2
+29176: b 3 0 3 1,2,2
+29176: c 3 0 3 1,2,2,2
+29176: a 4 0 4 1,2
+29176: join 18 2 5 0,2
+29176: meet 19 2 5 0,2,2
+NO CLASH, using fixed ground order
+29177: Facts:
+29177: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29177: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29177: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29177: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29177: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29177: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29177: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29177: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29177: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ join (meet ?26 (join ?28 (meet ?26 ?27)))
+ (meet ?26 (join ?27 (meet ?26 ?28)))
+ [28, 27, 26] by equation_H69 ?26 ?27 ?28
+29177: Goal:
+29177: Id : 1, {_}:
+ join a (meet b (join c (meet a d)))
+ =<=
+ join a (meet b (join c (meet d (join c (meet a b)))))
+ [] by prove_H40_dual
+29177: Order:
+29177: kbo
+29177: Leaf order:
+29177: d 2 0 2 2,2,2,2,2
+29177: b 3 0 3 1,2,2
+29177: c 3 0 3 1,2,2,2
+29177: a 4 0 4 1,2
+29177: join 18 2 5 0,2
+29177: meet 19 2 5 0,2,2
+NO CLASH, using fixed ground order
+29178: Facts:
+29178: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29178: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29178: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29178: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29178: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29178: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29178: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29178: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29178: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ join (meet ?26 (join ?28 (meet ?26 ?27)))
+ (meet ?26 (join ?27 (meet ?26 ?28)))
+ [28, 27, 26] by equation_H69 ?26 ?27 ?28
+29178: Goal:
+29178: Id : 1, {_}:
+ join a (meet b (join c (meet a d)))
+ =<=
+ join a (meet b (join c (meet d (join c (meet a b)))))
+ [] by prove_H40_dual
+29178: Order:
+29178: lpo
+29178: Leaf order:
+29178: d 2 0 2 2,2,2,2,2
+29178: b 3 0 3 1,2,2
+29178: c 3 0 3 1,2,2,2
+29178: a 4 0 4 1,2
+29178: join 18 2 5 0,2
+29178: meet 19 2 5 0,2,2
+% SZS status Timeout for LAT137-1.p
+NO CLASH, using fixed ground order
+29197: Facts:
+29197: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29197: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29197: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29197: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29197: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29197: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29197: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29197: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29197: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26 (join (meet ?26 ?27) (meet (join ?26 ?27) ?28))
+ [28, 27, 26] by equation_H61_dual ?26 ?27 ?28
+29197: Goal:
+29197: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+29197: Order:
+29197: nrkbo
+29197: Leaf order:
+29197: b 3 0 3 1,2,2
+29197: c 3 0 3 2,2,2,2
+29197: a 6 0 6 1,2
+29197: join 16 2 4 0,2,2
+29197: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+29198: Facts:
+29198: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29198: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29198: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29198: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29198: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29198: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29198: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29198: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29198: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26 (join (meet ?26 ?27) (meet (join ?26 ?27) ?28))
+ [28, 27, 26] by equation_H61_dual ?26 ?27 ?28
+29198: Goal:
+29198: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+29198: Order:
+29198: kbo
+29198: Leaf order:
+29198: b 3 0 3 1,2,2
+29198: c 3 0 3 2,2,2,2
+29198: a 6 0 6 1,2
+29198: join 16 2 4 0,2,2
+29198: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+29199: Facts:
+29199: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+29199: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+29199: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+29199: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+29199: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+29199: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+29199: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+29199: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+29199: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26 (join (meet ?26 ?27) (meet (join ?26 ?27) ?28))
+ [28, 27, 26] by equation_H61_dual ?26 ?27 ?28
+29199: Goal:
+29199: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+29199: Order:
+29199: lpo
+29199: Leaf order:
+29199: b 3 0 3 1,2,2
+29199: c 3 0 3 2,2,2,2
+29199: a 6 0 6 1,2
+29199: join 16 2 4 0,2,2
+29199: meet 20 2 6 0,2
+% SZS status Timeout for LAT171-1.p
+NO CLASH, using fixed ground order
+29274: Facts:
+29274: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+29274: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+29274: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+29274: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+29274: Id : 6, {_}: implies x y =>= implies y z [] by lemma_antecedent
+29274: Goal:
+29274: Id : 1, {_}: implies x z =>= truth [] by prove_wajsberg_lemma
+29274: Order:
+29274: nrkbo
+29274: Leaf order:
+29274: y 2 0 0
+29274: x 2 0 1 1,2
+29274: z 2 0 1 2,2
+29274: truth 4 0 1 3
+29274: not 2 1 0
+29274: implies 16 2 1 0,2
+NO CLASH, using fixed ground order
+29275: Facts:
+29275: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+29275: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+29275: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+29275: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+29275: Id : 6, {_}: implies x y =>= implies y z [] by lemma_antecedent
+29275: Goal:
+29275: Id : 1, {_}: implies x z =>= truth [] by prove_wajsberg_lemma
+29275: Order:
+29275: kbo
+29275: Leaf order:
+29275: y 2 0 0
+29275: x 2 0 1 1,2
+29275: z 2 0 1 2,2
+29275: truth 4 0 1 3
+29275: not 2 1 0
+29275: implies 16 2 1 0,2
+NO CLASH, using fixed ground order
+29276: Facts:
+29276: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+29276: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+29276: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+29276: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+29276: Id : 6, {_}: implies x y =>= implies y z [] by lemma_antecedent
+29276: Goal:
+29276: Id : 1, {_}: implies x z =>= truth [] by prove_wajsberg_lemma
+29276: Order:
+29276: lpo
+29276: Leaf order:
+29276: y 2 0 0
+29276: x 2 0 1 1,2
+29276: z 2 0 1 2,2
+29276: truth 4 0 1 3
+29276: not 2 1 0
+29276: implies 16 2 1 0,2
+% SZS status Timeout for LCL136-1.p
+NO CLASH, using fixed ground order
+29293: Facts:
+29293: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+29293: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+29293: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+29293: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+29293: Goal:
+29293: Id : 1, {_}:
+ implies (implies (implies x y) y)
+ (implies (implies y z) (implies x z))
+ =>=
+ truth
+ [] by prove_wajsberg_lemma
+29293: Order:
+29293: nrkbo
+29293: Leaf order:
+29293: x 2 0 2 1,1,1,2
+29293: z 2 0 2 2,1,2,2
+29293: y 3 0 3 2,1,1,2
+29293: truth 4 0 1 3
+29293: not 2 1 0
+29293: implies 19 2 6 0,2
+NO CLASH, using fixed ground order
+29294: Facts:
+29294: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+29294: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+29294: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+29294: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+29294: Goal:
+29294: Id : 1, {_}:
+ implies (implies (implies x y) y)
+ (implies (implies y z) (implies x z))
+ =>=
+ truth
+ [] by prove_wajsberg_lemma
+29294: Order:
+29294: kbo
+29294: Leaf order:
+29294: x 2 0 2 1,1,1,2
+29294: z 2 0 2 2,1,2,2
+29294: y 3 0 3 2,1,1,2
+29294: truth 4 0 1 3
+29294: not 2 1 0
+29294: implies 19 2 6 0,2
+NO CLASH, using fixed ground order
+29295: Facts:
+29295: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+29295: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+29295: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+29295: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+29295: Goal:
+29295: Id : 1, {_}:
+ implies (implies (implies x y) y)
+ (implies (implies y z) (implies x z))
+ =>=
+ truth
+ [] by prove_wajsberg_lemma
+29295: Order:
+29295: lpo
+29295: Leaf order:
+29295: x 2 0 2 1,1,1,2
+29295: z 2 0 2 2,1,2,2
+29295: y 3 0 3 2,1,1,2
+29295: truth 4 0 1 3
+29295: not 2 1 0
+29295: implies 19 2 6 0,2
+% SZS status Timeout for LCL137-1.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+29381: Facts:
+29381: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+29381: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+29381: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+29381: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+29381: Id : 6, {_}:
+ or ?14 ?15 =<= implies (not ?14) ?15
+ [15, 14] by or_definition ?14 ?15
+29381: Id : 7, {_}:
+ or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
+ [19, 18, 17] by or_associativity ?17 ?18 ?19
+29381: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
+29381: Id : 9, {_}:
+ and ?24 ?25 =<= not (or (not ?24) (not ?25))
+ [25, 24] by and_definition ?24 ?25
+29381: Id : 10, {_}:
+ and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
+ [29, 28, 27] by and_associativity ?27 ?28 ?29
+29381: Id : 11, {_}:
+ and ?31 ?32 =?= and ?32 ?31
+ [32, 31] by and_commutativity ?31 ?32
+29381: Goal:
+29381: Id : 1, {_}:
+ not (or (and x (or x x)) (and x x))
+ =<=
+ and (not x) (or (or (not x) (not x)) (and (not x) (not x)))
+ [] by prove_wajsberg_theorem
+29381: Order:
+29381: kbo
+29381: Leaf order:
+29381: truth 3 0 0
+29381: x 10 0 10 1,1,1,2
+29381: not 12 1 6 0,2
+29381: and 11 2 4 0,1,1,2
+29381: or 12 2 4 0,1,2
+29381: implies 14 2 0
+29380: Facts:
+29380: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+29380: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+29380: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+29380: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+29380: Id : 6, {_}:
+ or ?14 ?15 =<= implies (not ?14) ?15
+ [15, 14] by or_definition ?14 ?15
+29380: Id : 7, {_}:
+ or (or ?17 ?18) ?19 =?= or ?17 (or ?18 ?19)
+ [19, 18, 17] by or_associativity ?17 ?18 ?19
+29380: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
+29380: Id : 9, {_}:
+ and ?24 ?25 =<= not (or (not ?24) (not ?25))
+ [25, 24] by and_definition ?24 ?25
+29380: Id : 10, {_}:
+ and (and ?27 ?28) ?29 =?= and ?27 (and ?28 ?29)
+ [29, 28, 27] by and_associativity ?27 ?28 ?29
+29380: Id : 11, {_}:
+ and ?31 ?32 =?= and ?32 ?31
+ [32, 31] by and_commutativity ?31 ?32
+29380: Goal:
+29380: Id : 1, {_}:
+ not (or (and x (or x x)) (and x x))
+ =<=
+ and (not x) (or (or (not x) (not x)) (and (not x) (not x)))
+ [] by prove_wajsberg_theorem
+29380: Order:
+29380: nrkbo
+29380: Leaf order:
+29380: truth 3 0 0
+29380: x 10 0 10 1,1,1,2
+29380: not 12 1 6 0,2
+29380: and 11 2 4 0,1,1,2
+29380: or 12 2 4 0,1,2
+29380: implies 14 2 0
+NO CLASH, using fixed ground order
+29382: Facts:
+29382: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+29382: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+29382: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+29382: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+29382: Id : 6, {_}:
+ or ?14 ?15 =<= implies (not ?14) ?15
+ [15, 14] by or_definition ?14 ?15
+29382: Id : 7, {_}:
+ or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
+ [19, 18, 17] by or_associativity ?17 ?18 ?19
+29382: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
+29382: Id : 9, {_}:
+ and ?24 ?25 =<= not (or (not ?24) (not ?25))
+ [25, 24] by and_definition ?24 ?25
+29382: Id : 10, {_}:
+ and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
+ [29, 28, 27] by and_associativity ?27 ?28 ?29
+29382: Id : 11, {_}:
+ and ?31 ?32 =?= and ?32 ?31
+ [32, 31] by and_commutativity ?31 ?32
+29382: Goal:
+29382: Id : 1, {_}:
+ not (or (and x (or x x)) (and x x))
+ =<=
+ and (not x) (or (or (not x) (not x)) (and (not x) (not x)))
+ [] by prove_wajsberg_theorem
+29382: Order:
+29382: lpo
+29382: Leaf order:
+29382: truth 3 0 0
+29382: x 10 0 10 1,1,1,2
+29382: not 12 1 6 0,2
+29382: and 11 2 4 0,1,1,2
+29382: or 12 2 4 0,1,2
+29382: implies 14 2 0
+% SZS status Timeout for LCL165-1.p
+NO CLASH, using fixed ground order
+29399: Facts:
+29399: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29399: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29399: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29399: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29399: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29399: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29399: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29399: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29399: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29399: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29399: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29399: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29399: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29399: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29399: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29399: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+29399: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+29399: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+29399: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+29399: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+29399: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+29399: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+29399: Goal:
+29399: Id : 1, {_}:
+ associator x y (add u v)
+ =<=
+ add (associator x y u) (associator x y v)
+ [] by prove_linearised_form1
+29399: Order:
+29399: nrkbo
+29399: Leaf order:
+29399: u 2 0 2 1,3,2
+29399: v 2 0 2 2,3,2
+29399: x 3 0 3 1,2
+29399: y 3 0 3 2,2
+29399: additive_identity 8 0 0
+29399: additive_inverse 22 1 0
+29399: commutator 1 2 0
+29399: add 26 2 2 0,3,2
+29399: multiply 40 2 0
+29399: associator 4 3 3 0,2
+NO CLASH, using fixed ground order
+29400: Facts:
+29400: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29400: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29400: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29400: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29400: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29400: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29400: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29400: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29400: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29400: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29400: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29400: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29400: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29400: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29400: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29400: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+29400: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+29400: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+29400: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+29400: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+29400: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+29400: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+29400: Goal:
+29400: Id : 1, {_}:
+ associator x y (add u v)
+ =<=
+ add (associator x y u) (associator x y v)
+ [] by prove_linearised_form1
+29400: Order:
+29400: kbo
+29400: Leaf order:
+29400: u 2 0 2 1,3,2
+29400: v 2 0 2 2,3,2
+29400: x 3 0 3 1,2
+29400: y 3 0 3 2,2
+29400: additive_identity 8 0 0
+29400: additive_inverse 22 1 0
+29400: commutator 1 2 0
+29400: add 26 2 2 0,3,2
+29400: multiply 40 2 0
+29400: associator 4 3 3 0,2
+NO CLASH, using fixed ground order
+29401: Facts:
+29401: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29401: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29401: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29401: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29401: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29401: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29401: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29401: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29401: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29401: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29401: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29401: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29401: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29401: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29401: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29401: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+29401: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+29401: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+29401: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =>=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+29401: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =>=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+29401: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =>=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+29401: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =>=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+29401: Goal:
+29401: Id : 1, {_}:
+ associator x y (add u v)
+ =>=
+ add (associator x y u) (associator x y v)
+ [] by prove_linearised_form1
+29401: Order:
+29401: lpo
+29401: Leaf order:
+29401: u 2 0 2 1,3,2
+29401: v 2 0 2 2,3,2
+29401: x 3 0 3 1,2
+29401: y 3 0 3 2,2
+29401: additive_identity 8 0 0
+29401: additive_inverse 22 1 0
+29401: commutator 1 2 0
+29401: add 26 2 2 0,3,2
+29401: multiply 40 2 0
+29401: associator 4 3 3 0,2
+% SZS status Timeout for RNG019-7.p
+NO CLASH, using fixed ground order
+29433: Facts:
+29433: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29433: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29433: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29433: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29433: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29433: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29433: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29433: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29433: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29433: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29433: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29433: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29433: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29433: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29433: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29433: Goal:
+29433: Id : 1, {_}:
+ associator x (add u v) y
+ =<=
+ add (associator x u y) (associator x v y)
+ [] by prove_linearised_form2
+29433: Order:
+29433: kbo
+29433: Leaf order:
+29433: u 2 0 2 1,2,2
+29433: v 2 0 2 2,2,2
+29433: x 3 0 3 1,2
+29433: y 3 0 3 3,2
+29433: additive_identity 8 0 0
+29433: additive_inverse 6 1 0
+29433: commutator 1 2 0
+29433: add 18 2 2 0,2,2
+29433: multiply 22 2 0
+29433: associator 4 3 3 0,2
+NO CLASH, using fixed ground order
+29434: Facts:
+29434: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29434: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29434: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29434: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29434: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29434: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29434: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29434: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29434: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29434: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29434: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29434: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29434: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29434: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29434: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29434: Goal:
+29434: Id : 1, {_}:
+ associator x (add u v) y
+ =>=
+ add (associator x u y) (associator x v y)
+ [] by prove_linearised_form2
+29434: Order:
+29434: lpo
+29434: Leaf order:
+29434: u 2 0 2 1,2,2
+29434: v 2 0 2 2,2,2
+29434: x 3 0 3 1,2
+29434: y 3 0 3 3,2
+29434: additive_identity 8 0 0
+29434: additive_inverse 6 1 0
+29434: commutator 1 2 0
+29434: add 18 2 2 0,2,2
+29434: multiply 22 2 0
+29434: associator 4 3 3 0,2
+NO CLASH, using fixed ground order
+29432: Facts:
+29432: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29432: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29432: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29432: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29432: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29432: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29432: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29432: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29432: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29432: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29432: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29432: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29432: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29432: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29432: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29432: Goal:
+29432: Id : 1, {_}:
+ associator x (add u v) y
+ =<=
+ add (associator x u y) (associator x v y)
+ [] by prove_linearised_form2
+29432: Order:
+29432: nrkbo
+29432: Leaf order:
+29432: u 2 0 2 1,2,2
+29432: v 2 0 2 2,2,2
+29432: x 3 0 3 1,2
+29432: y 3 0 3 3,2
+29432: additive_identity 8 0 0
+29432: additive_inverse 6 1 0
+29432: commutator 1 2 0
+29432: add 18 2 2 0,2,2
+29432: multiply 22 2 0
+29432: associator 4 3 3 0,2
+% SZS status Timeout for RNG020-6.p
+NO CLASH, using fixed ground order
+29471: Facts:
+29471: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29471: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29471: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29471: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29471: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29471: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29471: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29471: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29471: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29471: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29471: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29471: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29471: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29471: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29471: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29471: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+29471: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+29471: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+29471: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+29471: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+29471: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+29471: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+29471: Goal:
+29471: Id : 1, {_}:
+ associator x (add u v) y
+ =<=
+ add (associator x u y) (associator x v y)
+ [] by prove_linearised_form2
+29471: Order:
+29471: nrkbo
+29471: Leaf order:
+29471: u 2 0 2 1,2,2
+29471: v 2 0 2 2,2,2
+29471: x 3 0 3 1,2
+29471: y 3 0 3 3,2
+29471: additive_identity 8 0 0
+29471: additive_inverse 22 1 0
+29471: commutator 1 2 0
+29471: add 26 2 2 0,2,2
+29471: multiply 40 2 0
+29471: associator 4 3 3 0,2
+NO CLASH, using fixed ground order
+29472: Facts:
+29472: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29472: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29472: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29472: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29472: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29472: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29472: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29472: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29472: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29472: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29472: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29472: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29472: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29472: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29472: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29472: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+29472: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+29472: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+29472: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+29472: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+29472: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+29472: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+29472: Goal:
+29472: Id : 1, {_}:
+ associator x (add u v) y
+ =<=
+ add (associator x u y) (associator x v y)
+ [] by prove_linearised_form2
+29472: Order:
+29472: kbo
+29472: Leaf order:
+29472: u 2 0 2 1,2,2
+29472: v 2 0 2 2,2,2
+29472: x 3 0 3 1,2
+29472: y 3 0 3 3,2
+29472: additive_identity 8 0 0
+29472: additive_inverse 22 1 0
+29472: commutator 1 2 0
+29472: add 26 2 2 0,2,2
+29472: multiply 40 2 0
+29472: associator 4 3 3 0,2
+NO CLASH, using fixed ground order
+29473: Facts:
+29473: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29473: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29473: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29473: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29473: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29473: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29473: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29473: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29473: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29473: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29473: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29473: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29473: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29473: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29473: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29473: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+29473: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+29473: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+29473: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =>=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+29473: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =>=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+29473: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =>=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+29473: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =>=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+29473: Goal:
+29473: Id : 1, {_}:
+ associator x (add u v) y
+ =>=
+ add (associator x u y) (associator x v y)
+ [] by prove_linearised_form2
+29473: Order:
+29473: lpo
+29473: Leaf order:
+29473: u 2 0 2 1,2,2
+29473: v 2 0 2 2,2,2
+29473: x 3 0 3 1,2
+29473: y 3 0 3 3,2
+29473: additive_identity 8 0 0
+29473: additive_inverse 22 1 0
+29473: commutator 1 2 0
+29473: add 26 2 2 0,2,2
+29473: multiply 40 2 0
+29473: associator 4 3 3 0,2
+% SZS status Timeout for RNG020-7.p
+NO CLASH, using fixed ground order
+29501: Facts:
+29501: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29501: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29501: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29501: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29501: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29501: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29501: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29501: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29501: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29501: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29501: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29501: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29501: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29501: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29501: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29501: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+29501: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+29501: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+29501: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+29501: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+29501: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+29501: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+29501: Goal:
+29501: Id : 1, {_}:
+ associator (add u v) x y
+ =<=
+ add (associator u x y) (associator v x y)
+ [] by prove_linearised_form3
+29501: Order:
+29501: nrkbo
+29501: Leaf order:
+29501: u 2 0 2 1,1,2
+29501: v 2 0 2 2,1,2
+29501: x 3 0 3 2,2
+29501: y 3 0 3 3,2
+29501: additive_identity 8 0 0
+29501: additive_inverse 22 1 0
+29501: commutator 1 2 0
+29501: add 26 2 2 0,1,2
+29501: multiply 40 2 0
+29501: associator 4 3 3 0,2
+NO CLASH, using fixed ground order
+29502: Facts:
+29502: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29502: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+NO CLASH, using fixed ground order
+29503: Facts:
+29502: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29502: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29502: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29502: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29502: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29502: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29502: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29502: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29502: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29502: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29502: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29502: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29502: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29502: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+29502: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+29502: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+29502: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+29502: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+29502: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+29502: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+29502: Goal:
+29502: Id : 1, {_}:
+ associator (add u v) x y
+ =<=
+ add (associator u x y) (associator v x y)
+ [] by prove_linearised_form3
+29502: Order:
+29502: kbo
+29502: Leaf order:
+29502: u 2 0 2 1,1,2
+29502: v 2 0 2 2,1,2
+29502: x 3 0 3 2,2
+29502: y 3 0 3 3,2
+29502: additive_identity 8 0 0
+29502: additive_inverse 22 1 0
+29502: commutator 1 2 0
+29502: add 26 2 2 0,1,2
+29502: multiply 40 2 0
+29502: associator 4 3 3 0,2
+29503: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29503: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29503: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29503: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29503: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29503: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29503: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29503: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29503: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29503: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29503: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29503: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29503: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29503: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29503: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29503: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+29503: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+29503: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+29503: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =>=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+29503: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =>=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+29503: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =>=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+29503: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =>=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+29503: Goal:
+29503: Id : 1, {_}:
+ associator (add u v) x y
+ =>=
+ add (associator u x y) (associator v x y)
+ [] by prove_linearised_form3
+29503: Order:
+29503: lpo
+29503: Leaf order:
+29503: u 2 0 2 1,1,2
+29503: v 2 0 2 2,1,2
+29503: x 3 0 3 2,2
+29503: y 3 0 3 3,2
+29503: additive_identity 8 0 0
+29503: additive_inverse 22 1 0
+29503: commutator 1 2 0
+29503: add 26 2 2 0,1,2
+29503: multiply 40 2 0
+29503: associator 4 3 3 0,2
+% SZS status Timeout for RNG021-7.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+29520: Facts:
+29520: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29520: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29520: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29520: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29520: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29520: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29520: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29520: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29520: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29520: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29520: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29520: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29520: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29520: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29520: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29520: Goal:
+29520: Id : 1, {_}:
+ add (associator x y z) (associator x z y) =>= additive_identity
+ [] by prove_equation
+29520: Order:
+29520: kbo
+29520: Leaf order:
+29520: x 2 0 2 1,1,2
+29520: y 2 0 2 2,1,2
+29520: z 2 0 2 3,1,2
+29520: additive_identity 9 0 1 3
+29520: additive_inverse 6 1 0
+29520: commutator 1 2 0
+29520: add 17 2 1 0,2
+29520: multiply 22 2 0
+29520: associator 3 3 2 0,1,2
+29519: Facts:
+29519: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29519: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29519: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29519: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29519: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29519: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29519: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29519: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29519: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29519: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29519: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29519: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29519: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29519: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29519: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29519: Goal:
+29519: Id : 1, {_}:
+ add (associator x y z) (associator x z y) =>= additive_identity
+ [] by prove_equation
+29519: Order:
+29519: nrkbo
+29519: Leaf order:
+29519: x 2 0 2 1,1,2
+29519: y 2 0 2 2,1,2
+29519: z 2 0 2 3,1,2
+29519: additive_identity 9 0 1 3
+29519: additive_inverse 6 1 0
+29519: commutator 1 2 0
+29519: add 17 2 1 0,2
+29519: multiply 22 2 0
+29519: associator 3 3 2 0,1,2
+NO CLASH, using fixed ground order
+29521: Facts:
+29521: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+29521: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+29521: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+29521: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+29521: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+29521: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+29521: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+29521: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+29521: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+29521: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+29521: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+29521: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29521: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29521: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+29521: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+29521: Goal:
+29521: Id : 1, {_}:
+ add (associator x y z) (associator x z y) =>= additive_identity
+ [] by prove_equation
+29521: Order:
+29521: lpo
+29521: Leaf order:
+29521: x 2 0 2 1,1,2
+29521: y 2 0 2 2,1,2
+29521: z 2 0 2 3,1,2
+29521: additive_identity 9 0 1 3
+29521: additive_inverse 6 1 0
+29521: commutator 1 2 0
+29521: add 17 2 1 0,2
+29521: multiply 22 2 0
+29521: associator 3 3 2 0,1,2
+% SZS status Timeout for RNG025-4.p
+NO CLASH, using fixed ground order
+29553: Facts:
+29553: Id : 2, {_}:
+ add ?2 ?3 =?= add ?3 ?2
+ [3, 2] by commutativity_for_addition ?2 ?3
+29553: Id : 3, {_}:
+ add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7
+ [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
+29553: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
+29553: Id : 5, {_}:
+ add ?11 additive_identity =>= ?11
+ [11] by right_additive_identity ?11
+29553: Id : 6, {_}:
+ multiply additive_identity ?13 =>= additive_identity
+ [13] by left_multiplicative_zero ?13
+29553: Id : 7, {_}:
+ multiply ?15 additive_identity =>= additive_identity
+ [15] by right_multiplicative_zero ?15
+29553: Id : 8, {_}:
+ add (additive_inverse ?17) ?17 =>= additive_identity
+ [17] by left_additive_inverse ?17
+29553: Id : 9, {_}:
+ add ?19 (additive_inverse ?19) =>= additive_identity
+ [19] by right_additive_inverse ?19
+29553: Id : 10, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+29553: Id : 11, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+29553: Id : 12, {_}:
+ additive_inverse (additive_inverse ?29) =>= ?29
+ [29] by additive_inverse_additive_inverse ?29
+29553: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29553: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29553: Id : 15, {_}:
+ associator ?37 ?38 (add ?39 ?40)
+ =<=
+ add (associator ?37 ?38 ?39) (associator ?37 ?38 ?40)
+ [40, 39, 38, 37] by linearised_associator1 ?37 ?38 ?39 ?40
+29553: Id : 16, {_}:
+ associator ?42 (add ?43 ?44) ?45
+ =<=
+ add (associator ?42 ?43 ?45) (associator ?42 ?44 ?45)
+ [45, 44, 43, 42] by linearised_associator2 ?42 ?43 ?44 ?45
+29553: Id : 17, {_}:
+ associator (add ?47 ?48) ?49 ?50
+ =<=
+ add (associator ?47 ?49 ?50) (associator ?48 ?49 ?50)
+ [50, 49, 48, 47] by linearised_associator3 ?47 ?48 ?49 ?50
+29553: Id : 18, {_}:
+ commutator ?52 ?53
+ =<=
+ add (multiply ?53 ?52) (additive_inverse (multiply ?52 ?53))
+ [53, 52] by commutator ?52 ?53
+29553: Goal:
+29553: Id : 1, {_}:
+ add (associator a b c) (associator a c b) =>= additive_identity
+ [] by prove_flexible_law
+29553: Order:
+29553: nrkbo
+29553: Leaf order:
+29553: a 2 0 2 1,1,2
+29553: b 2 0 2 2,1,2
+29553: c 2 0 2 3,1,2
+29553: additive_identity 9 0 1 3
+29553: additive_inverse 5 1 0
+29553: commutator 1 2 0
+29553: multiply 18 2 0
+29553: add 22 2 1 0,2
+29553: associator 11 3 2 0,1,2
+NO CLASH, using fixed ground order
+29554: Facts:
+29554: Id : 2, {_}:
+ add ?2 ?3 =?= add ?3 ?2
+ [3, 2] by commutativity_for_addition ?2 ?3
+29554: Id : 3, {_}:
+ add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
+ [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
+29554: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
+29554: Id : 5, {_}:
+ add ?11 additive_identity =>= ?11
+ [11] by right_additive_identity ?11
+29554: Id : 6, {_}:
+ multiply additive_identity ?13 =>= additive_identity
+ [13] by left_multiplicative_zero ?13
+29554: Id : 7, {_}:
+ multiply ?15 additive_identity =>= additive_identity
+ [15] by right_multiplicative_zero ?15
+29554: Id : 8, {_}:
+ add (additive_inverse ?17) ?17 =>= additive_identity
+ [17] by left_additive_inverse ?17
+29554: Id : 9, {_}:
+ add ?19 (additive_inverse ?19) =>= additive_identity
+ [19] by right_additive_inverse ?19
+29554: Id : 10, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+29554: Id : 11, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+29554: Id : 12, {_}:
+ additive_inverse (additive_inverse ?29) =>= ?29
+ [29] by additive_inverse_additive_inverse ?29
+29554: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29554: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29554: Id : 15, {_}:
+ associator ?37 ?38 (add ?39 ?40)
+ =<=
+ add (associator ?37 ?38 ?39) (associator ?37 ?38 ?40)
+ [40, 39, 38, 37] by linearised_associator1 ?37 ?38 ?39 ?40
+29554: Id : 16, {_}:
+ associator ?42 (add ?43 ?44) ?45
+ =<=
+ add (associator ?42 ?43 ?45) (associator ?42 ?44 ?45)
+ [45, 44, 43, 42] by linearised_associator2 ?42 ?43 ?44 ?45
+29554: Id : 17, {_}:
+ associator (add ?47 ?48) ?49 ?50
+ =<=
+ add (associator ?47 ?49 ?50) (associator ?48 ?49 ?50)
+ [50, 49, 48, 47] by linearised_associator3 ?47 ?48 ?49 ?50
+29554: Id : 18, {_}:
+ commutator ?52 ?53
+ =<=
+ add (multiply ?53 ?52) (additive_inverse (multiply ?52 ?53))
+ [53, 52] by commutator ?52 ?53
+29554: Goal:
+29554: Id : 1, {_}:
+ add (associator a b c) (associator a c b) =>= additive_identity
+ [] by prove_flexible_law
+29554: Order:
+29554: kbo
+29554: Leaf order:
+29554: a 2 0 2 1,1,2
+29554: b 2 0 2 2,1,2
+29554: c 2 0 2 3,1,2
+29554: additive_identity 9 0 1 3
+29554: additive_inverse 5 1 0
+29554: commutator 1 2 0
+29554: multiply 18 2 0
+29554: add 22 2 1 0,2
+29554: associator 11 3 2 0,1,2
+NO CLASH, using fixed ground order
+29555: Facts:
+29555: Id : 2, {_}:
+ add ?2 ?3 =?= add ?3 ?2
+ [3, 2] by commutativity_for_addition ?2 ?3
+29555: Id : 3, {_}:
+ add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
+ [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
+29555: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
+29555: Id : 5, {_}:
+ add ?11 additive_identity =>= ?11
+ [11] by right_additive_identity ?11
+29555: Id : 6, {_}:
+ multiply additive_identity ?13 =>= additive_identity
+ [13] by left_multiplicative_zero ?13
+29555: Id : 7, {_}:
+ multiply ?15 additive_identity =>= additive_identity
+ [15] by right_multiplicative_zero ?15
+29555: Id : 8, {_}:
+ add (additive_inverse ?17) ?17 =>= additive_identity
+ [17] by left_additive_inverse ?17
+29555: Id : 9, {_}:
+ add ?19 (additive_inverse ?19) =>= additive_identity
+ [19] by right_additive_inverse ?19
+29555: Id : 10, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+29555: Id : 11, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+29555: Id : 12, {_}:
+ additive_inverse (additive_inverse ?29) =>= ?29
+ [29] by additive_inverse_additive_inverse ?29
+29555: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+29555: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+29555: Id : 15, {_}:
+ associator ?37 ?38 (add ?39 ?40)
+ =>=
+ add (associator ?37 ?38 ?39) (associator ?37 ?38 ?40)
+ [40, 39, 38, 37] by linearised_associator1 ?37 ?38 ?39 ?40
+29555: Id : 16, {_}:
+ associator ?42 (add ?43 ?44) ?45
+ =>=
+ add (associator ?42 ?43 ?45) (associator ?42 ?44 ?45)
+ [45, 44, 43, 42] by linearised_associator2 ?42 ?43 ?44 ?45
+29555: Id : 17, {_}:
+ associator (add ?47 ?48) ?49 ?50
+ =>=
+ add (associator ?47 ?49 ?50) (associator ?48 ?49 ?50)
+ [50, 49, 48, 47] by linearised_associator3 ?47 ?48 ?49 ?50
+29555: Id : 18, {_}:
+ commutator ?52 ?53
+ =<=
+ add (multiply ?53 ?52) (additive_inverse (multiply ?52 ?53))
+ [53, 52] by commutator ?52 ?53
+29555: Goal:
+29555: Id : 1, {_}:
+ add (associator a b c) (associator a c b) =>= additive_identity
+ [] by prove_flexible_law
+29555: Order:
+29555: lpo
+29555: Leaf order:
+29555: a 2 0 2 1,1,2
+29555: b 2 0 2 2,1,2
+29555: c 2 0 2 3,1,2
+29555: additive_identity 9 0 1 3
+29555: additive_inverse 5 1 0
+29555: commutator 1 2 0
+29555: multiply 18 2 0
+29555: add 22 2 1 0,2
+29555: associator 11 3 2 0,1,2
+% SZS status Timeout for RNG025-8.p
+NO CLASH, using fixed ground order
+29571: Facts:
+29571: Id : 2, {_}:
+ multiply (additive_inverse ?2) (additive_inverse ?3)
+ =>=
+ multiply ?2 ?3
+ [3, 2] by product_of_inverses ?2 ?3
+29571: Id : 3, {_}:
+ multiply (additive_inverse ?5) ?6
+ =>=
+ additive_inverse (multiply ?5 ?6)
+ [6, 5] by inverse_product1 ?5 ?6
+29571: Id : 4, {_}:
+ multiply ?8 (additive_inverse ?9)
+ =>=
+ additive_inverse (multiply ?8 ?9)
+ [9, 8] by inverse_product2 ?8 ?9
+29571: Id : 5, {_}:
+ multiply ?11 (add ?12 (additive_inverse ?13))
+ =<=
+ add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
+ [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
+29571: Id : 6, {_}:
+ multiply (add ?15 (additive_inverse ?16)) ?17
+ =<=
+ add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
+ [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
+29571: Id : 7, {_}:
+ multiply (additive_inverse ?19) (add ?20 ?21)
+ =<=
+ add (additive_inverse (multiply ?19 ?20))
+ (additive_inverse (multiply ?19 ?21))
+ [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
+29571: Id : 8, {_}:
+ multiply (add ?23 ?24) (additive_inverse ?25)
+ =<=
+ add (additive_inverse (multiply ?23 ?25))
+ (additive_inverse (multiply ?24 ?25))
+ [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
+29571: Id : 9, {_}:
+ add ?27 ?28 =?= add ?28 ?27
+ [28, 27] by commutativity_for_addition ?27 ?28
+29571: Id : 10, {_}:
+ add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32
+ [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
+29571: Id : 11, {_}:
+ add additive_identity ?34 =>= ?34
+ [34] by left_additive_identity ?34
+29571: Id : 12, {_}:
+ add ?36 additive_identity =>= ?36
+ [36] by right_additive_identity ?36
+29571: Id : 13, {_}:
+ multiply additive_identity ?38 =>= additive_identity
+ [38] by left_multiplicative_zero ?38
+29571: Id : 14, {_}:
+ multiply ?40 additive_identity =>= additive_identity
+ [40] by right_multiplicative_zero ?40
+29571: Id : 15, {_}:
+ add (additive_inverse ?42) ?42 =>= additive_identity
+ [42] by left_additive_inverse ?42
+29571: Id : 16, {_}:
+ add ?44 (additive_inverse ?44) =>= additive_identity
+ [44] by right_additive_inverse ?44
+29571: Id : 17, {_}:
+ multiply ?46 (add ?47 ?48)
+ =<=
+ add (multiply ?46 ?47) (multiply ?46 ?48)
+ [48, 47, 46] by distribute1 ?46 ?47 ?48
+29571: Id : 18, {_}:
+ multiply (add ?50 ?51) ?52
+ =<=
+ add (multiply ?50 ?52) (multiply ?51 ?52)
+ [52, 51, 50] by distribute2 ?50 ?51 ?52
+29571: Id : 19, {_}:
+ additive_inverse (additive_inverse ?54) =>= ?54
+ [54] by additive_inverse_additive_inverse ?54
+29571: Id : 20, {_}:
+ multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57)
+ [57, 56] by right_alternative ?56 ?57
+29571: Id : 21, {_}:
+ multiply (multiply ?59 ?59) ?60 =?= multiply ?59 (multiply ?59 ?60)
+ [60, 59] by left_alternative ?59 ?60
+29571: Id : 22, {_}:
+ associator ?62 ?63 (add ?64 ?65)
+ =<=
+ add (associator ?62 ?63 ?64) (associator ?62 ?63 ?65)
+ [65, 64, 63, 62] by linearised_associator1 ?62 ?63 ?64 ?65
+29571: Id : 23, {_}:
+ associator ?67 (add ?68 ?69) ?70
+ =<=
+ add (associator ?67 ?68 ?70) (associator ?67 ?69 ?70)
+ [70, 69, 68, 67] by linearised_associator2 ?67 ?68 ?69 ?70
+29571: Id : 24, {_}:
+ associator (add ?72 ?73) ?74 ?75
+ =<=
+ add (associator ?72 ?74 ?75) (associator ?73 ?74 ?75)
+ [75, 74, 73, 72] by linearised_associator3 ?72 ?73 ?74 ?75
+29571: Id : 25, {_}:
+ commutator ?77 ?78
+ =<=
+ add (multiply ?78 ?77) (additive_inverse (multiply ?77 ?78))
+ [78, 77] by commutator ?77 ?78
+29571: Goal:
+29571: Id : 1, {_}:
+ add (associator a b c) (associator a c b) =>= additive_identity
+ [] by prove_flexible_law
+29571: Order:
+29571: nrkbo
+29571: Leaf order:
+29571: a 2 0 2 1,1,2
+29571: b 2 0 2 2,1,2
+29571: c 2 0 2 3,1,2
+29571: additive_identity 9 0 1 3
+29571: additive_inverse 21 1 0
+29571: commutator 1 2 0
+29571: add 30 2 1 0,2
+29571: multiply 36 2 0 add
+29571: associator 11 3 2 0,1,2
+NO CLASH, using fixed ground order
+29572: Facts:
+NO CLASH, using fixed ground order
+29572: Id : 2, {_}:
+ multiply (additive_inverse ?2) (additive_inverse ?3)
+ =>=
+ multiply ?2 ?3
+ [3, 2] by product_of_inverses ?2 ?3
+29572: Id : 3, {_}:
+ multiply (additive_inverse ?5) ?6
+ =>=
+ additive_inverse (multiply ?5 ?6)
+ [6, 5] by inverse_product1 ?5 ?6
+29572: Id : 4, {_}:
+ multiply ?8 (additive_inverse ?9)
+ =>=
+ additive_inverse (multiply ?8 ?9)
+ [9, 8] by inverse_product2 ?8 ?9
+29572: Id : 5, {_}:
+ multiply ?11 (add ?12 (additive_inverse ?13))
+ =<=
+ add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
+ [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
+29572: Id : 6, {_}:
+ multiply (add ?15 (additive_inverse ?16)) ?17
+ =<=
+ add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
+ [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
+29572: Id : 7, {_}:
+ multiply (additive_inverse ?19) (add ?20 ?21)
+ =<=
+ add (additive_inverse (multiply ?19 ?20))
+ (additive_inverse (multiply ?19 ?21))
+ [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
+29572: Id : 8, {_}:
+ multiply (add ?23 ?24) (additive_inverse ?25)
+ =<=
+ add (additive_inverse (multiply ?23 ?25))
+ (additive_inverse (multiply ?24 ?25))
+ [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
+29572: Id : 9, {_}:
+ add ?27 ?28 =?= add ?28 ?27
+ [28, 27] by commutativity_for_addition ?27 ?28
+29572: Id : 10, {_}:
+ add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
+ [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
+29572: Id : 11, {_}:
+ add additive_identity ?34 =>= ?34
+ [34] by left_additive_identity ?34
+29572: Id : 12, {_}:
+ add ?36 additive_identity =>= ?36
+ [36] by right_additive_identity ?36
+29572: Id : 13, {_}:
+ multiply additive_identity ?38 =>= additive_identity
+ [38] by left_multiplicative_zero ?38
+29572: Id : 14, {_}:
+ multiply ?40 additive_identity =>= additive_identity
+ [40] by right_multiplicative_zero ?40
+29572: Id : 15, {_}:
+ add (additive_inverse ?42) ?42 =>= additive_identity
+ [42] by left_additive_inverse ?42
+29572: Id : 16, {_}:
+ add ?44 (additive_inverse ?44) =>= additive_identity
+ [44] by right_additive_inverse ?44
+29572: Id : 17, {_}:
+ multiply ?46 (add ?47 ?48)
+ =<=
+ add (multiply ?46 ?47) (multiply ?46 ?48)
+ [48, 47, 46] by distribute1 ?46 ?47 ?48
+29572: Id : 18, {_}:
+ multiply (add ?50 ?51) ?52
+ =<=
+ add (multiply ?50 ?52) (multiply ?51 ?52)
+ [52, 51, 50] by distribute2 ?50 ?51 ?52
+29572: Id : 19, {_}:
+ additive_inverse (additive_inverse ?54) =>= ?54
+ [54] by additive_inverse_additive_inverse ?54
+29572: Id : 20, {_}:
+ multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
+ [57, 56] by right_alternative ?56 ?57
+29572: Id : 21, {_}:
+ multiply (multiply ?59 ?59) ?60 =>= multiply ?59 (multiply ?59 ?60)
+ [60, 59] by left_alternative ?59 ?60
+29572: Id : 22, {_}:
+ associator ?62 ?63 (add ?64 ?65)
+ =<=
+ add (associator ?62 ?63 ?64) (associator ?62 ?63 ?65)
+ [65, 64, 63, 62] by linearised_associator1 ?62 ?63 ?64 ?65
+29572: Id : 23, {_}:
+ associator ?67 (add ?68 ?69) ?70
+ =<=
+ add (associator ?67 ?68 ?70) (associator ?67 ?69 ?70)
+ [70, 69, 68, 67] by linearised_associator2 ?67 ?68 ?69 ?70
+29572: Id : 24, {_}:
+ associator (add ?72 ?73) ?74 ?75
+ =<=
+ add (associator ?72 ?74 ?75) (associator ?73 ?74 ?75)
+ [75, 74, 73, 72] by linearised_associator3 ?72 ?73 ?74 ?75
+29572: Id : 25, {_}:
+ commutator ?77 ?78
+ =<=
+ add (multiply ?78 ?77) (additive_inverse (multiply ?77 ?78))
+ [78, 77] by commutator ?77 ?78
+29572: Goal:
+29572: Id : 1, {_}:
+ add (associator a b c) (associator a c b) =>= additive_identity
+ [] by prove_flexible_law
+29572: Order:
+29572: kbo
+29572: Leaf order:
+29572: a 2 0 2 1,1,2
+29572: b 2 0 2 2,1,2
+29572: c 2 0 2 3,1,2
+29572: additive_identity 9 0 1 3
+29572: additive_inverse 21 1 0
+29572: commutator 1 2 0
+29572: add 30 2 1 0,2
+29572: multiply 36 2 0 add
+29572: associator 11 3 2 0,1,2
+29573: Facts:
+29573: Id : 2, {_}:
+ multiply (additive_inverse ?2) (additive_inverse ?3)
+ =>=
+ multiply ?2 ?3
+ [3, 2] by product_of_inverses ?2 ?3
+29573: Id : 3, {_}:
+ multiply (additive_inverse ?5) ?6
+ =>=
+ additive_inverse (multiply ?5 ?6)
+ [6, 5] by inverse_product1 ?5 ?6
+29573: Id : 4, {_}:
+ multiply ?8 (additive_inverse ?9)
+ =>=
+ additive_inverse (multiply ?8 ?9)
+ [9, 8] by inverse_product2 ?8 ?9
+29573: Id : 5, {_}:
+ multiply ?11 (add ?12 (additive_inverse ?13))
+ =>=
+ add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
+ [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
+29573: Id : 6, {_}:
+ multiply (add ?15 (additive_inverse ?16)) ?17
+ =>=
+ add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
+ [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
+29573: Id : 7, {_}:
+ multiply (additive_inverse ?19) (add ?20 ?21)
+ =>=
+ add (additive_inverse (multiply ?19 ?20))
+ (additive_inverse (multiply ?19 ?21))
+ [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
+29573: Id : 8, {_}:
+ multiply (add ?23 ?24) (additive_inverse ?25)
+ =>=
+ add (additive_inverse (multiply ?23 ?25))
+ (additive_inverse (multiply ?24 ?25))
+ [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
+29573: Id : 9, {_}:
+ add ?27 ?28 =?= add ?28 ?27
+ [28, 27] by commutativity_for_addition ?27 ?28
+29573: Id : 10, {_}:
+ add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
+ [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
+29573: Id : 11, {_}:
+ add additive_identity ?34 =>= ?34
+ [34] by left_additive_identity ?34
+29573: Id : 12, {_}:
+ add ?36 additive_identity =>= ?36
+ [36] by right_additive_identity ?36
+29573: Id : 13, {_}:
+ multiply additive_identity ?38 =>= additive_identity
+ [38] by left_multiplicative_zero ?38
+29573: Id : 14, {_}:
+ multiply ?40 additive_identity =>= additive_identity
+ [40] by right_multiplicative_zero ?40
+29573: Id : 15, {_}:
+ add (additive_inverse ?42) ?42 =>= additive_identity
+ [42] by left_additive_inverse ?42
+29573: Id : 16, {_}:
+ add ?44 (additive_inverse ?44) =>= additive_identity
+ [44] by right_additive_inverse ?44
+29573: Id : 17, {_}:
+ multiply ?46 (add ?47 ?48)
+ =>=
+ add (multiply ?46 ?47) (multiply ?46 ?48)
+ [48, 47, 46] by distribute1 ?46 ?47 ?48
+29573: Id : 18, {_}:
+ multiply (add ?50 ?51) ?52
+ =>=
+ add (multiply ?50 ?52) (multiply ?51 ?52)
+ [52, 51, 50] by distribute2 ?50 ?51 ?52
+29573: Id : 19, {_}:
+ additive_inverse (additive_inverse ?54) =>= ?54
+ [54] by additive_inverse_additive_inverse ?54
+29573: Id : 20, {_}:
+ multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
+ [57, 56] by right_alternative ?56 ?57
+29573: Id : 21, {_}:
+ multiply (multiply ?59 ?59) ?60 =>= multiply ?59 (multiply ?59 ?60)
+ [60, 59] by left_alternative ?59 ?60
+29573: Id : 22, {_}:
+ associator ?62 ?63 (add ?64 ?65)
+ =>=
+ add (associator ?62 ?63 ?64) (associator ?62 ?63 ?65)
+ [65, 64, 63, 62] by linearised_associator1 ?62 ?63 ?64 ?65
+29573: Id : 23, {_}:
+ associator ?67 (add ?68 ?69) ?70
+ =>=
+ add (associator ?67 ?68 ?70) (associator ?67 ?69 ?70)
+ [70, 69, 68, 67] by linearised_associator2 ?67 ?68 ?69 ?70
+29573: Id : 24, {_}:
+ associator (add ?72 ?73) ?74 ?75
+ =>=
+ add (associator ?72 ?74 ?75) (associator ?73 ?74 ?75)
+ [75, 74, 73, 72] by linearised_associator3 ?72 ?73 ?74 ?75
+29573: Id : 25, {_}:
+ commutator ?77 ?78
+ =<=
+ add (multiply ?78 ?77) (additive_inverse (multiply ?77 ?78))
+ [78, 77] by commutator ?77 ?78
+29573: Goal:
+29573: Id : 1, {_}:
+ add (associator a b c) (associator a c b) =>= additive_identity
+ [] by prove_flexible_law
+29573: Order:
+29573: lpo
+29573: Leaf order:
+29573: a 2 0 2 1,1,2
+29573: b 2 0 2 2,1,2
+29573: c 2 0 2 3,1,2
+29573: additive_identity 9 0 1 3
+29573: additive_inverse 21 1 0
+29573: commutator 1 2 0
+29573: add 30 2 1 0,2
+29573: multiply 36 2 0 add
+29573: associator 11 3 2 0,1,2
+% SZS status Timeout for RNG025-9.p
+NO CLASH, using fixed ground order
+29618: Facts:
+29618: Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3
+29618: Id : 3, {_}:
+ multiply ?5 (add ?6 ?7) =<= add (multiply ?6 ?5) (multiply ?7 ?5)
+ [7, 6, 5] by multiply_add_property ?5 ?6 ?7
+29618: Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9
+29618: Id : 5, {_}:
+ pixley ?11 ?12 ?13
+ =<=
+ add (multiply ?11 (inverse ?12))
+ (add (multiply ?11 ?13) (multiply (inverse ?12) ?13))
+ [13, 12, 11] by pixley_defn ?11 ?12 ?13
+29618: Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16
+29618: Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19
+29618: Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22
+29618: Goal:
+29618: Id : 1, {_}:
+ add a (multiply b c) =<= multiply (add a b) (add a c)
+ [] by prove_add_multiply_property
+29618: Order:
+29618: nrkbo
+29618: Leaf order:
+29618: n1 1 0 0
+29618: b 2 0 2 1,2,2
+29618: c 2 0 2 2,2,2
+29618: a 3 0 3 1,2
+29618: inverse 3 1 0
+29618: multiply 9 2 2 0,2,2
+29618: add 9 2 3 0,2
+29618: pixley 4 3 0
+NO CLASH, using fixed ground order
+29619: Facts:
+29619: Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3
+29619: Id : 3, {_}:
+ multiply ?5 (add ?6 ?7) =<= add (multiply ?6 ?5) (multiply ?7 ?5)
+ [7, 6, 5] by multiply_add_property ?5 ?6 ?7
+29619: Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9
+29619: Id : 5, {_}:
+ pixley ?11 ?12 ?13
+ =<=
+ add (multiply ?11 (inverse ?12))
+ (add (multiply ?11 ?13) (multiply (inverse ?12) ?13))
+ [13, 12, 11] by pixley_defn ?11 ?12 ?13
+29619: Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16
+29619: Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19
+29619: Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22
+29619: Goal:
+29619: Id : 1, {_}:
+ add a (multiply b c) =<= multiply (add a b) (add a c)
+ [] by prove_add_multiply_property
+29619: Order:
+29619: kbo
+29619: Leaf order:
+29619: n1 1 0 0
+29619: b 2 0 2 1,2,2
+29619: c 2 0 2 2,2,2
+29619: a 3 0 3 1,2
+29619: inverse 3 1 0
+29619: multiply 9 2 2 0,2,2
+29619: add 9 2 3 0,2
+29619: pixley 4 3 0
+NO CLASH, using fixed ground order
+29621: Facts:
+29621: Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3
+29621: Id : 3, {_}:
+ multiply ?5 (add ?6 ?7) =<= add (multiply ?6 ?5) (multiply ?7 ?5)
+ [7, 6, 5] by multiply_add_property ?5 ?6 ?7
+29621: Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9
+29621: Id : 5, {_}:
+ pixley ?11 ?12 ?13
+ =>=
+ add (multiply ?11 (inverse ?12))
+ (add (multiply ?11 ?13) (multiply (inverse ?12) ?13))
+ [13, 12, 11] by pixley_defn ?11 ?12 ?13
+29621: Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16
+29621: Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19
+29621: Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22
+29621: Goal:
+29621: Id : 1, {_}:
+ add a (multiply b c) =>= multiply (add a b) (add a c)
+ [] by prove_add_multiply_property
+29621: Order:
+29621: lpo
+29621: Leaf order:
+29621: n1 1 0 0
+29621: b 2 0 2 1,2,2
+29621: c 2 0 2 2,2,2
+29621: a 3 0 3 1,2
+29621: inverse 3 1 0
+29621: multiply 9 2 2 0,2,2
+29621: add 9 2 3 0,2
+29621: pixley 4 3 0
+Statistics :
+Max weight : 25
+Found proof, 25.954748s
+% SZS status Unsatisfiable for BOO023-1.p
+% SZS output start CNFRefutation for BOO023-1.p
+Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16
+Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22
+Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19
+Id : 5, {_}: pixley ?11 ?12 ?13 =<= add (multiply ?11 (inverse ?12)) (add (multiply ?11 ?13) (multiply (inverse ?12) ?13)) [13, 12, 11] by pixley_defn ?11 ?12 ?13
+Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9
+Id : 12, {_}: multiply ?33 (add ?34 ?35) =<= add (multiply ?34 ?33) (multiply ?35 ?33) [35, 34, 33] by multiply_add_property ?33 ?34 ?35
+Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3
+Id : 3, {_}: multiply ?5 (add ?6 ?7) =<= add (multiply ?6 ?5) (multiply ?7 ?5) [7, 6, 5] by multiply_add_property ?5 ?6 ?7
+Id : 45, {_}: multiply (multiply ?127 (add ?128 ?129)) (multiply ?129 ?127) =>= multiply ?129 ?127 [129, 128, 127] by Super 2 with 3 at 1,2
+Id : 52, {_}: multiply (add ?156 ?157) (multiply ?157 (add ?158 (add ?156 ?157))) =>= multiply ?157 (add ?158 (add ?156 ?157)) [158, 157, 156] by Super 45 with 2 at 1,2
+Id : 13, {_}: multiply ?37 (add ?38 (add ?39 ?37)) =>= add (multiply ?38 ?37) ?37 [39, 38, 37] by Super 12 with 2 at 2,3
+Id : 49, {_}: multiply (multiply ?143 n1) (multiply (inverse ?144) ?143) =>= multiply (inverse ?144) ?143 [144, 143] by Super 45 with 4 at 2,1,2
+Id : 21, {_}: pixley ?58 ?59 ?60 =<= add (multiply ?58 (inverse ?59)) (multiply ?60 (add ?58 (inverse ?59))) [60, 59, 58] by Demod 5 with 3 at 2,3
+Id : 24, {_}: pixley (add ?69 (inverse ?70)) ?70 ?71 =<= add (inverse ?70) (multiply ?71 (add (add ?69 (inverse ?70)) (inverse ?70))) [71, 70, 69] by Super 21 with 2 at 1,3
+Id : 19, {_}: pixley ?11 ?12 ?13 =<= add (multiply ?11 (inverse ?12)) (multiply ?13 (add ?11 (inverse ?12))) [13, 12, 11] by Demod 5 with 3 at 2,3
+Id : 162, {_}: multiply (pixley ?407 ?408 ?409) (multiply ?409 (add ?407 (inverse ?408))) =>= multiply ?409 (add ?407 (inverse ?408)) [409, 408, 407] by Super 2 with 19 at 1,2
+Id : 500, {_}: multiply ?959 (multiply ?960 (add ?959 (inverse ?960))) =>= multiply ?960 (add ?959 (inverse ?960)) [960, 959] by Super 162 with 7 at 1,2
+Id : 207, {_}: multiply (multiply ?494 n1) (multiply (inverse ?495) ?494) =>= multiply (inverse ?495) ?494 [495, 494] by Super 45 with 4 at 2,1,2
+Id : 211, {_}: multiply n1 (multiply (inverse ?507) (add ?508 n1)) =>= multiply (inverse ?507) (add ?508 n1) [508, 507] by Super 207 with 2 at 1,2
+Id : 16, {_}: multiply n1 (inverse ?49) =>= inverse ?49 [49] by Super 2 with 4 at 1,2
+Id : 60, {_}: multiply (inverse ?174) (add ?175 n1) =<= add (multiply ?175 (inverse ?174)) (inverse ?174) [175, 174] by Super 3 with 16 at 2,3
+Id : 61, {_}: multiply (inverse ?177) (add (add ?178 (inverse ?177)) n1) =>= add (inverse ?177) (inverse ?177) [178, 177] by Super 60 with 2 at 1,3
+Id : 14, {_}: multiply ?41 (add (add ?42 ?41) ?43) =>= add ?41 (multiply ?43 ?41) [43, 42, 41] by Super 12 with 2 at 1,3
+Id : 283, {_}: add (inverse ?177) (multiply n1 (inverse ?177)) =>= add (inverse ?177) (inverse ?177) [177] by Demod 61 with 14 at 2
+Id : 40, {_}: multiply (inverse ?110) (add n1 ?111) =<= add (inverse ?110) (multiply ?111 (inverse ?110)) [111, 110] by Super 3 with 16 at 1,3
+Id : 284, {_}: multiply (inverse ?177) (add n1 n1) =?= add (inverse ?177) (inverse ?177) [177] by Demod 283 with 40 at 2
+Id : 297, {_}: multiply n1 (add (inverse ?660) (inverse ?660)) =>= multiply (inverse ?660) (add n1 n1) [660] by Super 211 with 284 at 2,2
+Id : 505, {_}: multiply (inverse n1) (multiply (inverse n1) (add n1 n1)) =>= multiply n1 (add (inverse n1) (inverse n1)) [] by Super 500 with 297 at 2,2
+Id : 513, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= multiply n1 (add (inverse n1) (inverse n1)) [] by Demod 505 with 284 at 2,2
+Id : 514, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= multiply (inverse n1) (add n1 n1) [] by Demod 513 with 297 at 3
+Id : 515, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= add (inverse n1) (inverse n1) [] by Demod 514 with 284 at 3
+Id : 522, {_}: pixley (inverse n1) n1 (inverse n1) =<= add (multiply (inverse n1) (inverse n1)) (add (inverse n1) (inverse n1)) [] by Super 19 with 515 at 2,3
+Id : 525, {_}: inverse n1 =<= add (multiply (inverse n1) (inverse n1)) (add (inverse n1) (inverse n1)) [] by Demod 522 with 8 at 2
+Id : 543, {_}: multiply (inverse n1) (inverse n1) =<= add (multiply (multiply (inverse n1) (inverse n1)) (inverse n1)) (inverse n1) [] by Super 13 with 525 at 2,2
+Id : 39, {_}: multiply (inverse ?107) (add ?108 n1) =<= add (multiply ?108 (inverse ?107)) (inverse ?107) [108, 107] by Super 3 with 16 at 2,3
+Id : 557, {_}: multiply (inverse n1) (inverse n1) =<= multiply (inverse n1) (add (multiply (inverse n1) (inverse n1)) n1) [] by Demod 543 with 39 at 3
+Id : 22, {_}: pixley ?62 ?62 ?63 =<= add (multiply ?62 (inverse ?62)) (multiply ?63 n1) [63, 62] by Super 21 with 4 at 2,2,3
+Id : 116, {_}: ?322 =<= add (multiply ?323 (inverse ?323)) (multiply ?322 n1) [323, 322] by Demod 22 with 6 at 2
+Id : 131, {_}: ?358 =<= add (inverse n1) (multiply ?358 n1) [358] by Super 116 with 16 at 1,3
+Id : 144, {_}: add ?384 n1 =?= add (inverse n1) n1 [384] by Super 131 with 2 at 2,3
+Id : 132, {_}: add ?360 n1 =?= add (inverse n1) n1 [360] by Super 131 with 2 at 2,3
+Id : 145, {_}: add ?386 n1 =?= add ?387 n1 [387, 386] by Super 144 with 132 at 3
+Id : 730, {_}: multiply (inverse n1) (inverse n1) =<= multiply (inverse n1) (add ?1307 n1) [1307] by Super 557 with 145 at 2,3
+Id : 734, {_}: multiply (inverse n1) (inverse n1) =<= add (inverse n1) (inverse n1) [] by Super 730 with 284 at 3
+Id : 756, {_}: multiply (inverse n1) (multiply (inverse n1) (inverse n1)) =>= add (inverse n1) (inverse n1) [] by Demod 515 with 734 at 2,2
+Id : 757, {_}: multiply (inverse n1) (multiply (inverse n1) (inverse n1)) =>= multiply (inverse n1) (inverse n1) [] by Demod 756 with 734 at 3
+Id : 758, {_}: inverse n1 =<= add (multiply (inverse n1) (inverse n1)) (multiply (inverse n1) (inverse n1)) [] by Demod 525 with 734 at 2,3
+Id : 759, {_}: inverse n1 =<= multiply (inverse n1) (add (inverse n1) (inverse n1)) [] by Demod 758 with 3 at 3
+Id : 760, {_}: inverse n1 =<= multiply (inverse n1) (multiply (inverse n1) (inverse n1)) [] by Demod 759 with 734 at 2,3
+Id : 761, {_}: inverse n1 =<= multiply (inverse n1) (inverse n1) [] by Demod 757 with 760 at 2
+Id : 765, {_}: inverse n1 =<= add (inverse n1) (inverse n1) [] by Demod 734 with 761 at 2
+Id : 771, {_}: pixley (add (inverse n1) (inverse n1)) n1 ?1319 =<= add (inverse n1) (multiply ?1319 (add (inverse n1) (inverse n1))) [1319] by Super 24 with 765 at 1,2,2,3
+Id : 809, {_}: pixley (inverse n1) n1 ?1319 =<= add (inverse n1) (multiply ?1319 (add (inverse n1) (inverse n1))) [1319] by Demod 771 with 765 at 1,2
+Id : 810, {_}: pixley (inverse n1) n1 ?1319 =<= add (inverse n1) (multiply ?1319 (inverse n1)) [1319] by Demod 809 with 765 at 2,2,3
+Id : 859, {_}: pixley (inverse n1) n1 ?1388 =<= multiply (inverse n1) (add n1 ?1388) [1388] by Demod 810 with 40 at 3
+Id : 860, {_}: pixley (inverse n1) n1 (inverse n1) =>= multiply (inverse n1) n1 [] by Super 859 with 4 at 2,3
+Id : 885, {_}: inverse n1 =<= multiply (inverse n1) n1 [] by Demod 860 with 8 at 2
+Id : 902, {_}: multiply n1 (add ?1409 (inverse n1)) =<= add (multiply ?1409 n1) (inverse n1) [1409] by Super 3 with 885 at 2,3
+Id : 168, {_}: multiply ?429 (multiply ?430 (add ?429 (inverse ?430))) =>= multiply ?430 (add ?429 (inverse ?430)) [430, 429] by Super 162 with 7 at 1,2
+Id : 903, {_}: multiply n1 (add (inverse n1) ?1411) =<= add (inverse n1) (multiply ?1411 n1) [1411] by Super 3 with 885 at 1,3
+Id : 118, {_}: ?328 =<= add (inverse n1) (multiply ?328 n1) [328] by Super 116 with 16 at 1,3
+Id : 1013, {_}: multiply n1 (add (inverse n1) ?1510) =>= ?1510 [1510] by Demod 903 with 118 at 3
+Id : 1014, {_}: multiply n1 n1 =>= inverse (inverse n1) [] by Super 1013 with 4 at 2,2
+Id : 1051, {_}: multiply n1 (add n1 (inverse n1)) =<= add (inverse (inverse n1)) (inverse n1) [] by Super 902 with 1014 at 1,3
+Id : 1091, {_}: multiply n1 n1 =<= add (inverse (inverse n1)) (inverse n1) [] by Demod 1051 with 4 at 2,2
+Id : 1092, {_}: inverse (inverse n1) =<= add (inverse (inverse n1)) (inverse n1) [] by Demod 1091 with 1014 at 2
+Id : 1370, {_}: multiply (inverse (inverse n1)) (multiply n1 (inverse (inverse n1))) =>= multiply n1 (add (inverse (inverse n1)) (inverse n1)) [] by Super 168 with 1092 at 2,2,2
+Id : 1373, {_}: multiply (inverse (inverse n1)) (inverse (inverse n1)) =<= multiply n1 (add (inverse (inverse n1)) (inverse n1)) [] by Demod 1370 with 16 at 2,2
+Id : 1374, {_}: multiply (inverse (inverse n1)) (inverse (inverse n1)) =>= multiply n1 (inverse (inverse n1)) [] by Demod 1373 with 1092 at 2,3
+Id : 1375, {_}: multiply (inverse (inverse n1)) (inverse (inverse n1)) =>= inverse (inverse n1) [] by Demod 1374 with 16 at 3
+Id : 1407, {_}: multiply (inverse (inverse n1)) (add n1 (inverse (inverse n1))) =>= add (inverse (inverse n1)) (inverse (inverse n1)) [] by Super 40 with 1375 at 2,3
+Id : 1015, {_}: multiply n1 (add ?1513 n1) =>= n1 [1513] by Super 1013 with 145 at 2,2
+Id : 1292, {_}: n1 =<= add n1 (multiply n1 n1) [] by Super 14 with 1015 at 2
+Id : 1307, {_}: n1 =<= add n1 (inverse (inverse n1)) [] by Demod 1292 with 1014 at 2,3
+Id : 1421, {_}: multiply (inverse (inverse n1)) n1 =<= add (inverse (inverse n1)) (inverse (inverse n1)) [] by Demod 1407 with 1307 at 2,2
+Id : 1422, {_}: multiply (inverse (inverse n1)) n1 =<= multiply (inverse (inverse n1)) (add n1 n1) [] by Demod 1421 with 284 at 3
+Id : 111, {_}: ?63 =<= add (multiply ?62 (inverse ?62)) (multiply ?63 n1) [62, 63] by Demod 22 with 6 at 2
+Id : 359, {_}: multiply (multiply ?774 n1) (add ?774 ?775) =<= add (multiply ?774 n1) (multiply ?775 (multiply ?774 n1)) [775, 774] by Super 14 with 111 at 1,2,2
+Id : 114, {_}: multiply ?317 (multiply ?317 n1) =>= multiply ?317 n1 [317] by Super 2 with 111 at 1,2
+Id : 364, {_}: multiply (multiply ?788 n1) (add ?788 ?788) =?= add (multiply ?788 n1) (multiply ?788 n1) [788] by Super 359 with 114 at 2,3
+Id : 390, {_}: multiply (multiply ?814 n1) (add ?814 ?814) =>= multiply n1 (add ?814 ?814) [814] by Demod 364 with 3 at 3
+Id : 391, {_}: multiply (multiply n1 n1) (add ?816 n1) =>= multiply n1 (add n1 n1) [816] by Super 390 with 145 at 2,2
+Id : 1050, {_}: multiply (inverse (inverse n1)) (add ?816 n1) =>= multiply n1 (add n1 n1) [816] by Demod 391 with 1014 at 1,2
+Id : 1286, {_}: multiply (inverse (inverse n1)) (add ?816 n1) =>= n1 [816] by Demod 1050 with 1015 at 3
+Id : 1423, {_}: multiply (inverse (inverse n1)) n1 =>= n1 [] by Demod 1422 with 1286 at 3
+Id : 1449, {_}: multiply n1 (add (inverse (inverse n1)) (inverse n1)) =>= add n1 (inverse n1) [] by Super 902 with 1423 at 1,3
+Id : 1452, {_}: multiply n1 (inverse (inverse n1)) =>= add n1 (inverse n1) [] by Demod 1449 with 1092 at 2,2
+Id : 1453, {_}: multiply n1 (inverse (inverse n1)) =>= n1 [] by Demod 1452 with 4 at 3
+Id : 1454, {_}: inverse (inverse n1) =>= n1 [] by Demod 1453 with 16 at 2
+Id : 1500, {_}: multiply (multiply ?2051 n1) (multiply n1 ?2051) =>= multiply (inverse (inverse n1)) ?2051 [2051] by Super 49 with 1454 at 1,2,2
+Id : 3169, {_}: multiply (multiply ?3985 n1) (multiply n1 ?3985) =>= multiply n1 ?3985 [3985] by Demod 1500 with 1454 at 1,3
+Id : 933, {_}: multiply n1 (add (inverse n1) ?1411) =>= ?1411 [1411] by Demod 903 with 118 at 3
+Id : 3175, {_}: multiply (multiply (add (inverse n1) ?3998) n1) ?3998 =>= multiply n1 (add (inverse n1) ?3998) [3998] by Super 3169 with 933 at 2,2
+Id : 1440, {_}: inverse (inverse n1) =<= add (inverse n1) n1 [] by Super 118 with 1423 at 2,3
+Id : 1591, {_}: n1 =<= add (inverse n1) n1 [] by Demod 1440 with 1454 at 2
+Id : 1602, {_}: add ?2105 n1 =>= n1 [2105] by Super 145 with 1591 at 3
+Id : 1719, {_}: multiply ?2217 n1 =<= add ?2217 (multiply n1 ?2217) [2217] by Super 14 with 1602 at 2,2
+Id : 1478, {_}: n1 =<= add n1 n1 [] by Demod 1307 with 1454 at 2,3
+Id : 1483, {_}: multiply n1 (add (inverse ?660) (inverse ?660)) =>= multiply (inverse ?660) n1 [660] by Demod 297 with 1478 at 2,3
+Id : 1482, {_}: multiply (inverse ?177) n1 =<= add (inverse ?177) (inverse ?177) [177] by Demod 284 with 1478 at 2,2
+Id : 1484, {_}: multiply n1 (multiply (inverse ?660) n1) =>= multiply (inverse ?660) n1 [660] by Demod 1483 with 1482 at 2,2
+Id : 1727, {_}: multiply (multiply (inverse ?2233) n1) n1 =<= add (multiply (inverse ?2233) n1) (multiply (inverse ?2233) n1) [2233] by Super 1719 with 1484 at 2,3
+Id : 1763, {_}: multiply (multiply (inverse ?2233) n1) n1 =<= multiply n1 (add (inverse ?2233) (inverse ?2233)) [2233] by Demod 1727 with 3 at 3
+Id : 1764, {_}: multiply (multiply (inverse ?2233) n1) n1 =>= multiply n1 (multiply (inverse ?2233) n1) [2233] by Demod 1763 with 1482 at 2,3
+Id : 1765, {_}: multiply (multiply (inverse ?2233) n1) n1 =>= multiply (inverse ?2233) n1 [2233] by Demod 1764 with 1484 at 3
+Id : 1914, {_}: multiply (inverse ?2603) n1 =<= add (inverse n1) (multiply (inverse ?2603) n1) [2603] by Super 118 with 1765 at 2,3
+Id : 1949, {_}: multiply (inverse ?2603) n1 =>= inverse ?2603 [2603] by Demod 1914 with 118 at 3
+Id : 1994, {_}: multiply n1 (add (inverse ?2679) ?2680) =<= add (inverse ?2679) (multiply ?2680 n1) [2680, 2679] by Super 3 with 1949 at 1,3
+Id : 2422, {_}: multiply n1 (multiply n1 (add (inverse n1) ?3107)) =>= multiply ?3107 n1 [3107] by Super 933 with 1994 at 2,2
+Id : 2437, {_}: multiply n1 ?3107 =?= multiply ?3107 n1 [3107] by Demod 2422 with 933 at 2,2
+Id : 3237, {_}: multiply (multiply n1 (add (inverse n1) ?3998)) ?3998 =>= multiply n1 (add (inverse n1) ?3998) [3998] by Demod 3175 with 2437 at 1,2
+Id : 3238, {_}: multiply (multiply n1 (add (inverse n1) ?3998)) ?3998 =>= ?3998 [3998] by Demod 3237 with 933 at 3
+Id : 3239, {_}: multiply ?3998 ?3998 =>= ?3998 [3998] by Demod 3238 with 933 at 1,2
+Id : 3295, {_}: multiply ?4085 (add ?4086 ?4085) =<= add (multiply ?4086 ?4085) ?4085 [4086, 4085] by Super 3 with 3239 at 2,3
+Id : 3506, {_}: multiply ?37 (add ?38 (add ?39 ?37)) =>= multiply ?37 (add ?38 ?37) [39, 38, 37] by Demod 13 with 3295 at 3
+Id : 4221, {_}: multiply (add ?156 ?157) (multiply ?157 (add ?158 ?157)) =>= multiply ?157 (add ?158 (add ?156 ?157)) [158, 157, 156] by Demod 52 with 3506 at 2,2
+Id : 4233, {_}: multiply (add ?4966 ?4967) (multiply ?4967 (add ?4968 ?4967)) =>= multiply ?4967 (add ?4968 ?4967) [4968, 4967, 4966] by Demod 4221 with 3506 at 3
+Id : 1725, {_}: multiply (add (inverse n1) ?2230) n1 =<= add (add (inverse n1) ?2230) ?2230 [2230] by Super 1719 with 933 at 2,3
+Id : 2746, {_}: multiply n1 (add (inverse n1) ?2230) =<= add (add (inverse n1) ?2230) ?2230 [2230] by Demod 1725 with 2437 at 2
+Id : 2751, {_}: ?2230 =<= add (add (inverse n1) ?2230) ?2230 [2230] by Demod 2746 with 933 at 2
+Id : 4246, {_}: multiply (add ?5016 ?5017) (multiply ?5017 ?5017) =?= multiply ?5017 (add (add (inverse n1) ?5017) ?5017) [5017, 5016] by Super 4233 with 2751 at 2,2,2
+Id : 4327, {_}: multiply (add ?5016 ?5017) ?5017 =?= multiply ?5017 (add (add (inverse n1) ?5017) ?5017) [5017, 5016] by Demod 4246 with 3239 at 2,2
+Id : 3296, {_}: multiply ?4088 (add ?4088 ?4089) =<= add ?4088 (multiply ?4089 ?4088) [4089, 4088] by Super 3 with 3239 at 1,3
+Id : 3736, {_}: multiply ?41 (add (add ?42 ?41) ?43) =>= multiply ?41 (add ?41 ?43) [43, 42, 41] by Demod 14 with 3296 at 3
+Id : 4328, {_}: multiply (add ?5016 ?5017) ?5017 =?= multiply ?5017 (add ?5017 ?5017) [5017, 5016] by Demod 4327 with 3736 at 3
+Id : 4329, {_}: ?5017 =<= multiply ?5017 (add ?5017 ?5017) [5017] by Demod 4328 with 2 at 2
+Id : 3529, {_}: multiply ?4289 (add ?4290 ?4289) =<= add (multiply ?4290 ?4289) ?4289 [4290, 4289] by Super 3 with 3239 at 2,3
+Id : 3546, {_}: multiply ?4342 (add ?4342 ?4342) =>= add ?4342 ?4342 [4342] by Super 3529 with 3239 at 1,3
+Id : 4330, {_}: ?5017 =<= add ?5017 ?5017 [5017] by Demod 4329 with 3546 at 3
+Id : 4419, {_}: multiply ?5179 (add ?5180 ?5180) =>= multiply ?5180 ?5179 [5180, 5179] by Super 3 with 4330 at 3
+Id : 4472, {_}: multiply ?5179 ?5180 =?= multiply ?5180 ?5179 [5180, 5179] by Demod 4419 with 4330 at 2,2
+Id : 6559, {_}: multiply ?7216 (add ?7217 ?7218) =<= add (multiply ?7217 ?7216) (multiply ?7216 ?7218) [7218, 7217, 7216] by Super 3 with 4472 at 2,3
+Id : 4435, {_}: multiply ?5223 (add ?5224 ?5223) =<= multiply ?5223 (add ?5223 (add ?5224 ?5223)) [5224, 5223] by Super 3736 with 4330 at 2,2
+Id : 4446, {_}: multiply ?5223 (add ?5224 ?5223) =?= multiply ?5223 (add ?5223 ?5223) [5224, 5223] by Demod 4435 with 3506 at 3
+Id : 4447, {_}: multiply ?5223 (add ?5224 ?5223) =>= multiply ?5223 ?5223 [5224, 5223] by Demod 4446 with 4330 at 2,3
+Id : 4448, {_}: multiply ?5223 (add ?5224 ?5223) =>= ?5223 [5224, 5223] by Demod 4447 with 3239 at 3
+Id : 4587, {_}: multiply (add ?5347 ?5348) (add ?5349 ?5348) =<= add (multiply ?5349 (add ?5347 ?5348)) ?5348 [5349, 5348, 5347] by Super 3 with 4448 at 2,3
+Id : 13274, {_}: multiply ?16470 (add ?16471 ?16472) =<= add (multiply ?16471 ?16470) (multiply ?16470 ?16472) [16472, 16471, 16470] by Super 3 with 4472 at 2,3
+Id : 1990, {_}: inverse ?2668 =<= add (inverse n1) (inverse ?2668) [2668] by Super 118 with 1949 at 2,3
+Id : 2035, {_}: multiply (inverse n1) (multiply ?2698 (inverse ?2698)) =?= multiply ?2698 (add (inverse n1) (inverse ?2698)) [2698] by Super 168 with 1990 at 2,2,2
+Id : 2073, {_}: multiply (inverse n1) (multiply ?2698 (inverse ?2698)) =>= multiply ?2698 (inverse ?2698) [2698] by Demod 2035 with 1990 at 2,3
+Id : 3753, {_}: multiply n1 (multiply (inverse n1) (add (inverse n1) ?4498)) =>= multiply ?4498 (inverse n1) [4498] by Super 933 with 3296 at 2,2
+Id : 3737, {_}: multiply (inverse ?110) (add n1 ?111) =<= multiply (inverse ?110) (add (inverse ?110) ?111) [111, 110] by Demod 40 with 3296 at 3
+Id : 3799, {_}: multiply n1 (multiply (inverse n1) (add n1 ?4498)) =>= multiply ?4498 (inverse n1) [4498] by Demod 3753 with 3737 at 2,2
+Id : 811, {_}: pixley (inverse n1) n1 ?1319 =<= multiply (inverse n1) (add n1 ?1319) [1319] by Demod 810 with 40 at 3
+Id : 3800, {_}: multiply n1 (pixley (inverse n1) n1 ?4498) =>= multiply ?4498 (inverse n1) [4498] by Demod 3799 with 811 at 2,2
+Id : 1503, {_}: multiply (inverse (inverse n1)) (add n1 ?2058) =<= add (inverse (inverse n1)) (multiply ?2058 n1) [2058] by Super 40 with 1454 at 2,2,3
+Id : 1564, {_}: multiply n1 (add n1 ?2058) =<= add (inverse (inverse n1)) (multiply ?2058 n1) [2058] by Demod 1503 with 1454 at 1,2
+Id : 1565, {_}: multiply n1 (add n1 ?2058) =<= add n1 (multiply ?2058 n1) [2058] by Demod 1564 with 1454 at 1,3
+Id : 1981, {_}: multiply n1 (add n1 (inverse ?2643)) =>= add n1 (inverse ?2643) [2643] by Super 1565 with 1949 at 2,3
+Id : 2089, {_}: pixley n1 ?2784 n1 =<= add (multiply n1 (inverse ?2784)) (add n1 (inverse ?2784)) [2784] by Super 19 with 1981 at 2,3
+Id : 2096, {_}: n1 =<= add (multiply n1 (inverse ?2784)) (add n1 (inverse ?2784)) [2784] by Demod 2089 with 8 at 2
+Id : 2097, {_}: n1 =<= add (inverse ?2784) (add n1 (inverse ?2784)) [2784] by Demod 2096 with 16 at 1,3
+Id : 4563, {_}: ?4085 =<= add (multiply ?4086 ?4085) ?4085 [4086, 4085] by Demod 3295 with 4448 at 2
+Id : 4567, {_}: add ?5289 ?5290 =<= add ?5290 (add ?5289 ?5290) [5290, 5289] by Super 4563 with 4448 at 1,3
+Id : 5426, {_}: n1 =<= add n1 (inverse ?2784) [2784] by Demod 2097 with 4567 at 3
+Id : 5450, {_}: multiply n1 (multiply ?6117 n1) =<= multiply ?6117 (add n1 (inverse ?6117)) [6117] by Super 168 with 5426 at 2,2,2
+Id : 5478, {_}: multiply n1 (multiply ?6117 n1) =>= multiply ?6117 n1 [6117] by Demod 5450 with 5426 at 2,3
+Id : 2780, {_}: multiply n1 (add (inverse ?3598) ?3599) =<= add (inverse ?3598) (multiply n1 ?3599) [3599, 3598] by Super 1994 with 2437 at 2,3
+Id : 38, {_}: pixley n1 ?104 ?105 =<= add (inverse ?104) (multiply ?105 (add n1 (inverse ?104))) [105, 104] by Super 19 with 16 at 1,3
+Id : 5427, {_}: pixley n1 ?104 ?105 =<= add (inverse ?104) (multiply ?105 n1) [105, 104] by Demod 38 with 5426 at 2,2,3
+Id : 5431, {_}: pixley n1 ?104 ?105 =<= multiply n1 (add (inverse ?104) ?105) [105, 104] by Demod 5427 with 1994 at 3
+Id : 5434, {_}: pixley n1 ?3598 ?3599 =<= add (inverse ?3598) (multiply n1 ?3599) [3599, 3598] by Demod 2780 with 5431 at 2
+Id : 5505, {_}: pixley n1 ?6141 (multiply ?6142 n1) =>= add (inverse ?6141) (multiply ?6142 n1) [6142, 6141] by Super 5434 with 5478 at 2,3
+Id : 5432, {_}: pixley n1 ?2679 ?2680 =<= add (inverse ?2679) (multiply ?2680 n1) [2680, 2679] by Demod 1994 with 5431 at 2
+Id : 5574, {_}: pixley n1 ?6141 (multiply ?6142 n1) =>= pixley n1 ?6141 ?6142 [6142, 6141] by Demod 5505 with 5432 at 3
+Id : 5935, {_}: pixley n1 n1 ?6510 =>= multiply ?6510 n1 [6510] by Super 6 with 5574 at 2
+Id : 5952, {_}: ?6510 =<= multiply ?6510 n1 [6510] by Demod 5935 with 6 at 2
+Id : 5985, {_}: multiply n1 ?6117 =?= multiply ?6117 n1 [6117] by Demod 5478 with 5952 at 2,2
+Id : 5986, {_}: multiply n1 ?6117 =>= ?6117 [6117] by Demod 5985 with 5952 at 3
+Id : 5995, {_}: pixley (inverse n1) n1 ?4498 =>= multiply ?4498 (inverse n1) [4498] by Demod 3800 with 5986 at 2
+Id : 4560, {_}: multiply ?37 (add ?38 (add ?39 ?37)) =>= ?37 [39, 38, 37] by Demod 3506 with 4448 at 3
+Id : 4745, {_}: multiply n1 (add ?5532 (inverse n1)) =>= add ?5532 (inverse n1) [5532] by Super 933 with 4567 at 2,2
+Id : 4852, {_}: multiply ?5678 (add ?5678 (inverse n1)) =?= multiply n1 (add ?5678 (inverse n1)) [5678] by Super 168 with 4745 at 2,2
+Id : 4888, {_}: multiply ?5678 (add ?5678 (inverse n1)) =>= add ?5678 (inverse n1) [5678] by Demod 4852 with 4745 at 3
+Id : 5026, {_}: multiply (inverse ?5768) (add n1 (inverse n1)) =>= add (inverse ?5768) (inverse n1) [5768] by Super 3737 with 4888 at 3
+Id : 5122, {_}: multiply (inverse ?5768) n1 =<= add (inverse ?5768) (inverse n1) [5768] by Demod 5026 with 4 at 2,2
+Id : 5123, {_}: multiply n1 (inverse ?5768) =<= add (inverse ?5768) (inverse n1) [5768] by Demod 5122 with 2437 at 2
+Id : 5124, {_}: inverse ?5768 =<= add (inverse ?5768) (inverse n1) [5768] by Demod 5123 with 16 at 2
+Id : 5166, {_}: multiply (inverse n1) (add ?5860 (inverse ?5861)) =>= inverse n1 [5861, 5860] by Super 4560 with 5124 at 2,2,2
+Id : 6158, {_}: multiply ?6712 (inverse n1) =<= multiply (inverse n1) (add ?6712 (inverse (inverse n1))) [6712] by Super 168 with 5166 at 2,2
+Id : 6219, {_}: multiply ?6712 (inverse n1) =>= inverse n1 [6712] by Demod 6158 with 5166 at 3
+Id : 6251, {_}: pixley (inverse n1) n1 ?4498 =>= inverse n1 [4498] by Demod 5995 with 6219 at 3
+Id : 2037, {_}: pixley (inverse n1) ?2703 ?2704 =<= add (multiply (inverse n1) (inverse ?2703)) (multiply ?2704 (inverse ?2703)) [2704, 2703] by Super 19 with 1990 at 2,2,3
+Id : 2071, {_}: pixley (inverse n1) ?2703 ?2704 =<= multiply (inverse ?2703) (add (inverse n1) ?2704) [2704, 2703] by Demod 2037 with 3 at 3
+Id : 5976, {_}: ?63 =<= add (multiply ?62 (inverse ?62)) ?63 [62, 63] by Demod 111 with 5952 at 2,3
+Id : 6253, {_}: ?6806 =<= add (inverse n1) ?6806 [6806] by Super 5976 with 6219 at 1,3
+Id : 6304, {_}: pixley (inverse n1) ?2703 ?2704 =>= multiply (inverse ?2703) ?2704 [2704, 2703] by Demod 2071 with 6253 at 2,3
+Id : 6308, {_}: multiply (inverse n1) ?4498 =>= inverse n1 [4498] by Demod 6251 with 6304 at 2
+Id : 6315, {_}: inverse n1 =<= multiply ?2698 (inverse ?2698) [2698] by Demod 2073 with 6308 at 2
+Id : 6591, {_}: inverse n1 =<= multiply (inverse ?7342) ?7342 [7342] by Super 6315 with 4472 at 3
+Id : 13310, {_}: multiply (inverse ?16623) (add ?16624 ?16623) =?= add (multiply ?16624 (inverse ?16623)) (inverse n1) [16624, 16623] by Super 13274 with 6591 at 2,3
+Id : 6698, {_}: multiply ?7545 (add ?7545 (inverse ?7545)) =>= add ?7545 (inverse n1) [7545] by Super 3296 with 6591 at 2,3
+Id : 6721, {_}: multiply ?7545 n1 =<= add ?7545 (inverse n1) [7545] by Demod 6698 with 4 at 2,2
+Id : 6722, {_}: ?7545 =<= add ?7545 (inverse n1) [7545] by Demod 6721 with 5952 at 2
+Id : 13428, {_}: multiply (inverse ?16623) (add ?16624 ?16623) =>= multiply ?16624 (inverse ?16623) [16624, 16623] by Demod 13310 with 6722 at 3
+Id : 13655, {_}: multiply (add ?17100 ?17101) (add (inverse ?17101) ?17101) =>= add (multiply ?17100 (inverse ?17101)) ?17101 [17101, 17100] by Super 4587 with 13428 at 1,3
+Id : 6531, {_}: ?7094 =<= add (multiply ?7094 ?7095) ?7094 [7095, 7094] by Super 4563 with 4472 at 1,3
+Id : 6689, {_}: multiply ?7513 (add (inverse ?7513) ?7514) =?= add (inverse n1) (multiply ?7514 ?7513) [7514, 7513] by Super 3 with 6591 at 1,3
+Id : 7566, {_}: multiply ?8615 (add (inverse ?8615) ?8616) =>= multiply ?8616 ?8615 [8616, 8615] by Demod 6689 with 6253 at 3
+Id : 7568, {_}: multiply ?8620 n1 =<= multiply (inverse (inverse ?8620)) ?8620 [8620] by Super 7566 with 4 at 2,2
+Id : 7615, {_}: ?8620 =<= multiply (inverse (inverse ?8620)) ?8620 [8620] by Demod 7568 with 5952 at 2
+Id : 7635, {_}: inverse (inverse ?8669) =<= add ?8669 (inverse (inverse ?8669)) [8669] by Super 6531 with 7615 at 1,3
+Id : 7710, {_}: pixley ?8783 (inverse ?8783) ?8784 =<= add (multiply ?8783 (inverse (inverse ?8783))) (multiply ?8784 (inverse (inverse ?8783))) [8784, 8783] by Super 19 with 7635 at 2,2,3
+Id : 9183, {_}: pixley ?10684 (inverse ?10684) ?10685 =<= multiply (inverse (inverse ?10684)) (add ?10684 ?10685) [10685, 10684] by Demod 7710 with 3 at 3
+Id : 9184, {_}: pixley ?10687 (inverse ?10687) (inverse ?10687) =>= multiply (inverse (inverse ?10687)) n1 [10687] by Super 9183 with 4 at 2,3
+Id : 9239, {_}: ?10687 =<= multiply (inverse (inverse ?10687)) n1 [10687] by Demod 9184 with 7 at 2
+Id : 9240, {_}: ?10687 =<= multiply n1 (inverse (inverse ?10687)) [10687] by Demod 9239 with 4472 at 3
+Id : 9241, {_}: ?10687 =<= inverse (inverse ?10687) [10687] by Demod 9240 with 5986 at 3
+Id : 9328, {_}: add (inverse ?10804) ?10804 =>= n1 [10804] by Super 4 with 9241 at 2,2
+Id : 13791, {_}: multiply (add ?17100 ?17101) n1 =<= add (multiply ?17100 (inverse ?17101)) ?17101 [17101, 17100] by Demod 13655 with 9328 at 2,2
+Id : 13792, {_}: multiply n1 (add ?17100 ?17101) =<= add (multiply ?17100 (inverse ?17101)) ?17101 [17101, 17100] by Demod 13791 with 4472 at 2
+Id : 14391, {_}: add ?18258 ?18259 =<= add (multiply ?18258 (inverse ?18259)) ?18259 [18259, 18258] by Demod 13792 with 5986 at 2
+Id : 6742, {_}: multiply ?7513 (add (inverse ?7513) ?7514) =>= multiply ?7514 ?7513 [7514, 7513] by Demod 6689 with 6253 at 3
+Id : 7563, {_}: multiply (add (inverse ?8606) ?8607) ?8606 =>= multiply ?8607 ?8606 [8607, 8606] by Super 4472 with 6742 at 3
+Id : 14401, {_}: add (add (inverse (inverse ?18285)) ?18286) ?18285 =>= add (multiply ?18286 (inverse ?18285)) ?18285 [18286, 18285] by Super 14391 with 7563 at 1,3
+Id : 14494, {_}: add (add ?18285 ?18286) ?18285 =<= add (multiply ?18286 (inverse ?18285)) ?18285 [18286, 18285] by Demod 14401 with 9241 at 1,1,2
+Id : 13793, {_}: add ?17100 ?17101 =<= add (multiply ?17100 (inverse ?17101)) ?17101 [17101, 17100] by Demod 13792 with 5986 at 2
+Id : 14495, {_}: add (add ?18285 ?18286) ?18285 =>= add ?18286 ?18285 [18286, 18285] by Demod 14494 with 13793 at 3
+Id : 6533, {_}: multiply ?7100 (add ?7100 ?7101) =<= add ?7100 (multiply ?7100 ?7101) [7101, 7100] by Super 3296 with 4472 at 2,3
+Id : 7753, {_}: pixley ?8783 (inverse ?8783) ?8784 =<= multiply (inverse (inverse ?8783)) (add ?8783 ?8784) [8784, 8783] by Demod 7710 with 3 at 3
+Id : 9278, {_}: pixley ?8783 (inverse ?8783) ?8784 =>= multiply ?8783 (add ?8783 ?8784) [8784, 8783] by Demod 7753 with 9241 at 1,3
+Id : 7714, {_}: pixley (add ?8794 (inverse (inverse ?8794))) (inverse ?8794) ?8795 =<= add (inverse (inverse ?8794)) (multiply ?8795 (add (inverse (inverse ?8794)) (inverse (inverse ?8794)))) [8795, 8794] by Super 24 with 7635 at 1,2,2,3
+Id : 7746, {_}: pixley (inverse (inverse ?8794)) (inverse ?8794) ?8795 =<= add (inverse (inverse ?8794)) (multiply ?8795 (add (inverse (inverse ?8794)) (inverse (inverse ?8794)))) [8795, 8794] by Demod 7714 with 7635 at 1,2
+Id : 7747, {_}: pixley (inverse (inverse ?8794)) (inverse ?8794) ?8795 =<= add (inverse (inverse ?8794)) (multiply ?8795 (inverse (inverse ?8794))) [8795, 8794] by Demod 7746 with 4330 at 2,2,3
+Id : 7748, {_}: pixley (inverse (inverse ?8794)) (inverse ?8794) ?8795 =<= multiply (inverse (inverse ?8794)) (add (inverse (inverse ?8794)) ?8795) [8795, 8794] by Demod 7747 with 3296 at 3
+Id : 7749, {_}: pixley (inverse (inverse ?8794)) (inverse ?8794) ?8795 =>= multiply (inverse (inverse ?8794)) (add n1 ?8795) [8795, 8794] by Demod 7748 with 3737 at 3
+Id : 9298, {_}: pixley ?8794 (inverse ?8794) ?8795 =?= multiply (inverse (inverse ?8794)) (add n1 ?8795) [8795, 8794] by Demod 7749 with 9241 at 1,2
+Id : 9299, {_}: pixley ?8794 (inverse ?8794) ?8795 =>= multiply ?8794 (add n1 ?8795) [8795, 8794] by Demod 9298 with 9241 at 1,3
+Id : 9310, {_}: multiply ?8783 (add n1 ?8784) =?= multiply ?8783 (add ?8783 ?8784) [8784, 8783] by Demod 9278 with 9299 at 2
+Id : 9334, {_}: n1 =<= add n1 ?10824 [10824] by Super 5426 with 9241 at 2,3
+Id : 9392, {_}: multiply ?8783 n1 =<= multiply ?8783 (add ?8783 ?8784) [8784, 8783] by Demod 9310 with 9334 at 2,2
+Id : 9393, {_}: ?8783 =<= multiply ?8783 (add ?8783 ?8784) [8784, 8783] by Demod 9392 with 5952 at 2
+Id : 9397, {_}: ?7100 =<= add ?7100 (multiply ?7100 ?7101) [7101, 7100] by Demod 6533 with 9393 at 2
+Id : 7652, {_}: multiply ?8717 (add (inverse (inverse ?8717)) ?8718) =>= add ?8717 (multiply ?8718 ?8717) [8718, 8717] by Super 3 with 7615 at 1,3
+Id : 8997, {_}: multiply ?10489 (add (inverse (inverse ?10489)) ?10490) =>= multiply ?10489 (add ?10489 ?10490) [10490, 10489] by Demod 7652 with 3296 at 3
+Id : 9013, {_}: multiply (add (inverse (inverse ?10527)) ?10528) ?10527 =>= multiply ?10527 (add ?10527 ?10528) [10528, 10527] by Super 8997 with 4472 at 2
+Id : 11578, {_}: multiply (add ?10527 ?10528) ?10527 =?= multiply ?10527 (add ?10527 ?10528) [10528, 10527] by Demod 9013 with 9241 at 1,1,2
+Id : 11579, {_}: multiply (add ?10527 ?10528) ?10527 =>= ?10527 [10528, 10527] by Demod 11578 with 9393 at 3
+Id : 11608, {_}: add ?13907 ?13908 =<= add (add ?13907 ?13908) ?13907 [13908, 13907] by Super 9397 with 11579 at 2,3
+Id : 14496, {_}: add ?18285 ?18286 =?= add ?18286 ?18285 [18286, 18285] by Demod 14495 with 11608 at 2
+Id : 20857, {_}: multiply ?26392 (add ?26393 ?26394) =<= add (multiply ?26392 ?26394) (multiply ?26393 ?26392) [26394, 26393, 26392] by Super 6559 with 14496 at 3
+Id : 6561, {_}: multiply ?7224 (add ?7225 ?7226) =<= add (multiply ?7224 ?7225) (multiply ?7226 ?7224) [7226, 7225, 7224] by Super 3 with 4472 at 1,3
+Id : 45701, {_}: multiply ?26392 (add ?26393 ?26394) =?= multiply ?26392 (add ?26394 ?26393) [26394, 26393, 26392] by Demod 20857 with 6561 at 3
+Id : 92, {_}: pixley (add ?268 ?269) ?270 ?269 =<= add (multiply (add ?268 ?269) (inverse ?270)) (add ?269 (multiply (inverse ?270) ?269)) [270, 269, 268] by Super 19 with 14 at 2,3
+Id : 88314, {_}: pixley (add ?268 ?269) ?270 ?269 =<= add (multiply (inverse ?270) (add ?268 ?269)) (add ?269 (multiply (inverse ?270) ?269)) [270, 269, 268] by Demod 92 with 4472 at 1,3
+Id : 9395, {_}: ?4088 =<= add ?4088 (multiply ?4089 ?4088) [4089, 4088] by Demod 3296 with 9393 at 2
+Id : 88315, {_}: pixley (add ?268 ?269) ?270 ?269 =<= add (multiply (inverse ?270) (add ?268 ?269)) ?269 [270, 269, 268] by Demod 88314 with 9395 at 2,3
+Id : 88452, {_}: pixley (add ?145802 ?145803) ?145804 ?145803 =<= multiply (add ?145802 ?145803) (add (inverse ?145804) ?145803) [145804, 145803, 145802] by Demod 88315 with 4587 at 3
+Id : 88455, {_}: pixley (add ?145816 ?145817) (inverse ?145818) ?145817 =>= multiply (add ?145816 ?145817) (add ?145818 ?145817) [145818, 145817, 145816] by Super 88452 with 9241 at 1,2,3
+Id : 11, {_}: multiply (multiply ?29 (add ?30 ?31)) (multiply ?31 ?29) =>= multiply ?31 ?29 [31, 30, 29] by Super 2 with 3 at 1,2
+Id : 6691, {_}: multiply (inverse n1) (multiply ?7519 (inverse (add ?7520 ?7519))) =>= multiply ?7519 (inverse (add ?7520 ?7519)) [7520, 7519] by Super 11 with 6591 at 1,2
+Id : 6741, {_}: inverse n1 =<= multiply ?7519 (inverse (add ?7520 ?7519)) [7520, 7519] by Demod 6691 with 6308 at 2
+Id : 7453, {_}: pixley ?8439 (add ?8440 ?8439) ?8441 =<= add (inverse n1) (multiply ?8441 (add ?8439 (inverse (add ?8440 ?8439)))) [8441, 8440, 8439] by Super 19 with 6741 at 1,3
+Id : 7492, {_}: pixley ?8439 (add ?8440 ?8439) ?8441 =<= multiply ?8441 (add ?8439 (inverse (add ?8440 ?8439))) [8441, 8440, 8439] by Demod 7453 with 6253 at 3
+Id : 98274, {_}: pixley ?163996 (add ?163997 ?163996) n1 =>= add ?163996 (inverse (add ?163997 ?163996)) [163997, 163996] by Super 5986 with 7492 at 2
+Id : 4588, {_}: multiply (add ?5351 ?5352) (add ?5352 ?5353) =<= add ?5352 (multiply ?5353 (add ?5351 ?5352)) [5353, 5352, 5351] by Super 3 with 4448 at 1,3
+Id : 13309, {_}: multiply ?16620 (add ?16621 (inverse ?16620)) =?= add (multiply ?16621 ?16620) (inverse n1) [16621, 16620] by Super 13274 with 6315 at 2,3
+Id : 13427, {_}: multiply ?16620 (add ?16621 (inverse ?16620)) =>= multiply ?16621 ?16620 [16621, 16620] by Demod 13309 with 6722 at 3
+Id : 13531, {_}: multiply (add ?17007 (inverse ?17008)) (add (inverse ?17008) ?17008) =>= add (inverse ?17008) (multiply ?17007 ?17008) [17008, 17007] by Super 4588 with 13427 at 2,3
+Id : 11835, {_}: add ?14300 ?14301 =<= add (add ?14300 ?14301) ?14300 [14301, 14300] by Super 9397 with 11579 at 2,3
+Id : 11844, {_}: add ?14326 (add ?14327 ?14326) =?= add (add ?14327 ?14326) ?14326 [14327, 14326] by Super 11835 with 4567 at 1,3
+Id : 11909, {_}: add ?14327 ?14326 =<= add (add ?14327 ?14326) ?14326 [14326, 14327] by Demod 11844 with 4567 at 2
+Id : 11970, {_}: pixley (add ?69 (inverse ?70)) ?70 ?71 =<= add (inverse ?70) (multiply ?71 (add ?69 (inverse ?70))) [71, 70, 69] by Demod 24 with 11909 at 2,2,3
+Id : 12697, {_}: pixley (add ?69 (inverse ?70)) ?70 ?71 =<= multiply (add ?69 (inverse ?70)) (add (inverse ?70) ?71) [71, 70, 69] by Demod 11970 with 4588 at 3
+Id : 13561, {_}: pixley (add ?17007 (inverse ?17008)) ?17008 ?17008 =>= add (inverse ?17008) (multiply ?17007 ?17008) [17008, 17007] by Demod 13531 with 12697 at 2
+Id : 14017, {_}: add ?17647 (inverse ?17648) =<= add (inverse ?17648) (multiply ?17647 ?17648) [17648, 17647] by Demod 13561 with 7 at 2
+Id : 10227, {_}: multiply (inverse ?12001) (add ?12001 ?12002) =>= multiply ?12002 (inverse ?12001) [12002, 12001] by Super 6742 with 9241 at 1,2,2
+Id : 10243, {_}: multiply (inverse ?12047) ?12047 =<= multiply (multiply ?12047 ?12048) (inverse ?12047) [12048, 12047] by Super 10227 with 9397 at 2,2
+Id : 10311, {_}: inverse n1 =<= multiply (multiply ?12047 ?12048) (inverse ?12047) [12048, 12047] by Demod 10243 with 6591 at 2
+Id : 10454, {_}: inverse n1 =<= multiply (inverse ?12293) (multiply ?12293 ?12294) [12294, 12293] by Demod 10311 with 4472 at 3
+Id : 10488, {_}: inverse n1 =<= multiply ?12387 (multiply (inverse ?12387) ?12388) [12388, 12387] by Super 10454 with 9241 at 1,3
+Id : 14062, {_}: add ?17790 (inverse (multiply (inverse ?17790) ?17791)) =?= add (inverse (multiply (inverse ?17790) ?17791)) (inverse n1) [17791, 17790] by Super 14017 with 10488 at 2,3
+Id : 14147, {_}: add ?17790 (inverse (multiply (inverse ?17790) ?17791)) =>= inverse (multiply (inverse ?17790) ?17791) [17791, 17790] by Demod 14062 with 6722 at 3
+Id : 20167, {_}: add ?25476 (inverse (multiply (inverse ?25476) ?25477)) =?= add (inverse (multiply (inverse ?25476) ?25477)) ?25476 [25477, 25476] by Super 11608 with 14147 at 1,3
+Id : 20309, {_}: inverse (multiply (inverse ?25476) ?25477) =<= add (inverse (multiply (inverse ?25476) ?25477)) ?25476 [25477, 25476] by Demod 20167 with 14147 at 2
+Id : 98343, {_}: pixley ?164219 (inverse (multiply (inverse ?164219) ?164220)) n1 =<= add ?164219 (inverse (add (inverse (multiply (inverse ?164219) ?164220)) ?164219)) [164220, 164219] by Super 98274 with 20309 at 2,2
+Id : 98565, {_}: pixley ?164219 (inverse (multiply (inverse ?164219) ?164220)) n1 =>= add ?164219 (inverse (inverse (multiply (inverse ?164219) ?164220))) [164220, 164219] by Demod 98343 with 20309 at 1,2,3
+Id : 98566, {_}: pixley ?164219 (inverse (multiply (inverse ?164219) ?164220)) n1 =>= add ?164219 (multiply (inverse ?164219) ?164220) [164220, 164219] by Demod 98565 with 9241 at 2,3
+Id : 13654, {_}: multiply (add ?17097 ?17098) (add ?17098 (inverse ?17098)) =>= add ?17098 (multiply ?17097 (inverse ?17098)) [17098, 17097] by Super 4588 with 13428 at 2,3
+Id : 13794, {_}: multiply (add ?17097 ?17098) n1 =<= add ?17098 (multiply ?17097 (inverse ?17098)) [17098, 17097] by Demod 13654 with 4 at 2,2
+Id : 13795, {_}: multiply n1 (add ?17097 ?17098) =<= add ?17098 (multiply ?17097 (inverse ?17098)) [17098, 17097] by Demod 13794 with 4472 at 2
+Id : 14561, {_}: add ?18466 ?18467 =<= add ?18467 (multiply ?18466 (inverse ?18467)) [18467, 18466] by Demod 13795 with 5986 at 2
+Id : 14565, {_}: add ?18477 ?18478 =<= add ?18478 (multiply (inverse ?18478) ?18477) [18478, 18477] by Super 14561 with 4472 at 2,3
+Id : 98567, {_}: pixley ?164219 (inverse (multiply (inverse ?164219) ?164220)) n1 =>= add ?164220 ?164219 [164220, 164219] by Demod 98566 with 14565 at 3
+Id : 7451, {_}: multiply (inverse (add ?8431 ?8432)) (add ?8433 ?8432) =?= add (multiply ?8433 (inverse (add ?8431 ?8432))) (inverse n1) [8433, 8432, 8431] by Super 3 with 6741 at 2,3
+Id : 7493, {_}: multiply (inverse (add ?8431 ?8432)) (add ?8433 ?8432) =>= multiply ?8433 (inverse (add ?8431 ?8432)) [8433, 8432, 8431] by Demod 7451 with 6722 at 3
+Id : 105415, {_}: pixley (add ?172221 ?172222) (inverse (multiply ?172223 (inverse (add ?172221 ?172222)))) n1 =>= add (add ?172223 ?172222) (add ?172221 ?172222) [172223, 172222, 172221] by Super 98567 with 7493 at 1,2,2
+Id : 10242, {_}: multiply (inverse ?12044) ?12044 =<= multiply (multiply ?12045 ?12044) (inverse ?12044) [12045, 12044] by Super 10227 with 9395 at 2,2
+Id : 10309, {_}: inverse n1 =<= multiply (multiply ?12045 ?12044) (inverse ?12044) [12044, 12045] by Demod 10242 with 6591 at 2
+Id : 10337, {_}: inverse n1 =<= multiply (inverse ?12122) (multiply ?12123 ?12122) [12123, 12122] by Demod 10309 with 4472 at 3
+Id : 10370, {_}: inverse n1 =<= multiply ?12222 (multiply ?12223 (inverse ?12222)) [12223, 12222] by Super 10337 with 9241 at 1,3
+Id : 14061, {_}: add ?17787 (inverse (multiply ?17788 (inverse ?17787))) =?= add (inverse (multiply ?17788 (inverse ?17787))) (inverse n1) [17788, 17787] by Super 14017 with 10370 at 2,3
+Id : 14146, {_}: add ?17787 (inverse (multiply ?17788 (inverse ?17787))) =>= inverse (multiply ?17788 (inverse ?17787)) [17788, 17787] by Demod 14061 with 6722 at 3
+Id : 19953, {_}: add ?25324 (inverse (multiply ?25325 (inverse ?25324))) =?= add (inverse (multiply ?25325 (inverse ?25324))) ?25324 [25325, 25324] by Super 11608 with 14146 at 1,3
+Id : 20011, {_}: inverse (multiply ?25325 (inverse ?25324)) =<= add (inverse (multiply ?25325 (inverse ?25324))) ?25324 [25324, 25325] by Demod 19953 with 14146 at 2
+Id : 98342, {_}: pixley ?164216 (inverse (multiply ?164217 (inverse ?164216))) n1 =<= add ?164216 (inverse (add (inverse (multiply ?164217 (inverse ?164216))) ?164216)) [164217, 164216] by Super 98274 with 20011 at 2,2
+Id : 98562, {_}: pixley ?164216 (inverse (multiply ?164217 (inverse ?164216))) n1 =>= add ?164216 (inverse (inverse (multiply ?164217 (inverse ?164216)))) [164217, 164216] by Demod 98342 with 20011 at 1,2,3
+Id : 98563, {_}: pixley ?164216 (inverse (multiply ?164217 (inverse ?164216))) n1 =>= add ?164216 (multiply ?164217 (inverse ?164216)) [164217, 164216] by Demod 98562 with 9241 at 2,3
+Id : 13796, {_}: add ?17097 ?17098 =<= add ?17098 (multiply ?17097 (inverse ?17098)) [17098, 17097] by Demod 13795 with 5986 at 2
+Id : 98564, {_}: pixley ?164216 (inverse (multiply ?164217 (inverse ?164216))) n1 =>= add ?164217 ?164216 [164217, 164216] by Demod 98563 with 13796 at 3
+Id : 106322, {_}: add ?173840 (add ?173841 ?173842) =<= add (add ?173840 ?173842) (add ?173841 ?173842) [173842, 173841, 173840] by Demod 105415 with 98564 at 2
+Id : 106366, {_}: add ?174020 (add ?174021 (multiply ?174021 ?174022)) =?= add (add ?174020 (multiply ?174021 ?174022)) ?174021 [174022, 174021, 174020] by Super 106322 with 9397 at 2,3
+Id : 110603, {_}: add ?183991 ?183992 =<= add (add ?183991 (multiply ?183992 ?183993)) ?183992 [183993, 183992, 183991] by Demod 106366 with 9397 at 2,2
+Id : 111365, {_}: add (multiply ?185632 (inverse ?185633)) ?185634 =<= add (pixley ?185632 ?185633 ?185634) ?185634 [185634, 185633, 185632] by Super 110603 with 19 at 1,3
+Id : 5975, {_}: multiply ?143 (multiply (inverse ?144) ?143) =>= multiply (inverse ?144) ?143 [144, 143] by Demod 49 with 5952 at 1,2
+Id : 6517, {_}: multiply ?7054 (multiply ?7054 (inverse ?7055)) =>= multiply (inverse ?7055) ?7054 [7055, 7054] by Super 5975 with 4472 at 2,2
+Id : 7244, {_}: multiply (multiply ?8105 (inverse ?8106)) ?8105 =>= multiply (inverse ?8106) ?8105 [8106, 8105] by Super 4472 with 6517 at 3
+Id : 9315, {_}: multiply (multiply ?10762 ?10763) ?10762 =>= multiply (inverse (inverse ?10763)) ?10762 [10763, 10762] by Super 7244 with 9241 at 2,1,2
+Id : 9383, {_}: multiply (multiply ?10762 ?10763) ?10762 =>= multiply ?10763 ?10762 [10763, 10762] by Demod 9315 with 9241 at 1,3
+Id : 10069, {_}: pixley (multiply (inverse ?11745) ?11746) ?11745 ?11747 =<= add (multiply ?11746 (inverse ?11745)) (multiply ?11747 (add (multiply (inverse ?11745) ?11746) (inverse ?11745))) [11747, 11746, 11745] by Super 19 with 9383 at 1,3
+Id : 10131, {_}: pixley (multiply (inverse ?11745) ?11746) ?11745 ?11747 =<= add (multiply ?11746 (inverse ?11745)) (multiply ?11747 (inverse ?11745)) [11747, 11746, 11745] by Demod 10069 with 6531 at 2,2,3
+Id : 10132, {_}: pixley (multiply (inverse ?11745) ?11746) ?11745 ?11747 =>= multiply (inverse ?11745) (add ?11746 ?11747) [11747, 11746, 11745] by Demod 10131 with 3 at 3
+Id : 111375, {_}: add (multiply (multiply (inverse ?185663) ?185664) (inverse ?185663)) ?185665 =?= add (multiply (inverse ?185663) (add ?185664 ?185665)) ?185665 [185665, 185664, 185663] by Super 111365 with 10132 at 1,3
+Id : 111673, {_}: add (multiply (inverse ?185663) (multiply (inverse ?185663) ?185664)) ?185665 =?= add (multiply (inverse ?185663) (add ?185664 ?185665)) ?185665 [185665, 185664, 185663] by Demod 111375 with 4472 at 1,2
+Id : 111674, {_}: add (multiply (inverse ?185663) (multiply (inverse ?185663) ?185664)) ?185665 =?= multiply (add ?185664 ?185665) (add (inverse ?185663) ?185665) [185665, 185664, 185663] by Demod 111673 with 4587 at 3
+Id : 9338, {_}: multiply ?10835 (multiply ?10835 ?10836) =?= multiply (inverse (inverse ?10836)) ?10835 [10836, 10835] by Super 6517 with 9241 at 2,2,2
+Id : 9347, {_}: multiply ?10835 (multiply ?10835 ?10836) =>= multiply ?10836 ?10835 [10836, 10835] by Demod 9338 with 9241 at 1,3
+Id : 111675, {_}: add (multiply ?185664 (inverse ?185663)) ?185665 =<= multiply (add ?185664 ?185665) (add (inverse ?185663) ?185665) [185665, 185663, 185664] by Demod 111674 with 9347 at 1,2
+Id : 88316, {_}: pixley (add ?268 ?269) ?270 ?269 =<= multiply (add ?268 ?269) (add (inverse ?270) ?269) [270, 269, 268] by Demod 88315 with 4587 at 3
+Id : 111676, {_}: add (multiply ?185664 (inverse ?185663)) ?185665 =<= pixley (add ?185664 ?185665) ?185663 ?185665 [185665, 185663, 185664] by Demod 111675 with 88316 at 3
+Id : 111830, {_}: add (multiply ?145816 (inverse (inverse ?145818))) ?145817 =?= multiply (add ?145816 ?145817) (add ?145818 ?145817) [145817, 145818, 145816] by Demod 88455 with 111676 at 2
+Id : 111831, {_}: add (multiply ?145816 ?145818) ?145817 =<= multiply (add ?145816 ?145817) (add ?145818 ?145817) [145817, 145818, 145816] by Demod 111830 with 9241 at 2,1,2
+Id : 112319, {_}: add a (multiply b c) === add a (multiply b c) [] by Demod 112318 with 14496 at 3
+Id : 112318, {_}: add a (multiply b c) =<= add (multiply b c) a [] by Demod 112317 with 111831 at 3
+Id : 112317, {_}: add a (multiply b c) =<= multiply (add b a) (add c a) [] by Demod 112316 with 4472 at 3
+Id : 112316, {_}: add a (multiply b c) =<= multiply (add c a) (add b a) [] by Demod 112315 with 45701 at 3
+Id : 112315, {_}: add a (multiply b c) =<= multiply (add c a) (add a b) [] by Demod 112314 with 4472 at 3
+Id : 112314, {_}: add a (multiply b c) =<= multiply (add a b) (add c a) [] by Demod 1 with 45701 at 3
+Id : 1, {_}: add a (multiply b c) =<= multiply (add a b) (add a c) [] by prove_add_multiply_property
+% SZS output end CNFRefutation for BOO023-1.p
+29618: solved BOO023-1.p in 25.957622 using nrkbo
+29618: status Unsatisfiable for BOO023-1.p
+NO CLASH, using fixed ground order
+29626: Facts:
+29626: Id : 2, {_}:
+ multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
+ =>=
+ multiply ?2 ?3 (multiply ?4 ?5 ?6)
+ [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
+29626: Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
+29626: Id : 4, {_}:
+ multiply ?11 ?11 ?12 =>= ?11
+ [12, 11] by ternary_multiply_2 ?11 ?12
+29626: Id : 5, {_}:
+ multiply (inverse ?14) ?14 ?15 =>= ?15
+ [15, 14] by left_inverse ?14 ?15
+29626: Id : 6, {_}:
+ multiply ?17 ?18 (inverse ?18) =>= ?17
+ [18, 17] by right_inverse ?17 ?18
+29626: Goal:
+29626: Id : 1, {_}:
+ multiply (multiply a (inverse a) b)
+ (inverse (multiply (multiply c d e) f (multiply c d g)))
+ (multiply d (multiply g f e) c)
+ =>=
+ b
+ [] by prove_single_axiom
+29626: Order:
+29626: nrkbo
+29626: Leaf order:
+29626: a 2 0 2 1,1,2
+29626: f 2 0 2 2,1,2,2
+29626: e 2 0 2 3,1,1,2,2
+29626: b 2 0 2 3,1,2
+29626: g 2 0 2 3,3,1,2,2
+29626: c 3 0 3 1,1,1,2,2
+29626: d 3 0 3 2,1,1,2,2
+29626: inverse 4 1 2 0,2,1,2
+29626: multiply 16 3 7 0,2
+NO CLASH, using fixed ground order
+29627: Facts:
+29627: Id : 2, {_}:
+ multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
+ =>=
+ multiply ?2 ?3 (multiply ?4 ?5 ?6)
+ [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
+29627: Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
+29627: Id : 4, {_}:
+ multiply ?11 ?11 ?12 =>= ?11
+ [12, 11] by ternary_multiply_2 ?11 ?12
+29627: Id : 5, {_}:
+ multiply (inverse ?14) ?14 ?15 =>= ?15
+ [15, 14] by left_inverse ?14 ?15
+29627: Id : 6, {_}:
+ multiply ?17 ?18 (inverse ?18) =>= ?17
+ [18, 17] by right_inverse ?17 ?18
+29627: Goal:
+29627: Id : 1, {_}:
+ multiply (multiply a (inverse a) b)
+ (inverse (multiply (multiply c d e) f (multiply c d g)))
+ (multiply d (multiply g f e) c)
+ =>=
+ b
+ [] by prove_single_axiom
+29627: Order:
+29627: kbo
+29627: Leaf order:
+29627: a 2 0 2 1,1,2
+29627: f 2 0 2 2,1,2,2
+29627: e 2 0 2 3,1,1,2,2
+29627: b 2 0 2 3,1,2
+29627: g 2 0 2 3,3,1,2,2
+29627: c 3 0 3 1,1,1,2,2
+29627: d 3 0 3 2,1,1,2,2
+29627: inverse 4 1 2 0,2,1,2
+29627: multiply 16 3 7 0,2
+NO CLASH, using fixed ground order
+29628: Facts:
+29628: Id : 2, {_}:
+ multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6)
+ =>=
+ multiply ?2 ?3 (multiply ?4 ?5 ?6)
+ [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
+29628: Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
+29628: Id : 4, {_}:
+ multiply ?11 ?11 ?12 =>= ?11
+ [12, 11] by ternary_multiply_2 ?11 ?12
+29628: Id : 5, {_}:
+ multiply (inverse ?14) ?14 ?15 =>= ?15
+ [15, 14] by left_inverse ?14 ?15
+29628: Id : 6, {_}:
+ multiply ?17 ?18 (inverse ?18) =>= ?17
+ [18, 17] by right_inverse ?17 ?18
+29628: Goal:
+29628: Id : 1, {_}:
+ multiply (multiply a (inverse a) b)
+ (inverse (multiply (multiply c d e) f (multiply c d g)))
+ (multiply d (multiply g f e) c)
+ =>=
+ b
+ [] by prove_single_axiom
+29628: Order:
+29628: lpo
+29628: Leaf order:
+29628: a 2 0 2 1,1,2
+29628: f 2 0 2 2,1,2,2
+29628: e 2 0 2 3,1,1,2,2
+29628: b 2 0 2 3,1,2
+29628: g 2 0 2 3,3,1,2,2
+29628: c 3 0 3 1,1,1,2,2
+29628: d 3 0 3 2,1,1,2,2
+29628: inverse 4 1 2 0,2,1,2
+29628: multiply 16 3 7 0,2
+Statistics :
+Max weight : 24
+Found proof, 10.457305s
+% SZS status Unsatisfiable for BOO034-1.p
+% SZS output start CNFRefutation for BOO034-1.p
+Id : 5, {_}: multiply (inverse ?14) ?14 ?15 =>= ?15 [15, 14] by left_inverse ?14 ?15
+Id : 6, {_}: multiply ?17 ?18 (inverse ?18) =>= ?17 [18, 17] by right_inverse ?17 ?18
+Id : 4, {_}: multiply ?11 ?11 ?12 =>= ?11 [12, 11] by ternary_multiply_2 ?11 ?12
+Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9
+Id : 2, {_}: multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6) =>= multiply ?2 ?3 (multiply ?4 ?5 ?6) [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6
+Id : 13, {_}: multiply ?53 ?54 (multiply ?55 ?53 ?56) =?= multiply ?55 ?53 (multiply ?53 ?54 ?56) [56, 55, 54, 53] by Super 2 with 3 at 1,2
+Id : 12, {_}: multiply (multiply ?48 ?49 ?50) ?51 ?49 =?= multiply ?48 ?49 (multiply ?50 ?51 ?49) [51, 50, 49, 48] by Super 2 with 3 at 3,2
+Id : 919, {_}: multiply (multiply ?2933 ?2934 ?2935) ?2933 ?2934 =?= multiply ?2935 ?2933 (multiply ?2933 ?2934 ?2934) [2935, 2934, 2933] by Super 12 with 13 at 3
+Id : 1358, {_}: multiply (multiply ?4047 ?4048 ?4049) ?4047 ?4048 =>= multiply ?4049 ?4047 ?4048 [4049, 4048, 4047] by Demod 919 with 3 at 3,3
+Id : 518, {_}: multiply (multiply ?1782 ?1783 ?1784) ?1785 ?1783 =?= multiply ?1782 ?1783 (multiply ?1784 ?1785 ?1783) [1785, 1784, 1783, 1782] by Super 2 with 3 at 3,2
+Id : 658, {_}: multiply (multiply ?2168 ?2169 ?2170) ?2170 ?2169 =>= multiply ?2168 ?2169 ?2170 [2170, 2169, 2168] by Super 518 with 4 at 3,3
+Id : 663, {_}: multiply ?2187 (inverse ?2188) ?2188 =?= multiply ?2187 ?2188 (inverse ?2188) [2188, 2187] by Super 658 with 6 at 1,2
+Id : 700, {_}: multiply ?2187 (inverse ?2188) ?2188 =>= ?2187 [2188, 2187] by Demod 663 with 6 at 3
+Id : 1370, {_}: multiply ?4102 ?4102 (inverse ?4103) =?= multiply ?4103 ?4102 (inverse ?4103) [4103, 4102] by Super 1358 with 700 at 1,2
+Id : 1414, {_}: ?4102 =<= multiply ?4103 ?4102 (inverse ?4103) [4103, 4102] by Demod 1370 with 4 at 2
+Id : 1523, {_}: multiply ?4433 ?4434 (multiply ?4435 ?4433 (inverse ?4433)) =>= multiply ?4435 ?4433 ?4434 [4435, 4434, 4433] by Super 13 with 1414 at 3,3
+Id : 1537, {_}: multiply ?4433 ?4434 ?4435 =?= multiply ?4435 ?4433 ?4434 [4435, 4434, 4433] by Demod 1523 with 6 at 3,2
+Id : 1363, {_}: multiply ?4066 ?4066 ?4067 =?= multiply (inverse ?4067) ?4066 ?4067 [4067, 4066] by Super 1358 with 6 at 1,2
+Id : 1412, {_}: ?4066 =<= multiply (inverse ?4067) ?4066 ?4067 [4067, 4066] by Demod 1363 with 4 at 2
+Id : 1452, {_}: multiply (multiply ?4284 ?4285 (inverse ?4285)) ?4286 ?4285 =>= multiply ?4284 ?4285 ?4286 [4286, 4285, 4284] by Super 12 with 1412 at 3,3
+Id : 1474, {_}: multiply ?4284 ?4286 ?4285 =?= multiply ?4284 ?4285 ?4286 [4285, 4286, 4284] by Demod 1452 with 6 at 1,2
+Id : 726, {_}: inverse (inverse ?2325) =>= ?2325 [2325] by Super 5 with 700 at 2
+Id : 760, {_}: multiply ?2416 (inverse ?2416) ?2417 =>= ?2417 [2417, 2416] by Super 5 with 726 at 1,2
+Id : 41048, {_}: b === b [] by Demod 41047 with 700 at 2
+Id : 41047, {_}: multiply b (inverse (multiply c d (multiply f e g))) (multiply c d (multiply f e g)) =>= b [] by Demod 41046 with 1474 at 3,3,2
+Id : 41046, {_}: multiply b (inverse (multiply c d (multiply f e g))) (multiply c d (multiply f g e)) =>= b [] by Demod 41045 with 1537 at 3,3,2
+Id : 41045, {_}: multiply b (inverse (multiply c d (multiply f e g))) (multiply c d (multiply e f g)) =>= b [] by Demod 41044 with 1474 at 3,3,2
+Id : 41044, {_}: multiply b (inverse (multiply c d (multiply f e g))) (multiply c d (multiply e g f)) =>= b [] by Demod 41043 with 1537 at 3,3,2
+Id : 41043, {_}: multiply b (inverse (multiply c d (multiply f e g))) (multiply c d (multiply g f e)) =>= b [] by Demod 41042 with 1474 at 3,2
+Id : 41042, {_}: multiply b (inverse (multiply c d (multiply f e g))) (multiply c (multiply g f e) d) =>= b [] by Demod 41041 with 1537 at 3,2
+Id : 41041, {_}: multiply b (inverse (multiply c d (multiply f e g))) (multiply d c (multiply g f e)) =>= b [] by Demod 41040 with 1474 at 3,1,2,2
+Id : 41040, {_}: multiply b (inverse (multiply c d (multiply f g e))) (multiply d c (multiply g f e)) =>= b [] by Demod 41039 with 1474 at 2
+Id : 41039, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply c d (multiply f g e))) =>= b [] by Demod 41038 with 1537 at 2
+Id : 41038, {_}: multiply (inverse (multiply c d (multiply f g e))) b (multiply d c (multiply g f e)) =>= b [] by Demod 41037 with 1474 at 3,2
+Id : 41037, {_}: multiply (inverse (multiply c d (multiply f g e))) b (multiply d (multiply g f e) c) =>= b [] by Demod 41036 with 760 at 2,2
+Id : 41036, {_}: multiply (inverse (multiply c d (multiply f g e))) (multiply a (inverse a) b) (multiply d (multiply g f e) c) =>= b [] by Demod 41035 with 1537 at 3,1,1,2
+Id : 41035, {_}: multiply (inverse (multiply c d (multiply e f g))) (multiply a (inverse a) b) (multiply d (multiply g f e) c) =>= b [] by Demod 41034 with 1474 at 2
+Id : 41034, {_}: multiply (inverse (multiply c d (multiply e f g))) (multiply d (multiply g f e) c) (multiply a (inverse a) b) =>= b [] by Demod 11 with 1537 at 2
+Id : 11, {_}: multiply (multiply a (inverse a) b) (inverse (multiply c d (multiply e f g))) (multiply d (multiply g f e) c) =>= b [] by Demod 1 with 2 at 1,2,2
+Id : 1, {_}: multiply (multiply a (inverse a) b) (inverse (multiply (multiply c d e) f (multiply c d g))) (multiply d (multiply g f e) c) =>= b [] by prove_single_axiom
+% SZS output end CNFRefutation for BOO034-1.p
+29626: solved BOO034-1.p in 10.42465 using nrkbo
+29626: status Unsatisfiable for BOO034-1.p
+CLASH, statistics insufficient
+29634: Facts:
+29634: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+29634: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
+29634: Goal:
+29634: Id : 1, {_}:
+ apply (apply ?1 (f ?1)) (g ?1)
+ =<=
+ apply (g ?1) (apply (apply (f ?1) (f ?1)) (g ?1))
+ [1] by prove_u_combinator ?1
+29634: Order:
+29634: nrkbo
+29634: Leaf order:
+29634: s 1 0 0
+29634: k 1 0 0
+29634: f 3 1 3 0,2,1,2
+29634: g 3 1 3 0,2,2
+29634: apply 13 2 5 0,2
+CLASH, statistics insufficient
+29635: Facts:
+29635: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+29635: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
+29635: Goal:
+29635: Id : 1, {_}:
+ apply (apply ?1 (f ?1)) (g ?1)
+ =<=
+ apply (g ?1) (apply (apply (f ?1) (f ?1)) (g ?1))
+ [1] by prove_u_combinator ?1
+29635: Order:
+29635: kbo
+29635: Leaf order:
+29635: s 1 0 0
+29635: k 1 0 0
+29635: f 3 1 3 0,2,1,2
+29635: g 3 1 3 0,2,2
+29635: apply 13 2 5 0,2
+CLASH, statistics insufficient
+29636: Facts:
+29636: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+29636: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
+29636: Goal:
+29636: Id : 1, {_}:
+ apply (apply ?1 (f ?1)) (g ?1)
+ =<=
+ apply (g ?1) (apply (apply (f ?1) (f ?1)) (g ?1))
+ [1] by prove_u_combinator ?1
+29636: Order:
+29636: lpo
+29636: Leaf order:
+29636: s 1 0 0
+29636: k 1 0 0
+29636: f 3 1 3 0,2,1,2
+29636: g 3 1 3 0,2,2
+29636: apply 13 2 5 0,2
+% SZS status Timeout for COL004-1.p
+NO CLASH, using fixed ground order
+29663: Facts:
+29663: Id : 2, {_}:
+ apply (apply (apply s ?2) ?3) ?4
+ =?=
+ apply (apply ?2 ?4) (apply ?3 ?4)
+ [4, 3, 2] by s_definition ?2 ?3 ?4
+29663: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+29663: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply s
+ (apply k
+ (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
+ (apply (apply s (apply (apply s (apply k s)) k))
+ (apply k
+ (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
+ [] by strong_fixed_point
+29663: Goal:
+29663: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+29663: Order:
+29663: nrkbo
+29663: Leaf order:
+29663: strong_fixed_point 3 0 2 1,2
+29663: fixed_pt 3 0 3 2,2
+29663: s 11 0 0
+29663: k 13 0 0
+29663: apply 32 2 3 0,2
+NO CLASH, using fixed ground order
+29664: Facts:
+29664: Id : 2, {_}:
+ apply (apply (apply s ?2) ?3) ?4
+ =?=
+ apply (apply ?2 ?4) (apply ?3 ?4)
+ [4, 3, 2] by s_definition ?2 ?3 ?4
+29664: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+29664: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply s
+ (apply k
+ (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
+ (apply (apply s (apply (apply s (apply k s)) k))
+ (apply k
+ (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
+ [] by strong_fixed_point
+29664: Goal:
+29664: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+29664: Order:
+29664: kbo
+29664: Leaf order:
+29664: strong_fixed_point 3 0 2 1,2
+29664: fixed_pt 3 0 3 2,2
+29664: s 11 0 0
+29664: k 13 0 0
+29664: apply 32 2 3 0,2
+NO CLASH, using fixed ground order
+29665: Facts:
+29665: Id : 2, {_}:
+ apply (apply (apply s ?2) ?3) ?4
+ =?=
+ apply (apply ?2 ?4) (apply ?3 ?4)
+ [4, 3, 2] by s_definition ?2 ?3 ?4
+29665: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+29665: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply s
+ (apply k
+ (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
+ (apply (apply s (apply (apply s (apply k s)) k))
+ (apply k
+ (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
+ [] by strong_fixed_point
+29665: Goal:
+29665: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+29665: Order:
+29665: lpo
+29665: Leaf order:
+29665: strong_fixed_point 3 0 2 1,2
+29665: fixed_pt 3 0 3 2,2
+29665: s 11 0 0
+29665: k 13 0 0
+29665: apply 32 2 3 0,2
+% SZS status Timeout for COL006-6.p
+CLASH, statistics insufficient
+29690: Facts:
+29690: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+29690: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+29690: Id : 4, {_}:
+ apply (apply t ?11) ?12 =>= apply ?12 ?11
+ [12, 11] by t_definition ?11 ?12
+29690: Goal:
+29690: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+29690: Order:
+29690: nrkbo
+29690: Leaf order:
+29690: s 1 0 0
+29690: b 1 0 0
+29690: t 1 0 0
+29690: f 3 1 3 0,2,2
+29690: apply 17 2 3 0,2
+CLASH, statistics insufficient
+29691: Facts:
+29691: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+29691: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+29691: Id : 4, {_}:
+ apply (apply t ?11) ?12 =>= apply ?12 ?11
+ [12, 11] by t_definition ?11 ?12
+29691: Goal:
+29691: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+29691: Order:
+29691: kbo
+29691: Leaf order:
+29691: s 1 0 0
+29691: b 1 0 0
+29691: t 1 0 0
+29691: f 3 1 3 0,2,2
+29691: apply 17 2 3 0,2
+CLASH, statistics insufficient
+29692: Facts:
+29692: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+29692: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+29692: Id : 4, {_}:
+ apply (apply t ?11) ?12 =?= apply ?12 ?11
+ [12, 11] by t_definition ?11 ?12
+29692: Goal:
+29692: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+29692: Order:
+29692: lpo
+29692: Leaf order:
+29692: s 1 0 0
+29692: b 1 0 0
+29692: t 1 0 0
+29692: f 3 1 3 0,2,2
+29692: apply 17 2 3 0,2
+% SZS status Timeout for COL036-1.p
+CLASH, statistics insufficient
+29776: Facts:
+29776: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+29776: Id : 3, {_}:
+ apply (apply t ?7) ?8 =>= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+29776: Goal:
+29776: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (apply (h ?1) (g ?1)) (f ?1)
+ [1] by prove_f_combinator ?1
+29776: Order:
+29776: nrkbo
+29776: Leaf order:
+29776: b 1 0 0
+29776: t 1 0 0
+29776: f 2 1 2 0,2,1,1,2
+29776: g 2 1 2 0,2,1,2
+29776: h 2 1 2 0,2,2
+29776: apply 13 2 5 0,2
+CLASH, statistics insufficient
+29777: Facts:
+29777: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+29777: Id : 3, {_}:
+ apply (apply t ?7) ?8 =>= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+29777: Goal:
+29777: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (apply (h ?1) (g ?1)) (f ?1)
+ [1] by prove_f_combinator ?1
+29777: Order:
+29777: kbo
+29777: Leaf order:
+29777: b 1 0 0
+29777: t 1 0 0
+29777: f 2 1 2 0,2,1,1,2
+29777: g 2 1 2 0,2,1,2
+29777: h 2 1 2 0,2,2
+29777: apply 13 2 5 0,2
+CLASH, statistics insufficient
+29778: Facts:
+29778: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+29778: Id : 3, {_}:
+ apply (apply t ?7) ?8 =?= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+29778: Goal:
+29778: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (apply (h ?1) (g ?1)) (f ?1)
+ [1] by prove_f_combinator ?1
+29778: Order:
+29778: lpo
+29778: Leaf order:
+29778: b 1 0 0
+29778: t 1 0 0
+29778: f 2 1 2 0,2,1,1,2
+29778: g 2 1 2 0,2,1,2
+29778: h 2 1 2 0,2,2
+29778: apply 13 2 5 0,2
+Goal subsumed
+Statistics :
+Max weight : 100
+Found proof, 5.339173s
+% SZS status Unsatisfiable for COL063-1.p
+% SZS output start CNFRefutation for COL063-1.p
+Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
+Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
+Id : 3189, {_}: apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) === apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) [] by Super 3184 with 3 at 2
+Id : 3184, {_}: apply (apply ?10590 (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590))))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590))))) =>= apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590)))) [10590] by Super 3164 with 3 at 2,2
+Id : 3164, {_}: apply (apply ?10539 (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (apply (apply ?10540 (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) =>= apply (apply (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) [10540, 10539] by Super 442 with 2 at 2
+Id : 442, {_}: apply (apply (apply ?1394 (apply ?1395 (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (apply ?1396 (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) =>= apply (apply (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395))))) (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) [1396, 1395, 1394] by Super 277 with 2 at 1,1,2
+Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (apply (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) [901, 900] by Super 29 with 2 at 1,2
+Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (apply (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) [87, 86, 85] by Super 13 with 3 at 1,1,2
+Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (apply (h (apply (apply b ?33) (apply (apply b ?34) ?35))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (f (apply (apply b ?33) (apply (apply b ?34) ?35))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
+Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (apply (h (apply (apply b ?18) ?19)) (g (apply (apply b ?18) ?19))) (f (apply (apply b ?18) ?19)) [19, 18] by Super 1 with 2 at 1,1,2
+Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (h ?1) (g ?1)) (f ?1) [1] by prove_f_combinator ?1
+% SZS output end CNFRefutation for COL063-1.p
+29776: solved COL063-1.p in 5.300331 using nrkbo
+29776: status Unsatisfiable for COL063-1.p
+NO CLASH, using fixed ground order
+29785: Facts:
+29785: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+29785: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+29785: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+29785: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+29785: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+29785: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+29785: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+29785: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+29785: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+29785: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+29785: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+29785: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+29785: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+29785: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+29785: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+29785: Goal:
+29785: Id : 1, {_}:
+ a
+ =<=
+ multiply (least_upper_bound a identity)
+ (greatest_lower_bound a identity)
+ [] by prove_p19
+29785: Order:
+29785: nrkbo
+29785: Leaf order:
+29785: a 3 0 3 2
+29785: identity 4 0 2 2,1,3
+29785: inverse 1 1 0
+29785: least_upper_bound 14 2 1 0,1,3
+29785: greatest_lower_bound 14 2 1 0,2,3
+29785: multiply 19 2 1 0,3
+NO CLASH, using fixed ground order
+29786: Facts:
+29786: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+29786: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+29786: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+29786: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+29786: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+29786: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+29786: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+29786: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+29786: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+29786: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+29786: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+29786: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+29786: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+29786: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+29786: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+29786: Goal:
+29786: Id : 1, {_}:
+ a
+ =<=
+ multiply (least_upper_bound a identity)
+ (greatest_lower_bound a identity)
+ [] by prove_p19
+29786: Order:
+29786: kbo
+29786: Leaf order:
+29786: a 3 0 3 2
+29786: identity 4 0 2 2,1,3
+29786: inverse 1 1 0
+29786: least_upper_bound 14 2 1 0,1,3
+29786: greatest_lower_bound 14 2 1 0,2,3
+29786: multiply 19 2 1 0,3
+NO CLASH, using fixed ground order
+29787: Facts:
+29787: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+29787: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+29787: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+29787: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+29787: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+29787: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+29787: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+29787: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+29787: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+29787: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+29787: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+29787: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+29787: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+29787: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+29787: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+29787: Goal:
+29787: Id : 1, {_}:
+ a
+ =<=
+ multiply (least_upper_bound a identity)
+ (greatest_lower_bound a identity)
+ [] by prove_p19
+29787: Order:
+29787: lpo
+29787: Leaf order:
+29787: a 3 0 3 2
+29787: identity 4 0 2 2,1,3
+29787: inverse 1 1 0
+29787: least_upper_bound 14 2 1 0,1,3
+29787: greatest_lower_bound 14 2 1 0,2,3
+29787: multiply 19 2 1 0,3
+% SZS status Timeout for GRP167-3.p
+NO CLASH, using fixed ground order
+29831: Facts:
+29831: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+29831: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+29831: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+29831: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+29831: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+29831: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+29831: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+29831: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+29831: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+29831: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+29831: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+29831: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+29831: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+29831: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+29831: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+29831: Goal:
+29831: Id : 1, {_}:
+ inverse (least_upper_bound a b)
+ =<=
+ greatest_lower_bound (inverse a) (inverse b)
+ [] by prove_p10
+29831: Order:
+29831: nrkbo
+29831: Leaf order:
+29831: identity 2 0 0
+29831: a 2 0 2 1,1,2
+29831: b 2 0 2 2,1,2
+29831: inverse 4 1 3 0,2
+29831: least_upper_bound 14 2 1 0,1,2
+29831: greatest_lower_bound 14 2 1 0,3
+29831: multiply 18 2 0
+NO CLASH, using fixed ground order
+29832: Facts:
+29832: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+29832: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+29832: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+29832: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+29832: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+29832: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+29832: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+29832: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+NO CLASH, using fixed ground order
+29833: Facts:
+29833: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+29833: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+29833: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+29833: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+29833: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+29833: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+29832: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+29832: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+29832: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+29832: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+29832: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+29832: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+29832: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+29832: Goal:
+29832: Id : 1, {_}:
+ inverse (least_upper_bound a b)
+ =<=
+ greatest_lower_bound (inverse a) (inverse b)
+ [] by prove_p10
+29832: Order:
+29832: kbo
+29832: Leaf order:
+29832: identity 2 0 0
+29832: a 2 0 2 1,1,2
+29832: b 2 0 2 2,1,2
+29832: inverse 4 1 3 0,2
+29832: least_upper_bound 14 2 1 0,1,2
+29832: greatest_lower_bound 14 2 1 0,3
+29832: multiply 18 2 0
+29833: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+29833: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+29833: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+29833: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+29833: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+29833: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+29833: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+29833: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+29833: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+29833: Goal:
+29833: Id : 1, {_}:
+ inverse (least_upper_bound a b)
+ =<=
+ greatest_lower_bound (inverse a) (inverse b)
+ [] by prove_p10
+29833: Order:
+29833: lpo
+29833: Leaf order:
+29833: identity 2 0 0
+29833: a 2 0 2 1,1,2
+29833: b 2 0 2 2,1,2
+29833: inverse 4 1 3 0,2
+29833: least_upper_bound 14 2 1 0,1,2
+29833: greatest_lower_bound 14 2 1 0,3
+29833: multiply 18 2 0
+% SZS status Timeout for GRP179-1.p
+NO CLASH, using fixed ground order
+29866: Facts:
+29866: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+29866: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+29866: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+29866: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+29866: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+29866: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+29866: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+29866: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+29866: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+29866: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+29866: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+29866: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+29866: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+29866: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+29866: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+29866: Goal:
+29866: Id : 1, {_}:
+ least_upper_bound (inverse a) identity
+ =>=
+ inverse (greatest_lower_bound a identity)
+ [] by prove_p18
+29866: Order:
+29866: nrkbo
+29866: Leaf order:
+29866: a 2 0 2 1,1,2
+29866: identity 4 0 2 2,2
+29866: inverse 3 1 2 0,1,2
+29866: greatest_lower_bound 14 2 1 0,1,3
+29866: least_upper_bound 14 2 1 0,2
+29866: multiply 18 2 0
+NO CLASH, using fixed ground order
+29867: Facts:
+29867: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+29867: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+29867: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+29867: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+29867: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+29867: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+29867: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+29867: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+29867: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+29867: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+29867: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+29867: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+29867: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+29867: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+29867: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+29867: Goal:
+29867: Id : 1, {_}:
+ least_upper_bound (inverse a) identity
+ =>=
+ inverse (greatest_lower_bound a identity)
+ [] by prove_p18
+29867: Order:
+29867: kbo
+29867: Leaf order:
+29867: a 2 0 2 1,1,2
+29867: identity 4 0 2 2,2
+29867: inverse 3 1 2 0,1,2
+29867: greatest_lower_bound 14 2 1 0,1,3
+29867: least_upper_bound 14 2 1 0,2
+29867: multiply 18 2 0
+NO CLASH, using fixed ground order
+29868: Facts:
+29868: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+29868: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+29868: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+29868: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+29868: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+29868: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+29868: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+29868: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+29868: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+29868: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+29868: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+29868: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+29868: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+29868: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+29868: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+29868: Goal:
+29868: Id : 1, {_}:
+ least_upper_bound (inverse a) identity
+ =>=
+ inverse (greatest_lower_bound a identity)
+ [] by prove_p18
+29868: Order:
+29868: lpo
+29868: Leaf order:
+29868: a 2 0 2 1,1,2
+29868: identity 4 0 2 2,2
+29868: inverse 3 1 2 0,1,2
+29868: greatest_lower_bound 14 2 1 0,1,3
+29868: least_upper_bound 14 2 1 0,2
+29868: multiply 18 2 0
+% SZS status Timeout for GRP179-2.p
+NO CLASH, using fixed ground order
+29889: Facts:
+29889: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+29889: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+29889: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+29889: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+29889: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+29889: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+29889: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+29889: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+29889: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+29889: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+29889: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+29889: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+29889: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+29889: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+29889: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+29889: Goal:
+29889: Id : 1, {_}:
+ multiply a (multiply (inverse (greatest_lower_bound a b)) b)
+ =>=
+ least_upper_bound a b
+ [] by prove_p11
+29889: Order:
+29889: nrkbo
+29889: Leaf order:
+29889: identity 2 0 0
+29889: a 3 0 3 1,2
+29889: b 3 0 3 2,1,1,2,2
+29889: inverse 2 1 1 0,1,2,2
+29889: greatest_lower_bound 14 2 1 0,1,1,2,2
+29889: least_upper_bound 14 2 1 0,3
+29889: multiply 20 2 2 0,2
+NO CLASH, using fixed ground order
+29890: Facts:
+29890: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+29890: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+29890: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+29890: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+29890: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+29890: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+29890: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+29890: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+29890: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+29890: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+29890: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+29890: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+29890: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+29890: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+29890: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+29890: Goal:
+29890: Id : 1, {_}:
+ multiply a (multiply (inverse (greatest_lower_bound a b)) b)
+ =>=
+ least_upper_bound a b
+ [] by prove_p11
+29890: Order:
+29890: kbo
+29890: Leaf order:
+29890: identity 2 0 0
+29890: a 3 0 3 1,2
+29890: b 3 0 3 2,1,1,2,2
+29890: inverse 2 1 1 0,1,2,2
+29890: greatest_lower_bound 14 2 1 0,1,1,2,2
+29890: least_upper_bound 14 2 1 0,3
+29890: multiply 20 2 2 0,2
+NO CLASH, using fixed ground order
+29891: Facts:
+29891: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+29891: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+29891: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+29891: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+29891: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+29891: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+29891: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+29891: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+29891: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+29891: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+29891: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+29891: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+29891: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+29891: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+29891: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+29891: Goal:
+29891: Id : 1, {_}:
+ multiply a (multiply (inverse (greatest_lower_bound a b)) b)
+ =>=
+ least_upper_bound a b
+ [] by prove_p11
+29891: Order:
+29891: lpo
+29891: Leaf order:
+29891: identity 2 0 0
+29891: a 3 0 3 1,2
+29891: b 3 0 3 2,1,1,2,2
+29891: inverse 2 1 1 0,1,2,2
+29891: greatest_lower_bound 14 2 1 0,1,1,2,2
+29891: least_upper_bound 14 2 1 0,3
+29891: multiply 20 2 2 0,2
+% SZS status Timeout for GRP180-1.p
+NO CLASH, using fixed ground order
+29925: Facts:
+29925: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+29925: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+29925: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+29925: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+29925: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+29925: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+29925: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+29925: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+29925: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+29925: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+29925: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+29925: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+29925: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+29925: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+29925: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+29925: Id : 17, {_}: inverse identity =>= identity [] by p20_1
+29925: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20_2 ?51
+29925: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p20_3 ?53 ?54
+29925: Goal:
+29925: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =>=
+ identity
+ [] by prove_p20
+29925: Order:
+29925: nrkbo
+29925: Leaf order:
+29925: a 2 0 2 1,1,2
+29925: identity 7 0 3 2,1,2
+29925: inverse 8 1 1 0,2,2
+29925: least_upper_bound 14 2 1 0,1,2
+29925: greatest_lower_bound 15 2 2 0,2
+29925: multiply 20 2 0
+NO CLASH, using fixed ground order
+29926: Facts:
+29926: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+29926: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+29926: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+29926: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+29926: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+29926: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+29926: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+29926: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+29926: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+29926: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+29926: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+29926: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+29926: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+29926: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+29926: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+29926: Id : 17, {_}: inverse identity =>= identity [] by p20_1
+29926: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20_2 ?51
+29926: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p20_3 ?53 ?54
+29926: Goal:
+29926: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =>=
+ identity
+ [] by prove_p20
+29926: Order:
+29926: kbo
+29926: Leaf order:
+29926: a 2 0 2 1,1,2
+29926: identity 7 0 3 2,1,2
+29926: inverse 8 1 1 0,2,2
+29926: least_upper_bound 14 2 1 0,1,2
+29926: greatest_lower_bound 15 2 2 0,2
+29926: multiply 20 2 0
+NO CLASH, using fixed ground order
+29928: Facts:
+29928: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+29928: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+29928: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+29928: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+29928: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+29928: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+29928: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+29928: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+29928: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+29928: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+29928: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+29928: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+29928: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+29928: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+29928: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+29928: Id : 17, {_}: inverse identity =>= identity [] by p20_1
+29928: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20_2 ?51
+29928: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p20_3 ?53 ?54
+29928: Goal:
+29928: Id : 1, {_}:
+ greatest_lower_bound (least_upper_bound a identity)
+ (inverse (greatest_lower_bound a identity))
+ =>=
+ identity
+ [] by prove_p20
+29928: Order:
+29928: lpo
+29928: Leaf order:
+29928: a 2 0 2 1,1,2
+29928: identity 7 0 3 2,1,2
+29928: inverse 8 1 1 0,2,2
+29928: least_upper_bound 14 2 1 0,1,2
+29928: greatest_lower_bound 15 2 2 0,2
+29928: multiply 20 2 0
+% SZS status Timeout for GRP183-2.p
+NO CLASH, using fixed ground order
+29950: Facts:
+29950: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+29950: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+29950: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+29950: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+29950: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+29950: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+29950: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+29950: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+29950: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+29950: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+29950: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+29950: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+29950: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+29950: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+29950: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+29950: Goal:
+29950: Id : 1, {_}:
+ least_upper_bound (multiply a b) identity
+ =<=
+ multiply a (inverse (greatest_lower_bound a (inverse b)))
+ [] by prove_p23
+29950: Order:
+29950: nrkbo
+29950: Leaf order:
+29950: b 2 0 2 2,1,2
+29950: identity 3 0 1 2,2
+29950: a 3 0 3 1,1,2
+29950: inverse 3 1 2 0,2,3
+29950: greatest_lower_bound 14 2 1 0,1,2,3
+29950: least_upper_bound 14 2 1 0,2
+29950: multiply 20 2 2 0,1,2
+NO CLASH, using fixed ground order
+29951: Facts:
+29951: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+29951: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+29951: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+29951: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+29951: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+29951: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+29951: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+29951: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+29951: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+29951: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+29951: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+29951: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+29951: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+29951: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+29951: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+29951: Goal:
+29951: Id : 1, {_}:
+ least_upper_bound (multiply a b) identity
+ =<=
+ multiply a (inverse (greatest_lower_bound a (inverse b)))
+ [] by prove_p23
+29951: Order:
+29951: kbo
+29951: Leaf order:
+29951: b 2 0 2 2,1,2
+29951: identity 3 0 1 2,2
+29951: a 3 0 3 1,1,2
+29951: inverse 3 1 2 0,2,3
+29951: greatest_lower_bound 14 2 1 0,1,2,3
+29951: least_upper_bound 14 2 1 0,2
+29951: multiply 20 2 2 0,1,2
+NO CLASH, using fixed ground order
+29952: Facts:
+29952: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+29952: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+29952: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+29952: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+29952: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+29952: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+29952: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+29952: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+29952: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+29952: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+29952: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+29952: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+29952: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+29952: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+29952: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+29952: Goal:
+29952: Id : 1, {_}:
+ least_upper_bound (multiply a b) identity
+ =<=
+ multiply a (inverse (greatest_lower_bound a (inverse b)))
+ [] by prove_p23
+29952: Order:
+29952: lpo
+29952: Leaf order:
+29952: b 2 0 2 2,1,2
+29952: identity 3 0 1 2,2
+29952: a 3 0 3 1,1,2
+29952: inverse 3 1 2 0,2,3
+29952: greatest_lower_bound 14 2 1 0,1,2,3
+29952: least_upper_bound 14 2 1 0,2
+29952: multiply 20 2 2 0,1,2
+% SZS status Timeout for GRP186-1.p
+NO CLASH, using fixed ground order
+29976: Facts:
+29976: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
+29976: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
+29976: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
+29976: Id : 5, {_}:
+ meet ?9 ?10 =?= meet ?10 ?9
+ [10, 9] by commutativity_of_meet ?9 ?10
+29976: Id : 6, {_}:
+ join ?12 ?13 =?= join ?13 ?12
+ [13, 12] by commutativity_of_join ?12 ?13
+29976: Id : 7, {_}:
+ meet (meet ?15 ?16) ?17 =?= meet ?15 (meet ?16 ?17)
+ [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
+29976: Id : 8, {_}:
+ join (join ?19 ?20) ?21 =?= join ?19 (join ?20 ?21)
+ [21, 20, 19] by associativity_of_join ?19 ?20 ?21
+29976: Id : 9, {_}:
+ complement (complement ?23) =>= ?23
+ [23] by complement_involution ?23
+29976: Id : 10, {_}:
+ join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
+ [26, 25] by join_complement ?25 ?26
+29976: Id : 11, {_}:
+ meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
+ [29, 28] by meet_complement ?28 ?29
+29976: Goal:
+29976: Id : 1, {_}:
+ join a
+ (join
+ (meet (complement a) (meet (join a (complement b)) (join a b)))
+ (meet (complement a)
+ (join (meet (complement a) b)
+ (meet (complement a) (complement b)))))
+ =>=
+ n1
+ [] by prove_e2
+29976: Order:
+29976: nrkbo
+29976: Leaf order:
+29976: n0 1 0 0
+29976: n1 2 0 1 3
+29976: b 4 0 4 1,2,1,2,1,2,2
+29976: a 7 0 7 1,2
+29976: complement 15 1 6 0,1,1,2,2
+29976: meet 14 2 5 0,1,2,2
+29976: join 17 2 5 0,2
+NO CLASH, using fixed ground order
+29977: Facts:
+29977: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
+29977: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
+29977: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
+29977: Id : 5, {_}:
+ meet ?9 ?10 =?= meet ?10 ?9
+ [10, 9] by commutativity_of_meet ?9 ?10
+29977: Id : 6, {_}:
+ join ?12 ?13 =?= join ?13 ?12
+ [13, 12] by commutativity_of_join ?12 ?13
+29977: Id : 7, {_}:
+ meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
+ [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
+29977: Id : 8, {_}:
+ join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
+ [21, 20, 19] by associativity_of_join ?19 ?20 ?21
+29977: Id : 9, {_}:
+ complement (complement ?23) =>= ?23
+ [23] by complement_involution ?23
+29977: Id : 10, {_}:
+ join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
+ [26, 25] by join_complement ?25 ?26
+29977: Id : 11, {_}:
+ meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
+ [29, 28] by meet_complement ?28 ?29
+29977: Goal:
+29977: Id : 1, {_}:
+ join a
+ (join
+ (meet (complement a) (meet (join a (complement b)) (join a b)))
+ (meet (complement a)
+ (join (meet (complement a) b)
+ (meet (complement a) (complement b)))))
+ =>=
+ n1
+ [] by prove_e2
+29977: Order:
+29977: kbo
+29977: Leaf order:
+29977: n0 1 0 0
+29977: n1 2 0 1 3
+29977: b 4 0 4 1,2,1,2,1,2,2
+29977: a 7 0 7 1,2
+29977: complement 15 1 6 0,1,1,2,2
+29977: meet 14 2 5 0,1,2,2
+29977: join 17 2 5 0,2
+NO CLASH, using fixed ground order
+29978: Facts:
+29978: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
+29978: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
+29978: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
+29978: Id : 5, {_}:
+ meet ?9 ?10 =?= meet ?10 ?9
+ [10, 9] by commutativity_of_meet ?9 ?10
+29978: Id : 6, {_}:
+ join ?12 ?13 =?= join ?13 ?12
+ [13, 12] by commutativity_of_join ?12 ?13
+29978: Id : 7, {_}:
+ meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
+ [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
+29978: Id : 8, {_}:
+ join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
+ [21, 20, 19] by associativity_of_join ?19 ?20 ?21
+29978: Id : 9, {_}:
+ complement (complement ?23) =>= ?23
+ [23] by complement_involution ?23
+29978: Id : 10, {_}:
+ join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
+ [26, 25] by join_complement ?25 ?26
+29978: Id : 11, {_}:
+ meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
+ [29, 28] by meet_complement ?28 ?29
+29978: Goal:
+29978: Id : 1, {_}:
+ join a
+ (join
+ (meet (complement a) (meet (join a (complement b)) (join a b)))
+ (meet (complement a)
+ (join (meet (complement a) b)
+ (meet (complement a) (complement b)))))
+ =>=
+ n1
+ [] by prove_e2
+29978: Order:
+29978: lpo
+29978: Leaf order:
+29978: n0 1 0 0
+29978: n1 2 0 1 3
+29978: b 4 0 4 1,2,1,2,1,2,2
+29978: a 7 0 7 1,2
+29978: complement 15 1 6 0,1,1,2,2
+29978: meet 14 2 5 0,1,2,2
+29978: join 17 2 5 0,2
+% SZS status Timeout for LAT017-1.p
+NO CLASH, using fixed ground order
+30001: Facts:
+30001: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+30001: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+30001: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
+30001: Id : 5, {_}:
+ join ?9 ?10 =?= join ?10 ?9
+ [10, 9] by commutativity_of_join ?9 ?10
+30001: Id : 6, {_}:
+ meet (meet ?12 ?13) ?14 =?= meet ?12 (meet ?13 ?14)
+ [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
+30001: Id : 7, {_}:
+ join (join ?16 ?17) ?18 =?= join ?16 (join ?17 ?18)
+ [18, 17, 16] by associativity_of_join ?16 ?17 ?18
+30001: Id : 8, {_}:
+ join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
+ =>=
+ meet ?20 (join ?21 ?22)
+ [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
+30001: Id : 9, {_}:
+ meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
+ =>=
+ join ?24 (meet ?25 ?26)
+ [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
+30001: Id : 10, {_}:
+ join (meet (join (meet ?28 ?29) ?30) ?29) (meet ?30 ?28)
+ =<=
+ meet (join (meet (join ?28 ?29) ?30) ?29) (join ?30 ?28)
+ [30, 29, 28] by self_dual_distributivity ?28 ?29 ?30
+30001: Goal:
+30001: Id : 1, {_}:
+ meet a (join b c) =<= join (meet a b) (meet a c)
+ [] by prove_distributivity
+30001: Order:
+30001: nrkbo
+30001: Leaf order:
+30001: b 2 0 2 1,2,2
+30001: c 2 0 2 2,2,2
+30001: a 3 0 3 1,2
+30001: join 20 2 2 0,2,2
+30001: meet 21 2 3 0,2
+NO CLASH, using fixed ground order
+30002: Facts:
+30002: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+30002: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+30002: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
+30002: Id : 5, {_}:
+ join ?9 ?10 =?= join ?10 ?9
+ [10, 9] by commutativity_of_join ?9 ?10
+30002: Id : 6, {_}:
+ meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14)
+ [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
+30002: Id : 7, {_}:
+ join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18)
+ [18, 17, 16] by associativity_of_join ?16 ?17 ?18
+30002: Id : 8, {_}:
+ join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
+ =>=
+ meet ?20 (join ?21 ?22)
+ [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
+30002: Id : 9, {_}:
+ meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
+ =>=
+ join ?24 (meet ?25 ?26)
+ [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
+30002: Id : 10, {_}:
+ join (meet (join (meet ?28 ?29) ?30) ?29) (meet ?30 ?28)
+ =<=
+ meet (join (meet (join ?28 ?29) ?30) ?29) (join ?30 ?28)
+ [30, 29, 28] by self_dual_distributivity ?28 ?29 ?30
+30002: Goal:
+30002: Id : 1, {_}:
+ meet a (join b c) =<= join (meet a b) (meet a c)
+ [] by prove_distributivity
+30002: Order:
+30002: kbo
+30002: Leaf order:
+30002: b 2 0 2 1,2,2
+30002: c 2 0 2 2,2,2
+30002: a 3 0 3 1,2
+30002: join 20 2 2 0,2,2
+30002: meet 21 2 3 0,2
+NO CLASH, using fixed ground order
+30003: Facts:
+30003: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+30003: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+30003: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7
+30003: Id : 5, {_}:
+ join ?9 ?10 =?= join ?10 ?9
+ [10, 9] by commutativity_of_join ?9 ?10
+30003: Id : 6, {_}:
+ meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14)
+ [14, 13, 12] by associativity_of_meet ?12 ?13 ?14
+30003: Id : 7, {_}:
+ join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18)
+ [18, 17, 16] by associativity_of_join ?16 ?17 ?18
+30003: Id : 8, {_}:
+ join (meet ?20 (join ?21 ?22)) (meet ?20 ?21)
+ =>=
+ meet ?20 (join ?21 ?22)
+ [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22
+30003: Id : 9, {_}:
+ meet (join ?24 (meet ?25 ?26)) (join ?24 ?25)
+ =>=
+ join ?24 (meet ?25 ?26)
+ [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26
+30003: Id : 10, {_}:
+ join (meet (join (meet ?28 ?29) ?30) ?29) (meet ?30 ?28)
+ =<=
+ meet (join (meet (join ?28 ?29) ?30) ?29) (join ?30 ?28)
+ [30, 29, 28] by self_dual_distributivity ?28 ?29 ?30
+30003: Goal:
+30003: Id : 1, {_}:
+ meet a (join b c) =>= join (meet a b) (meet a c)
+ [] by prove_distributivity
+30003: Order:
+30003: lpo
+30003: Leaf order:
+30003: b 2 0 2 1,2,2
+30003: c 2 0 2 2,2,2
+30003: a 3 0 3 1,2
+30003: join 20 2 2 0,2,2
+30003: meet 21 2 3 0,2
+% SZS status Timeout for LAT020-1.p
+NO CLASH, using fixed ground order
+30025: Facts:
+30025: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+30025: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+30025: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+30025: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+30025: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+30025: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+30025: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+30025: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+30025: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+30025: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+30025: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+30025: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+30025: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+30025: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+30025: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+30025: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+30025: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+30025: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+30025: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+30025: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+30025: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+30025: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+30025: Goal:
+30025: Id : 1, {_}:
+ add (associator x y z) (associator x z y) =>= additive_identity
+ [] by prove_equation
+30025: Order:
+30025: nrkbo
+30025: Leaf order:
+30025: x 2 0 2 1,1,2
+30025: y 2 0 2 2,1,2
+30025: z 2 0 2 3,1,2
+30025: additive_identity 9 0 1 3
+30025: additive_inverse 22 1 0
+30025: commutator 1 2 0
+30025: add 25 2 1 0,2
+30025: multiply 40 2 0
+30025: associator 3 3 2 0,1,2
+NO CLASH, using fixed ground order
+30026: Facts:
+30026: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+30026: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+30026: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+30026: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+30026: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+30026: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+30026: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+30026: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+30026: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+30026: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+30026: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+30026: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+30026: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+30026: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+30026: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+30026: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+30026: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+30026: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+30026: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+30026: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+30026: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+30026: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+30026: Goal:
+30026: Id : 1, {_}:
+ add (associator x y z) (associator x z y) =>= additive_identity
+ [] by prove_equation
+30026: Order:
+30026: kbo
+30026: Leaf order:
+30026: x 2 0 2 1,1,2
+30026: y 2 0 2 2,1,2
+30026: z 2 0 2 3,1,2
+30026: additive_identity 9 0 1 3
+30026: additive_inverse 22 1 0
+30026: commutator 1 2 0
+30026: add 25 2 1 0,2
+30026: multiply 40 2 0
+30026: associator 3 3 2 0,1,2
+NO CLASH, using fixed ground order
+30027: Facts:
+30027: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+30027: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+30027: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+30027: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+30027: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+30027: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+30027: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+30027: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+30027: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+30027: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+30027: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+30027: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+30027: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+30027: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+30027: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+30027: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+30027: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+30027: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+30027: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =>=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+30027: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =>=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+30027: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =>=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+30027: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =>=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+30027: Goal:
+30027: Id : 1, {_}:
+ add (associator x y z) (associator x z y) =>= additive_identity
+ [] by prove_equation
+30027: Order:
+30027: lpo
+30027: Leaf order:
+30027: x 2 0 2 1,1,2
+30027: y 2 0 2 2,1,2
+30027: z 2 0 2 3,1,2
+30027: additive_identity 9 0 1 3
+30027: additive_inverse 22 1 0
+30027: commutator 1 2 0
+30027: add 25 2 1 0,2
+30027: multiply 40 2 0
+30027: associator 3 3 2 0,1,2
+% SZS status Timeout for RNG025-5.p
+NO CLASH, using fixed ground order
+30048: Facts:
+30048: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+30048: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+30048: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+30048: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+30048: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+30048: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+30048: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+30048: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+30048: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+30048: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+30048: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+30048: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+30048: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+30048: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+30048: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+30048: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+30048: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+30048: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+30048: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+30048: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+30048: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+30048: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+30048: Goal:
+30048: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
+30048: Order:
+30048: nrkbo
+30048: Leaf order:
+30048: y 1 0 1 2,2
+30048: x 2 0 2 1,2
+30048: additive_identity 9 0 1 3
+30048: additive_inverse 22 1 0
+30048: commutator 1 2 0
+30048: add 24 2 0
+30048: multiply 40 2 0
+30048: associator 2 3 1 0,2
+NO CLASH, using fixed ground order
+30049: Facts:
+30049: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+30049: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+30049: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+30049: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+30049: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+30049: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+30049: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+30049: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+30049: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+30049: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+30049: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+30049: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+30049: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+30049: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+30049: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+30049: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+30049: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+30049: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+30049: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+30049: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+30049: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+30049: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+30049: Goal:
+30049: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
+30049: Order:
+30049: kbo
+30049: Leaf order:
+30049: y 1 0 1 2,2
+30049: x 2 0 2 1,2
+30049: additive_identity 9 0 1 3
+30049: additive_inverse 22 1 0
+30049: commutator 1 2 0
+30049: add 24 2 0
+30049: multiply 40 2 0
+30049: associator 2 3 1 0,2
+NO CLASH, using fixed ground order
+30050: Facts:
+30050: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+30050: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+30050: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+30050: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+30050: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+30050: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+30050: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+30050: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+30050: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+30050: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+30050: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+30050: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+30050: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+30050: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+30050: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+30050: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+30050: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+30050: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+30050: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =>=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+30050: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =>=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+30050: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =>=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+30050: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =>=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+30050: Goal:
+30050: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law
+30050: Order:
+30050: lpo
+30050: Leaf order:
+30050: y 1 0 1 2,2
+30050: x 2 0 2 1,2
+30050: additive_identity 9 0 1 3
+30050: additive_inverse 22 1 0
+30050: commutator 1 2 0
+30050: add 24 2 0
+30050: multiply 40 2 0
+30050: associator 2 3 1 0,2
+% SZS status Timeout for RNG025-7.p
+CLASH, statistics insufficient
+30088: Facts:
+30088: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+30088: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
+30088: Goal:
+30088: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+30088: Order:
+30088: nrkbo
+30088: Leaf order:
+30088: s 1 0 0
+30088: k 1 0 0
+30088: f 3 1 3 0,2,2
+30088: apply 11 2 3 0,2
+CLASH, statistics insufficient
+30089: Facts:
+30089: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+30089: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
+30089: Goal:
+30089: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+30089: Order:
+30089: kbo
+30089: Leaf order:
+30089: s 1 0 0
+30089: k 1 0 0
+30089: f 3 1 3 0,2,2
+30089: apply 11 2 3 0,2
+CLASH, statistics insufficient
+30090: Facts:
+30090: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+30090: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8
+30090: Goal:
+30090: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+30090: Order:
+30090: lpo
+30090: Leaf order:
+30090: s 1 0 0
+30090: k 1 0 0
+30090: f 3 1 3 0,2,2
+30090: apply 11 2 3 0,2
+% SZS status Timeout for COL006-1.p
+NO CLASH, using fixed ground order
+30176: Facts:
+30176: Id : 2, {_}:
+ apply (apply (apply s ?2) ?3) ?4
+ =?=
+ apply (apply ?2 ?4) (apply ?3 ?4)
+ [4, 3, 2] by s_definition ?2 ?3 ?4
+30176: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+30176: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply s
+ (apply k
+ (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
+ (apply (apply s (apply k (apply (apply s s) (apply s k))))
+ (apply (apply s (apply k s)) k))
+ [] by strong_fixed_point
+30176: Goal:
+30176: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+30176: Order:
+30176: nrkbo
+30176: Leaf order:
+30176: strong_fixed_point 3 0 2 1,2
+30176: fixed_pt 3 0 3 2,2
+30176: k 10 0 0
+30176: s 11 0 0
+30176: apply 29 2 3 0,2
+NO CLASH, using fixed ground order
+30177: Facts:
+30177: Id : 2, {_}:
+ apply (apply (apply s ?2) ?3) ?4
+ =?=
+ apply (apply ?2 ?4) (apply ?3 ?4)
+ [4, 3, 2] by s_definition ?2 ?3 ?4
+30177: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+30177: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply s
+ (apply k
+ (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
+ (apply (apply s (apply k (apply (apply s s) (apply s k))))
+ (apply (apply s (apply k s)) k))
+ [] by strong_fixed_point
+30177: Goal:
+30177: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+30177: Order:
+30177: kbo
+30177: Leaf order:
+30177: strong_fixed_point 3 0 2 1,2
+30177: fixed_pt 3 0 3 2,2
+30177: k 10 0 0
+30177: s 11 0 0
+30177: apply 29 2 3 0,2
+NO CLASH, using fixed ground order
+30178: Facts:
+30178: Id : 2, {_}:
+ apply (apply (apply s ?2) ?3) ?4
+ =?=
+ apply (apply ?2 ?4) (apply ?3 ?4)
+ [4, 3, 2] by s_definition ?2 ?3 ?4
+30178: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+30178: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply s
+ (apply k
+ (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))
+ (apply (apply s (apply k (apply (apply s s) (apply s k))))
+ (apply (apply s (apply k s)) k))
+ [] by strong_fixed_point
+30178: Goal:
+30178: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+30178: Order:
+30178: lpo
+30178: Leaf order:
+30178: strong_fixed_point 3 0 2 1,2
+30178: fixed_pt 3 0 3 2,2
+30178: k 10 0 0
+30178: s 11 0 0
+30178: apply 29 2 3 0,2
+% SZS status Timeout for COL006-5.p
+NO CLASH, using fixed ground order
+30201: Facts:
+30201: Id : 2, {_}:
+ apply (apply (apply s ?2) ?3) ?4
+ =?=
+ apply (apply ?2 ?4) (apply ?3 ?4)
+ [4, 3, 2] by s_definition ?2 ?3 ?4
+30201: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+30201: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply s
+ (apply k
+ (apply (apply (apply s s) (apply (apply s k) k))
+ (apply (apply s s) (apply s k)))))
+ (apply (apply s (apply k s)) k)
+ [] by strong_fixed_point
+30201: Goal:
+30201: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+30201: Order:
+30201: nrkbo
+30201: Leaf order:
+30201: strong_fixed_point 3 0 2 1,2
+30201: fixed_pt 3 0 3 2,2
+30201: k 7 0 0
+30201: s 10 0 0
+30201: apply 25 2 3 0,2
+NO CLASH, using fixed ground order
+30202: Facts:
+30202: Id : 2, {_}:
+ apply (apply (apply s ?2) ?3) ?4
+ =?=
+ apply (apply ?2 ?4) (apply ?3 ?4)
+ [4, 3, 2] by s_definition ?2 ?3 ?4
+30202: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+30202: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply s
+ (apply k
+ (apply (apply (apply s s) (apply (apply s k) k))
+ (apply (apply s s) (apply s k)))))
+ (apply (apply s (apply k s)) k)
+ [] by strong_fixed_point
+30202: Goal:
+30202: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+30202: Order:
+30202: kbo
+30202: Leaf order:
+30202: strong_fixed_point 3 0 2 1,2
+30202: fixed_pt 3 0 3 2,2
+30202: k 7 0 0
+30202: s 10 0 0
+30202: apply 25 2 3 0,2
+NO CLASH, using fixed ground order
+30203: Facts:
+30203: Id : 2, {_}:
+ apply (apply (apply s ?2) ?3) ?4
+ =?=
+ apply (apply ?2 ?4) (apply ?3 ?4)
+ [4, 3, 2] by s_definition ?2 ?3 ?4
+30203: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7
+30203: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply s
+ (apply k
+ (apply (apply (apply s s) (apply (apply s k) k))
+ (apply (apply s s) (apply s k)))))
+ (apply (apply s (apply k s)) k)
+ [] by strong_fixed_point
+30203: Goal:
+30203: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+30203: Order:
+30203: lpo
+30203: Leaf order:
+30203: strong_fixed_point 3 0 2 1,2
+30203: fixed_pt 3 0 3 2,2
+30203: k 7 0 0
+30203: s 10 0 0
+30203: apply 25 2 3 0,2
+% SZS status Timeout for COL006-7.p
+NO CLASH, using fixed ground order
+30224: Facts:
+30224: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+30224: Id : 3, {_}:
+ apply (apply (apply n ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?8) ?7) ?8
+ [8, 7, 6] by n_definition ?6 ?7 ?8
+NO CLASH, using fixed ground order
+30225: Facts:
+30225: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+30225: Id : 3, {_}:
+ apply (apply (apply n ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?8) ?7) ?8
+ [8, 7, 6] by n_definition ?6 ?7 ?8
+30225: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply n
+ (apply (apply b b)
+ (apply (apply n (apply (apply b b) n)) n))) n)) b)) b
+ [] by strong_fixed_point
+30225: Goal:
+30225: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+30225: Order:
+30225: kbo
+30225: Leaf order:
+30225: strong_fixed_point 3 0 2 1,2
+30225: fixed_pt 3 0 3 2,2
+30225: n 6 0 0
+30225: b 9 0 0
+30225: apply 26 2 3 0,2
+NO CLASH, using fixed ground order
+30226: Facts:
+30226: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+30226: Id : 3, {_}:
+ apply (apply (apply n ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?8) ?7) ?8
+ [8, 7, 6] by n_definition ?6 ?7 ?8
+30226: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply n
+ (apply (apply b b)
+ (apply (apply n (apply (apply b b) n)) n))) n)) b)) b
+ [] by strong_fixed_point
+30226: Goal:
+30226: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+30226: Order:
+30226: lpo
+30226: Leaf order:
+30226: strong_fixed_point 3 0 2 1,2
+30226: fixed_pt 3 0 3 2,2
+30226: n 6 0 0
+30226: b 9 0 0
+30226: apply 26 2 3 0,2
+30224: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply n
+ (apply (apply b b)
+ (apply (apply n (apply (apply b b) n)) n))) n)) b)) b
+ [] by strong_fixed_point
+30224: Goal:
+30224: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+30224: Order:
+30224: nrkbo
+30224: Leaf order:
+30224: strong_fixed_point 3 0 2 1,2
+30224: fixed_pt 3 0 3 2,2
+30224: n 6 0 0
+30224: b 9 0 0
+30224: apply 26 2 3 0,2
+% SZS status Timeout for COL044-6.p
+NO CLASH, using fixed ground order
+30249: Facts:
+30249: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+30249: Id : 3, {_}:
+ apply (apply (apply n ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?8) ?7) ?8
+ [8, 7, 6] by n_definition ?6 ?7 ?8
+30249: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply n
+ (apply (apply b b)
+ (apply (apply n (apply n (apply b b))) n))) n)) b)) b
+ [] by strong_fixed_point
+30249: Goal:
+30249: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+30249: Order:
+30249: nrkbo
+30249: Leaf order:
+30249: strong_fixed_point 3 0 2 1,2
+30249: fixed_pt 3 0 3 2,2
+30249: n 6 0 0
+30249: b 9 0 0
+30249: apply 26 2 3 0,2
+NO CLASH, using fixed ground order
+30250: Facts:
+30250: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+30250: Id : 3, {_}:
+ apply (apply (apply n ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?8) ?7) ?8
+ [8, 7, 6] by n_definition ?6 ?7 ?8
+30250: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply n
+ (apply (apply b b)
+ (apply (apply n (apply n (apply b b))) n))) n)) b)) b
+ [] by strong_fixed_point
+30250: Goal:
+30250: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+30250: Order:
+30250: kbo
+30250: Leaf order:
+30250: strong_fixed_point 3 0 2 1,2
+30250: fixed_pt 3 0 3 2,2
+30250: n 6 0 0
+30250: b 9 0 0
+30250: apply 26 2 3 0,2
+NO CLASH, using fixed ground order
+30251: Facts:
+30251: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+30251: Id : 3, {_}:
+ apply (apply (apply n ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?8) ?7) ?8
+ [8, 7, 6] by n_definition ?6 ?7 ?8
+30251: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply n
+ (apply (apply b b)
+ (apply (apply n (apply n (apply b b))) n))) n)) b)) b
+ [] by strong_fixed_point
+30251: Goal:
+30251: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+30251: Order:
+30251: lpo
+30251: Leaf order:
+30251: strong_fixed_point 3 0 2 1,2
+30251: fixed_pt 3 0 3 2,2
+30251: n 6 0 0
+30251: b 9 0 0
+30251: apply 26 2 3 0,2
+% SZS status Timeout for COL044-7.p
+CLASH, statistics insufficient
+30275: Facts:
+30275: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+30275: Id : 3, {_}:
+ apply (apply t ?7) ?8 =>= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+30275: Goal:
+30275: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (apply (h ?1) (f ?1)) (g ?1)
+ [1] by prove_v_combinator ?1
+30275: Order:
+30275: nrkbo
+30275: Leaf order:
+30275: b 1 0 0
+30275: t 1 0 0
+30275: f 2 1 2 0,2,1,1,2
+30275: g 2 1 2 0,2,1,2
+30275: h 2 1 2 0,2,2
+30275: apply 13 2 5 0,2
+CLASH, statistics insufficient
+30276: Facts:
+30276: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+30276: Id : 3, {_}:
+ apply (apply t ?7) ?8 =>= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+30276: Goal:
+30276: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (apply (h ?1) (f ?1)) (g ?1)
+ [1] by prove_v_combinator ?1
+30276: Order:
+30276: kbo
+30276: Leaf order:
+30276: b 1 0 0
+30276: t 1 0 0
+30276: f 2 1 2 0,2,1,1,2
+30276: g 2 1 2 0,2,1,2
+30276: h 2 1 2 0,2,2
+30276: apply 13 2 5 0,2
+CLASH, statistics insufficient
+30277: Facts:
+30277: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+30277: Id : 3, {_}:
+ apply (apply t ?7) ?8 =?= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+30277: Goal:
+30277: Id : 1, {_}:
+ apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (apply (h ?1) (f ?1)) (g ?1)
+ [1] by prove_v_combinator ?1
+30277: Order:
+30277: lpo
+30277: Leaf order:
+30277: b 1 0 0
+30277: t 1 0 0
+30277: f 2 1 2 0,2,1,1,2
+30277: g 2 1 2 0,2,1,2
+30277: h 2 1 2 0,2,2
+30277: apply 13 2 5 0,2
+Goal subsumed
+Statistics :
+Max weight : 124
+Found proof, 34.381663s
+% SZS status Unsatisfiable for COL064-1.p
+% SZS output start CNFRefutation for COL064-1.p
+Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8
+Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5
+Id : 10997, {_}: apply (apply (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) === apply (apply (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) [] by Super 10996 with 3 at 2
+Id : 10996, {_}: apply (apply ?37685 (g (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t))))) (apply (h (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t))))) =>= apply (apply (h (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t)))) [37685] by Super 3193 with 2 at 2
+Id : 3193, {_}: apply (apply (apply ?10612 (apply ?10613 (g (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))))) (h (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))) =>= apply (apply (h (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))) [10613, 10612] by Super 3188 with 2 at 1,1,2
+Id : 3188, {_}: apply (apply (apply ?10602 (g (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t))))) (h (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t)))) =>= apply (apply (h (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t)))) [10602] by Super 3164 with 3 at 2
+Id : 3164, {_}: apply (apply ?10539 (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (apply (apply ?10540 (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) =>= apply (apply (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) [10540, 10539] by Super 442 with 2 at 2
+Id : 442, {_}: apply (apply (apply ?1394 (apply ?1395 (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (apply ?1396 (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) =>= apply (apply (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395))))) (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) [1396, 1395, 1394] by Super 277 with 2 at 1,1,2
+Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (apply (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) [901, 900] by Super 29 with 2 at 1,2
+Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (apply (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) [87, 86, 85] by Super 13 with 3 at 1,1,2
+Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (apply (h (apply (apply b ?33) (apply (apply b ?34) ?35))) (f (apply (apply b ?33) (apply (apply b ?34) ?35)))) (g (apply (apply b ?33) (apply (apply b ?34) ?35))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2
+Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (apply (h (apply (apply b ?18) ?19)) (f (apply (apply b ?18) ?19))) (g (apply (apply b ?18) ?19)) [19, 18] by Super 1 with 2 at 1,1,2
+Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (h ?1) (f ?1)) (g ?1) [1] by prove_v_combinator ?1
+% SZS output end CNFRefutation for COL064-1.p
+30275: solved COL064-1.p in 34.366147 using nrkbo
+30275: status Unsatisfiable for COL064-1.p
+CLASH, statistics insufficient
+30288: Facts:
+30288: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+30288: Id : 3, {_}:
+ apply (apply t ?7) ?8 =>= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+30288: Goal:
+30288: Id : 1, {_}:
+ apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1)
+ =>=
+ apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1))
+ [1] by prove_g_combinator ?1
+30288: Order:
+30288: nrkbo
+30288: Leaf order:
+30288: b 1 0 0
+30288: t 1 0 0
+30288: f 2 1 2 0,2,1,1,1,2
+30288: g 2 1 2 0,2,1,1,2
+30288: h 2 1 2 0,2,1,2
+30288: i 2 1 2 0,2,2
+30288: apply 15 2 7 0,2
+CLASH, statistics insufficient
+30289: Facts:
+30289: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+30289: Id : 3, {_}:
+ apply (apply t ?7) ?8 =>= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+30289: Goal:
+30289: Id : 1, {_}:
+ apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1)
+ =>=
+ apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1))
+ [1] by prove_g_combinator ?1
+30289: Order:
+30289: kbo
+30289: Leaf order:
+30289: b 1 0 0
+30289: t 1 0 0
+30289: f 2 1 2 0,2,1,1,1,2
+30289: g 2 1 2 0,2,1,1,2
+30289: h 2 1 2 0,2,1,2
+30289: i 2 1 2 0,2,2
+30289: apply 15 2 7 0,2
+CLASH, statistics insufficient
+30290: Facts:
+30290: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+30290: Id : 3, {_}:
+ apply (apply t ?7) ?8 =?= apply ?8 ?7
+ [8, 7] by t_definition ?7 ?8
+30290: Goal:
+30290: Id : 1, {_}:
+ apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1)
+ =>=
+ apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1))
+ [1] by prove_g_combinator ?1
+30290: Order:
+30290: lpo
+30290: Leaf order:
+30290: b 1 0 0
+30290: t 1 0 0
+30290: f 2 1 2 0,2,1,1,1,2
+30290: g 2 1 2 0,2,1,1,2
+30290: h 2 1 2 0,2,1,2
+30290: i 2 1 2 0,2,2
+30290: apply 15 2 7 0,2
+% SZS status Timeout for COL065-1.p
+CLASH, statistics insufficient
+30319: Facts:
+30319: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+30319: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+30319: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+30319: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+30319: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+30319: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+30319: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+30319: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+30319: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+30319: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+30319: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+30319: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+30319: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+30319: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+30319: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+30319: Id : 17, {_}:
+ greatest_lower_bound a c =>= greatest_lower_bound b c
+ [] by p12_1
+30319: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_2
+30319: Goal:
+30319: Id : 1, {_}: a =>= b [] by prove_p12
+30319: Order:
+30319: nrkbo
+30319: Leaf order:
+30319: identity 2 0 0
+30319: a 3 0 1 2
+30319: b 3 0 1 3
+30319: c 4 0 0
+30319: inverse 1 1 0
+30319: greatest_lower_bound 15 2 0
+30319: least_upper_bound 15 2 0
+30319: multiply 18 2 0
+CLASH, statistics insufficient
+30320: Facts:
+30320: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+30320: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+30320: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+30320: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+30320: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+30320: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+30320: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+30320: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+30320: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+30320: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+30320: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+30320: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+30320: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+30320: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+30320: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+30320: Id : 17, {_}:
+ greatest_lower_bound a c =>= greatest_lower_bound b c
+ [] by p12_1
+30320: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_2
+30320: Goal:
+30320: Id : 1, {_}: a =>= b [] by prove_p12
+30320: Order:
+30320: kbo
+30320: Leaf order:
+30320: identity 2 0 0
+30320: a 3 0 1 2
+30320: b 3 0 1 3
+30320: c 4 0 0
+30320: inverse 1 1 0
+30320: greatest_lower_bound 15 2 0
+30320: least_upper_bound 15 2 0
+30320: multiply 18 2 0
+CLASH, statistics insufficient
+30321: Facts:
+30321: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+30321: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+30321: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+30321: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+30321: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+30321: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+30321: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+30321: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+30321: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+30321: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+30321: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+30321: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+30321: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+30321: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+30321: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+30321: Id : 17, {_}:
+ greatest_lower_bound a c =>= greatest_lower_bound b c
+ [] by p12_1
+30321: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_2
+30321: Goal:
+30321: Id : 1, {_}: a =>= b [] by prove_p12
+30321: Order:
+30321: lpo
+30321: Leaf order:
+30321: identity 2 0 0
+30321: a 3 0 1 2
+30321: b 3 0 1 3
+30321: c 4 0 0
+30321: inverse 1 1 0
+30321: greatest_lower_bound 15 2 0
+30321: least_upper_bound 15 2 0
+30321: multiply 18 2 0
+% SZS status Timeout for GRP181-1.p
+CLASH, statistics insufficient
+30347: Facts:
+30347: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+30347: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+30347: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+30347: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+30347: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+30347: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+30347: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+30347: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+30347: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+30347: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+30347: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+30347: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+30347: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+30347: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+30347: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+30347: Id : 17, {_}: inverse identity =>= identity [] by p12_1
+30347: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12_2 ?51
+30347: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p12_3 ?53 ?54
+30347: Id : 20, {_}:
+ greatest_lower_bound a c =>= greatest_lower_bound b c
+ [] by p12_4
+30347: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_5
+30347: Goal:
+30347: Id : 1, {_}: a =>= b [] by prove_p12
+30347: Order:
+30347: nrkbo
+30347: Leaf order:
+30347: a 3 0 1 2
+30347: b 3 0 1 3
+30347: identity 4 0 0
+30347: c 4 0 0
+30347: inverse 7 1 0
+30347: greatest_lower_bound 15 2 0
+30347: least_upper_bound 15 2 0
+30347: multiply 20 2 0
+CLASH, statistics insufficient
+30348: Facts:
+30348: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+30348: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+30348: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+30348: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+30348: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+30348: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+30348: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+30348: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+30348: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+30348: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+30348: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+30348: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+30348: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+30348: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+30348: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+30348: Id : 17, {_}: inverse identity =>= identity [] by p12_1
+30348: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12_2 ?51
+30348: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p12_3 ?53 ?54
+30348: Id : 20, {_}:
+ greatest_lower_bound a c =>= greatest_lower_bound b c
+ [] by p12_4
+30348: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_5
+30348: Goal:
+30348: Id : 1, {_}: a =>= b [] by prove_p12
+30348: Order:
+30348: kbo
+30348: Leaf order:
+30348: a 3 0 1 2
+30348: b 3 0 1 3
+30348: identity 4 0 0
+30348: c 4 0 0
+30348: inverse 7 1 0
+30348: greatest_lower_bound 15 2 0
+30348: least_upper_bound 15 2 0
+30348: multiply 20 2 0
+CLASH, statistics insufficient
+30349: Facts:
+30349: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+30349: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+30349: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+30349: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+30349: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+30349: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+30349: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+30349: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+30349: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+30349: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+30349: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+30349: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+30349: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+30349: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+30349: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+30349: Id : 17, {_}: inverse identity =>= identity [] by p12_1
+30349: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12_2 ?51
+30349: Id : 19, {_}:
+ inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53)
+ [54, 53] by p12_3 ?53 ?54
+30349: Id : 20, {_}:
+ greatest_lower_bound a c =>= greatest_lower_bound b c
+ [] by p12_4
+30349: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_5
+30349: Goal:
+30349: Id : 1, {_}: a =>= b [] by prove_p12
+30349: Order:
+30349: lpo
+30349: Leaf order:
+30349: a 3 0 1 2
+30349: b 3 0 1 3
+30349: identity 4 0 0
+30349: c 4 0 0
+30349: inverse 7 1 0
+30349: greatest_lower_bound 15 2 0
+30349: least_upper_bound 15 2 0
+30349: multiply 20 2 0
+% SZS status Timeout for GRP181-2.p
+NO CLASH, using fixed ground order
+30391: Facts:
+30391: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+30391: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+30391: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+30391: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+30391: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+30391: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+30391: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+30391: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+30391: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+30391: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+30391: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+30391: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+30391: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+30391: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+30391: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+30391: Id : 17, {_}:
+ greatest_lower_bound (least_upper_bound a (inverse a))
+ (least_upper_bound b (inverse b))
+ =>=
+ identity
+ [] by p33_1
+30391: Goal:
+30391: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_p33
+30391: Order:
+30391: nrkbo
+30391: Leaf order:
+30391: identity 3 0 0
+30391: a 4 0 2 1,2
+30391: b 4 0 2 2,2
+30391: inverse 3 1 0
+30391: greatest_lower_bound 14 2 0
+30391: least_upper_bound 15 2 0
+30391: multiply 20 2 2 0,2
+NO CLASH, using fixed ground order
+30392: Facts:
+30392: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+30392: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+30392: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+30392: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+30392: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+30392: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+30392: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+30392: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+30392: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+30392: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+NO CLASH, using fixed ground order
+30393: Facts:
+30393: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+30393: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+30393: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+30393: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+30393: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+30393: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+30393: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+30393: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+30393: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+30393: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+30393: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+30393: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+30393: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+30393: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+30393: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+30393: Id : 17, {_}:
+ greatest_lower_bound (least_upper_bound a (inverse a))
+ (least_upper_bound b (inverse b))
+ =>=
+ identity
+ [] by p33_1
+30393: Goal:
+30393: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_p33
+30393: Order:
+30393: lpo
+30393: Leaf order:
+30393: identity 3 0 0
+30393: a 4 0 2 1,2
+30393: b 4 0 2 2,2
+30393: inverse 3 1 0
+30393: greatest_lower_bound 14 2 0
+30393: least_upper_bound 15 2 0
+30393: multiply 20 2 2 0,2
+30392: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+30392: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+30392: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+30392: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+30392: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+30392: Id : 17, {_}:
+ greatest_lower_bound (least_upper_bound a (inverse a))
+ (least_upper_bound b (inverse b))
+ =>=
+ identity
+ [] by p33_1
+30392: Goal:
+30392: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_p33
+30392: Order:
+30392: kbo
+30392: Leaf order:
+30392: identity 3 0 0
+30392: a 4 0 2 1,2
+30392: b 4 0 2 2,2
+30392: inverse 3 1 0
+30392: greatest_lower_bound 14 2 0
+30392: least_upper_bound 15 2 0
+30392: multiply 20 2 2 0,2
+% SZS status Timeout for GRP187-1.p
+NO CLASH, using fixed ground order
+30417: Facts:
+30417: Id : 2, {_}:
+ multiply
+ (inverse
+ (multiply
+ (inverse
+ (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
+ (multiply (inverse (multiply ?4 ?5))
+ (multiply ?4
+ (inverse
+ (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
+ ?7
+ =>=
+ ?6
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+30417: Goal:
+30417: Id : 1, {_}:
+ multiply (inverse a1) a1 =<= multiply (inverse b1) b1
+ [] by prove_these_axioms_1
+30417: Order:
+30417: nrkbo
+30417: Leaf order:
+30417: a1 2 0 2 1,1,2
+30417: b1 2 0 2 1,1,3
+30417: inverse 9 1 2 0,1,2
+30417: multiply 12 2 2 0,2
+NO CLASH, using fixed ground order
+30418: Facts:
+30418: Id : 2, {_}:
+ multiply
+ (inverse
+ (multiply
+ (inverse
+ (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
+ (multiply (inverse (multiply ?4 ?5))
+ (multiply ?4
+ (inverse
+ (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
+ ?7
+ =>=
+ ?6
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+30418: Goal:
+30418: Id : 1, {_}:
+ multiply (inverse a1) a1 =<= multiply (inverse b1) b1
+ [] by prove_these_axioms_1
+30418: Order:
+30418: kbo
+30418: Leaf order:
+30418: a1 2 0 2 1,1,2
+30418: b1 2 0 2 1,1,3
+30418: inverse 9 1 2 0,1,2
+30418: multiply 12 2 2 0,2
+NO CLASH, using fixed ground order
+30419: Facts:
+30419: Id : 2, {_}:
+ multiply
+ (inverse
+ (multiply
+ (inverse
+ (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
+ (multiply (inverse (multiply ?4 ?5))
+ (multiply ?4
+ (inverse
+ (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
+ ?7
+ =>=
+ ?6
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+30419: Goal:
+30419: Id : 1, {_}:
+ multiply (inverse a1) a1 =<= multiply (inverse b1) b1
+ [] by prove_these_axioms_1
+30419: Order:
+30419: lpo
+30419: Leaf order:
+30419: a1 2 0 2 1,1,2
+30419: b1 2 0 2 1,1,3
+30419: inverse 9 1 2 0,1,2
+30419: multiply 12 2 2 0,2
+% SZS status Timeout for GRP505-1.p
+NO CLASH, using fixed ground order
+30445: Facts:
+30445: Id : 2, {_}:
+ multiply
+ (inverse
+ (multiply
+ (inverse
+ (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
+ (multiply (inverse (multiply ?4 ?5))
+ (multiply ?4
+ (inverse
+ (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
+ ?7
+ =>=
+ ?6
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+30445: Goal:
+30445: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+30445: Order:
+30445: nrkbo
+30445: Leaf order:
+30445: a3 2 0 2 1,1,2
+30445: b3 2 0 2 2,1,2
+30445: c3 2 0 2 2,2
+30445: inverse 7 1 0
+30445: multiply 14 2 4 0,2
+NO CLASH, using fixed ground order
+30446: Facts:
+30446: Id : 2, {_}:
+ multiply
+ (inverse
+ (multiply
+ (inverse
+ (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
+ (multiply (inverse (multiply ?4 ?5))
+ (multiply ?4
+ (inverse
+ (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
+ ?7
+ =>=
+ ?6
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+30446: Goal:
+30446: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+30446: Order:
+30446: kbo
+30446: Leaf order:
+30446: a3 2 0 2 1,1,2
+30446: b3 2 0 2 2,1,2
+30446: c3 2 0 2 2,2
+30446: inverse 7 1 0
+30446: multiply 14 2 4 0,2
+NO CLASH, using fixed ground order
+30447: Facts:
+30447: Id : 2, {_}:
+ multiply
+ (inverse
+ (multiply
+ (inverse
+ (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
+ (multiply (inverse (multiply ?4 ?5))
+ (multiply ?4
+ (inverse
+ (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
+ ?7
+ =>=
+ ?6
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+30447: Goal:
+30447: Id : 1, {_}:
+ multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3)
+ [] by prove_these_axioms_3
+30447: Order:
+30447: lpo
+30447: Leaf order:
+30447: a3 2 0 2 1,1,2
+30447: b3 2 0 2 2,1,2
+30447: c3 2 0 2 2,2
+30447: inverse 7 1 0
+30447: multiply 14 2 4 0,2
+% SZS status Timeout for GRP507-1.p
+NO CLASH, using fixed ground order
+30481: Facts:
+30481: Id : 2, {_}:
+ multiply
+ (inverse
+ (multiply
+ (inverse
+ (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
+ (multiply (inverse (multiply ?4 ?5))
+ (multiply ?4
+ (inverse
+ (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
+ ?7
+ =>=
+ ?6
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+30481: Goal:
+30481: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_these_axioms_4
+30481: Order:
+30481: nrkbo
+30481: Leaf order:
+30481: a 2 0 2 1,2
+30481: b 2 0 2 2,2
+30481: inverse 7 1 0
+30481: multiply 12 2 2 0,2
+NO CLASH, using fixed ground order
+30482: Facts:
+30482: Id : 2, {_}:
+ multiply
+ (inverse
+ (multiply
+ (inverse
+ (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
+ (multiply (inverse (multiply ?4 ?5))
+ (multiply ?4
+ (inverse
+ (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
+ ?7
+ =>=
+ ?6
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+30482: Goal:
+30482: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_these_axioms_4
+30482: Order:
+30482: kbo
+30482: Leaf order:
+30482: a 2 0 2 1,2
+30482: b 2 0 2 2,2
+30482: inverse 7 1 0
+30482: multiply 12 2 2 0,2
+NO CLASH, using fixed ground order
+30483: Facts:
+30483: Id : 2, {_}:
+ multiply
+ (inverse
+ (multiply
+ (inverse
+ (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
+ (multiply (inverse (multiply ?4 ?5))
+ (multiply ?4
+ (inverse
+ (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
+ ?7
+ =>=
+ ?6
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+30483: Goal:
+30483: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_these_axioms_4
+30483: Order:
+30483: lpo
+30483: Leaf order:
+30483: a 2 0 2 1,2
+30483: b 2 0 2 2,2
+30483: inverse 7 1 0
+30483: multiply 12 2 2 0,2
+% SZS status Timeout for GRP508-1.p
+NO CLASH, using fixed ground order
+31468: Facts:
+31468: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+31468: Goal:
+31468: Id : 1, {_}: meet a a =>= a [] by prove_normal_axioms_1
+31468: Order:
+31468: nrkbo
+31468: Leaf order:
+31468: a 3 0 3 1,2
+31468: meet 19 2 1 0,2
+31468: join 20 2 0
+NO CLASH, using fixed ground order
+31469: Facts:
+31469: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+31469: Goal:
+31469: Id : 1, {_}: meet a a =>= a [] by prove_normal_axioms_1
+31469: Order:
+31469: kbo
+31469: Leaf order:
+31469: a 3 0 3 1,2
+31469: meet 19 2 1 0,2
+31469: join 20 2 0
+NO CLASH, using fixed ground order
+31470: Facts:
+31470: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+31470: Goal:
+31470: Id : 1, {_}: meet a a =>= a [] by prove_normal_axioms_1
+31470: Order:
+31470: lpo
+31470: Leaf order:
+31470: a 3 0 3 1,2
+31470: meet 19 2 1 0,2
+31470: join 20 2 0
+% SZS status Timeout for LAT080-1.p
+NO CLASH, using fixed ground order
+31492: Facts:
+31492: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+31492: Goal:
+31492: Id : 1, {_}: join a a =>= a [] by prove_normal_axioms_4
+31492: Order:
+31492: nrkbo
+31492: Leaf order:
+31492: a 3 0 3 1,2
+31492: meet 18 2 0
+31492: join 21 2 1 0,2
+NO CLASH, using fixed ground order
+31493: Facts:
+31493: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+31493: Goal:
+31493: Id : 1, {_}: join a a =>= a [] by prove_normal_axioms_4
+31493: Order:
+31493: kbo
+31493: Leaf order:
+31493: a 3 0 3 1,2
+31493: meet 18 2 0
+31493: join 21 2 1 0,2
+NO CLASH, using fixed ground order
+31494: Facts:
+31494: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+31494: Goal:
+31494: Id : 1, {_}: join a a =>= a [] by prove_normal_axioms_4
+31494: Order:
+31494: lpo
+31494: Leaf order:
+31494: a 3 0 3 1,2
+31494: meet 18 2 0
+31494: join 21 2 1 0,2
+% SZS status Timeout for LAT083-1.p
+NO CLASH, using fixed ground order
+31519: Facts:
+31519: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+31519: Goal:
+31519: Id : 1, {_}: meet a a =>= a [] by prove_wal_axioms_1
+31519: Order:
+31519: nrkbo
+31519: Leaf order:
+31519: a 3 0 3 1,2
+31519: join 18 2 0
+31519: meet 19 2 1 0,2
+NO CLASH, using fixed ground order
+31521: Facts:
+31521: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+31521: Goal:
+31521: Id : 1, {_}: meet a a =>= a [] by prove_wal_axioms_1
+31521: Order:
+31521: lpo
+31521: Leaf order:
+31521: a 3 0 3 1,2
+31521: join 18 2 0
+31521: meet 19 2 1 0,2
+NO CLASH, using fixed ground order
+31520: Facts:
+31520: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+31520: Goal:
+31520: Id : 1, {_}: meet a a =>= a [] by prove_wal_axioms_1
+31520: Order:
+31520: kbo
+31520: Leaf order:
+31520: a 3 0 3 1,2
+31520: join 18 2 0
+31520: meet 19 2 1 0,2
+% SZS status Timeout for LAT092-1.p
+NO CLASH, using fixed ground order
+31546: Facts:
+31546: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+31546: Goal:
+31546: Id : 1, {_}: meet b a =<= meet a b [] by prove_wal_axioms_2
+31546: Order:
+31546: nrkbo
+31546: Leaf order:
+31546: b 2 0 2 1,2
+31546: a 2 0 2 2,2
+31546: join 18 2 0
+31546: meet 20 2 2 0,2
+NO CLASH, using fixed ground order
+31547: Facts:
+31547: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+31547: Goal:
+31547: Id : 1, {_}: meet b a =<= meet a b [] by prove_wal_axioms_2
+31547: Order:
+31547: kbo
+31547: Leaf order:
+31547: b 2 0 2 1,2
+31547: a 2 0 2 2,2
+31547: join 18 2 0
+31547: meet 20 2 2 0,2
+NO CLASH, using fixed ground order
+31548: Facts:
+31548: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+31548: Goal:
+31548: Id : 1, {_}: meet b a =<= meet a b [] by prove_wal_axioms_2
+31548: Order:
+31548: lpo
+31548: Leaf order:
+31548: b 2 0 2 1,2
+31548: a 2 0 2 2,2
+31548: join 18 2 0
+31548: meet 20 2 2 0,2
+% SZS status Timeout for LAT093-1.p
+NO CLASH, using fixed ground order
+31571: Facts:
+31571: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+31571: Goal:
+31571: Id : 1, {_}: join a a =>= a [] by prove_wal_axioms_3
+31571: Order:
+31571: nrkbo
+31571: Leaf order:
+31571: a 3 0 3 1,2
+31571: meet 18 2 0
+31571: join 19 2 1 0,2
+NO CLASH, using fixed ground order
+31572: Facts:
+31572: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+31572: Goal:
+31572: Id : 1, {_}: join a a =>= a [] by prove_wal_axioms_3
+31572: Order:
+31572: kbo
+31572: Leaf order:
+31572: a 3 0 3 1,2
+31572: meet 18 2 0
+31572: join 19 2 1 0,2
+NO CLASH, using fixed ground order
+31573: Facts:
+31573: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+31573: Goal:
+31573: Id : 1, {_}: join a a =>= a [] by prove_wal_axioms_3
+31573: Order:
+31573: lpo
+31573: Leaf order:
+31573: a 3 0 3 1,2
+31573: meet 18 2 0
+31573: join 19 2 1 0,2
+% SZS status Timeout for LAT094-1.p
+NO CLASH, using fixed ground order
+31595: Facts:
+31595: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+31595: Goal:
+31595: Id : 1, {_}: join b a =<= join a b [] by prove_wal_axioms_4
+31595: Order:
+31595: nrkbo
+31595: Leaf order:
+31595: b 2 0 2 1,2
+31595: a 2 0 2 2,2
+31595: meet 18 2 0
+31595: join 20 2 2 0,2
+NO CLASH, using fixed ground order
+31596: Facts:
+31596: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+31596: Goal:
+31596: Id : 1, {_}: join b a =<= join a b [] by prove_wal_axioms_4
+31596: Order:
+31596: kbo
+31596: Leaf order:
+31596: b 2 0 2 1,2
+31596: a 2 0 2 2,2
+31596: meet 18 2 0
+31596: join 20 2 2 0,2
+NO CLASH, using fixed ground order
+31597: Facts:
+31597: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+31597: Goal:
+31597: Id : 1, {_}: join b a =<= join a b [] by prove_wal_axioms_4
+31597: Order:
+31597: lpo
+31597: Leaf order:
+31597: b 2 0 2 1,2
+31597: a 2 0 2 2,2
+31597: meet 18 2 0
+31597: join 20 2 2 0,2
+% SZS status Timeout for LAT095-1.p
+NO CLASH, using fixed ground order
+31621: Facts:
+31621: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+31621: Goal:
+31621: Id : 1, {_}:
+ meet (meet (join a b) (join c b)) b =>= b
+ [] by prove_wal_axioms_5
+31621: Order:
+31621: nrkbo
+31621: Leaf order:
+31621: a 1 0 1 1,1,1,2
+31621: c 1 0 1 1,2,1,2
+31621: b 4 0 4 2,1,1,2
+31621: join 20 2 2 0,1,1,2
+31621: meet 20 2 2 0,2
+NO CLASH, using fixed ground order
+31622: Facts:
+31622: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+31622: Goal:
+31622: Id : 1, {_}:
+ meet (meet (join a b) (join c b)) b =>= b
+ [] by prove_wal_axioms_5
+31622: Order:
+31622: kbo
+31622: Leaf order:
+31622: a 1 0 1 1,1,1,2
+31622: c 1 0 1 1,2,1,2
+31622: b 4 0 4 2,1,1,2
+31622: join 20 2 2 0,1,1,2
+31622: meet 20 2 2 0,2
+NO CLASH, using fixed ground order
+31623: Facts:
+31623: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+31623: Goal:
+31623: Id : 1, {_}:
+ meet (meet (join a b) (join c b)) b =>= b
+ [] by prove_wal_axioms_5
+31623: Order:
+31623: lpo
+31623: Leaf order:
+31623: a 1 0 1 1,1,1,2
+31623: c 1 0 1 1,2,1,2
+31623: b 4 0 4 2,1,1,2
+31623: join 20 2 2 0,1,1,2
+31623: meet 20 2 2 0,2
+% SZS status Timeout for LAT096-1.p
+NO CLASH, using fixed ground order
+31646: Facts:
+31646: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+31646: Goal:
+31646: Id : 1, {_}:
+ join (join (meet a b) (meet c b)) b =>= b
+ [] by prove_wal_axioms_6
+31646: Order:
+31646: nrkbo
+31646: Leaf order:
+31646: a 1 0 1 1,1,1,2
+31646: c 1 0 1 1,2,1,2
+31646: b 4 0 4 2,1,1,2
+31646: meet 20 2 2 0,1,1,2
+31646: join 20 2 2 0,2
+NO CLASH, using fixed ground order
+31647: Facts:
+31647: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+31647: Goal:
+31647: Id : 1, {_}:
+ join (join (meet a b) (meet c b)) b =>= b
+ [] by prove_wal_axioms_6
+31647: Order:
+31647: kbo
+31647: Leaf order:
+31647: a 1 0 1 1,1,1,2
+31647: c 1 0 1 1,2,1,2
+31647: b 4 0 4 2,1,1,2
+31647: meet 20 2 2 0,1,1,2
+31647: join 20 2 2 0,2
+NO CLASH, using fixed ground order
+31648: Facts:
+31648: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))
+ (meet
+ (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))
+ (meet ?7
+ (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3))))
+ (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+31648: Goal:
+31648: Id : 1, {_}:
+ join (join (meet a b) (meet c b)) b =>= b
+ [] by prove_wal_axioms_6
+31648: Order:
+31648: lpo
+31648: Leaf order:
+31648: a 1 0 1 1,1,1,2
+31648: c 1 0 1 1,2,1,2
+31648: b 4 0 4 2,1,1,2
+31648: meet 20 2 2 0,1,1,2
+31648: join 20 2 2 0,2
+% SZS status Timeout for LAT097-1.p
+NO CLASH, using fixed ground order
+31673: Facts:
+31673: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+31673: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+31673: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+31673: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+31673: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+31673: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+31673: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+31673: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+31673: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 ?29))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
+31673: Goal:
+31673: Id : 1, {_}:
+ meet a (join b (meet a (meet c d)))
+ =<=
+ meet a (join b (meet c (meet d (join a (meet b d)))))
+ [] by prove_H28
+31673: Order:
+31673: nrkbo
+31673: Leaf order:
+31673: c 2 0 2 1,2,2,2,2
+31673: b 3 0 3 1,2,2
+31673: d 3 0 3 2,2,2,2,2
+31673: a 4 0 4 1,2
+31673: join 16 2 3 0,2,2
+31673: meet 21 2 7 0,2
+NO CLASH, using fixed ground order
+31675: Facts:
+31675: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+31675: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+31675: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+31675: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+31675: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+31675: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+31675: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+31675: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+31675: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 ?29))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
+31675: Goal:
+31675: Id : 1, {_}:
+ meet a (join b (meet a (meet c d)))
+ =>=
+ meet a (join b (meet c (meet d (join a (meet b d)))))
+ [] by prove_H28
+31675: Order:
+31675: lpo
+31675: Leaf order:
+31675: c 2 0 2 1,2,2,2,2
+31675: b 3 0 3 1,2,2
+31675: d 3 0 3 2,2,2,2,2
+31675: a 4 0 4 1,2
+31675: join 16 2 3 0,2,2
+31675: meet 21 2 7 0,2
+NO CLASH, using fixed ground order
+31674: Facts:
+31674: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+31674: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+31674: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+31674: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+31674: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+31674: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+31674: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+31674: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+31674: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 ?29))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
+31674: Goal:
+31674: Id : 1, {_}:
+ meet a (join b (meet a (meet c d)))
+ =<=
+ meet a (join b (meet c (meet d (join a (meet b d)))))
+ [] by prove_H28
+31674: Order:
+31674: kbo
+31674: Leaf order:
+31674: c 2 0 2 1,2,2,2,2
+31674: b 3 0 3 1,2,2
+31674: d 3 0 3 2,2,2,2,2
+31674: a 4 0 4 1,2
+31674: join 16 2 3 0,2,2
+31674: meet 21 2 7 0,2
+% SZS status Timeout for LAT146-1.p
+NO CLASH, using fixed ground order
+31717: Facts:
+31717: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+31717: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+31717: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+31717: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+31717: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+31717: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+31717: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+31717: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+31717: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 ?29))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
+31717: Goal:
+31717: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
+ [] by prove_H7
+31717: Order:
+31717: nrkbo
+31717: Leaf order:
+31717: c 2 0 2 2,2,2,2
+31717: b 4 0 4 1,2,2
+31717: a 6 0 6 1,2
+31717: join 17 2 4 0,2,2
+31717: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+31718: Facts:
+31718: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+31718: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+31718: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+31718: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+31718: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+31718: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+31718: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+31718: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+31718: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 ?29))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
+31718: Goal:
+31718: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
+ [] by prove_H7
+31718: Order:
+31718: kbo
+31718: Leaf order:
+31718: c 2 0 2 2,2,2,2
+31718: b 4 0 4 1,2,2
+31718: a 6 0 6 1,2
+31718: join 17 2 4 0,2,2
+31718: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+31719: Facts:
+31719: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+31719: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+31719: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+31719: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+31719: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+31719: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+31719: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+31719: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+31719: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 ?29))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
+31719: Goal:
+31719: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
+ [] by prove_H7
+31719: Order:
+31719: lpo
+31719: Leaf order:
+31719: c 2 0 2 2,2,2,2
+31719: b 4 0 4 1,2,2
+31719: a 6 0 6 1,2
+31719: join 17 2 4 0,2,2
+31719: meet 20 2 6 0,2
+% SZS status Timeout for LAT148-1.p
+NO CLASH, using fixed ground order
+31740: Facts:
+31740: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+31740: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+31740: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+31740: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+31740: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+31740: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+31740: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+31740: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+31740: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
+ [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
+31740: Goal:
+31740: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+31740: Order:
+31740: nrkbo
+31740: Leaf order:
+31740: b 3 0 3 1,2,2
+31740: c 3 0 3 2,2,2,2
+31740: a 6 0 6 1,2
+31740: join 18 2 4 0,2,2
+31740: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+31741: Facts:
+31741: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+31741: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+31741: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+31741: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+31741: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+31741: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+31741: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+31741: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+31741: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
+ [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
+31741: Goal:
+31741: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+31741: Order:
+31741: kbo
+31741: Leaf order:
+31741: b 3 0 3 1,2,2
+31741: c 3 0 3 2,2,2,2
+31741: a 6 0 6 1,2
+31741: join 18 2 4 0,2,2
+31741: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+31742: Facts:
+31742: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+31742: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+31742: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+31742: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+31742: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+31742: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+31742: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+31742: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+31742: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =?=
+ meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
+ [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
+31742: Goal:
+31742: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+31742: Order:
+31742: lpo
+31742: Leaf order:
+31742: b 3 0 3 1,2,2
+31742: c 3 0 3 2,2,2,2
+31742: a 6 0 6 1,2
+31742: join 18 2 4 0,2,2
+31742: meet 20 2 6 0,2
+% SZS status Timeout for LAT156-1.p
+NO CLASH, using fixed ground order
+31822: Facts:
+31822: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+31822: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+31822: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+31822: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+31822: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+31822: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+31822: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+31822: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+31822: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (join (meet ?28 ?29) (meet ?28 (join ?26 ?27))))
+ [29, 28, 27, 26] by equation_H52 ?26 ?27 ?28 ?29
+31822: Goal:
+31822: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (join (meet a c) (meet c d)))
+ [] by prove_H51
+31822: Order:
+31822: nrkbo
+31822: Leaf order:
+31822: b 2 0 2 1,2,2
+31822: d 2 0 2 2,2,2,2,2
+31822: c 3 0 3 1,2,2,2
+31822: a 4 0 4 1,2
+31822: join 18 2 4 0,2,2
+31822: meet 19 2 5 0,2
+NO CLASH, using fixed ground order
+31823: Facts:
+31823: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+31823: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+31823: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+31823: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+31823: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+31823: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+31823: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+31823: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+31823: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (join (meet ?28 ?29) (meet ?28 (join ?26 ?27))))
+ [29, 28, 27, 26] by equation_H52 ?26 ?27 ?28 ?29
+31823: Goal:
+31823: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (join (meet a c) (meet c d)))
+ [] by prove_H51
+31823: Order:
+31823: kbo
+31823: Leaf order:
+31823: b 2 0 2 1,2,2
+31823: d 2 0 2 2,2,2,2,2
+31823: c 3 0 3 1,2,2,2
+31823: a 4 0 4 1,2
+31823: join 18 2 4 0,2,2
+31823: meet 19 2 5 0,2
+NO CLASH, using fixed ground order
+31824: Facts:
+31824: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+31824: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+31824: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+31824: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+31824: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+31824: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+31824: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+31824: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+31824: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =?=
+ meet ?26 (join ?27 (join (meet ?28 ?29) (meet ?28 (join ?26 ?27))))
+ [29, 28, 27, 26] by equation_H52 ?26 ?27 ?28 ?29
+31824: Goal:
+31824: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (join (meet a c) (meet c d)))
+ [] by prove_H51
+31824: Order:
+31824: lpo
+31824: Leaf order:
+31824: b 2 0 2 1,2,2
+31824: d 2 0 2 2,2,2,2,2
+31824: c 3 0 3 1,2,2,2
+31824: a 4 0 4 1,2
+31824: join 18 2 4 0,2,2
+31824: meet 19 2 5 0,2
+% SZS status Timeout for LAT160-1.p
+NO CLASH, using fixed ground order
+31846: Facts:
+31846: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+31846: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+31846: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+31846: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+31846: Id : 6, {_}:
+ or ?14 ?15 =<= implies (not ?14) ?15
+ [15, 14] by or_definition ?14 ?15
+31846: Id : 7, {_}:
+ or (or ?17 ?18) ?19 =?= or ?17 (or ?18 ?19)
+ [19, 18, 17] by or_associativity ?17 ?18 ?19
+31846: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
+31846: Id : 9, {_}:
+ and ?24 ?25 =<= not (or (not ?24) (not ?25))
+ [25, 24] by and_definition ?24 ?25
+31846: Id : 10, {_}:
+ and (and ?27 ?28) ?29 =?= and ?27 (and ?28 ?29)
+ [29, 28, 27] by and_associativity ?27 ?28 ?29
+31846: Id : 11, {_}:
+ and ?31 ?32 =?= and ?32 ?31
+ [32, 31] by and_commutativity ?31 ?32
+31846: Id : 12, {_}:
+ xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
+ [35, 34] by xor_definition ?34 ?35
+31846: Id : 13, {_}:
+ xor ?37 ?38 =?= xor ?38 ?37
+ [38, 37] by xor_commutativity ?37 ?38
+31846: Id : 14, {_}:
+ and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
+ [41, 40] by and_star_definition ?40 ?41
+31846: Id : 15, {_}:
+ and_star (and_star ?43 ?44) ?45 =?= and_star ?43 (and_star ?44 ?45)
+ [45, 44, 43] by and_star_associativity ?43 ?44 ?45
+31846: Id : 16, {_}:
+ and_star ?47 ?48 =?= and_star ?48 ?47
+ [48, 47] by and_star_commutativity ?47 ?48
+31846: Id : 17, {_}: not truth =>= falsehood [] by false_definition
+31846: Goal:
+31846: Id : 1, {_}:
+ and_star (xor (and_star (xor truth x) y) truth) y
+ =<=
+ and_star (xor (and_star (xor truth y) x) truth) x
+ [] by prove_alternative_wajsberg_axiom
+31846: Order:
+31846: nrkbo
+31846: Leaf order:
+31846: falsehood 1 0 0
+31846: x 3 0 3 2,1,1,1,2
+31846: y 3 0 3 2,1,1,2
+31846: truth 8 0 4 1,1,1,1,2
+31846: not 12 1 0
+31846: xor 7 2 4 0,1,2
+31846: and 9 2 0
+31846: or 10 2 0
+31846: and_star 11 2 4 0,2
+31846: implies 14 2 0
+NO CLASH, using fixed ground order
+31847: Facts:
+31847: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+31847: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+31847: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+31847: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+31847: Id : 6, {_}:
+ or ?14 ?15 =<= implies (not ?14) ?15
+ [15, 14] by or_definition ?14 ?15
+31847: Id : 7, {_}:
+ or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
+ [19, 18, 17] by or_associativity ?17 ?18 ?19
+31847: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
+31847: Id : 9, {_}:
+ and ?24 ?25 =<= not (or (not ?24) (not ?25))
+ [25, 24] by and_definition ?24 ?25
+31847: Id : 10, {_}:
+ and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
+ [29, 28, 27] by and_associativity ?27 ?28 ?29
+31847: Id : 11, {_}:
+ and ?31 ?32 =?= and ?32 ?31
+ [32, 31] by and_commutativity ?31 ?32
+31847: Id : 12, {_}:
+ xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
+ [35, 34] by xor_definition ?34 ?35
+31847: Id : 13, {_}:
+ xor ?37 ?38 =?= xor ?38 ?37
+ [38, 37] by xor_commutativity ?37 ?38
+31847: Id : 14, {_}:
+ and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
+ [41, 40] by and_star_definition ?40 ?41
+31847: Id : 15, {_}:
+ and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45)
+ [45, 44, 43] by and_star_associativity ?43 ?44 ?45
+31847: Id : 16, {_}:
+ and_star ?47 ?48 =?= and_star ?48 ?47
+ [48, 47] by and_star_commutativity ?47 ?48
+31847: Id : 17, {_}: not truth =>= falsehood [] by false_definition
+31847: Goal:
+31847: Id : 1, {_}:
+ and_star (xor (and_star (xor truth x) y) truth) y
+ =?=
+ and_star (xor (and_star (xor truth y) x) truth) x
+ [] by prove_alternative_wajsberg_axiom
+31847: Order:
+31847: kbo
+31847: Leaf order:
+31847: falsehood 1 0 0
+31847: x 3 0 3 2,1,1,1,2
+31847: y 3 0 3 2,1,1,2
+31847: truth 8 0 4 1,1,1,1,2
+31847: not 12 1 0
+31847: xor 7 2 4 0,1,2
+31847: and 9 2 0
+31847: or 10 2 0
+31847: and_star 11 2 4 0,2
+31847: implies 14 2 0
+NO CLASH, using fixed ground order
+31848: Facts:
+31848: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
+31848: Id : 3, {_}:
+ implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
+ =>=
+ truth
+ [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
+31848: Id : 4, {_}:
+ implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
+ [9, 8] by wajsberg_3 ?8 ?9
+31848: Id : 5, {_}:
+ implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
+ [12, 11] by wajsberg_4 ?11 ?12
+31848: Id : 6, {_}:
+ or ?14 ?15 =<= implies (not ?14) ?15
+ [15, 14] by or_definition ?14 ?15
+31848: Id : 7, {_}:
+ or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19)
+ [19, 18, 17] by or_associativity ?17 ?18 ?19
+31848: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
+31848: Id : 9, {_}:
+ and ?24 ?25 =<= not (or (not ?24) (not ?25))
+ [25, 24] by and_definition ?24 ?25
+31848: Id : 10, {_}:
+ and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29)
+ [29, 28, 27] by and_associativity ?27 ?28 ?29
+31848: Id : 11, {_}:
+ and ?31 ?32 =?= and ?32 ?31
+ [32, 31] by and_commutativity ?31 ?32
+31848: Id : 12, {_}:
+ xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
+ [35, 34] by xor_definition ?34 ?35
+31848: Id : 13, {_}:
+ xor ?37 ?38 =?= xor ?38 ?37
+ [38, 37] by xor_commutativity ?37 ?38
+31848: Id : 14, {_}:
+ and_star ?40 ?41 =>= not (or (not ?40) (not ?41))
+ [41, 40] by and_star_definition ?40 ?41
+31848: Id : 15, {_}:
+ and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45)
+ [45, 44, 43] by and_star_associativity ?43 ?44 ?45
+31848: Id : 16, {_}:
+ and_star ?47 ?48 =?= and_star ?48 ?47
+ [48, 47] by and_star_commutativity ?47 ?48
+31848: Id : 17, {_}: not truth =>= falsehood [] by false_definition
+31848: Goal:
+31848: Id : 1, {_}:
+ and_star (xor (and_star (xor truth x) y) truth) y
+ =<=
+ and_star (xor (and_star (xor truth y) x) truth) x
+ [] by prove_alternative_wajsberg_axiom
+31848: Order:
+31848: lpo
+31848: Leaf order:
+31848: falsehood 1 0 0
+31848: x 3 0 3 2,1,1,1,2
+31848: y 3 0 3 2,1,1,2
+31848: truth 8 0 4 1,1,1,1,2
+31848: not 12 1 0
+31848: xor 7 2 4 0,1,2
+31848: and 9 2 0
+31848: or 10 2 0
+31848: and_star 11 2 4 0,2
+31848: implies 14 2 0
+% SZS status Timeout for LCL160-1.p
+NO CLASH, using fixed ground order
+31871: Facts:
+31871: Id : 2, {_}: add ?2 additive_identity =>= ?2 [2] by right_identity ?2
+31871: Id : 3, {_}:
+ add ?4 (additive_inverse ?4) =>= additive_identity
+ [4] by right_additive_inverse ?4
+31871: Id : 4, {_}:
+ multiply ?6 (add ?7 ?8) =<= add (multiply ?6 ?7) (multiply ?6 ?8)
+ [8, 7, 6] by distribute1 ?6 ?7 ?8
+31871: Id : 5, {_}:
+ multiply (add ?10 ?11) ?12
+ =<=
+ add (multiply ?10 ?12) (multiply ?11 ?12)
+ [12, 11, 10] by distribute2 ?10 ?11 ?12
+31871: Id : 6, {_}:
+ add (add ?14 ?15) ?16 =?= add ?14 (add ?15 ?16)
+ [16, 15, 14] by associative_addition ?14 ?15 ?16
+31871: Id : 7, {_}:
+ add ?18 ?19 =?= add ?19 ?18
+ [19, 18] by commutative_addition ?18 ?19
+31871: Id : 8, {_}:
+ multiply (multiply ?21 ?22) ?23 =?= multiply ?21 (multiply ?22 ?23)
+ [23, 22, 21] by associative_multiplication ?21 ?22 ?23
+31871: Id : 9, {_}: multiply ?25 (multiply ?25 ?25) =>= ?25 [25] by x_cubed_is_x ?25
+31871: Goal:
+31871: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_commutativity
+31871: Order:
+31871: nrkbo
+31871: Leaf order:
+31871: additive_identity 2 0 0
+31871: a 2 0 2 1,2
+31871: b 2 0 2 2,2
+31871: additive_inverse 1 1 0
+31871: add 12 2 0
+31871: multiply 14 2 2 0,2
+NO CLASH, using fixed ground order
+31872: Facts:
+31872: Id : 2, {_}: add ?2 additive_identity =>= ?2 [2] by right_identity ?2
+31872: Id : 3, {_}:
+ add ?4 (additive_inverse ?4) =>= additive_identity
+ [4] by right_additive_inverse ?4
+31872: Id : 4, {_}:
+ multiply ?6 (add ?7 ?8) =<= add (multiply ?6 ?7) (multiply ?6 ?8)
+ [8, 7, 6] by distribute1 ?6 ?7 ?8
+31872: Id : 5, {_}:
+ multiply (add ?10 ?11) ?12
+ =<=
+ add (multiply ?10 ?12) (multiply ?11 ?12)
+ [12, 11, 10] by distribute2 ?10 ?11 ?12
+31872: Id : 6, {_}:
+ add (add ?14 ?15) ?16 =>= add ?14 (add ?15 ?16)
+ [16, 15, 14] by associative_addition ?14 ?15 ?16
+31872: Id : 7, {_}:
+ add ?18 ?19 =?= add ?19 ?18
+ [19, 18] by commutative_addition ?18 ?19
+31872: Id : 8, {_}:
+ multiply (multiply ?21 ?22) ?23 =>= multiply ?21 (multiply ?22 ?23)
+ [23, 22, 21] by associative_multiplication ?21 ?22 ?23
+31872: Id : 9, {_}: multiply ?25 (multiply ?25 ?25) =>= ?25 [25] by x_cubed_is_x ?25
+31872: Goal:
+31872: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_commutativity
+31872: Order:
+31872: kbo
+31872: Leaf order:
+31872: additive_identity 2 0 0
+31872: a 2 0 2 1,2
+31872: b 2 0 2 2,2
+31872: additive_inverse 1 1 0
+31872: add 12 2 0
+31872: multiply 14 2 2 0,2
+NO CLASH, using fixed ground order
+31873: Facts:
+31873: Id : 2, {_}: add ?2 additive_identity =>= ?2 [2] by right_identity ?2
+31873: Id : 3, {_}:
+ add ?4 (additive_inverse ?4) =>= additive_identity
+ [4] by right_additive_inverse ?4
+31873: Id : 4, {_}:
+ multiply ?6 (add ?7 ?8) =>= add (multiply ?6 ?7) (multiply ?6 ?8)
+ [8, 7, 6] by distribute1 ?6 ?7 ?8
+31873: Id : 5, {_}:
+ multiply (add ?10 ?11) ?12
+ =>=
+ add (multiply ?10 ?12) (multiply ?11 ?12)
+ [12, 11, 10] by distribute2 ?10 ?11 ?12
+31873: Id : 6, {_}:
+ add (add ?14 ?15) ?16 =>= add ?14 (add ?15 ?16)
+ [16, 15, 14] by associative_addition ?14 ?15 ?16
+31873: Id : 7, {_}:
+ add ?18 ?19 =?= add ?19 ?18
+ [19, 18] by commutative_addition ?18 ?19
+31873: Id : 8, {_}:
+ multiply (multiply ?21 ?22) ?23 =>= multiply ?21 (multiply ?22 ?23)
+ [23, 22, 21] by associative_multiplication ?21 ?22 ?23
+31873: Id : 9, {_}: multiply ?25 (multiply ?25 ?25) =>= ?25 [25] by x_cubed_is_x ?25
+31873: Goal:
+31873: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_commutativity
+31873: Order:
+31873: lpo
+31873: Leaf order:
+31873: additive_identity 2 0 0
+31873: a 2 0 2 1,2
+31873: b 2 0 2 2,2
+31873: additive_inverse 1 1 0
+31873: add 12 2 0
+31873: multiply 14 2 2 0,2
+% SZS status Timeout for RNG009-5.p
+NO CLASH, using fixed ground order
+31898: Facts:
+31898: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+31898: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+31898: Id : 4, {_}:
+ add (additive_inverse ?6) ?6 =>= additive_identity
+ [6] by left_additive_inverse ?6
+31898: Id : 5, {_}:
+ add ?8 (additive_inverse ?8) =>= additive_identity
+ [8] by right_additive_inverse ?8
+31898: Id : 6, {_}:
+ add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12
+ [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
+31898: Id : 7, {_}:
+ add ?14 ?15 =?= add ?15 ?14
+ [15, 14] by commutativity_for_addition ?14 ?15
+31898: Id : 8, {_}:
+ multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19
+ [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
+31898: Id : 9, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+31898: Id : 10, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+31898: Id : 11, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29
+31898: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
+31898: Goal:
+31898: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
+31898: Order:
+31898: nrkbo
+31898: Leaf order:
+31898: b 2 0 1 1,2
+31898: a 2 0 1 2,2
+31898: c 2 0 1 3
+31898: additive_identity 4 0 0
+31898: additive_inverse 2 1 0
+31898: add 14 2 0
+31898: multiply 14 2 1 0,2
+NO CLASH, using fixed ground order
+31899: Facts:
+31899: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+31899: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+31899: Id : 4, {_}:
+ add (additive_inverse ?6) ?6 =>= additive_identity
+ [6] by left_additive_inverse ?6
+31899: Id : 5, {_}:
+ add ?8 (additive_inverse ?8) =>= additive_identity
+ [8] by right_additive_inverse ?8
+31899: Id : 6, {_}:
+ add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
+ [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
+31899: Id : 7, {_}:
+ add ?14 ?15 =?= add ?15 ?14
+ [15, 14] by commutativity_for_addition ?14 ?15
+31899: Id : 8, {_}:
+ multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
+ [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
+31899: Id : 9, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+31899: Id : 10, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+31899: Id : 11, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29
+31899: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
+31899: Goal:
+31899: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
+31899: Order:
+31899: kbo
+31899: Leaf order:
+31899: b 2 0 1 1,2
+31899: a 2 0 1 2,2
+31899: c 2 0 1 3
+31899: additive_identity 4 0 0
+31899: additive_inverse 2 1 0
+31899: add 14 2 0
+31899: multiply 14 2 1 0,2
+NO CLASH, using fixed ground order
+31900: Facts:
+31900: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+31900: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+31900: Id : 4, {_}:
+ add (additive_inverse ?6) ?6 =>= additive_identity
+ [6] by left_additive_inverse ?6
+31900: Id : 5, {_}:
+ add ?8 (additive_inverse ?8) =>= additive_identity
+ [8] by right_additive_inverse ?8
+31900: Id : 6, {_}:
+ add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
+ [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
+31900: Id : 7, {_}:
+ add ?14 ?15 =?= add ?15 ?14
+ [15, 14] by commutativity_for_addition ?14 ?15
+31900: Id : 8, {_}:
+ multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
+ [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
+31900: Id : 9, {_}:
+ multiply ?21 (add ?22 ?23)
+ =>=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+31900: Id : 10, {_}:
+ multiply (add ?25 ?26) ?27
+ =>=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+31900: Id : 11, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29
+31900: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
+31900: Goal:
+31900: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
+31900: Order:
+31900: lpo
+31900: Leaf order:
+31900: b 2 0 1 1,2
+31900: a 2 0 1 2,2
+31900: c 2 0 1 3
+31900: additive_identity 4 0 0
+31900: additive_inverse 2 1 0
+31900: add 14 2 0
+31900: multiply 14 2 1 0,2
+% SZS status Timeout for RNG009-7.p
+NO CLASH, using fixed ground order
+31923: Facts:
+31923: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+31923: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+31923: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+31923: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+31923: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+31923: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+31923: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+31923: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+31923: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+31923: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+31923: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+31923: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+31923: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+31923: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+31923: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+31923: Goal:
+31923: Id : 1, {_}:
+ add
+ (add (associator (multiply a b) c d)
+ (associator a b (multiply c d)))
+ (additive_inverse
+ (add
+ (add (associator a (multiply b c) d)
+ (multiply a (associator b c d)))
+ (multiply (associator a b c) d)))
+ =>=
+ additive_identity
+ [] by prove_teichmuller_identity
+31923: Order:
+31923: nrkbo
+31923: Leaf order:
+31923: a 5 0 5 1,1,1,1,2
+31923: b 5 0 5 2,1,1,1,2
+31923: c 5 0 5 2,1,1,2
+31923: d 5 0 5 3,1,1,2
+31923: additive_identity 9 0 1 3
+31923: additive_inverse 7 1 1 0,2,2
+31923: commutator 1 2 0
+31923: add 20 2 4 0,2
+31923: multiply 27 2 5 0,1,1,1,2
+31923: associator 6 3 5 0,1,1,2
+NO CLASH, using fixed ground order
+31924: Facts:
+31924: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+31924: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+31924: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+31924: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+31924: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+31924: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+31924: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+31924: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+31924: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+31924: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+31924: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+31924: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+31924: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+31924: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+31924: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+31924: Goal:
+31924: Id : 1, {_}:
+ add
+ (add (associator (multiply a b) c d)
+ (associator a b (multiply c d)))
+ (additive_inverse
+ (add
+ (add (associator a (multiply b c) d)
+ (multiply a (associator b c d)))
+ (multiply (associator a b c) d)))
+ =>=
+ additive_identity
+ [] by prove_teichmuller_identity
+31924: Order:
+31924: kbo
+31924: Leaf order:
+31924: a 5 0 5 1,1,1,1,2
+31924: b 5 0 5 2,1,1,1,2
+31924: c 5 0 5 2,1,1,2
+31924: d 5 0 5 3,1,1,2
+31924: additive_identity 9 0 1 3
+31924: additive_inverse 7 1 1 0,2,2
+31924: commutator 1 2 0
+31924: add 20 2 4 0,2
+31924: multiply 27 2 5 0,1,1,1,2
+31924: associator 6 3 5 0,1,1,2
+NO CLASH, using fixed ground order
+31925: Facts:
+31925: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+31925: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+31925: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+31925: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+31925: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+31925: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+31925: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+31925: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+31925: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+31925: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+31925: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+31925: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+31925: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+31925: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+31925: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+31925: Goal:
+31925: Id : 1, {_}:
+ add
+ (add (associator (multiply a b) c d)
+ (associator a b (multiply c d)))
+ (additive_inverse
+ (add
+ (add (associator a (multiply b c) d)
+ (multiply a (associator b c d)))
+ (multiply (associator a b c) d)))
+ =>=
+ additive_identity
+ [] by prove_teichmuller_identity
+31925: Order:
+31925: lpo
+31925: Leaf order:
+31925: a 5 0 5 1,1,1,1,2
+31925: b 5 0 5 2,1,1,1,2
+31925: c 5 0 5 2,1,1,2
+31925: d 5 0 5 3,1,1,2
+31925: additive_identity 9 0 1 3
+31925: additive_inverse 7 1 1 0,2,2
+31925: commutator 1 2 0
+31925: add 20 2 4 0,2
+31925: multiply 27 2 5 0,1,1,1,2
+31925: associator 6 3 5 0,1,1,2
+% SZS status Timeout for RNG026-6.p
+NO CLASH, using fixed ground order
+31946: Facts:
+31946: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+31946: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+31946: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+31946: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+31946: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+31946: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+31946: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+31946: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+31946: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+31946: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+31946: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+31946: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+31946: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+31946: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+31946: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+31946: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+31946: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+31946: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+31946: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+31946: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+31946: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+31946: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+31946: Goal:
+31946: Id : 1, {_}:
+ add
+ (add (associator (multiply a b) c d)
+ (associator a b (multiply c d)))
+ (additive_inverse
+ (add
+ (add (associator a (multiply b c) d)
+ (multiply a (associator b c d)))
+ (multiply (associator a b c) d)))
+ =>=
+ additive_identity
+ [] by prove_teichmuller_identity
+31946: Order:
+31946: nrkbo
+31946: Leaf order:
+31946: a 5 0 5 1,1,1,1,2
+31946: b 5 0 5 2,1,1,1,2
+31946: c 5 0 5 2,1,1,2
+31946: d 5 0 5 3,1,1,2
+31946: additive_identity 9 0 1 3
+31946: additive_inverse 23 1 1 0,2,2
+31946: commutator 1 2 0
+31946: add 28 2 4 0,2
+31946: multiply 45 2 5 0,1,1,1,2
+31946: associator 6 3 5 0,1,1,2
+NO CLASH, using fixed ground order
+31947: Facts:
+31947: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+31947: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+31947: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+31947: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+31947: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+31947: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+31947: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+31947: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+31947: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+31947: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+31947: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+31947: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+31947: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+31947: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+31947: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+31947: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+31947: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+31947: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+31947: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+31947: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+31947: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+31947: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+31947: Goal:
+31947: Id : 1, {_}:
+ add
+ (add (associator (multiply a b) c d)
+ (associator a b (multiply c d)))
+ (additive_inverse
+ (add
+ (add (associator a (multiply b c) d)
+ (multiply a (associator b c d)))
+ (multiply (associator a b c) d)))
+ =>=
+ additive_identity
+ [] by prove_teichmuller_identity
+31947: Order:
+31947: kbo
+31947: Leaf order:
+31947: a 5 0 5 1,1,1,1,2
+31947: b 5 0 5 2,1,1,1,2
+31947: c 5 0 5 2,1,1,2
+31947: d 5 0 5 3,1,1,2
+31947: additive_identity 9 0 1 3
+31947: additive_inverse 23 1 1 0,2,2
+31947: commutator 1 2 0
+31947: add 28 2 4 0,2
+31947: multiply 45 2 5 0,1,1,1,2
+31947: associator 6 3 5 0,1,1,2
+NO CLASH, using fixed ground order
+31948: Facts:
+31948: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+31948: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+31948: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+31948: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+31948: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+31948: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+31948: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+31948: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+31948: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+31948: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+31948: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+31948: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+31948: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+31948: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+31948: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+31948: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+31948: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+31948: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+31948: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =>=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+31948: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =>=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+31948: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =>=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+31948: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =>=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+31948: Goal:
+31948: Id : 1, {_}:
+ add
+ (add (associator (multiply a b) c d)
+ (associator a b (multiply c d)))
+ (additive_inverse
+ (add
+ (add (associator a (multiply b c) d)
+ (multiply a (associator b c d)))
+ (multiply (associator a b c) d)))
+ =>=
+ additive_identity
+ [] by prove_teichmuller_identity
+31948: Order:
+31948: lpo
+31948: Leaf order:
+31948: a 5 0 5 1,1,1,1,2
+31948: b 5 0 5 2,1,1,1,2
+31948: c 5 0 5 2,1,1,2
+31948: d 5 0 5 3,1,1,2
+31948: additive_identity 9 0 1 3
+31948: additive_inverse 23 1 1 0,2,2
+31948: commutator 1 2 0
+31948: add 28 2 4 0,2
+31948: multiply 45 2 5 0,1,1,1,2
+31948: associator 6 3 5 0,1,1,2
+% SZS status Timeout for RNG026-7.p
+NO CLASH, using fixed ground order
+31979: Facts:
+31979: Id : 2, {_}:
+ nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by sh_1 ?2 ?3 ?4
+31979: Goal:
+31979: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+31979: Order:
+31979: nrkbo
+31979: Leaf order:
+31979: c 2 0 2 2,2,2,2
+31979: a 3 0 3 1,2
+31979: b 3 0 3 1,2,2
+31979: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+31980: Facts:
+31980: Id : 2, {_}:
+ nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by sh_1 ?2 ?3 ?4
+31980: Goal:
+31980: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+31980: Order:
+31980: kbo
+31980: Leaf order:
+31980: c 2 0 2 2,2,2,2
+31980: a 3 0 3 1,2
+31980: b 3 0 3 1,2,2
+31980: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+31981: Facts:
+31981: Id : 2, {_}:
+ nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by sh_1 ?2 ?3 ?4
+31981: Goal:
+31981: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+31981: Order:
+31981: lpo
+31981: Leaf order:
+31981: c 2 0 2 2,2,2,2
+31981: a 3 0 3 1,2
+31981: b 3 0 3 1,2,2
+31981: nand 12 2 6 0,2
+% SZS status Timeout for BOO076-1.p
+CLASH, statistics insufficient
+32007: Facts:
+32007: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+32007: Id : 3, {_}:
+ apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
+ [8, 7] by w_definition ?7 ?8
+32007: Goal:
+32007: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_strong_fixed_point ?1
+32007: Order:
+32007: nrkbo
+32007: Leaf order:
+32007: b 1 0 0
+32007: w 1 0 0
+32007: f 3 1 3 0,2,2
+32007: apply 12 2 3 0,2
+CLASH, statistics insufficient
+32008: Facts:
+32008: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+32008: Id : 3, {_}:
+ apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
+ [8, 7] by w_definition ?7 ?8
+32008: Goal:
+32008: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_strong_fixed_point ?1
+32008: Order:
+32008: kbo
+32008: Leaf order:
+32008: b 1 0 0
+32008: w 1 0 0
+32008: f 3 1 3 0,2,2
+32008: apply 12 2 3 0,2
+CLASH, statistics insufficient
+32009: Facts:
+32009: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+32009: Id : 3, {_}:
+ apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8
+ [8, 7] by w_definition ?7 ?8
+32009: Goal:
+32009: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_strong_fixed_point ?1
+32009: Order:
+32009: lpo
+32009: Leaf order:
+32009: b 1 0 0
+32009: w 1 0 0
+32009: f 3 1 3 0,2,2
+32009: apply 12 2 3 0,2
+% SZS status Timeout for COL003-1.p
+CLASH, statistics insufficient
+32036: Facts:
+32036: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+CLASH, statistics insufficient
+32037: Facts:
+32037: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+32037: Id : 3, {_}:
+ apply (apply w1 ?7) ?8 =?= apply (apply ?8 ?7) ?7
+ [8, 7] by w1_definition ?7 ?8
+32037: Goal:
+32037: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+32037: Order:
+32037: kbo
+32037: Leaf order:
+32037: b 1 0 0
+32037: w1 1 0 0
+32037: f 3 1 3 0,2,2
+32037: apply 12 2 3 0,2
+32036: Id : 3, {_}:
+ apply (apply w1 ?7) ?8 =?= apply (apply ?8 ?7) ?7
+ [8, 7] by w1_definition ?7 ?8
+32036: Goal:
+32036: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+32036: Order:
+32036: nrkbo
+32036: Leaf order:
+32036: b 1 0 0
+32036: w1 1 0 0
+32036: f 3 1 3 0,2,2
+32036: apply 12 2 3 0,2
+CLASH, statistics insufficient
+32038: Facts:
+32038: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+32038: Id : 3, {_}:
+ apply (apply w1 ?7) ?8 =?= apply (apply ?8 ?7) ?7
+ [8, 7] by w1_definition ?7 ?8
+32038: Goal:
+32038: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+32038: Order:
+32038: lpo
+32038: Leaf order:
+32038: b 1 0 0
+32038: w1 1 0 0
+32038: f 3 1 3 0,2,2
+32038: apply 12 2 3 0,2
+% SZS status Timeout for COL042-1.p
+NO CLASH, using fixed ground order
+32071: Facts:
+32071: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+32071: Id : 3, {_}:
+ apply (apply (apply h ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?7) ?8) ?7
+ [8, 7, 6] by h_definition ?6 ?7 ?8
+32071: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply h
+ (apply (apply b (apply (apply b h) (apply b b)))
+ (apply h (apply (apply b h) (apply b b))))) h)) b)) b
+ [] by strong_fixed_point
+32071: Goal:
+32071: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+32071: Order:
+32071: nrkbo
+32071: Leaf order:
+32071: strong_fixed_point 3 0 2 1,2
+32071: fixed_pt 3 0 3 2,2
+32071: h 6 0 0
+32071: b 12 0 0
+32071: apply 29 2 3 0,2
+NO CLASH, using fixed ground order
+32072: Facts:
+32072: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+32072: Id : 3, {_}:
+ apply (apply (apply h ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?7) ?8) ?7
+ [8, 7, 6] by h_definition ?6 ?7 ?8
+32072: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply h
+ (apply (apply b (apply (apply b h) (apply b b)))
+ (apply h (apply (apply b h) (apply b b))))) h)) b)) b
+ [] by strong_fixed_point
+32072: Goal:
+32072: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+32072: Order:
+32072: kbo
+32072: Leaf order:
+32072: strong_fixed_point 3 0 2 1,2
+32072: fixed_pt 3 0 3 2,2
+32072: h 6 0 0
+32072: b 12 0 0
+32072: apply 29 2 3 0,2
+NO CLASH, using fixed ground order
+32073: Facts:
+32073: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+32073: Id : 3, {_}:
+ apply (apply (apply h ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?7) ?8) ?7
+ [8, 7, 6] by h_definition ?6 ?7 ?8
+32073: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply h
+ (apply (apply b (apply (apply b h) (apply b b)))
+ (apply h (apply (apply b h) (apply b b))))) h)) b)) b
+ [] by strong_fixed_point
+32073: Goal:
+32073: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+32073: Order:
+32073: lpo
+32073: Leaf order:
+32073: strong_fixed_point 3 0 2 1,2
+32073: fixed_pt 3 0 3 2,2
+32073: h 6 0 0
+32073: b 12 0 0
+32073: apply 29 2 3 0,2
+% SZS status Timeout for COL043-3.p
+NO CLASH, using fixed ground order
+32095: Facts:
+NO CLASH, using fixed ground order
+32096: Facts:
+32096: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+32096: Id : 3, {_}:
+ apply (apply (apply n ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?8) ?7) ?8
+ [8, 7, 6] by n_definition ?6 ?7 ?8
+32096: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply n
+ (apply n
+ (apply (apply b (apply b b))
+ (apply n (apply (apply b b) n))))) n)) b)) b
+ [] by strong_fixed_point
+32096: Goal:
+32096: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+32096: Order:
+32096: kbo
+32096: Leaf order:
+32096: strong_fixed_point 3 0 2 1,2
+32096: fixed_pt 3 0 3 2,2
+32096: n 6 0 0
+32096: b 10 0 0
+32096: apply 27 2 3 0,2
+NO CLASH, using fixed ground order
+32097: Facts:
+32097: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+32097: Id : 3, {_}:
+ apply (apply (apply n ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?8) ?7) ?8
+ [8, 7, 6] by n_definition ?6 ?7 ?8
+32097: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply n
+ (apply n
+ (apply (apply b (apply b b))
+ (apply n (apply (apply b b) n))))) n)) b)) b
+ [] by strong_fixed_point
+32097: Goal:
+32097: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+32097: Order:
+32097: lpo
+32097: Leaf order:
+32097: strong_fixed_point 3 0 2 1,2
+32097: fixed_pt 3 0 3 2,2
+32097: n 6 0 0
+32097: b 10 0 0
+32097: apply 27 2 3 0,2
+32095: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+32095: Id : 3, {_}:
+ apply (apply (apply n ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?8) ?7) ?8
+ [8, 7, 6] by n_definition ?6 ?7 ?8
+32095: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply n
+ (apply n
+ (apply (apply b (apply b b))
+ (apply n (apply (apply b b) n))))) n)) b)) b
+ [] by strong_fixed_point
+32095: Goal:
+32095: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+32095: Order:
+32095: nrkbo
+32095: Leaf order:
+32095: strong_fixed_point 3 0 2 1,2
+32095: fixed_pt 3 0 3 2,2
+32095: n 6 0 0
+32095: b 10 0 0
+32095: apply 27 2 3 0,2
+% SZS status Timeout for COL044-8.p
+NO CLASH, using fixed ground order
+32149: Facts:
+32149: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+32149: Id : 3, {_}:
+ apply (apply (apply n ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?8) ?7) ?8
+ [8, 7, 6] by n_definition ?6 ?7 ?8
+32149: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply n
+ (apply n
+ (apply (apply b (apply b b))
+ (apply n (apply n (apply b b)))))) n)) b)) b
+ [] by strong_fixed_point
+32149: Goal:
+32149: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+32149: Order:
+32149: nrkbo
+32149: Leaf order:
+32149: strong_fixed_point 3 0 2 1,2
+32149: fixed_pt 3 0 3 2,2
+32149: n 6 0 0
+32149: b 10 0 0
+32149: apply 27 2 3 0,2
+NO CLASH, using fixed ground order
+32150: Facts:
+32150: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+32150: Id : 3, {_}:
+ apply (apply (apply n ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?8) ?7) ?8
+ [8, 7, 6] by n_definition ?6 ?7 ?8
+32150: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply n
+ (apply n
+ (apply (apply b (apply b b))
+ (apply n (apply n (apply b b)))))) n)) b)) b
+ [] by strong_fixed_point
+32150: Goal:
+32150: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+32150: Order:
+32150: kbo
+32150: Leaf order:
+32150: strong_fixed_point 3 0 2 1,2
+32150: fixed_pt 3 0 3 2,2
+32150: n 6 0 0
+32150: b 10 0 0
+32150: apply 27 2 3 0,2
+NO CLASH, using fixed ground order
+32151: Facts:
+32151: Id : 2, {_}:
+ apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4)
+ [4, 3, 2] by b_definition ?2 ?3 ?4
+32151: Id : 3, {_}:
+ apply (apply (apply n ?6) ?7) ?8
+ =?=
+ apply (apply (apply ?6 ?8) ?7) ?8
+ [8, 7, 6] by n_definition ?6 ?7 ?8
+32151: Id : 4, {_}:
+ strong_fixed_point
+ =<=
+ apply
+ (apply b
+ (apply
+ (apply b
+ (apply
+ (apply n
+ (apply n
+ (apply (apply b (apply b b))
+ (apply n (apply n (apply b b)))))) n)) b)) b
+ [] by strong_fixed_point
+32151: Goal:
+32151: Id : 1, {_}:
+ apply strong_fixed_point fixed_pt
+ =<=
+ apply fixed_pt (apply strong_fixed_point fixed_pt)
+ [] by prove_strong_fixed_point
+32151: Order:
+32151: lpo
+32151: Leaf order:
+32151: strong_fixed_point 3 0 2 1,2
+32151: fixed_pt 3 0 3 2,2
+32151: n 6 0 0
+32151: b 10 0 0
+32151: apply 27 2 3 0,2
+% SZS status Timeout for COL044-9.p
+NO CLASH, using fixed ground order
+32174: Facts:
+32174: Id : 2, {_}:
+ multiply
+ (inverse
+ (multiply
+ (inverse
+ (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
+ (multiply (inverse (multiply ?4 ?5))
+ (multiply ?4
+ (inverse
+ (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
+ ?7
+ =>=
+ ?6
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+32174: Goal:
+32174: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+32174: Order:
+32174: nrkbo
+32174: Leaf order:
+32174: b2 2 0 2 1,1,1,2
+32174: a2 2 0 2 2,2
+32174: inverse 8 1 1 0,1,1,2
+32174: multiply 12 2 2 0,2
+NO CLASH, using fixed ground order
+32175: Facts:
+32175: Id : 2, {_}:
+ multiply
+ (inverse
+ (multiply
+ (inverse
+ (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
+ (multiply (inverse (multiply ?4 ?5))
+ (multiply ?4
+ (inverse
+ (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
+ ?7
+ =>=
+ ?6
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+32175: Goal:
+32175: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+32175: Order:
+32175: kbo
+32175: Leaf order:
+32175: b2 2 0 2 1,1,1,2
+32175: a2 2 0 2 2,2
+32175: inverse 8 1 1 0,1,1,2
+32175: multiply 12 2 2 0,2
+NO CLASH, using fixed ground order
+32176: Facts:
+32176: Id : 2, {_}:
+ multiply
+ (inverse
+ (multiply
+ (inverse
+ (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2)))
+ (multiply (inverse (multiply ?4 ?5))
+ (multiply ?4
+ (inverse
+ (multiply (multiply ?6 (inverse ?7)) (inverse ?5)))))))
+ ?7
+ =>=
+ ?6
+ [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7
+32176: Goal:
+32176: Id : 1, {_}:
+ multiply (multiply (inverse b2) b2) a2 =>= a2
+ [] by prove_these_axioms_2
+32176: Order:
+32176: lpo
+32176: Leaf order:
+32176: b2 2 0 2 1,1,1,2
+32176: a2 2 0 2 2,2
+32176: inverse 8 1 1 0,1,1,2
+32176: multiply 12 2 2 0,2
+% SZS status Timeout for GRP506-1.p
+NO CLASH, using fixed ground order
+32197: Facts:
+32197: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32197: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+NO CLASH, using fixed ground order
+32198: Facts:
+32198: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32198: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32198: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32198: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32198: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32198: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32198: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32198: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32198: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+32198: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+32198: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+32198: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+32198: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+32197: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32197: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32197: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32197: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32197: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32197: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32197: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+NO CLASH, using fixed ground order
+32197: Id : 11, {_}:
+ complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+32197: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+32197: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+32197: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+32197: Id : 15, {_}:
+ join (meet (complement ?38) (join ?38 ?39))
+ (join (complement ?39) (meet ?38 ?39))
+ =>=
+ n1
+ [39, 38] by megill ?38 ?39
+32197: Goal:
+32197: Id : 1, {_}:
+ meet a (join b (meet a (join (complement a) (meet a b))))
+ =>=
+ meet a (join (complement a) (meet a b))
+ [] by prove_this
+32197: Order:
+32197: nrkbo
+32197: Leaf order:
+32197: n0 1 0 0
+32197: n1 2 0 0
+32197: b 3 0 3 1,2,2
+32197: a 7 0 7 1,2
+32197: complement 14 1 2 0,1,2,2,2,2
+32197: join 18 2 3 0,2,2
+32197: meet 19 2 5 0,2
+32199: Facts:
+32199: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32199: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32199: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32199: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32199: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32199: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32199: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32199: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32199: Id : 10, {_}:
+ complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27)
+ [27, 26] by compatibility1 ?26 ?27
+32199: Id : 11, {_}:
+ complement (meet ?29 ?30) =>= join (complement ?29) (complement ?30)
+ [30, 29] by compatibility2 ?29 ?30
+32199: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32
+32199: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34
+32199: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36
+32199: Id : 15, {_}:
+ join (meet (complement ?38) (join ?38 ?39))
+ (join (complement ?39) (meet ?38 ?39))
+ =>=
+ n1
+ [39, 38] by megill ?38 ?39
+32199: Goal:
+32199: Id : 1, {_}:
+ meet a (join b (meet a (join (complement a) (meet a b))))
+ =>=
+ meet a (join (complement a) (meet a b))
+ [] by prove_this
+32199: Order:
+32199: lpo
+32199: Leaf order:
+32199: n0 1 0 0
+32199: n1 2 0 0
+32199: b 3 0 3 1,2,2
+32199: a 7 0 7 1,2
+32199: complement 14 1 2 0,1,2,2,2,2
+32199: join 18 2 3 0,2,2
+32199: meet 19 2 5 0,2
+32198: Id : 15, {_}:
+ join (meet (complement ?38) (join ?38 ?39))
+ (join (complement ?39) (meet ?38 ?39))
+ =>=
+ n1
+ [39, 38] by megill ?38 ?39
+32198: Goal:
+32198: Id : 1, {_}:
+ meet a (join b (meet a (join (complement a) (meet a b))))
+ =>=
+ meet a (join (complement a) (meet a b))
+ [] by prove_this
+32198: Order:
+32198: kbo
+32198: Leaf order:
+32198: n0 1 0 0
+32198: n1 2 0 0
+32198: b 3 0 3 1,2,2
+32198: a 7 0 7 1,2
+32198: complement 14 1 2 0,1,2,2,2,2
+32198: join 18 2 3 0,2,2
+32198: meet 19 2 5 0,2
+% SZS status Timeout for LAT053-1.p
+NO CLASH, using fixed ground order
+32222: Facts:
+32222: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+32222: Goal:
+32222: Id : 1, {_}: meet a b =<= meet b a [] by prove_normal_axioms_2
+32222: Order:
+32222: nrkbo
+32222: Leaf order:
+32222: a 2 0 2 1,2
+32222: b 2 0 2 2,2
+32222: join 20 2 0
+32222: meet 20 2 2 0,2
+NO CLASH, using fixed ground order
+32223: Facts:
+32223: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+32223: Goal:
+32223: Id : 1, {_}: meet a b =<= meet b a [] by prove_normal_axioms_2
+32223: Order:
+32223: kbo
+32223: Leaf order:
+32223: a 2 0 2 1,2
+32223: b 2 0 2 2,2
+32223: join 20 2 0
+32223: meet 20 2 2 0,2
+NO CLASH, using fixed ground order
+32224: Facts:
+32224: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+32224: Goal:
+32224: Id : 1, {_}: meet a b =<= meet b a [] by prove_normal_axioms_2
+32224: Order:
+32224: lpo
+32224: Leaf order:
+32224: a 2 0 2 1,2
+32224: b 2 0 2 2,2
+32224: join 20 2 0
+32224: meet 20 2 2 0,2
+% SZS status Timeout for LAT081-1.p
+NO CLASH, using fixed ground order
+32257: Facts:
+32257: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+32257: Goal:
+32257: Id : 1, {_}: join a b =<= join b a [] by prove_normal_axioms_5
+32257: Order:
+32257: nrkbo
+32257: Leaf order:
+32257: a 2 0 2 1,2
+32257: b 2 0 2 2,2
+32257: meet 18 2 0
+32257: join 22 2 2 0,2
+NO CLASH, using fixed ground order
+32258: Facts:
+32258: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+32258: Goal:
+32258: Id : 1, {_}: join a b =<= join b a [] by prove_normal_axioms_5
+32258: Order:
+32258: kbo
+32258: Leaf order:
+32258: a 2 0 2 1,2
+32258: b 2 0 2 2,2
+32258: meet 18 2 0
+32258: join 22 2 2 0,2
+NO CLASH, using fixed ground order
+32259: Facts:
+32259: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+32259: Goal:
+32259: Id : 1, {_}: join a b =<= join b a [] by prove_normal_axioms_5
+32259: Order:
+32259: lpo
+32259: Leaf order:
+32259: a 2 0 2 1,2
+32259: b 2 0 2 2,2
+32259: meet 18 2 0
+32259: join 22 2 2 0,2
+% SZS status Timeout for LAT084-1.p
+NO CLASH, using fixed ground order
+32283: Facts:
+32283: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+32283: Goal:
+32283: Id : 1, {_}: meet a (join a b) =>= a [] by prove_normal_axioms_7
+32283: Order:
+32283: nrkbo
+32283: Leaf order:
+32283: b 1 0 1 2,2,2
+32283: a 3 0 3 1,2
+32283: meet 19 2 1 0,2
+32283: join 21 2 1 0,2,2
+NO CLASH, using fixed ground order
+32284: Facts:
+32284: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+32284: Goal:
+32284: Id : 1, {_}: meet a (join a b) =>= a [] by prove_normal_axioms_7
+32284: Order:
+32284: kbo
+32284: Leaf order:
+32284: b 1 0 1 2,2,2
+32284: a 3 0 3 1,2
+32284: meet 19 2 1 0,2
+32284: join 21 2 1 0,2,2
+NO CLASH, using fixed ground order
+32285: Facts:
+32285: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+32285: Goal:
+32285: Id : 1, {_}: meet a (join a b) =>= a [] by prove_normal_axioms_7
+32285: Order:
+32285: lpo
+32285: Leaf order:
+32285: b 1 0 1 2,2,2
+32285: a 3 0 3 1,2
+32285: meet 19 2 1 0,2
+32285: join 21 2 1 0,2,2
+% SZS status Timeout for LAT086-1.p
+NO CLASH, using fixed ground order
+32311: Facts:
+32311: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+32311: Goal:
+32311: Id : 1, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8
+32311: Order:
+32311: nrkbo
+32311: Leaf order:
+32311: b 1 0 1 2,2,2
+32311: a 3 0 3 1,2
+32311: meet 19 2 1 0,2,2
+32311: join 21 2 1 0,2
+NO CLASH, using fixed ground order
+32312: Facts:
+32312: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+32312: Goal:
+32312: Id : 1, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8
+32312: Order:
+32312: kbo
+32312: Leaf order:
+32312: b 1 0 1 2,2,2
+32312: a 3 0 3 1,2
+32312: meet 19 2 1 0,2,2
+32312: join 21 2 1 0,2
+NO CLASH, using fixed ground order
+32313: Facts:
+32313: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+32313: Goal:
+32313: Id : 1, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8
+32313: Order:
+32313: lpo
+32313: Leaf order:
+32313: b 1 0 1 2,2,2
+32313: a 3 0 3 1,2
+32313: meet 19 2 1 0,2,2
+32313: join 21 2 1 0,2
+% SZS status Timeout for LAT087-1.p
+NO CLASH, using fixed ground order
+32355: Facts:
+32355: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32355: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32355: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32355: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32355: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32355: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32355: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32355: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32355: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?28 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))))
+ [28, 27, 26] by equation_H3 ?26 ?27 ?28
+32355: Goal:
+32355: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+32355: Order:
+32355: nrkbo
+32355: Leaf order:
+32355: a 4 0 4 1,2
+32355: b 4 0 4 1,2,2
+32355: c 4 0 4 2,2,2,2
+32355: join 17 2 4 0,2,2
+32355: meet 21 2 6 0,2
+NO CLASH, using fixed ground order
+32356: Facts:
+32356: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32356: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32356: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32356: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32356: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32356: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32356: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32356: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32356: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?28 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))))
+ [28, 27, 26] by equation_H3 ?26 ?27 ?28
+32356: Goal:
+32356: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+32356: Order:
+32356: kbo
+32356: Leaf order:
+32356: a 4 0 4 1,2
+32356: b 4 0 4 1,2,2
+32356: c 4 0 4 2,2,2,2
+32356: join 17 2 4 0,2,2
+32356: meet 21 2 6 0,2
+NO CLASH, using fixed ground order
+32357: Facts:
+32357: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32357: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32357: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32357: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32357: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32357: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32357: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32357: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32357: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?28 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))))
+ [28, 27, 26] by equation_H3 ?26 ?27 ?28
+32357: Goal:
+32357: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+32357: Order:
+32357: lpo
+32357: Leaf order:
+32357: a 4 0 4 1,2
+32357: b 4 0 4 1,2,2
+32357: c 4 0 4 2,2,2,2
+32357: join 17 2 4 0,2,2
+32357: meet 21 2 6 0,2
+% SZS status Timeout for LAT099-1.p
+NO CLASH, using fixed ground order
+32378: Facts:
+32378: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32378: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32378: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32378: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32378: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32378: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32378: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32378: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32378: Id : 10, {_}:
+ meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
+32378: Goal:
+32378: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+32378: Order:
+32378: nrkbo
+32378: Leaf order:
+32378: d 2 0 2 2,2,2,2,2
+32378: b 3 0 3 1,2,2
+32378: c 3 0 3 1,2,2,2
+32378: a 4 0 4 1,2
+32378: meet 19 2 5 0,2
+32378: join 19 2 5 0,2,2
+NO CLASH, using fixed ground order
+32379: Facts:
+32379: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32379: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32379: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32379: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32379: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32379: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32379: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32379: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32379: Id : 10, {_}:
+ meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
+32379: Goal:
+32379: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+32379: Order:
+32379: kbo
+32379: Leaf order:
+32379: d 2 0 2 2,2,2,2,2
+32379: b 3 0 3 1,2,2
+32379: c 3 0 3 1,2,2,2
+32379: a 4 0 4 1,2
+32379: meet 19 2 5 0,2
+32379: join 19 2 5 0,2,2
+NO CLASH, using fixed ground order
+32380: Facts:
+32380: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32380: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32380: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32380: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32380: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32380: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32380: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32380: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32380: Id : 10, {_}:
+ meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
+ =?=
+ meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
+32380: Goal:
+32380: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =>=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+32380: Order:
+32380: lpo
+32380: Leaf order:
+32380: d 2 0 2 2,2,2,2,2
+32380: b 3 0 3 1,2,2
+32380: c 3 0 3 1,2,2,2
+32380: a 4 0 4 1,2
+32380: meet 19 2 5 0,2
+32380: join 19 2 5 0,2,2
+% SZS status Timeout for LAT110-1.p
+NO CLASH, using fixed ground order
+32414: Facts:
+32414: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32414: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32414: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32414: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32414: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32414: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32414: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32414: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32414: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join (meet ?26 (join ?27 (meet ?26 ?28))) (meet ?28 ?29))
+ [29, 28, 27, 26] by equation_H79 ?26 ?27 ?28 ?29
+32414: Goal:
+32414: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+32414: Order:
+32414: nrkbo
+32414: Leaf order:
+32414: b 3 0 3 1,2,2
+32414: c 3 0 3 2,2,2
+32414: a 5 0 5 1,2
+32414: join 17 2 4 0,2,2
+32414: meet 20 2 5 0,2
+NO CLASH, using fixed ground order
+32415: Facts:
+32415: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32415: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32415: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32415: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32415: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32415: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32415: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32415: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32415: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join (meet ?26 (join ?27 (meet ?26 ?28))) (meet ?28 ?29))
+ [29, 28, 27, 26] by equation_H79 ?26 ?27 ?28 ?29
+32415: Goal:
+32415: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+32415: Order:
+32415: kbo
+32415: Leaf order:
+32415: b 3 0 3 1,2,2
+32415: c 3 0 3 2,2,2
+32415: a 5 0 5 1,2
+32415: join 17 2 4 0,2,2
+32415: meet 20 2 5 0,2
+NO CLASH, using fixed ground order
+32416: Facts:
+32416: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32416: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32416: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32416: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32416: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32416: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32416: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32416: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32416: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =?=
+ meet ?26 (join (meet ?26 (join ?27 (meet ?26 ?28))) (meet ?28 ?29))
+ [29, 28, 27, 26] by equation_H79 ?26 ?27 ?28 ?29
+32416: Goal:
+32416: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ join (meet a (join c (meet a b))) (meet a (join b (meet a c)))
+ [] by prove_H69
+32416: Order:
+32416: lpo
+32416: Leaf order:
+32416: b 3 0 3 1,2,2
+32416: c 3 0 3 2,2,2
+32416: a 5 0 5 1,2
+32416: join 17 2 4 0,2,2
+32416: meet 20 2 5 0,2
+% SZS status Timeout for LAT118-1.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+32445: Facts:
+32445: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32445: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32445: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32445: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32445: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32445: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32445: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32445: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32445: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?28 (meet ?26 ?27)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H22 ?26 ?27 ?28
+32445: Goal:
+32445: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+32445: Order:
+32445: kbo
+32445: Leaf order:
+32445: b 3 0 3 1,2,2
+32445: c 3 0 3 2,2,2,2
+32445: a 6 0 6 1,2
+32445: join 17 2 4 0,2,2
+32445: meet 21 2 6 0,2
+NO CLASH, using fixed ground order
+32446: Facts:
+32446: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32446: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32446: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32446: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32446: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32446: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32446: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32446: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32446: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?28 (meet ?26 ?27)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H22 ?26 ?27 ?28
+32446: Goal:
+32446: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+32446: Order:
+32446: lpo
+32446: Leaf order:
+32446: b 3 0 3 1,2,2
+32446: c 3 0 3 2,2,2,2
+32446: a 6 0 6 1,2
+32446: join 17 2 4 0,2,2
+32446: meet 21 2 6 0,2
+32444: Facts:
+32444: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32444: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32444: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32444: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32444: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32444: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32444: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32444: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32444: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?28 (meet ?26 ?27)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H22 ?26 ?27 ?28
+32444: Goal:
+32444: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+32444: Order:
+32444: nrkbo
+32444: Leaf order:
+32444: b 3 0 3 1,2,2
+32444: c 3 0 3 2,2,2,2
+32444: a 6 0 6 1,2
+32444: join 17 2 4 0,2,2
+32444: meet 21 2 6 0,2
+% SZS status Timeout for LAT142-1.p
+NO CLASH, using fixed ground order
+32541: Facts:
+32541: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32541: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32541: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32541: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32541: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32541: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32541: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32541: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32541: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 ?29))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
+32541: Goal:
+32541: Id : 1, {_}:
+ meet a (meet b (join c (meet a d)))
+ =<=
+ meet a (meet b (join c (meet d (join a (meet b c)))))
+ [] by prove_H45
+32541: Order:
+32541: nrkbo
+32541: Leaf order:
+32541: d 2 0 2 2,2,2,2,2
+32541: b 3 0 3 1,2,2
+32541: c 3 0 3 1,2,2,2
+32541: a 4 0 4 1,2
+32541: join 16 2 3 0,2,2,2
+32541: meet 21 2 7 0,2
+NO CLASH, using fixed ground order
+32542: Facts:
+32542: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32542: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32542: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32542: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32542: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32542: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32542: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32542: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32542: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 ?29))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
+32542: Goal:
+32542: Id : 1, {_}:
+ meet a (meet b (join c (meet a d)))
+ =<=
+ meet a (meet b (join c (meet d (join a (meet b c)))))
+ [] by prove_H45
+32542: Order:
+32542: kbo
+32542: Leaf order:
+32542: d 2 0 2 2,2,2,2,2
+32542: b 3 0 3 1,2,2
+32542: c 3 0 3 1,2,2,2
+32542: a 4 0 4 1,2
+32542: join 16 2 3 0,2,2,2
+32542: meet 21 2 7 0,2
+NO CLASH, using fixed ground order
+32543: Facts:
+32543: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32543: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32543: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32543: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32543: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32543: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32543: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32543: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32543: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 ?29))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29
+32543: Goal:
+32543: Id : 1, {_}:
+ meet a (meet b (join c (meet a d)))
+ =>=
+ meet a (meet b (join c (meet d (join a (meet b c)))))
+ [] by prove_H45
+32543: Order:
+32543: lpo
+32543: Leaf order:
+32543: d 2 0 2 2,2,2,2,2
+32543: b 3 0 3 1,2,2
+32543: c 3 0 3 1,2,2,2
+32543: a 4 0 4 1,2
+32543: join 16 2 3 0,2,2,2
+32543: meet 21 2 7 0,2
+% SZS status Timeout for LAT147-1.p
+NO CLASH, using fixed ground order
+32564: Facts:
+32564: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32564: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32564: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32564: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32564: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32564: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32564: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32564: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32564: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?27 (join ?29 (meet ?26 ?28)))))
+ [29, 28, 27, 26] by equation_H42 ?26 ?27 ?28 ?29
+32564: Goal:
+32564: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+32564: Order:
+32564: nrkbo
+32564: Leaf order:
+32564: b 3 0 3 1,2,2
+32564: c 3 0 3 2,2,2,2
+32564: a 6 0 6 1,2
+32564: join 18 2 4 0,2,2
+32564: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+32565: Facts:
+32565: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32565: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32565: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32565: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32565: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32565: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32565: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32565: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32565: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?27 (join ?29 (meet ?26 ?28)))))
+ [29, 28, 27, 26] by equation_H42 ?26 ?27 ?28 ?29
+32565: Goal:
+32565: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+32565: Order:
+32565: kbo
+32565: Leaf order:
+32565: b 3 0 3 1,2,2
+32565: c 3 0 3 2,2,2,2
+32565: a 6 0 6 1,2
+32565: join 18 2 4 0,2,2
+32565: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+32566: Facts:
+32566: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32566: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32566: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32566: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32566: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32566: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32566: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32566: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32566: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join ?27 (join ?29 (meet ?26 ?28)))))
+ [29, 28, 27, 26] by equation_H42 ?26 ?27 ?28 ?29
+32566: Goal:
+32566: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+32566: Order:
+32566: lpo
+32566: Leaf order:
+32566: b 3 0 3 1,2,2
+32566: c 3 0 3 2,2,2,2
+32566: a 6 0 6 1,2
+32566: join 18 2 4 0,2,2
+32566: meet 20 2 6 0,2
+% SZS status Timeout for LAT154-1.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+32589: Facts:
+32589: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32589: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32589: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32589: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32589: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32589: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32589: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32589: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32589: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
+ [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
+32589: Goal:
+32589: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+32589: Order:
+32589: kbo
+32589: Leaf order:
+32589: a 4 0 4 1,2
+32589: b 4 0 4 1,2,2
+32589: c 4 0 4 2,2,2,2
+32589: join 18 2 4 0,2,2
+32589: meet 20 2 6 0,2
+32588: Facts:
+32588: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32588: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32588: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32588: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32588: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32588: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32588: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32588: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32588: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
+ [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
+32588: Goal:
+32588: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+32588: Order:
+32588: nrkbo
+32588: Leaf order:
+32588: a 4 0 4 1,2
+32588: b 4 0 4 1,2,2
+32588: c 4 0 4 2,2,2,2
+32588: join 18 2 4 0,2,2
+32588: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+32590: Facts:
+32590: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32590: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32590: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32590: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32590: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32590: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32590: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32590: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32590: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =?=
+ meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29))))
+ [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29
+32590: Goal:
+32590: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+32590: Order:
+32590: lpo
+32590: Leaf order:
+32590: a 4 0 4 1,2
+32590: b 4 0 4 1,2,2
+32590: c 4 0 4 2,2,2,2
+32590: join 18 2 4 0,2,2
+32590: meet 20 2 6 0,2
+% SZS status Timeout for LAT155-1.p
+NO CLASH, using fixed ground order
+32615: Facts:
+32615: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32615: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32615: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32615: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32615: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32615: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32615: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32615: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32615: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29))))
+ [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29
+32615: Goal:
+32615: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H58
+32615: Order:
+32615: nrkbo
+32615: Leaf order:
+32615: c 2 0 2 2,2,2
+32615: a 4 0 4 1,2
+32615: b 4 0 4 1,2,2
+32615: meet 18 2 4 0,2
+32615: join 18 2 4 0,2,2
+NO CLASH, using fixed ground order
+32616: Facts:
+32616: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32616: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32616: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32616: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32616: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32616: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32616: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32616: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32616: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29))))
+ [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29
+32616: Goal:
+32616: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H58
+32616: Order:
+32616: kbo
+32616: Leaf order:
+32616: c 2 0 2 2,2,2
+32616: a 4 0 4 1,2
+32616: b 4 0 4 1,2,2
+32616: meet 18 2 4 0,2
+32616: join 18 2 4 0,2,2
+NO CLASH, using fixed ground order
+32617: Facts:
+32617: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+32617: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+32617: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+32617: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+32617: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+32617: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+32617: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+32617: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+32617: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =?=
+ join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29))))
+ [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29
+32617: Goal:
+32617: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H58
+32617: Order:
+32617: lpo
+32617: Leaf order:
+32617: c 2 0 2 2,2,2
+32617: a 4 0 4 1,2
+32617: b 4 0 4 1,2,2
+32617: meet 18 2 4 0,2
+32617: join 18 2 4 0,2,2
+% SZS status Timeout for LAT170-1.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+32640: Facts:
+32640: Id : 2, {_}:
+ add ?2 ?3 =?= add ?3 ?2
+ [3, 2] by commutativity_for_addition ?2 ?3
+32640: Id : 3, {_}:
+ add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
+ [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
+32640: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
+32640: Id : 5, {_}:
+ add ?11 additive_identity =>= ?11
+ [11] by right_additive_identity ?11
+32640: Id : 6, {_}:
+ multiply additive_identity ?13 =>= additive_identity
+ [13] by left_multiplicative_zero ?13
+32640: Id : 7, {_}:
+ multiply ?15 additive_identity =>= additive_identity
+ [15] by right_multiplicative_zero ?15
+32640: Id : 8, {_}:
+ add (additive_inverse ?17) ?17 =>= additive_identity
+ [17] by left_additive_inverse ?17
+32640: Id : 9, {_}:
+ add ?19 (additive_inverse ?19) =>= additive_identity
+ [19] by right_additive_inverse ?19
+32640: Id : 10, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+32640: Id : 11, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+32640: Id : 12, {_}:
+ additive_inverse (additive_inverse ?29) =>= ?29
+ [29] by additive_inverse_additive_inverse ?29
+32640: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+32640: Id : 14, {_}:
+ associator ?34 ?35 ?36
+ =<=
+ add (multiply (multiply ?34 ?35) ?36)
+ (additive_inverse (multiply ?34 (multiply ?35 ?36)))
+ [36, 35, 34] by associator ?34 ?35 ?36
+NO CLASH, using fixed ground order
+32641: Facts:
+32641: Id : 2, {_}:
+ add ?2 ?3 =?= add ?3 ?2
+ [3, 2] by commutativity_for_addition ?2 ?3
+32641: Id : 3, {_}:
+ add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
+ [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
+32641: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
+32641: Id : 5, {_}:
+ add ?11 additive_identity =>= ?11
+ [11] by right_additive_identity ?11
+32641: Id : 6, {_}:
+ multiply additive_identity ?13 =>= additive_identity
+ [13] by left_multiplicative_zero ?13
+32641: Id : 7, {_}:
+ multiply ?15 additive_identity =>= additive_identity
+ [15] by right_multiplicative_zero ?15
+32641: Id : 8, {_}:
+ add (additive_inverse ?17) ?17 =>= additive_identity
+ [17] by left_additive_inverse ?17
+32641: Id : 9, {_}:
+ add ?19 (additive_inverse ?19) =>= additive_identity
+ [19] by right_additive_inverse ?19
+32641: Id : 10, {_}:
+ multiply ?21 (add ?22 ?23)
+ =>=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+32641: Id : 11, {_}:
+ multiply (add ?25 ?26) ?27
+ =>=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+32641: Id : 12, {_}:
+ additive_inverse (additive_inverse ?29) =>= ?29
+ [29] by additive_inverse_additive_inverse ?29
+32641: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+32641: Id : 14, {_}:
+ associator ?34 ?35 ?36
+ =>=
+ add (multiply (multiply ?34 ?35) ?36)
+ (additive_inverse (multiply ?34 (multiply ?35 ?36)))
+ [36, 35, 34] by associator ?34 ?35 ?36
+32641: Id : 15, {_}:
+ commutator ?38 ?39
+ =<=
+ add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
+ [39, 38] by commutator ?38 ?39
+32641: Goal:
+32641: Id : 1, {_}:
+ multiply
+ (multiply (multiply (associator x x y) (associator x x y)) x)
+ (multiply (associator x x y) (associator x x y))
+ =>=
+ additive_identity
+ [] by prove_conjecture_2
+32641: Order:
+32641: lpo
+32641: Leaf order:
+32641: y 4 0 4 3,1,1,1,2
+32641: additive_identity 9 0 1 3
+32641: x 9 0 9 1,1,1,1,2
+32641: additive_inverse 6 1 0
+32641: commutator 1 2 0
+32641: add 16 2 0
+32641: multiply 22 2 4 0,2
+32641: associator 5 3 4 0,1,1,1,2
+32639: Facts:
+32639: Id : 2, {_}:
+ add ?2 ?3 =?= add ?3 ?2
+ [3, 2] by commutativity_for_addition ?2 ?3
+32639: Id : 3, {_}:
+ add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7
+ [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
+32639: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
+32639: Id : 5, {_}:
+ add ?11 additive_identity =>= ?11
+ [11] by right_additive_identity ?11
+32639: Id : 6, {_}:
+ multiply additive_identity ?13 =>= additive_identity
+ [13] by left_multiplicative_zero ?13
+32639: Id : 7, {_}:
+ multiply ?15 additive_identity =>= additive_identity
+ [15] by right_multiplicative_zero ?15
+32639: Id : 8, {_}:
+ add (additive_inverse ?17) ?17 =>= additive_identity
+ [17] by left_additive_inverse ?17
+32639: Id : 9, {_}:
+ add ?19 (additive_inverse ?19) =>= additive_identity
+ [19] by right_additive_inverse ?19
+32639: Id : 10, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+32639: Id : 11, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+32639: Id : 12, {_}:
+ additive_inverse (additive_inverse ?29) =>= ?29
+ [29] by additive_inverse_additive_inverse ?29
+32639: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+32639: Id : 14, {_}:
+ associator ?34 ?35 ?36
+ =<=
+ add (multiply (multiply ?34 ?35) ?36)
+ (additive_inverse (multiply ?34 (multiply ?35 ?36)))
+ [36, 35, 34] by associator ?34 ?35 ?36
+32639: Id : 15, {_}:
+ commutator ?38 ?39
+ =<=
+ add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
+ [39, 38] by commutator ?38 ?39
+32639: Goal:
+32639: Id : 1, {_}:
+ multiply
+ (multiply (multiply (associator x x y) (associator x x y)) x)
+ (multiply (associator x x y) (associator x x y))
+ =>=
+ additive_identity
+ [] by prove_conjecture_2
+32639: Order:
+32639: nrkbo
+32639: Leaf order:
+32639: y 4 0 4 3,1,1,1,2
+32639: additive_identity 9 0 1 3
+32639: x 9 0 9 1,1,1,1,2
+32639: additive_inverse 6 1 0
+32639: commutator 1 2 0
+32639: add 16 2 0
+32639: multiply 22 2 4 0,2
+32639: associator 5 3 4 0,1,1,1,2
+32640: Id : 15, {_}:
+ commutator ?38 ?39
+ =<=
+ add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
+ [39, 38] by commutator ?38 ?39
+32640: Goal:
+32640: Id : 1, {_}:
+ multiply
+ (multiply (multiply (associator x x y) (associator x x y)) x)
+ (multiply (associator x x y) (associator x x y))
+ =>=
+ additive_identity
+ [] by prove_conjecture_2
+32640: Order:
+32640: kbo
+32640: Leaf order:
+32640: y 4 0 4 3,1,1,1,2
+32640: additive_identity 9 0 1 3
+32640: x 9 0 9 1,1,1,1,2
+32640: additive_inverse 6 1 0
+32640: commutator 1 2 0
+32640: add 16 2 0
+32640: multiply 22 2 4 0,2
+32640: associator 5 3 4 0,1,1,1,2
+% SZS status Timeout for RNG031-6.p
+NO CLASH, using fixed ground order
+32666: Facts:
+32666: Id : 2, {_}:
+ multiply (additive_inverse ?2) (additive_inverse ?3)
+ =>=
+ multiply ?2 ?3
+ [3, 2] by product_of_inverses ?2 ?3
+32666: Id : 3, {_}:
+ multiply (additive_inverse ?5) ?6
+ =>=
+ additive_inverse (multiply ?5 ?6)
+ [6, 5] by inverse_product1 ?5 ?6
+32666: Id : 4, {_}:
+ multiply ?8 (additive_inverse ?9)
+ =>=
+ additive_inverse (multiply ?8 ?9)
+ [9, 8] by inverse_product2 ?8 ?9
+32666: Id : 5, {_}:
+ multiply ?11 (add ?12 (additive_inverse ?13))
+ =<=
+ add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
+ [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
+32666: Id : 6, {_}:
+ multiply (add ?15 (additive_inverse ?16)) ?17
+ =<=
+ add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
+ [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
+32666: Id : 7, {_}:
+ multiply (additive_inverse ?19) (add ?20 ?21)
+ =<=
+ add (additive_inverse (multiply ?19 ?20))
+ (additive_inverse (multiply ?19 ?21))
+ [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
+32666: Id : 8, {_}:
+ multiply (add ?23 ?24) (additive_inverse ?25)
+ =<=
+ add (additive_inverse (multiply ?23 ?25))
+ (additive_inverse (multiply ?24 ?25))
+ [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
+32666: Id : 9, {_}:
+ add ?27 ?28 =?= add ?28 ?27
+ [28, 27] by commutativity_for_addition ?27 ?28
+32666: Id : 10, {_}:
+ add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32
+ [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
+32666: Id : 11, {_}:
+ add additive_identity ?34 =>= ?34
+ [34] by left_additive_identity ?34
+32666: Id : 12, {_}:
+ add ?36 additive_identity =>= ?36
+ [36] by right_additive_identity ?36
+32666: Id : 13, {_}:
+ multiply additive_identity ?38 =>= additive_identity
+ [38] by left_multiplicative_zero ?38
+32666: Id : 14, {_}:
+ multiply ?40 additive_identity =>= additive_identity
+ [40] by right_multiplicative_zero ?40
+32666: Id : 15, {_}:
+ add (additive_inverse ?42) ?42 =>= additive_identity
+ [42] by left_additive_inverse ?42
+32666: Id : 16, {_}:
+ add ?44 (additive_inverse ?44) =>= additive_identity
+ [44] by right_additive_inverse ?44
+32666: Id : 17, {_}:
+ multiply ?46 (add ?47 ?48)
+ =<=
+ add (multiply ?46 ?47) (multiply ?46 ?48)
+ [48, 47, 46] by distribute1 ?46 ?47 ?48
+32666: Id : 18, {_}:
+ multiply (add ?50 ?51) ?52
+ =<=
+ add (multiply ?50 ?52) (multiply ?51 ?52)
+ [52, 51, 50] by distribute2 ?50 ?51 ?52
+32666: Id : 19, {_}:
+ additive_inverse (additive_inverse ?54) =>= ?54
+ [54] by additive_inverse_additive_inverse ?54
+32666: Id : 20, {_}:
+ multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57)
+ [57, 56] by right_alternative ?56 ?57
+32666: Id : 21, {_}:
+ associator ?59 ?60 ?61
+ =<=
+ add (multiply (multiply ?59 ?60) ?61)
+ (additive_inverse (multiply ?59 (multiply ?60 ?61)))
+ [61, 60, 59] by associator ?59 ?60 ?61
+32666: Id : 22, {_}:
+ commutator ?63 ?64
+ =<=
+ add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
+ [64, 63] by commutator ?63 ?64
+32666: Goal:
+32666: Id : 1, {_}:
+ multiply
+ (multiply (multiply (associator x x y) (associator x x y)) x)
+ (multiply (associator x x y) (associator x x y))
+ =>=
+ additive_identity
+ [] by prove_conjecture_2
+32666: Order:
+32666: nrkbo
+32666: Leaf order:
+32666: y 4 0 4 3,1,1,1,2
+32666: additive_identity 9 0 1 3
+32666: x 9 0 9 1,1,1,1,2
+32666: additive_inverse 22 1 0
+32666: commutator 1 2 0
+32666: add 24 2 0
+32666: multiply 40 2 4 0,2add
+32666: associator 5 3 4 0,1,1,1,2
+NO CLASH, using fixed ground order
+32667: Facts:
+32667: Id : 2, {_}:
+ multiply (additive_inverse ?2) (additive_inverse ?3)
+ =>=
+ multiply ?2 ?3
+ [3, 2] by product_of_inverses ?2 ?3
+32667: Id : 3, {_}:
+ multiply (additive_inverse ?5) ?6
+ =>=
+ additive_inverse (multiply ?5 ?6)
+ [6, 5] by inverse_product1 ?5 ?6
+32667: Id : 4, {_}:
+ multiply ?8 (additive_inverse ?9)
+ =>=
+ additive_inverse (multiply ?8 ?9)
+ [9, 8] by inverse_product2 ?8 ?9
+32667: Id : 5, {_}:
+ multiply ?11 (add ?12 (additive_inverse ?13))
+ =<=
+ add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
+ [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
+32667: Id : 6, {_}:
+ multiply (add ?15 (additive_inverse ?16)) ?17
+ =<=
+ add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
+ [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
+32667: Id : 7, {_}:
+ multiply (additive_inverse ?19) (add ?20 ?21)
+ =<=
+ add (additive_inverse (multiply ?19 ?20))
+ (additive_inverse (multiply ?19 ?21))
+ [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
+32667: Id : 8, {_}:
+ multiply (add ?23 ?24) (additive_inverse ?25)
+ =<=
+ add (additive_inverse (multiply ?23 ?25))
+ (additive_inverse (multiply ?24 ?25))
+ [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
+32667: Id : 9, {_}:
+ add ?27 ?28 =?= add ?28 ?27
+ [28, 27] by commutativity_for_addition ?27 ?28
+32667: Id : 10, {_}:
+ add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
+ [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
+32667: Id : 11, {_}:
+ add additive_identity ?34 =>= ?34
+ [34] by left_additive_identity ?34
+32667: Id : 12, {_}:
+ add ?36 additive_identity =>= ?36
+ [36] by right_additive_identity ?36
+32667: Id : 13, {_}:
+ multiply additive_identity ?38 =>= additive_identity
+ [38] by left_multiplicative_zero ?38
+32667: Id : 14, {_}:
+ multiply ?40 additive_identity =>= additive_identity
+ [40] by right_multiplicative_zero ?40
+32667: Id : 15, {_}:
+ add (additive_inverse ?42) ?42 =>= additive_identity
+ [42] by left_additive_inverse ?42
+32667: Id : 16, {_}:
+ add ?44 (additive_inverse ?44) =>= additive_identity
+ [44] by right_additive_inverse ?44
+32667: Id : 17, {_}:
+ multiply ?46 (add ?47 ?48)
+ =<=
+ add (multiply ?46 ?47) (multiply ?46 ?48)
+ [48, 47, 46] by distribute1 ?46 ?47 ?48
+32667: Id : 18, {_}:
+ multiply (add ?50 ?51) ?52
+ =<=
+ add (multiply ?50 ?52) (multiply ?51 ?52)
+ [52, 51, 50] by distribute2 ?50 ?51 ?52
+32667: Id : 19, {_}:
+ additive_inverse (additive_inverse ?54) =>= ?54
+ [54] by additive_inverse_additive_inverse ?54
+32667: Id : 20, {_}:
+ multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
+ [57, 56] by right_alternative ?56 ?57
+32667: Id : 21, {_}:
+ associator ?59 ?60 ?61
+ =<=
+ add (multiply (multiply ?59 ?60) ?61)
+ (additive_inverse (multiply ?59 (multiply ?60 ?61)))
+ [61, 60, 59] by associator ?59 ?60 ?61
+32667: Id : 22, {_}:
+ commutator ?63 ?64
+ =<=
+ add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
+ [64, 63] by commutator ?63 ?64
+32667: Goal:
+32667: Id : 1, {_}:
+ multiply
+ (multiply (multiply (associator x x y) (associator x x y)) x)
+ (multiply (associator x x y) (associator x x y))
+ =>=
+ additive_identity
+ [] by prove_conjecture_2
+32667: Order:
+32667: kbo
+32667: Leaf order:
+32667: y 4 0 4 3,1,1,1,2
+32667: additive_identity 9 0 1 3
+32667: x 9 0 9 1,1,1,1,2
+32667: additive_inverse 22 1 0
+32667: commutator 1 2 0
+32667: add 24 2 0
+32667: multiply 40 2 4 0,2add
+32667: associator 5 3 4 0,1,1,1,2
+NO CLASH, using fixed ground order
+32668: Facts:
+32668: Id : 2, {_}:
+ multiply (additive_inverse ?2) (additive_inverse ?3)
+ =>=
+ multiply ?2 ?3
+ [3, 2] by product_of_inverses ?2 ?3
+32668: Id : 3, {_}:
+ multiply (additive_inverse ?5) ?6
+ =>=
+ additive_inverse (multiply ?5 ?6)
+ [6, 5] by inverse_product1 ?5 ?6
+32668: Id : 4, {_}:
+ multiply ?8 (additive_inverse ?9)
+ =>=
+ additive_inverse (multiply ?8 ?9)
+ [9, 8] by inverse_product2 ?8 ?9
+32668: Id : 5, {_}:
+ multiply ?11 (add ?12 (additive_inverse ?13))
+ =>=
+ add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
+ [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
+32668: Id : 6, {_}:
+ multiply (add ?15 (additive_inverse ?16)) ?17
+ =>=
+ add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
+ [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
+32668: Id : 7, {_}:
+ multiply (additive_inverse ?19) (add ?20 ?21)
+ =>=
+ add (additive_inverse (multiply ?19 ?20))
+ (additive_inverse (multiply ?19 ?21))
+ [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
+32668: Id : 8, {_}:
+ multiply (add ?23 ?24) (additive_inverse ?25)
+ =>=
+ add (additive_inverse (multiply ?23 ?25))
+ (additive_inverse (multiply ?24 ?25))
+ [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
+32668: Id : 9, {_}:
+ add ?27 ?28 =?= add ?28 ?27
+ [28, 27] by commutativity_for_addition ?27 ?28
+32668: Id : 10, {_}:
+ add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
+ [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
+32668: Id : 11, {_}:
+ add additive_identity ?34 =>= ?34
+ [34] by left_additive_identity ?34
+32668: Id : 12, {_}:
+ add ?36 additive_identity =>= ?36
+ [36] by right_additive_identity ?36
+32668: Id : 13, {_}:
+ multiply additive_identity ?38 =>= additive_identity
+ [38] by left_multiplicative_zero ?38
+32668: Id : 14, {_}:
+ multiply ?40 additive_identity =>= additive_identity
+ [40] by right_multiplicative_zero ?40
+32668: Id : 15, {_}:
+ add (additive_inverse ?42) ?42 =>= additive_identity
+ [42] by left_additive_inverse ?42
+32668: Id : 16, {_}:
+ add ?44 (additive_inverse ?44) =>= additive_identity
+ [44] by right_additive_inverse ?44
+32668: Id : 17, {_}:
+ multiply ?46 (add ?47 ?48)
+ =>=
+ add (multiply ?46 ?47) (multiply ?46 ?48)
+ [48, 47, 46] by distribute1 ?46 ?47 ?48
+32668: Id : 18, {_}:
+ multiply (add ?50 ?51) ?52
+ =>=
+ add (multiply ?50 ?52) (multiply ?51 ?52)
+ [52, 51, 50] by distribute2 ?50 ?51 ?52
+32668: Id : 19, {_}:
+ additive_inverse (additive_inverse ?54) =>= ?54
+ [54] by additive_inverse_additive_inverse ?54
+32668: Id : 20, {_}:
+ multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
+ [57, 56] by right_alternative ?56 ?57
+32668: Id : 21, {_}:
+ associator ?59 ?60 ?61
+ =>=
+ add (multiply (multiply ?59 ?60) ?61)
+ (additive_inverse (multiply ?59 (multiply ?60 ?61)))
+ [61, 60, 59] by associator ?59 ?60 ?61
+32668: Id : 22, {_}:
+ commutator ?63 ?64
+ =<=
+ add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
+ [64, 63] by commutator ?63 ?64
+32668: Goal:
+32668: Id : 1, {_}:
+ multiply
+ (multiply (multiply (associator x x y) (associator x x y)) x)
+ (multiply (associator x x y) (associator x x y))
+ =>=
+ additive_identity
+ [] by prove_conjecture_2
+32668: Order:
+32668: lpo
+32668: Leaf order:
+32668: y 4 0 4 3,1,1,1,2
+32668: additive_identity 9 0 1 3
+32668: x 9 0 9 1,1,1,1,2
+32668: additive_inverse 22 1 0
+32668: commutator 1 2 0
+32668: add 24 2 0
+32668: multiply 40 2 4 0,2add
+32668: associator 5 3 4 0,1,1,1,2
+% SZS status Timeout for RNG031-7.p
+NO CLASH, using fixed ground order
+32691: Facts:
+32691: Id : 2, {_}: f (g1 ?3) =>= ?3 [3] by clause1 ?3
+32691: Id : 3, {_}: f (g2 ?5) =>= ?5 [5] by clause2 ?5
+32691: Goal:
+32691: Id : 1, {_}: g1 ?1 =<= g2 ?1 [1] by clause3 ?1
+32691: Order:
+32691: nrkbo
+32691: Leaf order:
+32691: f 2 1 0
+32691: g1 2 1 1 0,2
+32691: g2 2 1 1 0,3
+NO CLASH, using fixed ground order
+32692: Facts:
+32692: Id : 2, {_}: f (g1 ?3) =>= ?3 [3] by clause1 ?3
+32692: Id : 3, {_}: f (g2 ?5) =>= ?5 [5] by clause2 ?5
+32692: Goal:
+32692: Id : 1, {_}: g1 ?1 =<= g2 ?1 [1] by clause3 ?1
+32692: Order:
+32692: kbo
+32692: Leaf order:
+32692: f 2 1 0
+32692: g1 2 1 1 0,2
+32692: g2 2 1 1 0,3
+NO CLASH, using fixed ground order
+32693: Facts:
+32693: Id : 2, {_}: f (g1 ?3) =>= ?3 [3] by clause1 ?3
+32693: Id : 3, {_}: f (g2 ?5) =>= ?5 [5] by clause2 ?5
+32693: Goal:
+32693: Id : 1, {_}: g1 ?1 =<= g2 ?1 [1] by clause3 ?1
+32693: Order:
+32693: lpo
+32693: Leaf order:
+32693: f 2 1 0
+32693: g1 2 1 1 0,2
+32693: g2 2 1 1 0,3
+32691: status GaveUp for SYN305-1.p
+32693: status GaveUp for SYN305-1.p
+32692: status GaveUp for SYN305-1.p
+% SZS status Timeout for SYN305-1.p
+CLASH, statistics insufficient
+32698: Facts:
+32698: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+32698: Id : 3, {_}:
+ apply (apply (apply h ?7) ?8) ?9
+ =?=
+ apply (apply (apply ?7 ?8) ?9) ?8
+ [9, 8, 7] by h_definition ?7 ?8 ?9
+32698: Goal:
+32698: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+32698: Order:
+32698: nrkbo
+32698: Leaf order:
+32698: b 1 0 0
+32698: h 1 0 0
+32698: f 3 1 3 0,2,2
+32698: apply 14 2 3 0,2
+CLASH, statistics insufficient
+32699: Facts:
+32699: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+32699: Id : 3, {_}:
+ apply (apply (apply h ?7) ?8) ?9
+ =?=
+ apply (apply (apply ?7 ?8) ?9) ?8
+ [9, 8, 7] by h_definition ?7 ?8 ?9
+32699: Goal:
+32699: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+32699: Order:
+32699: kbo
+32699: Leaf order:
+32699: b 1 0 0
+32699: h 1 0 0
+32699: f 3 1 3 0,2,2
+32699: apply 14 2 3 0,2
+CLASH, statistics insufficient
+32700: Facts:
+32700: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+32700: Id : 3, {_}:
+ apply (apply (apply h ?7) ?8) ?9
+ =?=
+ apply (apply (apply ?7 ?8) ?9) ?8
+ [9, 8, 7] by h_definition ?7 ?8 ?9
+32700: Goal:
+32700: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+32700: Order:
+32700: lpo
+32700: Leaf order:
+32700: b 1 0 0
+32700: h 1 0 0
+32700: f 3 1 3 0,2,2
+32700: apply 14 2 3 0,2
+% SZS status Timeout for COL043-1.p
+CLASH, statistics insufficient
+32721: Facts:
+32721: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+32721: Id : 3, {_}:
+ apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
+ [9, 8, 7] by q_definition ?7 ?8 ?9
+32721: Id : 4, {_}:
+ apply (apply w ?11) ?12 =?= apply (apply ?11 ?12) ?12
+ [12, 11] by w_definition ?11 ?12
+32721: Goal:
+32721: Id : 1, {_}:
+ apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (g ?1)) (h ?1)
+ =<=
+ apply (apply (f ?1) (g ?1)) (apply (apply (f ?1) (g ?1)) (h ?1))
+ [1] by prove_p_combinator ?1
+32721: Order:
+32721: nrkbo
+32721: Leaf order:
+32721: b 1 0 0
+32721: q 1 0 0
+32721: w 1 0 0
+32721: h 2 1 2 0,2,2
+32721: f 3 1 3 0,2,1,1,1,2
+32721: g 4 1 4 0,2,1,1,2
+32721: apply 22 2 8 0,2
+CLASH, statistics insufficient
+32722: Facts:
+32722: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+32722: Id : 3, {_}:
+ apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
+ [9, 8, 7] by q_definition ?7 ?8 ?9
+32722: Id : 4, {_}:
+ apply (apply w ?11) ?12 =?= apply (apply ?11 ?12) ?12
+ [12, 11] by w_definition ?11 ?12
+32722: Goal:
+32722: Id : 1, {_}:
+ apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (g ?1)) (h ?1)
+ =<=
+ apply (apply (f ?1) (g ?1)) (apply (apply (f ?1) (g ?1)) (h ?1))
+ [1] by prove_p_combinator ?1
+32722: Order:
+32722: kbo
+32722: Leaf order:
+32722: b 1 0 0
+32722: q 1 0 0
+32722: w 1 0 0
+32722: h 2 1 2 0,2,2
+32722: f 3 1 3 0,2,1,1,1,2
+32722: g 4 1 4 0,2,1,1,2
+32722: apply 22 2 8 0,2
+CLASH, statistics insufficient
+32723: Facts:
+32723: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+32723: Id : 3, {_}:
+ apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9)
+ [9, 8, 7] by q_definition ?7 ?8 ?9
+32723: Id : 4, {_}:
+ apply (apply w ?11) ?12 =?= apply (apply ?11 ?12) ?12
+ [12, 11] by w_definition ?11 ?12
+32723: Goal:
+32723: Id : 1, {_}:
+ apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (g ?1)) (h ?1)
+ =>=
+ apply (apply (f ?1) (g ?1)) (apply (apply (f ?1) (g ?1)) (h ?1))
+ [1] by prove_p_combinator ?1
+32723: Order:
+32723: lpo
+32723: Leaf order:
+32723: b 1 0 0
+32723: q 1 0 0
+32723: w 1 0 0
+32723: h 2 1 2 0,2,2
+32723: f 3 1 3 0,2,1,1,1,2
+32723: g 4 1 4 0,2,1,1,2
+32723: apply 22 2 8 0,2
+% SZS status Timeout for COL066-1.p
+NO CLASH, using fixed ground order
+32745: Facts:
+32745: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
+32745: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
+32745: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
+32745: Id : 5, {_}:
+ meet ?9 ?10 =?= meet ?10 ?9
+ [10, 9] by commutativity_of_meet ?9 ?10
+32745: Id : 6, {_}:
+ join ?12 ?13 =?= join ?13 ?12
+ [13, 12] by commutativity_of_join ?12 ?13
+32745: Id : 7, {_}:
+ meet (meet ?15 ?16) ?17 =?= meet ?15 (meet ?16 ?17)
+ [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
+32745: Id : 8, {_}:
+ join (join ?19 ?20) ?21 =?= join ?19 (join ?20 ?21)
+ [21, 20, 19] by associativity_of_join ?19 ?20 ?21
+32745: Id : 9, {_}:
+ complement (complement ?23) =>= ?23
+ [23] by complement_involution ?23
+32745: Id : 10, {_}:
+ join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
+ [26, 25] by join_complement ?25 ?26
+32745: Id : 11, {_}:
+ meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
+ [29, 28] by meet_complement ?28 ?29
+32745: Goal:
+32745: Id : 1, {_}:
+ join
+ (complement
+ (join
+ (join (meet (complement a) b)
+ (meet (complement a) (complement b)))
+ (meet a (join (complement a) b)))) (join (complement a) b)
+ =>=
+ n1
+ [] by prove_e3
+32745: Order:
+32745: nrkbo
+32745: Leaf order:
+32745: n0 1 0 0
+32745: n1 2 0 1 3
+32745: b 4 0 4 2,1,1,1,1,2
+32745: a 5 0 5 1,1,1,1,1,1,2
+32745: complement 15 1 6 0,1,2
+32745: meet 12 2 3 0,1,1,1,1,2
+32745: join 17 2 5 0,2
+NO CLASH, using fixed ground order
+32746: Facts:
+32746: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
+32746: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
+32746: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
+32746: Id : 5, {_}:
+ meet ?9 ?10 =?= meet ?10 ?9
+ [10, 9] by commutativity_of_meet ?9 ?10
+32746: Id : 6, {_}:
+ join ?12 ?13 =?= join ?13 ?12
+ [13, 12] by commutativity_of_join ?12 ?13
+32746: Id : 7, {_}:
+ meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
+ [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
+32746: Id : 8, {_}:
+ join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
+ [21, 20, 19] by associativity_of_join ?19 ?20 ?21
+32746: Id : 9, {_}:
+ complement (complement ?23) =>= ?23
+ [23] by complement_involution ?23
+32746: Id : 10, {_}:
+ join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
+ [26, 25] by join_complement ?25 ?26
+NO CLASH, using fixed ground order
+32747: Facts:
+32747: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2
+32747: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4
+32747: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7
+32747: Id : 5, {_}:
+ meet ?9 ?10 =?= meet ?10 ?9
+ [10, 9] by commutativity_of_meet ?9 ?10
+32747: Id : 6, {_}:
+ join ?12 ?13 =?= join ?13 ?12
+ [13, 12] by commutativity_of_join ?12 ?13
+32747: Id : 7, {_}:
+ meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17)
+ [17, 16, 15] by associativity_of_meet ?15 ?16 ?17
+32747: Id : 8, {_}:
+ join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21)
+ [21, 20, 19] by associativity_of_join ?19 ?20 ?21
+32747: Id : 9, {_}:
+ complement (complement ?23) =>= ?23
+ [23] by complement_involution ?23
+32747: Id : 10, {_}:
+ join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26)
+ [26, 25] by join_complement ?25 ?26
+32747: Id : 11, {_}:
+ meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
+ [29, 28] by meet_complement ?28 ?29
+32747: Goal:
+32747: Id : 1, {_}:
+ join
+ (complement
+ (join
+ (join (meet (complement a) b)
+ (meet (complement a) (complement b)))
+ (meet a (join (complement a) b)))) (join (complement a) b)
+ =>=
+ n1
+ [] by prove_e3
+32747: Order:
+32747: lpo
+32747: Leaf order:
+32747: n0 1 0 0
+32747: n1 2 0 1 3
+32747: b 4 0 4 2,1,1,1,1,2
+32747: a 5 0 5 1,1,1,1,1,1,2
+32747: complement 15 1 6 0,1,2
+32747: meet 12 2 3 0,1,1,1,1,2
+32747: join 17 2 5 0,2
+32746: Id : 11, {_}:
+ meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29))
+ [29, 28] by meet_complement ?28 ?29
+32746: Goal:
+32746: Id : 1, {_}:
+ join
+ (complement
+ (join
+ (join (meet (complement a) b)
+ (meet (complement a) (complement b)))
+ (meet a (join (complement a) b)))) (join (complement a) b)
+ =>=
+ n1
+ [] by prove_e3
+32746: Order:
+32746: kbo
+32746: Leaf order:
+32746: n0 1 0 0
+32746: n1 2 0 1 3
+32746: b 4 0 4 2,1,1,1,1,2
+32746: a 5 0 5 1,1,1,1,1,1,2
+32746: complement 15 1 6 0,1,2
+32746: meet 12 2 3 0,1,1,1,1,2
+32746: join 17 2 5 0,2
+% SZS status Timeout for LAT018-1.p
+NO CLASH, using fixed ground order
+301: Facts:
+301: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+301: Goal:
+301: Id : 1, {_}:
+ meet (meet a b) c =>= meet a (meet b c)
+ [] by prove_normal_axioms_3
+301: Order:
+301: nrkbo
+301: Leaf order:
+301: a 2 0 2 1,1,2
+301: b 2 0 2 2,1,2
+301: c 2 0 2 2,2
+301: join 20 2 0
+301: meet 22 2 4 0,2
+NO CLASH, using fixed ground order
+302: Facts:
+302: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+302: Goal:
+302: Id : 1, {_}:
+ meet (meet a b) c =>= meet a (meet b c)
+ [] by prove_normal_axioms_3
+302: Order:
+302: kbo
+302: Leaf order:
+302: a 2 0 2 1,1,2
+302: b 2 0 2 2,1,2
+302: c 2 0 2 2,2
+302: join 20 2 0
+302: meet 22 2 4 0,2
+NO CLASH, using fixed ground order
+303: Facts:
+303: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+303: Goal:
+303: Id : 1, {_}:
+ meet (meet a b) c =>= meet a (meet b c)
+ [] by prove_normal_axioms_3
+303: Order:
+303: lpo
+303: Leaf order:
+303: a 2 0 2 1,1,2
+303: b 2 0 2 2,1,2
+303: c 2 0 2 2,2
+303: join 20 2 0
+303: meet 22 2 4 0,2
+% SZS status Timeout for LAT082-1.p
+NO CLASH, using fixed ground order
+337: Facts:
+337: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+337: Goal:
+337: Id : 1, {_}:
+ join (join a b) c =>= join a (join b c)
+ [] by prove_normal_axioms_6
+337: Order:
+337: nrkbo
+337: Leaf order:
+337: a 2 0 2 1,1,2
+337: b 2 0 2 2,1,2
+337: c 2 0 2 2,2
+337: meet 18 2 0
+337: join 24 2 4 0,2
+NO CLASH, using fixed ground order
+338: Facts:
+338: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+338: Goal:
+338: Id : 1, {_}:
+ join (join a b) c =>= join a (join b c)
+ [] by prove_normal_axioms_6
+338: Order:
+338: kbo
+338: Leaf order:
+338: a 2 0 2 1,1,2
+338: b 2 0 2 2,1,2
+338: c 2 0 2 2,2
+338: meet 18 2 0
+338: join 24 2 4 0,2
+NO CLASH, using fixed ground order
+339: Facts:
+339: Id : 2, {_}:
+ join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)
+ (meet
+ (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))
+ (meet
+ (join
+ (meet ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))
+ (meet ?8
+ (join ?3
+ (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3))))
+ (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3))))
+ (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4))
+ =>=
+ ?3
+ [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8
+339: Goal:
+339: Id : 1, {_}:
+ join (join a b) c =>= join a (join b c)
+ [] by prove_normal_axioms_6
+339: Order:
+339: lpo
+339: Leaf order:
+339: a 2 0 2 1,1,2
+339: b 2 0 2 2,1,2
+339: c 2 0 2 2,2
+339: meet 18 2 0
+339: join 24 2 4 0,2
+% SZS status Timeout for LAT085-1.p
+NO CLASH, using fixed ground order
+1422: Facts:
+1422: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+1422: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+1422: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+1422: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+1422: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+1422: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+1422: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+1422: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+1422: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
+ [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
+1422: Goal:
+1422: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+1422: Order:
+1422: nrkbo
+1422: Leaf order:
+1422: a 4 0 4 1,2
+1422: b 4 0 4 1,2,2
+1422: c 4 0 4 2,2,2,2
+1422: join 16 2 4 0,2,2
+1422: meet 22 2 6 0,2
+NO CLASH, using fixed ground order
+1423: Facts:
+1423: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+1423: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+1423: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+1423: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+1423: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+1423: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+1423: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+1423: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+1423: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
+ [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
+1423: Goal:
+1423: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+1423: Order:
+1423: kbo
+1423: Leaf order:
+1423: a 4 0 4 1,2
+1423: b 4 0 4 1,2,2
+1423: c 4 0 4 2,2,2,2
+1423: join 16 2 4 0,2,2
+1423: meet 22 2 6 0,2
+NO CLASH, using fixed ground order
+1424: Facts:
+1424: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+1424: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+1424: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+1424: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+1424: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+1424: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+1424: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+1424: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+1424: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
+ [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
+1424: Goal:
+1424: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+1424: Order:
+1424: lpo
+1424: Leaf order:
+1424: a 4 0 4 1,2
+1424: b 4 0 4 1,2,2
+1424: c 4 0 4 2,2,2,2
+1424: join 16 2 4 0,2,2
+1424: meet 22 2 6 0,2
+% SZS status Timeout for LAT144-1.p
+NO CLASH, using fixed ground order
+1797: Facts:
+1797: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+1797: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+1797: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+1797: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+1797: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+1797: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+1797: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+1797: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+1797: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
+ [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
+1797: Goal:
+1797: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+1797: Order:
+1797: nrkbo
+1797: Leaf order:
+1797: d 2 0 2 2,2,2,2,2
+1797: b 3 0 3 1,2,2
+1797: c 3 0 3 1,2,2,2
+1797: a 4 0 4 1,2
+1797: join 18 2 5 0,2,2
+1797: meet 19 2 5 0,2
+NO CLASH, using fixed ground order
+1798: Facts:
+1798: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+1798: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+1798: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+1798: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+1798: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+1798: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+1798: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+1798: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+1798: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
+ [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
+1798: Goal:
+1798: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+1798: Order:
+1798: kbo
+1798: Leaf order:
+1798: d 2 0 2 2,2,2,2,2
+1798: b 3 0 3 1,2,2
+1798: c 3 0 3 1,2,2,2
+1798: a 4 0 4 1,2
+1798: join 18 2 5 0,2,2
+1798: meet 19 2 5 0,2
+NO CLASH, using fixed ground order
+1799: Facts:
+1799: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+1799: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+1799: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+1799: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+1799: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+1799: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+1799: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+1799: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+1799: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
+ [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
+1799: Goal:
+1799: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+1799: Order:
+1799: lpo
+1799: Leaf order:
+1799: d 2 0 2 2,2,2,2,2
+1799: b 3 0 3 1,2,2
+1799: c 3 0 3 1,2,2,2
+1799: a 4 0 4 1,2
+1799: join 18 2 5 0,2,2
+1799: meet 19 2 5 0,2
+% SZS status Timeout for LAT150-1.p
+NO CLASH, using fixed ground order
+3353: Facts:
+3353: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+3353: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+3353: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+3353: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+3353: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+3353: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+3353: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+3353: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+3353: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
+ [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
+3353: Goal:
+3353: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+3353: Order:
+3353: nrkbo
+3353: Leaf order:
+3353: d 2 0 2 2,2,2,2,2
+3353: b 3 0 3 1,2,2
+3353: c 3 0 3 1,2,2,2
+3353: a 4 0 4 1,2
+3353: join 18 2 5 0,2,2
+3353: meet 19 2 5 0,2
+NO CLASH, using fixed ground order
+3358: Facts:
+3358: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+3358: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+3358: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+3358: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+3358: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+3358: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+3358: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+3358: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+3358: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
+ [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
+3358: Goal:
+3358: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+3358: Order:
+3358: kbo
+3358: Leaf order:
+3358: d 2 0 2 2,2,2,2,2
+3358: b 3 0 3 1,2,2
+3358: c 3 0 3 1,2,2,2
+3358: a 4 0 4 1,2
+3358: join 18 2 5 0,2,2
+3358: meet 19 2 5 0,2
+NO CLASH, using fixed ground order
+3361: Facts:
+3361: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+3361: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+3361: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+3361: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+3361: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+3361: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+3361: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+3361: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+3361: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28))))
+ [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29
+3361: Goal:
+3361: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+3361: Order:
+3361: lpo
+3361: Leaf order:
+3361: d 2 0 2 2,2,2,2,2
+3361: b 3 0 3 1,2,2
+3361: c 3 0 3 1,2,2,2
+3361: a 4 0 4 1,2
+3361: join 18 2 5 0,2,2
+3361: meet 19 2 5 0,2
+% SZS status Timeout for LAT151-1.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+4534: Facts:
+4534: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+4534: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+4534: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+4534: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+4534: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+4534: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+4534: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+4534: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+4534: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
+ [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
+4534: Goal:
+4534: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+4534: Order:
+4534: kbo
+4534: Leaf order:
+4534: b 3 0 3 1,2,2
+4534: c 3 0 3 2,2,2,2
+4534: a 6 0 6 1,2
+4534: join 18 2 4 0,2,2
+4534: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+4537: Facts:
+4537: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+4537: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+4537: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+4537: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+4537: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+4537: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+4537: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+4537: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+4537: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
+ [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
+4537: Goal:
+4537: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+4537: Order:
+4537: lpo
+4537: Leaf order:
+4537: b 3 0 3 1,2,2
+4537: c 3 0 3 2,2,2,2
+4537: a 6 0 6 1,2
+4537: join 18 2 4 0,2,2
+4537: meet 20 2 6 0,2
+4533: Facts:
+4533: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+4533: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+4533: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+4533: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+4533: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+4533: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+4533: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+4533: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+4533: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
+ [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
+4533: Goal:
+4533: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+4533: Order:
+4533: nrkbo
+4533: Leaf order:
+4533: b 3 0 3 1,2,2
+4533: c 3 0 3 2,2,2,2
+4533: a 6 0 6 1,2
+4533: join 18 2 4 0,2,2
+4533: meet 20 2 6 0,2
+% SZS status Timeout for LAT152-1.p
+NO CLASH, using fixed ground order
+5952: Facts:
+5952: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+5952: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+5952: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+5952: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+5952: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+5952: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+5952: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+5952: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+5952: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
+ [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
+5952: Goal:
+5952: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
+ [] by prove_H7
+5952: Order:
+5952: nrkbo
+5952: Leaf order:
+5952: c 2 0 2 2,2,2,2
+5952: b 4 0 4 1,2,2
+5952: a 6 0 6 1,2
+5952: join 18 2 4 0,2,2
+5952: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+5958: Facts:
+5958: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+5958: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+5958: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+5958: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+5958: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+5958: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+5958: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+5958: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+5958: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
+ [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
+5958: Goal:
+5958: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
+ [] by prove_H7
+5958: Order:
+5958: kbo
+5958: Leaf order:
+5958: c 2 0 2 2,2,2,2
+5958: b 4 0 4 1,2,2
+5958: a 6 0 6 1,2
+5958: join 18 2 4 0,2,2
+5958: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+5959: Facts:
+5959: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+5959: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+5959: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+5959: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+5959: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+5959: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+5959: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+5959: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+5959: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
+ [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
+5959: Goal:
+5959: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
+ [] by prove_H7
+5959: Order:
+5959: lpo
+5959: Leaf order:
+5959: c 2 0 2 2,2,2,2
+5959: b 4 0 4 1,2,2
+5959: a 6 0 6 1,2
+5959: join 18 2 4 0,2,2
+5959: meet 20 2 6 0,2
+% SZS status Timeout for LAT159-1.p
+NO CLASH, using fixed ground order
+7548: Facts:
+7548: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+7548: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+7548: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+7548: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+7548: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+7548: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+7548: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+7548: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+7548: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
+ [28, 27, 26] by equation_H68 ?26 ?27 ?28
+7548: Goal:
+7548: Id : 1, {_}:
+ meet a (meet b (join c d))
+ =<=
+ meet a (meet b (join c (meet a (join d (meet b c)))))
+ [] by prove_H73
+7548: Order:
+7548: nrkbo
+7548: Leaf order:
+7548: d 2 0 2 2,2,2,2
+7548: a 3 0 3 1,2
+7548: b 3 0 3 1,2,2
+7548: c 3 0 3 1,2,2,2
+7548: join 15 2 3 0,2,2,2
+7548: meet 19 2 6 0,2
+NO CLASH, using fixed ground order
+7549: Facts:
+7549: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+7549: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+7549: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+7549: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+7549: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+7549: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+7549: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+7549: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+7549: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
+ [28, 27, 26] by equation_H68 ?26 ?27 ?28
+7549: Goal:
+7549: Id : 1, {_}:
+ meet a (meet b (join c d))
+ =<=
+ meet a (meet b (join c (meet a (join d (meet b c)))))
+ [] by prove_H73
+7549: Order:
+7549: kbo
+7549: Leaf order:
+7549: d 2 0 2 2,2,2,2
+7549: a 3 0 3 1,2
+7549: b 3 0 3 1,2,2
+7549: c 3 0 3 1,2,2,2
+7549: join 15 2 3 0,2,2,2
+7549: meet 19 2 6 0,2
+NO CLASH, using fixed ground order
+7552: Facts:
+7552: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+7552: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+7552: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+7552: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+7552: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+7552: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+7552: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+7552: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+7552: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27))))
+ [28, 27, 26] by equation_H68 ?26 ?27 ?28
+7552: Goal:
+7552: Id : 1, {_}:
+ meet a (meet b (join c d))
+ =<=
+ meet a (meet b (join c (meet a (join d (meet b c)))))
+ [] by prove_H73
+7552: Order:
+7552: lpo
+7552: Leaf order:
+7552: d 2 0 2 2,2,2,2
+7552: a 3 0 3 1,2
+7552: b 3 0 3 1,2,2
+7552: c 3 0 3 1,2,2,2
+7552: join 15 2 3 0,2,2,2
+7552: meet 19 2 6 0,2
+% SZS status Timeout for LAT162-1.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+8627: Facts:
+8627: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+8627: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+8627: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+8627: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+8627: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+8627: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+8627: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+8627: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+8627: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
+8627: Goal:
+8627: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+8627: Order:
+8627: kbo
+8627: Leaf order:
+8627: b 3 0 3 1,2,2
+8627: c 3 0 3 2,2,2,2
+8627: a 6 0 6 1,2
+8627: join 17 2 4 0,2,2
+8627: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+8628: Facts:
+8628: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+8628: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+8628: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+8628: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+8628: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+8628: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+8628: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+8628: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+8628: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
+8628: Goal:
+8628: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+8628: Order:
+8628: lpo
+8628: Leaf order:
+8628: b 3 0 3 1,2,2
+8628: c 3 0 3 2,2,2,2
+8628: a 6 0 6 1,2
+8628: join 17 2 4 0,2,2
+8628: meet 20 2 6 0,2
+8626: Facts:
+8626: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+8626: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+8626: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+8626: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+8626: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+8626: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+8626: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+8626: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+8626: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
+8626: Goal:
+8626: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+8626: Order:
+8626: nrkbo
+8626: Leaf order:
+8626: b 3 0 3 1,2,2
+8626: c 3 0 3 2,2,2,2
+8626: a 6 0 6 1,2
+8626: join 17 2 4 0,2,2
+8626: meet 20 2 6 0,2
+% SZS status Timeout for LAT164-1.p
+NO CLASH, using fixed ground order
+10913: Facts:
+10913: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+10913: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+10913: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+10913: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+10913: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+10913: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+10913: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+10913: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+10913: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?27 (meet ?26 (join ?27 ?28)))
+ (join ?28 (meet ?26 ?27)))
+ [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
+10913: Goal:
+10913: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H58
+10913: Order:
+10913: nrkbo
+10913: Leaf order:
+10913: c 2 0 2 2,2,2
+10913: a 4 0 4 1,2
+10913: b 4 0 4 1,2,2
+10913: meet 17 2 4 0,2
+10913: join 19 2 4 0,2,2
+NO CLASH, using fixed ground order
+10920: Facts:
+10920: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+10920: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+10920: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+10920: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+10920: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+10920: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+10920: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+10920: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+10920: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?27 (meet ?26 (join ?27 ?28)))
+ (join ?28 (meet ?26 ?27)))
+ [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
+10920: Goal:
+10920: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H58
+10920: Order:
+10920: kbo
+10920: Leaf order:
+10920: c 2 0 2 2,2,2
+10920: a 4 0 4 1,2
+10920: b 4 0 4 1,2,2
+10920: meet 17 2 4 0,2
+10920: join 19 2 4 0,2,2
+NO CLASH, using fixed ground order
+10926: Facts:
+10926: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+10926: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+10926: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+10926: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+10926: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+10926: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+10926: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+10926: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+10926: Id : 10, {_}:
+ meet (join ?26 ?27) (join ?26 ?28)
+ =<=
+ join ?26
+ (meet (join ?27 (meet ?26 (join ?27 ?28)))
+ (join ?28 (meet ?26 ?27)))
+ [28, 27, 26] by equation_H21_dual ?26 ?27 ?28
+10926: Goal:
+10926: Id : 1, {_}:
+ meet a (join b c)
+ =<=
+ meet a (join b (meet (join a b) (join c (meet a b))))
+ [] by prove_H58
+10926: Order:
+10926: lpo
+10926: Leaf order:
+10926: c 2 0 2 2,2,2
+10926: a 4 0 4 1,2
+10926: b 4 0 4 1,2,2
+10926: meet 17 2 4 0,2
+10926: join 19 2 4 0,2,2
+% SZS status Timeout for LAT169-1.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+11323: Facts:
+11323: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+11323: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+11323: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+11323: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+11323: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+11323: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+11323: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+11323: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+11323: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
+11323: Goal:
+11323: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+11323: Order:
+11323: kbo
+11323: Leaf order:
+11323: b 3 0 3 1,2,2
+11323: c 3 0 3 2,2,2,2
+11323: a 6 0 6 1,2
+11323: join 18 2 4 0,2,2
+11323: meet 19 2 6 0,2
+NO CLASH, using fixed ground order
+11324: Facts:
+11324: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+11324: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+11324: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+11324: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+11324: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+11324: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+11324: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+11324: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+11324: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
+ =?=
+ join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
+11324: Goal:
+11324: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+11324: Order:
+11324: lpo
+11324: Leaf order:
+11324: b 3 0 3 1,2,2
+11324: c 3 0 3 2,2,2,2
+11324: a 6 0 6 1,2
+11324: join 18 2 4 0,2,2
+11324: meet 19 2 6 0,2
+11322: Facts:
+11322: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+11322: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+11322: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+11322: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+11322: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+11322: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+11322: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+11322: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+11322: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
+11322: Goal:
+11322: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+11322: Order:
+11322: nrkbo
+11322: Leaf order:
+11322: b 3 0 3 1,2,2
+11322: c 3 0 3 2,2,2,2
+11322: a 6 0 6 1,2
+11322: join 18 2 4 0,2,2
+11322: meet 19 2 6 0,2
+% SZS status Timeout for LAT174-1.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+11474: Facts:
+11474: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+11474: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+11474: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+11474: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+11474: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+11474: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+11474: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+11474: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+11474: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+11474: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+11474: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+11474: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+11474: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+11474: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+11474: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+11474: Goal:
+11474: Id : 1, {_}:
+ multiply cz (multiply cx (multiply cy cx))
+ =<=
+ multiply (multiply (multiply cz cx) cy) cx
+ [] by prove_right_moufang
+11474: Order:
+11474: kbo
+11474: Leaf order:
+11474: cz 2 0 2 1,2
+11474: cy 2 0 2 1,2,2,2
+11474: cx 4 0 4 1,2,2
+11474: additive_identity 8 0 0
+11474: additive_inverse 6 1 0
+11474: commutator 1 2 0
+11474: add 16 2 0
+11474: multiply 28 2 6 0,2
+11474: associator 1 3 0
+NO CLASH, using fixed ground order
+11475: Facts:
+11475: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+11475: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+11475: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+11475: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+11475: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+11475: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+11475: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+11475: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+11475: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+11475: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+11475: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+11475: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+11475: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+11475: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+11475: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+11475: Goal:
+11475: Id : 1, {_}:
+ multiply cz (multiply cx (multiply cy cx))
+ =<=
+ multiply (multiply (multiply cz cx) cy) cx
+ [] by prove_right_moufang
+11475: Order:
+11475: lpo
+11475: Leaf order:
+11475: cz 2 0 2 1,2
+11475: cy 2 0 2 1,2,2,2
+11475: cx 4 0 4 1,2,2
+11475: additive_identity 8 0 0
+11475: additive_inverse 6 1 0
+11475: commutator 1 2 0
+11475: add 16 2 0
+11475: multiply 28 2 6 0,2
+11475: associator 1 3 0
+11473: Facts:
+11473: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+11473: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+11473: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+11473: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+11473: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+11473: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+11473: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+11473: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+11473: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+11473: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+11473: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+11473: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+11473: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+11473: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+11473: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+11473: Goal:
+11473: Id : 1, {_}:
+ multiply cz (multiply cx (multiply cy cx))
+ =<=
+ multiply (multiply (multiply cz cx) cy) cx
+ [] by prove_right_moufang
+11473: Order:
+11473: nrkbo
+11473: Leaf order:
+11473: cz 2 0 2 1,2
+11473: cy 2 0 2 1,2,2,2
+11473: cx 4 0 4 1,2,2
+11473: additive_identity 8 0 0
+11473: additive_inverse 6 1 0
+11473: commutator 1 2 0
+11473: add 16 2 0
+11473: multiply 28 2 6 0,2
+11473: associator 1 3 0
+% SZS status Timeout for RNG027-5.p
+NO CLASH, using fixed ground order
+12546: Facts:
+12546: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+12546: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+12546: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+12546: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+12546: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+12546: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+12546: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+12546: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+12546: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+12546: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+12546: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+12546: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+12546: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+12546: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+NO CLASH, using fixed ground order
+12546: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+12546: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+12546: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+12546: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+12546: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+12546: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+12547: Facts:
+12546: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+12546: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+12546: Goal:
+12546: Id : 1, {_}:
+ multiply cz (multiply cx (multiply cy cx))
+ =<=
+ multiply (multiply (multiply cz cx) cy) cx
+ [] by prove_right_moufang
+12546: Order:
+12546: nrkbo
+12546: Leaf order:
+12546: cz 2 0 2 1,2
+12546: cy 2 0 2 1,2,2,2
+12546: cx 4 0 4 1,2,2
+12546: additive_identity 8 0 0
+12546: additive_inverse 22 1 0
+12546: commutator 1 2 0
+12546: add 24 2 0
+12546: multiply 46 2 6 0,2
+12547: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+12547: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+12547: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+12547: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+12547: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+12547: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+12547: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+12546: associator 1 3 0
+12547: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+12547: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+12547: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+12547: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+12547: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+12547: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+12547: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+12547: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+12547: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+12547: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+12547: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+12547: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+12547: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+12547: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+12547: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+12547: Goal:
+12547: Id : 1, {_}:
+ multiply cz (multiply cx (multiply cy cx))
+ =<=
+ multiply (multiply (multiply cz cx) cy) cx
+ [] by prove_right_moufang
+12547: Order:
+12547: kbo
+12547: Leaf order:
+12547: cz 2 0 2 1,2
+12547: cy 2 0 2 1,2,2,2
+12547: cx 4 0 4 1,2,2
+12547: additive_identity 8 0 0
+12547: additive_inverse 22 1 0
+12547: commutator 1 2 0
+12547: add 24 2 0
+12547: multiply 46 2 6 0,2
+12547: associator 1 3 0
+NO CLASH, using fixed ground order
+12548: Facts:
+12548: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+12548: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+12548: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+12548: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+12548: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+12548: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+12548: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+12548: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+12548: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+12548: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+12548: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+12548: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+12548: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+12548: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+12548: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+12548: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+12548: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+12548: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+12548: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =>=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+12548: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =>=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+12548: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =>=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+12548: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =>=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+12548: Goal:
+12548: Id : 1, {_}:
+ multiply cz (multiply cx (multiply cy cx))
+ =<=
+ multiply (multiply (multiply cz cx) cy) cx
+ [] by prove_right_moufang
+12548: Order:
+12548: lpo
+12548: Leaf order:
+12548: cz 2 0 2 1,2
+12548: cy 2 0 2 1,2,2,2
+12548: cx 4 0 4 1,2,2
+12548: additive_identity 8 0 0
+12548: additive_inverse 22 1 0
+12548: commutator 1 2 0
+12548: add 24 2 0
+12548: multiply 46 2 6 0,2
+12548: associator 1 3 0
+% SZS status Timeout for RNG027-7.p
+NO CLASH, using fixed ground order
+14022: Facts:
+14022: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+14022: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+14022: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+14022: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+14022: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+14022: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+14022: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+14022: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+NO CLASH, using fixed ground order
+14022: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+14022: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+14022: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+14022: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+14022: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+14022: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+14022: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+14022: Goal:
+14022: Id : 1, {_}:
+ associator x (multiply x y) z =>= multiply (associator x y z) x
+ [] by prove_right_moufang
+14022: Order:
+14022: nrkbo
+14022: Leaf order:
+14022: y 2 0 2 2,2,2
+14022: z 2 0 2 3,2
+14022: x 4 0 4 1,2
+14022: additive_identity 8 0 0
+14022: additive_inverse 6 1 0
+14022: commutator 1 2 0
+14022: add 16 2 0
+14022: multiply 24 2 2 0,2,2
+14022: associator 3 3 2 0,2
+14023: Facts:
+14023: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+14023: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+14023: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+14023: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+14023: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+14023: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+14023: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+14023: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+14023: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+14023: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+14023: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+14023: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+14023: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+14023: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+14023: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+14023: Goal:
+14023: Id : 1, {_}:
+ associator x (multiply x y) z =>= multiply (associator x y z) x
+ [] by prove_right_moufang
+14023: Order:
+14023: kbo
+14023: Leaf order:
+14023: y 2 0 2 2,2,2
+14023: z 2 0 2 3,2
+14023: x 4 0 4 1,2
+14023: additive_identity 8 0 0
+14023: additive_inverse 6 1 0
+14023: commutator 1 2 0
+14023: add 16 2 0
+14023: multiply 24 2 2 0,2,2
+14023: associator 3 3 2 0,2
+NO CLASH, using fixed ground order
+14025: Facts:
+14025: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+14025: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+14025: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+14025: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+14025: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+14025: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+14025: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+14025: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+14025: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+14025: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+14025: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+14025: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+14025: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+14025: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+14025: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+14025: Goal:
+14025: Id : 1, {_}:
+ associator x (multiply x y) z =>= multiply (associator x y z) x
+ [] by prove_right_moufang
+14025: Order:
+14025: lpo
+14025: Leaf order:
+14025: y 2 0 2 2,2,2
+14025: z 2 0 2 3,2
+14025: x 4 0 4 1,2
+14025: additive_identity 8 0 0
+14025: additive_inverse 6 1 0
+14025: commutator 1 2 0
+14025: add 16 2 0
+14025: multiply 24 2 2 0,2,2
+14025: associator 3 3 2 0,2
+% SZS status Timeout for RNG027-8.p
+NO CLASH, using fixed ground order
+15720: Facts:
+15720: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+15720: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+15720: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+15720: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+15720: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+15720: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+15720: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+15720: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+15720: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+15720: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+15720: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+15720: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+15720: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+15720: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+15720: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+15720: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+15720: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+15720: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+15720: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+15720: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+15720: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+15720: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+15720: Goal:
+15720: Id : 1, {_}:
+ associator x (multiply x y) z =>= multiply (associator x y z) x
+ [] by prove_right_moufang
+15720: Order:
+15720: nrkbo
+15720: Leaf order:
+15720: y 2 0 2 2,2,2
+15720: z 2 0 2 3,2
+15720: x 4 0 4 1,2
+15720: additive_identity 8 0 0
+15720: additive_inverse 22 1 0
+15720: commutator 1 2 0
+15720: add 24 2 0
+15720: multiply 42 2 2 0,2,2
+15720: associator 3 3 2 0,2
+NO CLASH, using fixed ground order
+15721: Facts:
+15721: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+15721: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+15721: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+15721: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+15721: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+15721: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+15721: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+15721: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+15721: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+15721: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+15721: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+15721: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+15721: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+15721: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+15721: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+15721: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+15721: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+15721: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+15721: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+15721: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+15721: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+15721: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+15721: Goal:
+15721: Id : 1, {_}:
+ associator x (multiply x y) z =>= multiply (associator x y z) x
+ [] by prove_right_moufang
+15721: Order:
+15721: kbo
+15721: Leaf order:
+15721: y 2 0 2 2,2,2
+15721: z 2 0 2 3,2
+15721: x 4 0 4 1,2
+15721: additive_identity 8 0 0
+15721: additive_inverse 22 1 0
+15721: commutator 1 2 0
+15721: add 24 2 0
+15721: multiply 42 2 2 0,2,2
+15721: associator 3 3 2 0,2
+NO CLASH, using fixed ground order
+15722: Facts:
+15722: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+15722: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+15722: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+15722: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+15722: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+15722: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+15722: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+15722: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+15722: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+15722: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+15722: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+15722: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+15722: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+15722: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+15722: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+15722: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+15722: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+15722: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+15722: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =>=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+15722: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =>=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+15722: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =>=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+15722: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =>=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+15722: Goal:
+15722: Id : 1, {_}:
+ associator x (multiply x y) z =>= multiply (associator x y z) x
+ [] by prove_right_moufang
+15722: Order:
+15722: lpo
+15722: Leaf order:
+15722: y 2 0 2 2,2,2
+15722: z 2 0 2 3,2
+15722: x 4 0 4 1,2
+15722: additive_identity 8 0 0
+15722: additive_inverse 22 1 0
+15722: commutator 1 2 0
+15722: add 24 2 0
+15722: multiply 42 2 2 0,2,2
+15722: associator 3 3 2 0,2
+% SZS status Timeout for RNG027-9.p
+NO CLASH, using fixed ground order
+16372: Facts:
+16372: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+16372: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+16372: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+16372: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+16372: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+16372: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+16372: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+16372: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+16372: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+16372: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+16372: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+16372: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+16372: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+16372: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+16372: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+16372: Goal:
+16372: Id : 1, {_}:
+ multiply (multiply cx (multiply cy cx)) cz
+ =>=
+ multiply cx (multiply cy (multiply cx cz))
+ [] by prove_left_moufang
+16372: Order:
+16372: nrkbo
+16372: Leaf order:
+16372: cy 2 0 2 1,2,1,2
+16372: cz 2 0 2 2,2
+16372: cx 4 0 4 1,1,2
+16372: additive_identity 8 0 0
+16372: additive_inverse 6 1 0
+16372: commutator 1 2 0
+16372: add 16 2 0
+16372: multiply 28 2 6 0,2
+16372: associator 1 3 0
+NO CLASH, using fixed ground order
+16373: Facts:
+16373: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+16373: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+16373: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+16373: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+16373: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+16373: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+16373: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+16373: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+16373: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+NO CLASH, using fixed ground order
+16374: Facts:
+16374: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+16374: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+16374: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+16374: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+16374: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+16374: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+16374: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+16374: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+16374: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+16373: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+16373: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+16373: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+16373: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+16373: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+16373: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+16373: Goal:
+16373: Id : 1, {_}:
+ multiply (multiply cx (multiply cy cx)) cz
+ =>=
+ multiply cx (multiply cy (multiply cx cz))
+ [] by prove_left_moufang
+16373: Order:
+16373: kbo
+16373: Leaf order:
+16373: cy 2 0 2 1,2,1,2
+16373: cz 2 0 2 2,2
+16373: cx 4 0 4 1,1,2
+16373: additive_identity 8 0 0
+16373: additive_inverse 6 1 0
+16373: commutator 1 2 0
+16373: add 16 2 0
+16373: multiply 28 2 6 0,2
+16373: associator 1 3 0
+16374: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+16374: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+16374: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+16374: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+16374: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+16374: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+16374: Goal:
+16374: Id : 1, {_}:
+ multiply (multiply cx (multiply cy cx)) cz
+ =>=
+ multiply cx (multiply cy (multiply cx cz))
+ [] by prove_left_moufang
+16374: Order:
+16374: lpo
+16374: Leaf order:
+16374: cy 2 0 2 1,2,1,2
+16374: cz 2 0 2 2,2
+16374: cx 4 0 4 1,1,2
+16374: additive_identity 8 0 0
+16374: additive_inverse 6 1 0
+16374: commutator 1 2 0
+16374: add 16 2 0
+16374: multiply 28 2 6 0,2
+16374: associator 1 3 0
+% SZS status Timeout for RNG028-5.p
+NO CLASH, using fixed ground order
+18637: Facts:
+18637: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+18637: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+18637: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+18637: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+18637: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+18637: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+18637: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+18637: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+18637: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+18637: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+18637: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+18637: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+18637: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+18637: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+18637: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+18637: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+18637: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+18637: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+18637: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+18637: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+18637: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+18637: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+18637: Goal:
+18637: Id : 1, {_}:
+ multiply (multiply cx (multiply cy cx)) cz
+ =>=
+ multiply cx (multiply cy (multiply cx cz))
+ [] by prove_left_moufang
+18637: Order:
+18637: nrkbo
+18637: Leaf order:
+18637: cy 2 0 2 1,2,1,2
+18637: cz 2 0 2 2,2
+18637: cx 4 0 4 1,1,2
+18637: additive_identity 8 0 0
+18637: additive_inverse 22 1 0
+18637: commutator 1 2 0
+18637: add 24 2 0
+18637: multiply 46 2 6 0,2
+18637: associator 1 3 0
+NO CLASH, using fixed ground order
+18660: Facts:
+18660: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+18660: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+18660: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+18660: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+18660: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+18660: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+18660: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+18660: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+18660: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+18660: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+18660: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+18660: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+18660: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+18660: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+18660: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+18660: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+18660: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+18660: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+18660: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+18660: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+18660: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+18660: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+18660: Goal:
+18660: Id : 1, {_}:
+ multiply (multiply cx (multiply cy cx)) cz
+ =>=
+ multiply cx (multiply cy (multiply cx cz))
+ [] by prove_left_moufang
+18660: Order:
+18660: kbo
+18660: Leaf order:
+18660: cy 2 0 2 1,2,1,2
+18660: cz 2 0 2 2,2
+18660: cx 4 0 4 1,1,2
+18660: additive_identity 8 0 0
+18660: additive_inverse 22 1 0
+18660: commutator 1 2 0
+18660: add 24 2 0
+18660: multiply 46 2 6 0,2
+18660: associator 1 3 0
+NO CLASH, using fixed ground order
+18670: Facts:
+18670: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+18670: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+18670: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+18670: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+18670: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+18670: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+18670: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+18670: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+18670: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+18670: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+18670: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+18670: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+18670: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+18670: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+18670: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+18670: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+18670: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+18670: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+18670: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =>=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+18670: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =>=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+18670: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =>=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+18670: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =>=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+18670: Goal:
+18670: Id : 1, {_}:
+ multiply (multiply cx (multiply cy cx)) cz
+ =>=
+ multiply cx (multiply cy (multiply cx cz))
+ [] by prove_left_moufang
+18670: Order:
+18670: lpo
+18670: Leaf order:
+18670: cy 2 0 2 1,2,1,2
+18670: cz 2 0 2 2,2
+18670: cx 4 0 4 1,1,2
+18670: additive_identity 8 0 0
+18670: additive_inverse 22 1 0
+18670: commutator 1 2 0
+18670: add 24 2 0
+18670: multiply 46 2 6 0,2
+18670: associator 1 3 0
+% SZS status Timeout for RNG028-7.p
+NO CLASH, using fixed ground order
+20636: Facts:
+20636: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+20636: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+20636: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+20636: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+20636: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+20636: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+20636: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+20636: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+20636: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+20636: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+20636: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+20636: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+20636: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+20636: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+20636: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+20636: Goal:
+20636: Id : 1, {_}:
+ associator x (multiply y x) z =>= multiply x (associator x y z)
+ [] by prove_left_moufang
+20636: Order:
+20636: nrkbo
+20636: Leaf order:
+20636: y 2 0 2 1,2,2
+20636: z 2 0 2 3,2
+20636: x 4 0 4 1,2
+20636: additive_identity 8 0 0
+20636: additive_inverse 6 1 0
+20636: commutator 1 2 0
+20636: add 16 2 0
+20636: multiply 24 2 2 0,2,2
+20636: associator 3 3 2 0,2
+NO CLASH, using fixed ground order
+20637: Facts:
+20637: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+20637: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+20637: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+20637: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+20637: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+20637: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+20637: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+20637: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+20637: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+20637: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+20637: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+20637: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+20637: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+20637: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+20637: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+20637: Goal:
+20637: Id : 1, {_}:
+ associator x (multiply y x) z =>= multiply x (associator x y z)
+ [] by prove_left_moufang
+20637: Order:
+20637: kbo
+20637: Leaf order:
+20637: y 2 0 2 1,2,2
+20637: z 2 0 2 3,2
+20637: x 4 0 4 1,2
+20637: additive_identity 8 0 0
+20637: additive_inverse 6 1 0
+20637: commutator 1 2 0
+20637: add 16 2 0
+20637: multiply 24 2 2 0,2,2
+20637: associator 3 3 2 0,2
+NO CLASH, using fixed ground order
+20638: Facts:
+20638: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+20638: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+20638: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+20638: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+20638: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+20638: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+20638: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+20638: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+20638: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+20638: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+20638: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+20638: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+20638: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+20638: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+20638: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+20638: Goal:
+20638: Id : 1, {_}:
+ associator x (multiply y x) z =>= multiply x (associator x y z)
+ [] by prove_left_moufang
+20638: Order:
+20638: lpo
+20638: Leaf order:
+20638: y 2 0 2 1,2,2
+20638: z 2 0 2 3,2
+20638: x 4 0 4 1,2
+20638: additive_identity 8 0 0
+20638: additive_inverse 6 1 0
+20638: commutator 1 2 0
+20638: add 16 2 0
+20638: multiply 24 2 2 0,2,2
+20638: associator 3 3 2 0,2
+% SZS status Timeout for RNG028-8.p
+NO CLASH, using fixed ground order
+22095: Facts:
+22095: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+22095: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+22095: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+22095: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+22095: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+22095: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+22095: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+22095: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+22095: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+22095: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+22095: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+22095: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+22095: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+22095: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+22095: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+22095: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+22095: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+22095: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+22095: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+22095: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+22095: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+22095: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+22095: Goal:
+22095: Id : 1, {_}:
+ associator x (multiply y x) z =>= multiply x (associator x y z)
+ [] by prove_left_moufang
+22095: Order:
+22095: nrkbo
+22095: Leaf order:
+22095: y 2 0 2 1,2,2
+22095: z 2 0 2 3,2
+22095: x 4 0 4 1,2
+22095: additive_identity 8 0 0
+22095: additive_inverse 22 1 0
+22095: commutator 1 2 0
+22095: add 24 2 0
+22095: multiply 42 2 2 0,2,2
+22095: associator 3 3 2 0,2
+NO CLASH, using fixed ground order
+22098: Facts:
+NO CLASH, using fixed ground order
+22098: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+22098: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+22098: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+22098: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+22098: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+22098: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+22098: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+22098: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+22098: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+22098: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+22098: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+22098: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+22098: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+22098: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+22098: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+22098: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+22098: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+22098: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+22098: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+22098: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+22098: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+22098: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+22098: Goal:
+22098: Id : 1, {_}:
+ associator x (multiply y x) z =>= multiply x (associator x y z)
+ [] by prove_left_moufang
+22098: Order:
+22098: kbo
+22098: Leaf order:
+22098: y 2 0 2 1,2,2
+22098: z 2 0 2 3,2
+22098: x 4 0 4 1,2
+22098: additive_identity 8 0 0
+22098: additive_inverse 22 1 0
+22098: commutator 1 2 0
+22098: add 24 2 0
+22098: multiply 42 2 2 0,2,2
+22098: associator 3 3 2 0,2
+22100: Facts:
+22100: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+22100: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+22100: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+22100: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+22100: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+22100: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+22100: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+22100: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+22100: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+22100: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+22100: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+22100: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+22100: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+22100: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+22100: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+22100: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+22100: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+22100: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+22100: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =>=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+22100: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =>=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+22100: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =>=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+22100: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =>=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+22100: Goal:
+22100: Id : 1, {_}:
+ associator x (multiply y x) z =>= multiply x (associator x y z)
+ [] by prove_left_moufang
+22100: Order:
+22100: lpo
+22100: Leaf order:
+22100: y 2 0 2 1,2,2
+22100: z 2 0 2 3,2
+22100: x 4 0 4 1,2
+22100: additive_identity 8 0 0
+22100: additive_inverse 22 1 0
+22100: commutator 1 2 0
+22100: add 24 2 0
+22100: multiply 42 2 2 0,2,2
+22100: associator 3 3 2 0,2
+% SZS status Timeout for RNG028-9.p
+NO CLASH, using fixed ground order
+23750: Facts:
+23750: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+23750: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+23750: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+23750: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+23750: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+23750: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+23750: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+23750: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+23750: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+23750: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+23750: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+23750: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+23750: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+23750: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+23750: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+23750: Goal:
+23750: Id : 1, {_}:
+ multiply (multiply cx cy) (multiply cz cx)
+ =>=
+ multiply cx (multiply (multiply cy cz) cx)
+ [] by prove_middle_law
+23750: Order:
+23750: nrkbo
+23750: Leaf order:
+23750: cz 2 0 2 1,2,2
+23750: cy 2 0 2 2,1,2
+23750: cx 4 0 4 1,1,2
+23750: additive_identity 8 0 0
+23750: additive_inverse 6 1 0
+23750: commutator 1 2 0
+23750: add 16 2 0
+23750: multiply 28 2 6 0,2
+23750: associator 1 3 0
+NO CLASH, using fixed ground order
+23751: Facts:
+23751: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+23751: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+23751: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+23751: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+23751: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+23751: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+23751: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+23751: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+23751: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+23751: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+23751: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+23751: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+23751: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+23751: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+23751: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+23751: Goal:
+23751: Id : 1, {_}:
+ multiply (multiply cx cy) (multiply cz cx)
+ =>=
+ multiply cx (multiply (multiply cy cz) cx)
+ [] by prove_middle_law
+23751: Order:
+23751: kbo
+23751: Leaf order:
+23751: cz 2 0 2 1,2,2
+23751: cy 2 0 2 2,1,2
+23751: cx 4 0 4 1,1,2
+23751: additive_identity 8 0 0
+23751: additive_inverse 6 1 0
+23751: commutator 1 2 0
+23751: add 16 2 0
+23751: multiply 28 2 6 0,2
+23751: associator 1 3 0
+NO CLASH, using fixed ground order
+23752: Facts:
+23752: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+23752: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+23752: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+23752: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+23752: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+23752: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+23752: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+23752: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+23752: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+23752: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+23752: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+23752: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+23752: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+23752: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+23752: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+23752: Goal:
+23752: Id : 1, {_}:
+ multiply (multiply cx cy) (multiply cz cx)
+ =>=
+ multiply cx (multiply (multiply cy cz) cx)
+ [] by prove_middle_law
+23752: Order:
+23752: lpo
+23752: Leaf order:
+23752: cz 2 0 2 1,2,2
+23752: cy 2 0 2 2,1,2
+23752: cx 4 0 4 1,1,2
+23752: additive_identity 8 0 0
+23752: additive_inverse 6 1 0
+23752: commutator 1 2 0
+23752: add 16 2 0
+23752: multiply 28 2 6 0,2
+23752: associator 1 3 0
+% SZS status Timeout for RNG029-5.p
+NO CLASH, using fixed ground order
+24862: Facts:
+24862: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+24862: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+24862: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+24862: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+24862: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+24862: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+24862: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+24862: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+24862: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+24862: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+24862: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+24862: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+24862: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+24862: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+24862: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+24862: Goal:
+24862: Id : 1, {_}:
+ multiply (multiply x y) (multiply z x)
+ =<=
+ multiply (multiply x (multiply y z)) x
+ [] by prove_middle_moufang
+24862: Order:
+24862: nrkbo
+24862: Leaf order:
+24862: z 2 0 2 1,2,2
+24862: y 2 0 2 2,1,2
+24862: x 4 0 4 1,1,2
+24862: additive_identity 8 0 0
+24862: additive_inverse 6 1 0
+24862: commutator 1 2 0
+24862: add 16 2 0
+24862: multiply 28 2 6 0,2
+24862: associator 1 3 0
+NO CLASH, using fixed ground order
+24863: Facts:
+24863: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+24863: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+24863: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+24863: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+24863: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+24863: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+24863: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+24863: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+24863: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+24863: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+24863: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+24863: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+24863: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+24863: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+24863: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+24863: Goal:
+24863: Id : 1, {_}:
+ multiply (multiply x y) (multiply z x)
+ =<=
+ multiply (multiply x (multiply y z)) x
+ [] by prove_middle_moufang
+24863: Order:
+24863: kbo
+24863: Leaf order:
+24863: z 2 0 2 1,2,2
+24863: y 2 0 2 2,1,2
+24863: x 4 0 4 1,1,2
+24863: additive_identity 8 0 0
+24863: additive_inverse 6 1 0
+24863: commutator 1 2 0
+24863: add 16 2 0
+24863: multiply 28 2 6 0,2
+24863: associator 1 3 0
+NO CLASH, using fixed ground order
+24864: Facts:
+24864: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+24864: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+24864: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+24864: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+24864: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+24864: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+24864: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+24864: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+24864: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+24864: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+24864: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+24864: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+24864: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+24864: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+24864: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+24864: Goal:
+24864: Id : 1, {_}:
+ multiply (multiply x y) (multiply z x)
+ =<=
+ multiply (multiply x (multiply y z)) x
+ [] by prove_middle_moufang
+24864: Order:
+24864: lpo
+24864: Leaf order:
+24864: z 2 0 2 1,2,2
+24864: y 2 0 2 2,1,2
+24864: x 4 0 4 1,1,2
+24864: additive_identity 8 0 0
+24864: additive_inverse 6 1 0
+24864: commutator 1 2 0
+24864: add 16 2 0
+24864: multiply 28 2 6 0,2
+24864: associator 1 3 0
+% SZS status Timeout for RNG029-6.p
+NO CLASH, using fixed ground order
+26436: Facts:
+26436: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+26436: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+26436: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+26436: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+26436: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+26436: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+26436: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+26436: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+26436: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+26436: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+26436: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+26436: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+26436: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+26436: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+26436: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+26436: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+26436: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+26436: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+26436: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+26436: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+26436: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+26436: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+26436: Goal:
+26436: Id : 1, {_}:
+ multiply (multiply x y) (multiply z x)
+ =<=
+ multiply (multiply x (multiply y z)) x
+ [] by prove_middle_moufang
+26436: Order:
+26436: nrkbo
+26436: Leaf order:
+26436: z 2 0 2 1,2,2
+26436: y 2 0 2 2,1,2
+26436: x 4 0 4 1,1,2
+26436: additive_identity 8 0 0
+26436: additive_inverse 22 1 0
+26436: commutator 1 2 0
+26436: add 24 2 0
+26436: multiply 46 2 6 0,2
+26436: associator 1 3 0
+NO CLASH, using fixed ground order
+26437: Facts:
+26437: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+26437: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+26437: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+26437: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+26437: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+26437: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+NO CLASH, using fixed ground order
+26438: Facts:
+26438: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+26438: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+26438: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+26438: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+26438: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+26438: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+26438: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+26438: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+26438: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+26438: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+26438: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+26438: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+26438: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+26438: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+26438: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+26438: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+26438: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+26438: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+26438: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =>=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+26438: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =>=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+26438: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =>=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+26438: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =>=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+26438: Goal:
+26438: Id : 1, {_}:
+ multiply (multiply x y) (multiply z x)
+ =<=
+ multiply (multiply x (multiply y z)) x
+ [] by prove_middle_moufang
+26438: Order:
+26438: lpo
+26438: Leaf order:
+26438: z 2 0 2 1,2,2
+26438: y 2 0 2 2,1,2
+26438: x 4 0 4 1,1,2
+26438: additive_identity 8 0 0
+26438: additive_inverse 22 1 0
+26438: commutator 1 2 0
+26438: add 24 2 0
+26438: multiply 46 2 6 0,2
+26438: associator 1 3 0
+26437: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+26437: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+26437: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+26437: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+26437: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+26437: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+26437: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+26437: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+26437: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+26437: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+26437: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+26437: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+26437: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+26437: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+26437: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+26437: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+26437: Goal:
+26437: Id : 1, {_}:
+ multiply (multiply x y) (multiply z x)
+ =<=
+ multiply (multiply x (multiply y z)) x
+ [] by prove_middle_moufang
+26437: Order:
+26437: kbo
+26437: Leaf order:
+26437: z 2 0 2 1,2,2
+26437: y 2 0 2 2,1,2
+26437: x 4 0 4 1,1,2
+26437: additive_identity 8 0 0
+26437: additive_inverse 22 1 0
+26437: commutator 1 2 0
+26437: add 24 2 0
+26437: multiply 46 2 6 0,2
+26437: associator 1 3 0
+% SZS status Timeout for RNG029-7.p
+NO CLASH, using fixed ground order
+28162: Facts:
+28162: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+28162: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+28162: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+28162: Id : 5, {_}: add c d =>= d [] by absorbtion
+28162: Goal:
+28162: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+28162: Order:
+28162: nrkbo
+28162: Leaf order:
+28162: c 1 0 0
+28162: d 2 0 0
+28162: a 2 0 2 1,1,1,2
+28162: b 3 0 3 1,2,1,1,2
+28162: negate 9 1 5 0,1,2
+28162: add 13 2 3 0,2
+NO CLASH, using fixed ground order
+28167: Facts:
+28167: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+28167: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+28167: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+28167: Id : 5, {_}: add c d =>= d [] by absorbtion
+28167: Goal:
+28167: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+28167: Order:
+28167: kbo
+28167: Leaf order:
+28167: c 1 0 0
+28167: d 2 0 0
+28167: a 2 0 2 1,1,1,2
+28167: b 3 0 3 1,2,1,1,2
+28167: negate 9 1 5 0,1,2
+28167: add 13 2 3 0,2
+NO CLASH, using fixed ground order
+28168: Facts:
+28168: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+28168: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+28168: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+28168: Id : 5, {_}: add c d =>= d [] by absorbtion
+28168: Goal:
+28168: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+28168: Order:
+28168: lpo
+28168: Leaf order:
+28168: c 1 0 0
+28168: d 2 0 0
+28168: a 2 0 2 1,1,1,2
+28168: b 3 0 3 1,2,1,1,2
+28168: negate 9 1 5 0,1,2
+28168: add 13 2 3 0,2
+% SZS status Timeout for ROB006-1.p
+NO CLASH, using fixed ground order
+30020: Facts:
+30020: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
+30020: Id : 3, {_}:
+ add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8)
+ [8, 7, 6] by associativity_of_add ?6 ?7 ?8
+30020: Id : 4, {_}:
+ negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
+ =>=
+ ?10
+ [11, 10] by robbins_axiom ?10 ?11
+30020: Id : 5, {_}: add c d =>= d [] by absorbtion
+30020: Goal:
+30020: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
+30020: Order:
+30020: nrkbo
+30020: Leaf order:
+30020: c 1 0 0
+30020: d 2 0 0
+30020: negate 4 1 0
+30020: add 11 2 1 0,2
+NO CLASH, using fixed ground order
+30021: Facts:
+30021: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
+30021: Id : 3, {_}:
+ add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
+ [8, 7, 6] by associativity_of_add ?6 ?7 ?8
+30021: Id : 4, {_}:
+ negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
+ =>=
+ ?10
+ [11, 10] by robbins_axiom ?10 ?11
+30021: Id : 5, {_}: add c d =>= d [] by absorbtion
+30021: Goal:
+30021: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
+30021: Order:
+30021: kbo
+30021: Leaf order:
+30021: c 1 0 0
+30021: d 2 0 0
+30021: negate 4 1 0
+30021: add 11 2 1 0,2
+NO CLASH, using fixed ground order
+30022: Facts:
+30022: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
+30022: Id : 3, {_}:
+ add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
+ [8, 7, 6] by associativity_of_add ?6 ?7 ?8
+30022: Id : 4, {_}:
+ negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
+ =>=
+ ?10
+ [11, 10] by robbins_axiom ?10 ?11
+30022: Id : 5, {_}: add c d =>= d [] by absorbtion
+30022: Goal:
+30022: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
+30022: Order:
+30022: lpo
+30022: Leaf order:
+30022: c 1 0 0
+30022: d 2 0 0
+30022: negate 4 1 0
+30022: add 11 2 1 0,2
+% SZS status Timeout for ROB006-2.p
+NO CLASH, using fixed ground order
+31074: Facts:
+31074: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+31074: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+31074: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+31074: Id : 5, {_}: add c d =>= c [] by identity_constant
+31074: Goal:
+31074: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+31074: Order:
+31074: nrkbo
+31074: Leaf order:
+31074: d 1 0 0
+31074: c 2 0 0
+31074: a 2 0 2 1,1,1,2
+31074: b 3 0 3 1,2,1,1,2
+31074: negate 9 1 5 0,1,2
+31074: add 13 2 3 0,2
+NO CLASH, using fixed ground order
+31075: Facts:
+31075: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+31075: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+31075: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+31075: Id : 5, {_}: add c d =>= c [] by identity_constant
+31075: Goal:
+31075: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+31075: Order:
+31075: kbo
+31075: Leaf order:
+31075: d 1 0 0
+31075: c 2 0 0
+31075: a 2 0 2 1,1,1,2
+31075: b 3 0 3 1,2,1,1,2
+31075: negate 9 1 5 0,1,2
+31075: add 13 2 3 0,2
+NO CLASH, using fixed ground order
+31076: Facts:
+31076: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+31076: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+31076: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+31076: Id : 5, {_}: add c d =>= c [] by identity_constant
+31076: Goal:
+31076: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+31076: Order:
+31076: lpo
+31076: Leaf order:
+31076: d 1 0 0
+31076: c 2 0 0
+31076: a 2 0 2 1,1,1,2
+31076: b 3 0 3 1,2,1,1,2
+31076: negate 9 1 5 0,1,2
+31076: add 13 2 3 0,2
+% SZS status Timeout for ROB026-1.p
+NO CLASH, using fixed ground order
+32629: Facts:
+32629: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+32629: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+32629: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+32629: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+32629: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+32629: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+32629: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+32629: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+32629: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+32629: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+32629: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+32629: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+32629: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+32629: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+32629: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+32629: Goal:
+32629: Id : 1, {_}:
+ least_upper_bound a (greatest_lower_bound b c)
+ =<=
+ greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c)
+ [] by prove_distrnu
+32629: Order:
+32629: nrkbo
+32629: Leaf order:
+32629: identity 2 0 0
+32629: b 2 0 2 1,2,2
+32629: c 2 0 2 2,2,2
+32629: a 3 0 3 1,2
+32629: inverse 1 1 0
+32629: greatest_lower_bound 15 2 2 0,2,2
+32629: least_upper_bound 16 2 3 0,2
+32629: multiply 18 2 0
+NO CLASH, using fixed ground order
+32630: Facts:
+32630: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+32630: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+32630: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+32630: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+32630: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+32630: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+32630: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+32630: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+32630: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+32630: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+32630: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+32630: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+32630: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+32630: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+32630: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+32630: Goal:
+32630: Id : 1, {_}:
+ least_upper_bound a (greatest_lower_bound b c)
+ =<=
+ greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c)
+ [] by prove_distrnu
+32630: Order:
+32630: kbo
+32630: Leaf order:
+32630: identity 2 0 0
+32630: b 2 0 2 1,2,2
+32630: c 2 0 2 2,2,2
+32630: a 3 0 3 1,2
+32630: inverse 1 1 0
+32630: greatest_lower_bound 15 2 2 0,2,2
+32630: least_upper_bound 16 2 3 0,2
+32630: multiply 18 2 0
+NO CLASH, using fixed ground order
+32631: Facts:
+32631: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+32631: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+32631: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+32631: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+32631: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+32631: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+32631: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+32631: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+32631: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+32631: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+32631: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+32631: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+32631: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+32631: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+32631: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+32631: Goal:
+32631: Id : 1, {_}:
+ least_upper_bound a (greatest_lower_bound b c)
+ =>=
+ greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c)
+ [] by prove_distrnu
+32631: Order:
+32631: lpo
+32631: Leaf order:
+32631: identity 2 0 0
+32631: b 2 0 2 1,2,2
+32631: c 2 0 2 2,2,2
+32631: a 3 0 3 1,2
+32631: inverse 1 1 0
+32631: greatest_lower_bound 15 2 2 0,2,2
+32631: least_upper_bound 16 2 3 0,2
+32631: multiply 18 2 0
+% SZS status Timeout for GRP164-1.p
+NO CLASH, using fixed ground order
+2296: Facts:
+2296: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+2296: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+2296: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+2296: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+2296: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+2296: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+2296: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+2296: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+2296: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+2296: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+2296: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+2296: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+2296: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+2296: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+2296: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+2296: Goal:
+2296: Id : 1, {_}:
+ greatest_lower_bound a (least_upper_bound b c)
+ =<=
+ least_upper_bound (greatest_lower_bound a b)
+ (greatest_lower_bound a c)
+ [] by prove_distrun
+2296: Order:
+2296: nrkbo
+2296: Leaf order:
+2296: identity 2 0 0
+2296: b 2 0 2 1,2,2
+2296: c 2 0 2 2,2,2
+2296: a 3 0 3 1,2
+2296: inverse 1 1 0
+2296: least_upper_bound 15 2 2 0,2,2
+2296: greatest_lower_bound 16 2 3 0,2
+2296: multiply 18 2 0
+NO CLASH, using fixed ground order
+2305: Facts:
+2305: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+2305: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+2305: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+2305: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+2305: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+2305: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+2305: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+2305: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+2305: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+2305: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+2305: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+2305: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+2305: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+2305: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+2305: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+2305: Goal:
+2305: Id : 1, {_}:
+ greatest_lower_bound a (least_upper_bound b c)
+ =<=
+ least_upper_bound (greatest_lower_bound a b)
+ (greatest_lower_bound a c)
+ [] by prove_distrun
+2305: Order:
+2305: kbo
+2305: Leaf order:
+2305: identity 2 0 0
+2305: b 2 0 2 1,2,2
+2305: c 2 0 2 2,2,2
+2305: a 3 0 3 1,2
+2305: inverse 1 1 0
+2305: least_upper_bound 15 2 2 0,2,2
+2305: greatest_lower_bound 16 2 3 0,2
+2305: multiply 18 2 0
+NO CLASH, using fixed ground order
+2309: Facts:
+2309: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+2309: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+2309: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+2309: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+2309: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+2309: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+2309: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+2309: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+2309: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+2309: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+2309: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+2309: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+2309: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+2309: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+2309: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+2309: Goal:
+2309: Id : 1, {_}:
+ greatest_lower_bound a (least_upper_bound b c)
+ =>=
+ least_upper_bound (greatest_lower_bound a b)
+ (greatest_lower_bound a c)
+ [] by prove_distrun
+2309: Order:
+2309: lpo
+2309: Leaf order:
+2309: identity 2 0 0
+2309: b 2 0 2 1,2,2
+2309: c 2 0 2 2,2,2
+2309: a 3 0 3 1,2
+2309: inverse 1 1 0
+2309: least_upper_bound 15 2 2 0,2,2
+2309: greatest_lower_bound 16 2 3 0,2
+2309: multiply 18 2 0
+% SZS status Timeout for GRP164-2.p
+NO CLASH, using fixed ground order
+4004: Facts:
+4004: Id : 2, {_}:
+ multiply (multiply ?2 ?3) ?4 =?= multiply ?2 (multiply ?3 ?4)
+ [4, 3, 2] by associativity_of_multiply ?2 ?3 ?4
+4004: Id : 3, {_}:
+ multiply ?6 (multiply ?7 (multiply ?7 ?7))
+ =?=
+ multiply ?7 (multiply ?7 (multiply ?7 ?6))
+ [7, 6] by condition ?6 ?7
+4004: Goal:
+4004: Id : 1, {_}:
+ multiply a
+ (multiply b
+ (multiply a
+ (multiply b
+ (multiply a
+ (multiply b
+ (multiply a
+ (multiply b
+ (multiply a
+ (multiply b
+ (multiply a
+ (multiply b
+ (multiply a
+ (multiply b
+ (multiply a (multiply b (multiply a b))))))))))))))))
+ =>=
+ multiply a
+ (multiply a
+ (multiply a
+ (multiply a
+ (multiply a
+ (multiply a
+ (multiply a
+ (multiply a
+ (multiply a
+ (multiply b
+ (multiply b
+ (multiply b
+ (multiply b
+ (multiply b
+ (multiply b (multiply b (multiply b b))))))))))))))))
+ [] by prove_this
+4004: Order:
+4004: nrkbo
+4004: Leaf order:
+4004: a 18 0 18 1,2
+4004: b 18 0 18 1,2,2
+4004: multiply 44 2 34 0,2
+NO CLASH, using fixed ground order
+4005: Facts:
+4005: Id : 2, {_}:
+ multiply (multiply ?2 ?3) ?4 =>= multiply ?2 (multiply ?3 ?4)
+ [4, 3, 2] by associativity_of_multiply ?2 ?3 ?4
+4005: Id : 3, {_}:
+ multiply ?6 (multiply ?7 (multiply ?7 ?7))
+ =?=
+ multiply ?7 (multiply ?7 (multiply ?7 ?6))
+ [7, 6] by condition ?6 ?7
+4005: Goal:
+4005: Id : 1, {_}:
+ multiply a
+ (multiply b
+ (multiply a
+ (multiply b
+ (multiply a
+ (multiply b
+ (multiply a
+ (multiply b
+ (multiply a
+ (multiply b
+ (multiply a
+ (multiply b
+ (multiply a
+ (multiply b
+ (multiply a (multiply b (multiply a b))))))))))))))))
+ =?=
+ multiply a
+ (multiply a
+ (multiply a
+ (multiply a
+ (multiply a
+ (multiply a
+ (multiply a
+ (multiply a
+ (multiply a
+ (multiply b
+ (multiply b
+ (multiply b
+ (multiply b
+ (multiply b
+ (multiply b (multiply b (multiply b b))))))))))))))))
+ [] by prove_this
+4005: Order:
+4005: kbo
+4005: Leaf order:
+4005: a 18 0 18 1,2
+4005: b 18 0 18 1,2,2
+4005: multiply 44 2 34 0,2
+NO CLASH, using fixed ground order
+% SZS status Timeout for GRP196-1.p
+NO CLASH, using fixed ground order
+7093: Facts:
+7093: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
+ (f ?3 (f (f ?3 (f (f ?2 ?2) ?2)) ?4))
+ =>=
+ ?3
+ [5, 4, 3, 2] by ol_23A ?2 ?3 ?4 ?5
+7093: Goal:
+7093: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
+ [] by associativity
+7093: Order:
+7093: nrkbo
+7093: Leaf order:
+7093: a 3 0 3 1,2
+7093: c 3 0 3 2,1,2,2
+7093: b 4 0 4 1,1,2,2
+7093: f 18 2 8 0,2
+NO CLASH, using fixed ground order
+7104: Facts:
+7104: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
+ (f ?3 (f (f ?3 (f (f ?2 ?2) ?2)) ?4))
+ =>=
+ ?3
+ [5, 4, 3, 2] by ol_23A ?2 ?3 ?4 ?5
+7104: Goal:
+7104: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
+ [] by associativity
+7104: Order:
+7104: kbo
+7104: Leaf order:
+7104: a 3 0 3 1,2
+7104: c 3 0 3 2,1,2,2
+7104: b 4 0 4 1,1,2,2
+7104: f 18 2 8 0,2
+NO CLASH, using fixed ground order
+7109: Facts:
+7109: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
+ (f ?3 (f (f ?3 (f (f ?2 ?2) ?2)) ?4))
+ =>=
+ ?3
+ [5, 4, 3, 2] by ol_23A ?2 ?3 ?4 ?5
+7109: Goal:
+7109: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
+ [] by associativity
+7109: Order:
+7109: lpo
+7109: Leaf order:
+7109: a 3 0 3 1,2
+7109: c 3 0 3 2,1,2,2
+7109: b 4 0 4 1,1,2,2
+7109: f 18 2 8 0,2
+% SZS status Timeout for LAT070-1.p
+NO CLASH, using fixed ground order
+9646: Facts:
+9646: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+9646: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+9646: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+9646: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+9646: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+9646: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+9646: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+9646: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+9646: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
+ [28, 27, 26] by equation_H7 ?26 ?27 ?28
+9646: Goal:
+9646: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+9646: Order:
+9646: nrkbo
+9646: Leaf order:
+9646: b 3 0 3 1,2,2
+9646: c 3 0 3 2,2,2,2
+9646: a 6 0 6 1,2
+9646: join 17 2 4 0,2,2
+9646: meet 21 2 6 0,2
+NO CLASH, using fixed ground order
+9648: Facts:
+9648: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+9648: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+9648: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+9648: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+9648: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+9648: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+9648: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+9648: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+9648: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
+ [28, 27, 26] by equation_H7 ?26 ?27 ?28
+9648: Goal:
+9648: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+9648: Order:
+9648: kbo
+9648: Leaf order:
+9648: b 3 0 3 1,2,2
+9648: c 3 0 3 2,2,2,2
+9648: a 6 0 6 1,2
+9648: join 17 2 4 0,2,2
+9648: meet 21 2 6 0,2
+NO CLASH, using fixed ground order
+9649: Facts:
+9649: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+9649: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+9649: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+9649: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+9649: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+9649: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+9649: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+9649: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+9649: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))))
+ [28, 27, 26] by equation_H7 ?26 ?27 ?28
+9649: Goal:
+9649: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+9649: Order:
+9649: lpo
+9649: Leaf order:
+9649: b 3 0 3 1,2,2
+9649: c 3 0 3 2,2,2,2
+9649: a 6 0 6 1,2
+9649: join 17 2 4 0,2,2
+9649: meet 21 2 6 0,2
+% SZS status Timeout for LAT138-1.p
+NO CLASH, using fixed ground order
+11119: Facts:
+11119: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+11119: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+11119: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+11119: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+11119: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+11119: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+11119: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+11119: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+11119: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?26 (meet ?27 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H21 ?26 ?27 ?28
+11119: Goal:
+11119: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+11119: Order:
+11119: kbo
+11119: Leaf order:
+11119: a 4 0 4 1,2
+11119: b 4 0 4 1,2,2
+11119: c 4 0 4 2,2,2,2
+11119: join 17 2 4 0,2,2
+11119: meet 21 2 6 0,2
+NO CLASH, using fixed ground order
+11120: Facts:
+11120: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+11120: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+11120: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+11120: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+11120: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+11120: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+11120: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+11120: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+11120: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?26 (meet ?27 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H21 ?26 ?27 ?28
+11120: Goal:
+11120: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+11120: Order:
+11120: lpo
+11120: Leaf order:
+11120: a 4 0 4 1,2
+11120: b 4 0 4 1,2,2
+11120: c 4 0 4 2,2,2,2
+11120: join 17 2 4 0,2,2
+11120: meet 21 2 6 0,2
+NO CLASH, using fixed ground order
+11118: Facts:
+11118: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+11118: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+11118: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+11118: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+11118: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+11118: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+11118: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+11118: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+11118: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?26 (meet ?27 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H21 ?26 ?27 ?28
+11118: Goal:
+11118: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+11118: Order:
+11118: nrkbo
+11118: Leaf order:
+11118: a 4 0 4 1,2
+11118: b 4 0 4 1,2,2
+11118: c 4 0 4 2,2,2,2
+11118: join 17 2 4 0,2,2
+11118: meet 21 2 6 0,2
+% SZS status Timeout for LAT140-1.p
+NO CLASH, using fixed ground order
+12763: Facts:
+12763: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+12763: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+12763: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+12763: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+12763: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+12763: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+12763: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+12763: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+12763: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
+ [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
+12763: Goal:
+12763: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+12763: Order:
+12763: nrkbo
+12763: Leaf order:
+12763: b 3 0 3 1,2,2
+12763: c 3 0 3 2,2,2,2
+12763: a 6 0 6 1,2
+12763: join 16 2 4 0,2,2
+12763: meet 22 2 6 0,2
+NO CLASH, using fixed ground order
+12764: Facts:
+12764: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+12764: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+12764: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+12764: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+12764: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+12764: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+12764: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+12764: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+12764: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
+ [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
+12764: Goal:
+12764: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+12764: Order:
+12764: kbo
+12764: Leaf order:
+12764: b 3 0 3 1,2,2
+12764: c 3 0 3 2,2,2,2
+12764: a 6 0 6 1,2
+12764: join 16 2 4 0,2,2
+12764: meet 22 2 6 0,2
+NO CLASH, using fixed ground order
+12765: Facts:
+12765: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+12765: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+12765: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+12765: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+12765: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+12765: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+12765: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+12765: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+12765: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 (meet ?28 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29))))
+ [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29
+12765: Goal:
+12765: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+12765: Order:
+12765: lpo
+12765: Leaf order:
+12765: b 3 0 3 1,2,2
+12765: c 3 0 3 2,2,2,2
+12765: a 6 0 6 1,2
+12765: join 16 2 4 0,2,2
+12765: meet 22 2 6 0,2
+% SZS status Timeout for LAT145-1.p
+NO CLASH, using fixed ground order
+13612: Facts:
+13612: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13612: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13612: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13612: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13612: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13612: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13612: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13612: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13612: Id : 10, {_}:
+ meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
+13612: Goal:
+13612: Id : 1, {_}:
+ meet a (join b (meet c (join b d)))
+ =<=
+ meet a (join b (meet c (join d (meet a (join b d)))))
+ [] by prove_H43
+13612: Order:
+13612: nrkbo
+13612: Leaf order:
+13612: c 2 0 2 1,2,2,2
+13612: a 3 0 3 1,2
+13612: d 3 0 3 2,2,2,2,2
+13612: b 4 0 4 1,2,2
+13612: meet 19 2 5 0,2
+13612: join 19 2 5 0,2,2
+NO CLASH, using fixed ground order
+13613: Facts:
+13613: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13613: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13613: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13613: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13613: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13613: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13613: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13613: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13613: Id : 10, {_}:
+ meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
+13613: Goal:
+13613: Id : 1, {_}:
+ meet a (join b (meet c (join b d)))
+ =<=
+ meet a (join b (meet c (join d (meet a (join b d)))))
+ [] by prove_H43
+13613: Order:
+13613: kbo
+13613: Leaf order:
+13613: c 2 0 2 1,2,2,2
+13613: a 3 0 3 1,2
+13613: d 3 0 3 2,2,2,2,2
+13613: b 4 0 4 1,2,2
+13613: meet 19 2 5 0,2
+13613: join 19 2 5 0,2,2
+NO CLASH, using fixed ground order
+13614: Facts:
+13614: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+13614: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+13614: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+13614: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+13614: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+13614: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+13614: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+13614: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+13614: Id : 10, {_}:
+ meet ?26 (join ?27 (join ?28 (meet ?26 ?29)))
+ =?=
+ meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29
+13614: Goal:
+13614: Id : 1, {_}:
+ meet a (join b (meet c (join b d)))
+ =<=
+ meet a (join b (meet c (join d (meet a (join b d)))))
+ [] by prove_H43
+13614: Order:
+13614: lpo
+13614: Leaf order:
+13614: c 2 0 2 1,2,2,2
+13614: a 3 0 3 1,2
+13614: d 3 0 3 2,2,2,2,2
+13614: b 4 0 4 1,2,2
+13614: meet 19 2 5 0,2
+13614: join 19 2 5 0,2,2
+% SZS status Timeout for LAT149-1.p
+NO CLASH, using fixed ground order
+14638: Facts:
+14638: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14638: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14638: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14638: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14638: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14638: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14638: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14638: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14638: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
+ [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
+14638: Goal:
+14638: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
+ [] by prove_H7
+14638: Order:
+14638: nrkbo
+14638: Leaf order:
+14638: c 2 0 2 2,2,2,2
+14638: b 4 0 4 1,2,2
+14638: a 6 0 6 1,2
+14638: join 18 2 4 0,2,2
+14638: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+14639: Facts:
+14639: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14639: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14639: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14639: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14639: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14639: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14639: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14639: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14639: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
+ [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
+14639: Goal:
+14639: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
+ [] by prove_H7
+14639: Order:
+NO CLASH, using fixed ground order
+14640: Facts:
+14640: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+14640: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+14640: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+14640: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+14640: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+14640: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+14640: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+14640: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+14640: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27)))))
+ [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29
+14640: Goal:
+14640: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet a (join (meet a b) (meet c (join a b)))))
+ [] by prove_H7
+14640: Order:
+14640: lpo
+14640: Leaf order:
+14640: c 2 0 2 2,2,2,2
+14640: b 4 0 4 1,2,2
+14640: a 6 0 6 1,2
+14640: join 18 2 4 0,2,2
+14640: meet 20 2 6 0,2
+14639: kbo
+14639: Leaf order:
+14639: c 2 0 2 2,2,2,2
+14639: b 4 0 4 1,2,2
+14639: a 6 0 6 1,2
+14639: join 18 2 4 0,2,2
+14639: meet 20 2 6 0,2
+% SZS status Timeout for LAT153-1.p
+NO CLASH, using fixed ground order
+15430: Facts:
+15430: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+15430: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+15430: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+15430: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+15430: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+15430: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+15430: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+15430: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+15430: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
+ [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
+15430: Goal:
+15430: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+15430: Order:
+15430: nrkbo
+15430: Leaf order:
+15430: a 4 0 4 1,2
+15430: b 4 0 4 1,2,2
+15430: c 4 0 4 2,2,2,2
+15430: join 18 2 4 0,2,2
+15430: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+15431: Facts:
+15431: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+15431: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+15431: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+15431: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+15431: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+15431: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+15431: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+15431: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+15431: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
+ [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
+15431: Goal:
+15431: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+15431: Order:
+15431: kbo
+15431: Leaf order:
+15431: a 4 0 4 1,2
+15431: b 4 0 4 1,2,2
+15431: c 4 0 4 2,2,2,2
+15431: join 18 2 4 0,2,2
+15431: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+15432: Facts:
+15432: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+15432: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+15432: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+15432: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+15432: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+15432: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+15432: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+15432: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+15432: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
+ [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
+15432: Goal:
+15432: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join (meet a (join b c)) (meet b c))))
+ [] by prove_H2
+15432: Order:
+15432: lpo
+15432: Leaf order:
+15432: a 4 0 4 1,2
+15432: b 4 0 4 1,2,2
+15432: c 4 0 4 2,2,2,2
+15432: join 18 2 4 0,2,2
+15432: meet 20 2 6 0,2
+% SZS status Timeout for LAT157-1.p
+NO CLASH, using fixed ground order
+16370: Facts:
+16370: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+16370: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+16370: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+16370: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+16370: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+16370: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+16370: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+16370: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+16370: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
+ [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
+16370: Goal:
+16370: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (join (meet a c) (meet c (join b d))))
+ [] by prove_H49
+16370: Order:
+16370: nrkbo
+16370: Leaf order:
+16370: d 2 0 2 2,2,2,2,2
+16370: b 3 0 3 1,2,2
+16370: c 3 0 3 1,2,2,2
+16370: a 4 0 4 1,2
+16370: meet 19 2 5 0,2
+16370: join 19 2 5 0,2,2
+NO CLASH, using fixed ground order
+16387: Facts:
+16387: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+16387: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+16387: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+16387: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+16387: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+16387: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+16387: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+16387: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+16387: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
+ [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
+16387: Goal:
+16387: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (join (meet a c) (meet c (join b d))))
+ [] by prove_H49
+16387: Order:
+16387: kbo
+16387: Leaf order:
+16387: d 2 0 2 2,2,2,2,2
+16387: b 3 0 3 1,2,2
+16387: c 3 0 3 1,2,2,2
+16387: a 4 0 4 1,2
+16387: meet 19 2 5 0,2
+16387: join 19 2 5 0,2,2
+NO CLASH, using fixed ground order
+16398: Facts:
+16398: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+16398: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+16398: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+16398: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+16398: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+16398: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+16398: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+16398: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+16398: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?26 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29)))))
+ [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29
+16398: Goal:
+16398: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (join (meet a c) (meet c (join b d))))
+ [] by prove_H49
+16398: Order:
+16398: lpo
+16398: Leaf order:
+16398: d 2 0 2 2,2,2,2,2
+16398: b 3 0 3 1,2,2
+16398: c 3 0 3 1,2,2,2
+16398: a 4 0 4 1,2
+16398: meet 19 2 5 0,2
+16398: join 19 2 5 0,2,2
+% SZS status Timeout for LAT158-1.p
+NO CLASH, using fixed ground order
+17619: Facts:
+17619: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+17619: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+17619: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+17619: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+17619: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+17619: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+17619: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+17619: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+17619: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
+17619: Goal:
+17619: Id : 1, {_}:
+ meet a (join b (meet a (meet c d)))
+ =<=
+ meet a (join b (meet c (join (meet a d) (meet b d))))
+ [] by prove_H32
+17619: Order:
+17619: nrkbo
+17619: Leaf order:
+17619: c 2 0 2 1,2,2,2,2
+17619: b 3 0 3 1,2,2
+17619: d 3 0 3 2,2,2,2,2
+17619: a 4 0 4 1,2
+17619: join 16 2 3 0,2,2
+17619: meet 21 2 7 0,2
+NO CLASH, using fixed ground order
+17620: Facts:
+17620: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+17620: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+17620: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+17620: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+17620: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+17620: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+17620: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+17620: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+17620: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
+17620: Goal:
+NO CLASH, using fixed ground order
+17620: Id : 1, {_}:
+ meet a (join b (meet a (meet c d)))
+ =<=
+ meet a (join b (meet c (join (meet a d) (meet b d))))
+ [] by prove_H32
+17620: Order:
+17620: kbo
+17620: Leaf order:
+17620: c 2 0 2 1,2,2,2,2
+17620: b 3 0 3 1,2,2
+17620: d 3 0 3 2,2,2,2,2
+17620: a 4 0 4 1,2
+17620: join 16 2 3 0,2,2
+17620: meet 21 2 7 0,2
+17622: Facts:
+17622: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+17622: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+17622: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+17622: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+17622: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+17622: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+17622: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+17622: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+17622: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
+17622: Goal:
+17622: Id : 1, {_}:
+ meet a (join b (meet a (meet c d)))
+ =>=
+ meet a (join b (meet c (join (meet a d) (meet b d))))
+ [] by prove_H32
+17622: Order:
+17622: lpo
+17622: Leaf order:
+17622: c 2 0 2 1,2,2,2,2
+17622: b 3 0 3 1,2,2
+17622: d 3 0 3 2,2,2,2,2
+17622: a 4 0 4 1,2
+17622: join 16 2 3 0,2,2
+17622: meet 21 2 7 0,2
+% SZS status Timeout for LAT163-1.p
+NO CLASH, using fixed ground order
+17778: Facts:
+17778: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+17778: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+17778: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+17778: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+17778: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+17778: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+17778: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+17778: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+17778: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
+17778: Goal:
+17778: Id : 1, {_}:
+ meet a (join b (meet c (join b d)))
+ =<=
+ meet a (join b (meet c (join d (meet a (meet b c)))))
+ [] by prove_H77
+17778: Order:
+17778: nrkbo
+17778: Leaf order:
+17778: d 2 0 2 2,2,2,2,2
+17778: a 3 0 3 1,2
+17778: c 3 0 3 1,2,2,2
+17778: b 4 0 4 1,2,2
+17778: join 17 2 4 0,2,2
+17778: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+17779: Facts:
+17779: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+17779: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+17779: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+17779: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+17779: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+17779: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+17779: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+17779: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+17779: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
+17779: Goal:
+17779: Id : 1, {_}:
+ meet a (join b (meet c (join b d)))
+ =<=
+ meet a (join b (meet c (join d (meet a (meet b c)))))
+ [] by prove_H77
+17779: Order:
+17779: kbo
+17779: Leaf order:
+17779: d 2 0 2 2,2,2,2,2
+17779: a 3 0 3 1,2
+17779: c 3 0 3 1,2,2,2
+17779: b 4 0 4 1,2,2
+17779: join 17 2 4 0,2,2
+17779: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+17780: Facts:
+17780: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+17780: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+17780: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+17780: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+17780: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+17780: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+17780: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+17780: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+17780: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29
+17780: Goal:
+17780: Id : 1, {_}:
+ meet a (join b (meet c (join b d)))
+ =<=
+ meet a (join b (meet c (join d (meet a (meet b c)))))
+ [] by prove_H77
+17780: Order:
+17780: lpo
+17780: Leaf order:
+17780: d 2 0 2 2,2,2,2,2
+17780: a 3 0 3 1,2
+17780: c 3 0 3 1,2,2,2
+17780: b 4 0 4 1,2,2
+17780: join 17 2 4 0,2,2
+17780: meet 20 2 6 0,2
+% SZS status Timeout for LAT165-1.p
+NO CLASH, using fixed ground order
+18025: Facts:
+18025: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+18025: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+18025: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+18025: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+18025: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+18025: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+18025: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+18025: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+18025: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29
+18025: Goal:
+18025: Id : 1, {_}:
+ meet a (join b (meet c (join b d)))
+ =<=
+ meet a (join b (meet c (join d (meet b (join a d)))))
+ [] by prove_H78
+18025: Order:
+18025: nrkbo
+18025: Leaf order:
+18025: c 2 0 2 1,2,2,2
+18025: a 3 0 3 1,2
+18025: d 3 0 3 2,2,2,2,2
+18025: b 4 0 4 1,2,2
+18025: join 18 2 5 0,2,2
+18025: meet 20 2 5 0,2
+NO CLASH, using fixed ground order
+18026: Facts:
+18026: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+18026: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+18026: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+18026: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+18026: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+18026: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+18026: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+18026: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+18026: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29
+18026: Goal:
+18026: Id : 1, {_}:
+ meet a (join b (meet c (join b d)))
+ =<=
+ meet a (join b (meet c (join d (meet b (join a d)))))
+ [] by prove_H78
+18026: Order:
+18026: kbo
+18026: Leaf order:
+18026: c 2 0 2 1,2,2,2
+18026: a 3 0 3 1,2
+18026: d 3 0 3 2,2,2,2,2
+18026: b 4 0 4 1,2,2
+18026: join 18 2 5 0,2,2
+18026: meet 20 2 5 0,2
+NO CLASH, using fixed ground order
+18027: Facts:
+18027: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+18027: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+18027: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+18027: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+18027: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+18027: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+18027: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+18027: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+18027: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =?=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28)))))
+ [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29
+18027: Goal:
+18027: Id : 1, {_}:
+ meet a (join b (meet c (join b d)))
+ =<=
+ meet a (join b (meet c (join d (meet b (join a d)))))
+ [] by prove_H78
+18027: Order:
+18027: lpo
+18027: Leaf order:
+18027: c 2 0 2 1,2,2,2
+18027: a 3 0 3 1,2
+18027: d 3 0 3 2,2,2,2,2
+18027: b 4 0 4 1,2,2
+18027: join 18 2 5 0,2,2
+18027: meet 20 2 5 0,2
+% SZS status Timeout for LAT166-1.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+18051: Facts:
+18051: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+18051: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+18051: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+18051: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+18051: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+18051: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+18051: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+18051: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+18051: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?27 (join ?26 ?29)))))
+ [29, 28, 27, 26] by equation_H78 ?26 ?27 ?28 ?29
+18051: Goal:
+18051: Id : 1, {_}:
+ meet a (join b (meet c (join b d)))
+ =<=
+ meet a (join b (meet c (join d (meet a (meet b c)))))
+ [] by prove_H77
+18051: Order:
+18051: kbo
+18051: Leaf order:
+18051: d 2 0 2 2,2,2,2,2
+18051: a 3 0 3 1,2
+18051: c 3 0 3 1,2,2,2
+18051: b 4 0 4 1,2,2
+18051: join 18 2 4 0,2,2
+18051: meet 20 2 6 0,2
+NO CLASH, using fixed ground order
+18052: Facts:
+18052: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+18052: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+18052: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+18052: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+18052: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+18052: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+18052: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+18052: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+18052: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?27 (join ?26 ?29)))))
+ [29, 28, 27, 26] by equation_H78 ?26 ?27 ?28 ?29
+18052: Goal:
+18052: Id : 1, {_}:
+ meet a (join b (meet c (join b d)))
+ =<=
+ meet a (join b (meet c (join d (meet a (meet b c)))))
+ [] by prove_H77
+18052: Order:
+18052: lpo
+18052: Leaf order:
+18052: d 2 0 2 2,2,2,2,2
+18052: a 3 0 3 1,2
+18052: c 3 0 3 1,2,2,2
+18052: b 4 0 4 1,2,2
+18052: join 18 2 4 0,2,2
+18052: meet 20 2 6 0,2
+18050: Facts:
+18050: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+18050: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+18050: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+18050: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+18050: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+18050: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+18050: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+18050: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+18050: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?28 (join ?27 ?29)))
+ =<=
+ meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?27 (join ?26 ?29)))))
+ [29, 28, 27, 26] by equation_H78 ?26 ?27 ?28 ?29
+18050: Goal:
+18050: Id : 1, {_}:
+ meet a (join b (meet c (join b d)))
+ =<=
+ meet a (join b (meet c (join d (meet a (meet b c)))))
+ [] by prove_H77
+18050: Order:
+18050: nrkbo
+18050: Leaf order:
+18050: d 2 0 2 2,2,2,2,2
+18050: a 3 0 3 1,2
+18050: c 3 0 3 1,2,2,2
+18050: b 4 0 4 1,2,2
+18050: join 18 2 4 0,2,2
+18050: meet 20 2 6 0,2
+% SZS status Timeout for LAT167-1.p
+NO CLASH, using fixed ground order
+18084: Facts:
+18084: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+18084: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+18084: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+18084: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+18084: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+18084: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+18084: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+18084: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+18084: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
+18084: Goal:
+18084: Id : 1, {_}:
+ meet a (join b (meet a (meet c d)))
+ =<=
+ meet a (join b (meet c (join (meet a d) (meet b d))))
+ [] by prove_H32
+18084: Order:
+18084: nrkbo
+18084: Leaf order:
+18084: c 2 0 2 1,2,2,2,2
+18084: b 3 0 3 1,2,2
+18084: d 3 0 3 2,2,2,2,2
+18084: a 4 0 4 1,2
+18084: join 17 2 3 0,2,2
+18084: meet 20 2 7 0,2
+NO CLASH, using fixed ground order
+18085: Facts:
+18085: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+18085: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+18085: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+18085: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+18085: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+18085: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+18085: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+18085: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+18085: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
+18085: Goal:
+18085: Id : 1, {_}:
+ meet a (join b (meet a (meet c d)))
+ =<=
+ meet a (join b (meet c (join (meet a d) (meet b d))))
+ [] by prove_H32
+18085: Order:
+18085: kbo
+18085: Leaf order:
+18085: c 2 0 2 1,2,2,2,2
+18085: b 3 0 3 1,2,2
+18085: d 3 0 3 2,2,2,2,2
+18085: a 4 0 4 1,2
+18085: join 17 2 3 0,2,2
+18085: meet 20 2 7 0,2
+NO CLASH, using fixed ground order
+18086: Facts:
+18086: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+18086: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+18086: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+18086: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+18086: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+18086: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+18086: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+18086: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+18086: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
+ =?=
+ join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
+18086: Goal:
+18086: Id : 1, {_}:
+ meet a (join b (meet a (meet c d)))
+ =>=
+ meet a (join b (meet c (join (meet a d) (meet b d))))
+ [] by prove_H32
+18086: Order:
+18086: lpo
+18086: Leaf order:
+18086: c 2 0 2 1,2,2,2,2
+18086: b 3 0 3 1,2,2
+18086: d 3 0 3 2,2,2,2,2
+18086: a 4 0 4 1,2
+18086: join 17 2 3 0,2,2
+18086: meet 20 2 7 0,2
+% SZS status Timeout for LAT172-1.p
+NO CLASH, using fixed ground order
+18325: Facts:
+18325: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+18325: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+18325: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+18325: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+18325: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+18325: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+18325: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+18325: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+18325: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
+18325: Goal:
+18325: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+18325: Order:
+18325: nrkbo
+18325: Leaf order:
+18325: d 2 0 2 2,2,2,2,2
+18325: b 3 0 3 1,2,2
+18325: c 3 0 3 1,2,2,2
+18325: a 4 0 4 1,2
+18325: meet 18 2 5 0,2
+18325: join 19 2 5 0,2,2
+NO CLASH, using fixed ground order
+18329: Facts:
+18329: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+18329: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+18329: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+18329: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+18329: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+18329: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+18329: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+18329: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+18329: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
+ =<=
+ join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
+18329: Goal:
+18329: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+18329: Order:
+18329: kbo
+18329: Leaf order:
+18329: d 2 0 2 2,2,2,2,2
+18329: b 3 0 3 1,2,2
+18329: c 3 0 3 1,2,2,2
+18329: a 4 0 4 1,2
+18329: meet 18 2 5 0,2
+18329: join 19 2 5 0,2,2
+NO CLASH, using fixed ground order
+18330: Facts:
+18330: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+18330: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+18330: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+18330: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+18330: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+18330: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+18330: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+18330: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+18330: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?27 ?29)))
+ =?=
+ join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27))))
+ [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29
+18330: Goal:
+18330: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join d (meet c (join a b)))))
+ [] by prove_H40
+18330: Order:
+18330: lpo
+18330: Leaf order:
+18330: d 2 0 2 2,2,2,2,2
+18330: b 3 0 3 1,2,2
+18330: c 3 0 3 1,2,2,2
+18330: a 4 0 4 1,2
+18330: meet 18 2 5 0,2
+18330: join 19 2 5 0,2,2
+% SZS status Timeout for LAT173-1.p
+NO CLASH, using fixed ground order
+19752: Facts:
+19752: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19752: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19752: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19752: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19752: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19752: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19752: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+NO CLASH, using fixed ground order
+19755: Facts:
+19755: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19755: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19755: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19755: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19755: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19755: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19755: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19755: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+NO CLASH, using fixed ground order
+19757: Facts:
+19757: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+19757: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+19757: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+19757: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+19757: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+19757: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+19757: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+19757: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19757: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
+ [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
+19757: Goal:
+19757: Id : 1, {_}:
+ meet a (join b (meet a (meet c d)))
+ =>=
+ meet a (join b (meet c (join (meet a d) (meet b d))))
+ [] by prove_H32
+19757: Order:
+19757: lpo
+19757: Leaf order:
+19757: c 2 0 2 1,2,2,2,2
+19757: b 3 0 3 1,2,2
+19757: d 3 0 3 2,2,2,2,2
+19757: a 4 0 4 1,2
+19757: join 18 2 3 0,2,2
+19757: meet 20 2 7 0,2
+19752: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+19752: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
+ [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
+19752: Goal:
+19752: Id : 1, {_}:
+ meet a (join b (meet a (meet c d)))
+ =<=
+ meet a (join b (meet c (join (meet a d) (meet b d))))
+ [] by prove_H32
+19752: Order:
+19752: nrkbo
+19752: Leaf order:
+19752: c 2 0 2 1,2,2,2,2
+19752: b 3 0 3 1,2,2
+19752: d 3 0 3 2,2,2,2,2
+19752: a 4 0 4 1,2
+19752: join 18 2 3 0,2,2
+19752: meet 20 2 7 0,2
+19755: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
+ [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
+19755: Goal:
+19755: Id : 1, {_}:
+ meet a (join b (meet a (meet c d)))
+ =<=
+ meet a (join b (meet c (join (meet a d) (meet b d))))
+ [] by prove_H32
+19755: Order:
+19755: kbo
+19755: Leaf order:
+19755: c 2 0 2 1,2,2,2,2
+19755: b 3 0 3 1,2,2
+19755: d 3 0 3 2,2,2,2,2
+19755: a 4 0 4 1,2
+19755: join 18 2 3 0,2,2
+19755: meet 20 2 7 0,2
+% SZS status Timeout for LAT175-1.p
+NO CLASH, using fixed ground order
+21153: Facts:
+21153: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+21153: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+21153: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+21153: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+21153: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+21153: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+21153: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+21153: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+21153: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
+ [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
+21153: Goal:
+21153: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+21153: Order:
+21153: nrkbo
+21153: Leaf order:
+21153: d 2 0 2 2,2,2,2,2
+21153: b 3 0 3 1,2,2
+21153: c 3 0 3 1,2,2,2
+21153: a 4 0 4 1,2
+21153: meet 18 2 5 0,2
+21153: join 20 2 5 0,2,2
+NO CLASH, using fixed ground order
+21154: Facts:
+21154: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+21154: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+21154: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+21154: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+21154: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+21154: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+21154: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+21154: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+21154: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
+ [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
+21154: Goal:
+21154: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =<=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+21154: Order:
+21154: kbo
+21154: Leaf order:
+21154: d 2 0 2 2,2,2,2,2
+21154: b 3 0 3 1,2,2
+21154: c 3 0 3 1,2,2,2
+21154: a 4 0 4 1,2
+21154: meet 18 2 5 0,2
+21154: join 20 2 5 0,2,2
+NO CLASH, using fixed ground order
+21155: Facts:
+21155: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+21155: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+21155: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+21155: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+21155: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+21155: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+21155: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+21155: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+21155: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =?=
+ join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
+ [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
+21155: Goal:
+21155: Id : 1, {_}:
+ meet a (join b (meet c (join a d)))
+ =>=
+ meet a (join b (meet c (join b (join d (meet a c)))))
+ [] by prove_H42
+21155: Order:
+21155: lpo
+21155: Leaf order:
+21155: d 2 0 2 2,2,2,2,2
+21155: b 3 0 3 1,2,2
+21155: c 3 0 3 1,2,2,2
+21155: a 4 0 4 1,2
+21155: meet 18 2 5 0,2
+21155: join 20 2 5 0,2,2
+% SZS status Timeout for LAT176-1.p
+NO CLASH, using fixed ground order
+23137: Facts:
+23137: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+23137: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+23137: Id : 4, {_}:
+ add (additive_inverse ?6) ?6 =>= additive_identity
+ [6] by left_additive_inverse ?6
+23137: Id : 5, {_}:
+ add ?8 (additive_inverse ?8) =>= additive_identity
+ [8] by right_additive_inverse ?8
+23137: Id : 6, {_}:
+ add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12
+ [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
+23137: Id : 7, {_}:
+ add ?14 ?15 =?= add ?15 ?14
+ [15, 14] by commutativity_for_addition ?14 ?15
+23137: Id : 8, {_}:
+ multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19
+ [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
+23137: Id : 9, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+23137: Id : 10, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+23137: Id : 11, {_}:
+ multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29
+ [29] by x_fourthed_is_x ?29
+23137: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
+23137: Goal:
+23137: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
+23137: Order:
+23137: nrkbo
+23137: Leaf order:
+23137: b 2 0 1 1,2
+23137: a 2 0 1 2,2
+23137: c 2 0 1 3
+23137: additive_identity 4 0 0
+23137: additive_inverse 2 1 0
+23137: add 14 2 0
+23137: multiply 15 2 1 0,2
+NO CLASH, using fixed ground order
+23138: Facts:
+23138: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+23138: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+23138: Id : 4, {_}:
+ add (additive_inverse ?6) ?6 =>= additive_identity
+ [6] by left_additive_inverse ?6
+23138: Id : 5, {_}:
+ add ?8 (additive_inverse ?8) =>= additive_identity
+ [8] by right_additive_inverse ?8
+23138: Id : 6, {_}:
+ add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
+ [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
+23138: Id : 7, {_}:
+ add ?14 ?15 =?= add ?15 ?14
+ [15, 14] by commutativity_for_addition ?14 ?15
+23138: Id : 8, {_}:
+ multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
+ [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
+23138: Id : 9, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+23138: Id : 10, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+23138: Id : 11, {_}:
+ multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29
+ [29] by x_fourthed_is_x ?29
+23138: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
+23138: Goal:
+23138: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
+23138: Order:
+23138: kbo
+23138: Leaf order:
+23138: b 2 0 1 1,2
+23138: a 2 0 1 2,2
+23138: c 2 0 1 3
+23138: additive_identity 4 0 0
+23138: additive_inverse 2 1 0
+23138: add 14 2 0
+23138: multiply 15 2 1 0,2
+NO CLASH, using fixed ground order
+23139: Facts:
+23139: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+23139: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+23139: Id : 4, {_}:
+ add (additive_inverse ?6) ?6 =>= additive_identity
+ [6] by left_additive_inverse ?6
+23139: Id : 5, {_}:
+ add ?8 (additive_inverse ?8) =>= additive_identity
+ [8] by right_additive_inverse ?8
+23139: Id : 6, {_}:
+ add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
+ [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
+23139: Id : 7, {_}:
+ add ?14 ?15 =?= add ?15 ?14
+ [15, 14] by commutativity_for_addition ?14 ?15
+23139: Id : 8, {_}:
+ multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
+ [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
+23139: Id : 9, {_}:
+ multiply ?21 (add ?22 ?23)
+ =>=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+23139: Id : 10, {_}:
+ multiply (add ?25 ?26) ?27
+ =>=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+23139: Id : 11, {_}:
+ multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29
+ [29] by x_fourthed_is_x ?29
+23139: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
+23139: Goal:
+23139: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
+23139: Order:
+23139: lpo
+23139: Leaf order:
+23139: b 2 0 1 1,2
+23139: a 2 0 1 2,2
+23139: c 2 0 1 3
+23139: additive_identity 4 0 0
+23139: additive_inverse 2 1 0
+23139: add 14 2 0
+23139: multiply 15 2 1 0,2
+% SZS status Timeout for RNG035-7.p
+NO CLASH, using fixed ground order
+23161: Facts:
+NO CLASH, using fixed ground order
+23162: Facts:
+23162: Id : 2, {_}:
+ nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c1 ?2 ?3 ?4
+23162: Goal:
+23162: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23162: Order:
+23162: kbo
+23162: Leaf order:
+23162: b 1 0 1 1,2,2
+23162: a 4 0 4 1,1,2
+23162: nand 9 2 3 0,2
+23161: Id : 2, {_}:
+ nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c1 ?2 ?3 ?4
+23161: Goal:
+23161: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23161: Order:
+23161: nrkbo
+23161: Leaf order:
+23161: b 1 0 1 1,2,2
+23161: a 4 0 4 1,1,2
+23161: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+23163: Facts:
+23163: Id : 2, {_}:
+ nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c1 ?2 ?3 ?4
+23163: Goal:
+23163: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23163: Order:
+23163: lpo
+23163: Leaf order:
+23163: b 1 0 1 1,2,2
+23163: a 4 0 4 1,1,2
+23163: nand 9 2 3 0,2
+% SZS status Timeout for BOO077-1.p
+NO CLASH, using fixed ground order
+23212: Facts:
+23212: Id : 2, {_}:
+ nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c1 ?2 ?3 ?4
+23212: Goal:
+23212: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23212: Order:
+23212: nrkbo
+23212: Leaf order:
+23212: c 2 0 2 2,2,2,2
+23212: a 3 0 3 1,2
+23212: b 3 0 3 1,2,2
+23212: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+23213: Facts:
+23213: Id : 2, {_}:
+ nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c1 ?2 ?3 ?4
+23213: Goal:
+23213: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23213: Order:
+23213: kbo
+23213: Leaf order:
+23213: c 2 0 2 2,2,2,2
+23213: a 3 0 3 1,2
+23213: b 3 0 3 1,2,2
+23213: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+23214: Facts:
+23214: Id : 2, {_}:
+ nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c1 ?2 ?3 ?4
+23214: Goal:
+23214: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23214: Order:
+23214: lpo
+23214: Leaf order:
+23214: c 2 0 2 2,2,2,2
+23214: a 3 0 3 1,2
+23214: b 3 0 3 1,2,2
+23214: nand 12 2 6 0,2
+% SZS status Timeout for BOO078-1.p
+NO CLASH, using fixed ground order
+23320: Facts:
+23320: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c2 ?2 ?3 ?4
+23320: Goal:
+23320: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23320: Order:
+23320: nrkbo
+23320: Leaf order:
+23320: b 1 0 1 1,2,2
+23320: a 4 0 4 1,1,2
+23320: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+23321: Facts:
+23321: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c2 ?2 ?3 ?4
+23321: Goal:
+23321: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23321: Order:
+23321: kbo
+23321: Leaf order:
+23321: b 1 0 1 1,2,2
+23321: a 4 0 4 1,1,2
+23321: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+23322: Facts:
+23322: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c2 ?2 ?3 ?4
+23322: Goal:
+23322: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23322: Order:
+23322: lpo
+23322: Leaf order:
+23322: b 1 0 1 1,2,2
+23322: a 4 0 4 1,1,2
+23322: nand 9 2 3 0,2
+% SZS status Timeout for BOO079-1.p
+NO CLASH, using fixed ground order
+23351: Facts:
+23351: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c2 ?2 ?3 ?4
+23351: Goal:
+NO CLASH, using fixed ground order
+23352: Facts:
+23352: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c2 ?2 ?3 ?4
+23352: Goal:
+23352: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23352: Order:
+23352: kbo
+23352: Leaf order:
+23352: c 2 0 2 2,2,2,2
+23352: a 3 0 3 1,2
+23352: b 3 0 3 1,2,2
+23352: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+23353: Facts:
+23353: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c2 ?2 ?3 ?4
+23353: Goal:
+23353: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23353: Order:
+23353: lpo
+23353: Leaf order:
+23353: c 2 0 2 2,2,2,2
+23353: a 3 0 3 1,2
+23353: b 3 0 3 1,2,2
+23353: nand 12 2 6 0,2
+23351: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23351: Order:
+23351: nrkbo
+23351: Leaf order:
+23351: c 2 0 2 2,2,2,2
+23351: a 3 0 3 1,2
+23351: b 3 0 3 1,2,2
+23351: nand 12 2 6 0,2
+% SZS status Timeout for BOO080-1.p
+NO CLASH, using fixed ground order
+23376: Facts:
+23376: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c3 ?2 ?3 ?4
+23376: Goal:
+23376: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23376: Order:
+23376: nrkbo
+23376: Leaf order:
+23376: b 1 0 1 1,2,2
+23376: a 4 0 4 1,1,2
+23376: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+23377: Facts:
+23377: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c3 ?2 ?3 ?4
+23377: Goal:
+23377: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23377: Order:
+23377: kbo
+23377: Leaf order:
+23377: b 1 0 1 1,2,2
+23377: a 4 0 4 1,1,2
+23377: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+23378: Facts:
+23378: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c3 ?2 ?3 ?4
+23378: Goal:
+23378: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23378: Order:
+23378: lpo
+23378: Leaf order:
+23378: b 1 0 1 1,2,2
+23378: a 4 0 4 1,1,2
+23378: nand 9 2 3 0,2
+% SZS status Timeout for BOO081-1.p
+NO CLASH, using fixed ground order
+23400: Facts:
+23400: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c3 ?2 ?3 ?4
+23400: Goal:
+23400: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23400: Order:
+23400: nrkbo
+23400: Leaf order:
+23400: c 2 0 2 2,2,2,2
+23400: a 3 0 3 1,2
+23400: b 3 0 3 1,2,2
+23400: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+23401: Facts:
+23401: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c3 ?2 ?3 ?4
+23401: Goal:
+23401: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23401: Order:
+23401: kbo
+23401: Leaf order:
+23401: c 2 0 2 2,2,2,2
+23401: a 3 0 3 1,2
+23401: b 3 0 3 1,2,2
+23401: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+23402: Facts:
+23402: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c3 ?2 ?3 ?4
+23402: Goal:
+23402: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23402: Order:
+23402: lpo
+23402: Leaf order:
+23402: c 2 0 2 2,2,2,2
+23402: a 3 0 3 1,2
+23402: b 3 0 3 1,2,2
+23402: nand 12 2 6 0,2
+% SZS status Timeout for BOO082-1.p
+NO CLASH, using fixed ground order
+23425: Facts:
+23425: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c4 ?2 ?3 ?4
+23425: Goal:
+23425: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23425: Order:
+23425: nrkbo
+23425: Leaf order:
+23425: b 1 0 1 1,2,2
+23425: a 4 0 4 1,1,2
+23425: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+23426: Facts:
+23426: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c4 ?2 ?3 ?4
+23426: Goal:
+23426: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23426: Order:
+23426: kbo
+23426: Leaf order:
+23426: b 1 0 1 1,2,2
+23426: a 4 0 4 1,1,2
+23426: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+23427: Facts:
+23427: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c4 ?2 ?3 ?4
+23427: Goal:
+23427: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23427: Order:
+23427: lpo
+23427: Leaf order:
+23427: b 1 0 1 1,2,2
+23427: a 4 0 4 1,1,2
+23427: nand 9 2 3 0,2
+% SZS status Timeout for BOO083-1.p
+NO CLASH, using fixed ground order
+23456: Facts:
+23456: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c4 ?2 ?3 ?4
+23456: Goal:
+23456: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23456: Order:
+23456: nrkbo
+23456: Leaf order:
+23456: c 2 0 2 2,2,2,2
+23456: a 3 0 3 1,2
+23456: b 3 0 3 1,2,2
+23456: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+23458: Facts:
+23458: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c4 ?2 ?3 ?4
+23458: Goal:
+23458: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23458: Order:
+23458: lpo
+23458: Leaf order:
+23458: c 2 0 2 2,2,2,2
+23458: a 3 0 3 1,2
+23458: b 3 0 3 1,2,2
+23458: nand 12 2 6 0,2
+23457: Facts:
+23457: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c4 ?2 ?3 ?4
+23457: Goal:
+23457: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23457: Order:
+23457: kbo
+23457: Leaf order:
+23457: c 2 0 2 2,2,2,2
+23457: a 3 0 3 1,2
+23457: b 3 0 3 1,2,2
+23457: nand 12 2 6 0,2
+% SZS status Timeout for BOO084-1.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+23485: Facts:
+23485: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c5 ?2 ?3 ?4
+23485: Goal:
+23485: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23485: Order:
+23485: kbo
+23485: Leaf order:
+23485: b 1 0 1 1,2,2
+23485: a 4 0 4 1,1,2
+23485: nand 9 2 3 0,2
+23484: Facts:
+23484: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c5 ?2 ?3 ?4
+23484: Goal:
+23484: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23484: Order:
+23484: nrkbo
+23484: Leaf order:
+23484: b 1 0 1 1,2,2
+23484: a 4 0 4 1,1,2
+23484: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+23486: Facts:
+23486: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c5 ?2 ?3 ?4
+23486: Goal:
+23486: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23486: Order:
+23486: lpo
+23486: Leaf order:
+23486: b 1 0 1 1,2,2
+23486: a 4 0 4 1,1,2
+23486: nand 9 2 3 0,2
+% SZS status Timeout for BOO085-1.p
+NO CLASH, using fixed ground order
+23521: Facts:
+23521: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c5 ?2 ?3 ?4
+23521: Goal:
+23521: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23521: Order:
+23521: nrkbo
+23521: Leaf order:
+23521: c 2 0 2 2,2,2,2
+23521: a 3 0 3 1,2
+23521: b 3 0 3 1,2,2
+23521: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+23522: Facts:
+23522: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c5 ?2 ?3 ?4
+23522: Goal:
+23522: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23522: Order:
+23522: kbo
+23522: Leaf order:
+23522: c 2 0 2 2,2,2,2
+23522: a 3 0 3 1,2
+23522: b 3 0 3 1,2,2
+23522: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+23523: Facts:
+23523: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c5 ?2 ?3 ?4
+23523: Goal:
+23523: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23523: Order:
+23523: lpo
+23523: Leaf order:
+23523: c 2 0 2 2,2,2,2
+23523: a 3 0 3 1,2
+23523: b 3 0 3 1,2,2
+23523: nand 12 2 6 0,2
+% SZS status Timeout for BOO086-1.p
+NO CLASH, using fixed ground order
+23545: Facts:
+23545: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
+ [4, 3, 2] by c6 ?2 ?3 ?4
+23545: Goal:
+23545: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23545: Order:
+23545: nrkbo
+23545: Leaf order:
+23545: b 1 0 1 1,2,2
+23545: a 4 0 4 1,1,2
+23545: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+23546: Facts:
+23546: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
+ [4, 3, 2] by c6 ?2 ?3 ?4
+23546: Goal:
+23546: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23546: Order:
+23546: kbo
+23546: Leaf order:
+23546: b 1 0 1 1,2,2
+23546: a 4 0 4 1,1,2
+23546: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+23547: Facts:
+23547: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
+ [4, 3, 2] by c6 ?2 ?3 ?4
+23547: Goal:
+23547: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23547: Order:
+23547: lpo
+23547: Leaf order:
+23547: b 1 0 1 1,2,2
+23547: a 4 0 4 1,1,2
+23547: nand 9 2 3 0,2
+% SZS status Timeout for BOO087-1.p
+NO CLASH, using fixed ground order
+23572: Facts:
+23572: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
+ [4, 3, 2] by c6 ?2 ?3 ?4
+23572: Goal:
+23572: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23572: Order:
+23572: nrkbo
+23572: Leaf order:
+23572: c 2 0 2 2,2,2,2
+23572: a 3 0 3 1,2
+23572: b 3 0 3 1,2,2
+23572: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+23573: Facts:
+23573: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
+ [4, 3, 2] by c6 ?2 ?3 ?4
+23573: Goal:
+23573: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23573: Order:
+23573: kbo
+23573: Leaf order:
+23573: c 2 0 2 2,2,2,2
+23573: a 3 0 3 1,2
+23573: b 3 0 3 1,2,2
+23573: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+23574: Facts:
+23574: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4
+ [4, 3, 2] by c6 ?2 ?3 ?4
+23574: Goal:
+23574: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23574: Order:
+23574: lpo
+23574: Leaf order:
+23574: c 2 0 2 2,2,2,2
+23574: a 3 0 3 1,2
+23574: b 3 0 3 1,2,2
+23574: nand 12 2 6 0,2
+% SZS status Timeout for BOO088-1.p
+NO CLASH, using fixed ground order
+23605: Facts:
+23605: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c7 ?2 ?3 ?4
+23605: Goal:
+23605: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23605: Order:
+23605: nrkbo
+23605: Leaf order:
+23605: b 1 0 1 1,2,2
+23605: a 4 0 4 1,1,2
+23605: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+23606: Facts:
+23606: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c7 ?2 ?3 ?4
+23606: Goal:
+23606: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23606: Order:
+23606: kbo
+23606: Leaf order:
+23606: b 1 0 1 1,2,2
+23606: a 4 0 4 1,1,2
+23606: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+23607: Facts:
+23607: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c7 ?2 ?3 ?4
+23607: Goal:
+23607: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23607: Order:
+23607: lpo
+23607: Leaf order:
+23607: b 1 0 1 1,2,2
+23607: a 4 0 4 1,1,2
+23607: nand 9 2 3 0,2
+% SZS status Timeout for BOO089-1.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+23696: Facts:
+23696: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c7 ?2 ?3 ?4
+23696: Goal:
+23696: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23696: Order:
+23696: kbo
+23696: Leaf order:
+23696: c 2 0 2 2,2,2,2
+23696: a 3 0 3 1,2
+23696: b 3 0 3 1,2,2
+23696: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+23697: Facts:
+23697: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c7 ?2 ?3 ?4
+23697: Goal:
+23697: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23697: Order:
+23697: lpo
+23697: Leaf order:
+23697: c 2 0 2 2,2,2,2
+23697: a 3 0 3 1,2
+23697: b 3 0 3 1,2,2
+23697: nand 12 2 6 0,2
+23695: Facts:
+23695: Id : 2, {_}:
+ nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c7 ?2 ?3 ?4
+23695: Goal:
+23695: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23695: Order:
+23695: nrkbo
+23695: Leaf order:
+23695: c 2 0 2 2,2,2,2
+23695: a 3 0 3 1,2
+23695: b 3 0 3 1,2,2
+23695: nand 12 2 6 0,2
+% SZS status Timeout for BOO090-1.p
+NO CLASH, using fixed ground order
+23723: Facts:
+23723: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c8 ?2 ?3 ?4
+23723: Goal:
+23723: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23723: Order:
+23723: nrkbo
+23723: Leaf order:
+23723: b 1 0 1 1,2,2
+23723: a 4 0 4 1,1,2
+23723: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+23724: Facts:
+23724: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c8 ?2 ?3 ?4
+23724: Goal:
+23724: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23724: Order:
+23724: kbo
+23724: Leaf order:
+23724: b 1 0 1 1,2,2
+23724: a 4 0 4 1,1,2
+23724: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+23725: Facts:
+23725: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c8 ?2 ?3 ?4
+23725: Goal:
+23725: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23725: Order:
+23725: lpo
+23725: Leaf order:
+23725: b 1 0 1 1,2,2
+23725: a 4 0 4 1,1,2
+23725: nand 9 2 3 0,2
+% SZS status Timeout for BOO091-1.p
+NO CLASH, using fixed ground order
+23747: Facts:
+23747: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c8 ?2 ?3 ?4
+23747: Goal:
+23747: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23747: Order:
+23747: nrkbo
+23747: Leaf order:
+23747: c 2 0 2 2,2,2,2
+23747: a 3 0 3 1,2
+23747: b 3 0 3 1,2,2
+23747: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+23748: Facts:
+23748: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c8 ?2 ?3 ?4
+23748: Goal:
+23748: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23748: Order:
+23748: kbo
+23748: Leaf order:
+23748: c 2 0 2 2,2,2,2
+23748: a 3 0 3 1,2
+23748: b 3 0 3 1,2,2
+23748: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+23749: Facts:
+23749: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c8 ?2 ?3 ?4
+23749: Goal:
+23749: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23749: Order:
+23749: lpo
+23749: Leaf order:
+23749: c 2 0 2 2,2,2,2
+23749: a 3 0 3 1,2
+23749: b 3 0 3 1,2,2
+23749: nand 12 2 6 0,2
+% SZS status Timeout for BOO092-1.p
+NO CLASH, using fixed ground order
+23772: Facts:
+23772: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c9 ?2 ?3 ?4
+23772: Goal:
+NO CLASH, using fixed ground order
+23773: Facts:
+23773: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c9 ?2 ?3 ?4
+23773: Goal:
+23773: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23773: Order:
+23773: kbo
+23773: Leaf order:
+23773: b 1 0 1 1,2,2
+23773: a 4 0 4 1,1,2
+23773: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+23774: Facts:
+23774: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c9 ?2 ?3 ?4
+23774: Goal:
+23774: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23774: Order:
+23774: lpo
+23774: Leaf order:
+23774: b 1 0 1 1,2,2
+23774: a 4 0 4 1,1,2
+23774: nand 9 2 3 0,2
+23772: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23772: Order:
+23772: nrkbo
+23772: Leaf order:
+23772: b 1 0 1 1,2,2
+23772: a 4 0 4 1,1,2
+23772: nand 9 2 3 0,2
+% SZS status Timeout for BOO093-1.p
+NO CLASH, using fixed ground order
+23798: Facts:
+23798: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c9 ?2 ?3 ?4
+23798: Goal:
+23798: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23798: Order:
+23798: nrkbo
+23798: Leaf order:
+23798: c 2 0 2 2,2,2,2
+23798: a 3 0 3 1,2
+23798: b 3 0 3 1,2,2
+23798: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+23799: Facts:
+23799: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c9 ?2 ?3 ?4
+23799: Goal:
+23799: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23799: Order:
+23799: kbo
+23799: Leaf order:
+23799: c 2 0 2 2,2,2,2
+23799: a 3 0 3 1,2
+23799: b 3 0 3 1,2,2
+23799: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+23800: Facts:
+23800: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c9 ?2 ?3 ?4
+23800: Goal:
+23800: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23800: Order:
+23800: lpo
+23800: Leaf order:
+23800: c 2 0 2 2,2,2,2
+23800: a 3 0 3 1,2
+23800: b 3 0 3 1,2,2
+23800: nand 12 2 6 0,2
+% SZS status Timeout for BOO094-1.p
+NO CLASH, using fixed ground order
+23822: Facts:
+23822: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c10 ?2 ?3 ?4
+23822: Goal:
+23822: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23822: Order:
+23822: nrkbo
+23822: Leaf order:
+23822: b 1 0 1 1,2,2
+23822: a 4 0 4 1,1,2
+23822: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+23823: Facts:
+23823: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c10 ?2 ?3 ?4
+23823: Goal:
+23823: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23823: Order:
+23823: kbo
+23823: Leaf order:
+23823: b 1 0 1 1,2,2
+23823: a 4 0 4 1,1,2
+23823: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+23824: Facts:
+23824: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c10 ?2 ?3 ?4
+23824: Goal:
+23824: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23824: Order:
+23824: lpo
+23824: Leaf order:
+23824: b 1 0 1 1,2,2
+23824: a 4 0 4 1,1,2
+23824: nand 9 2 3 0,2
+% SZS status Timeout for BOO095-1.p
+NO CLASH, using fixed ground order
+23854: Facts:
+23854: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c10 ?2 ?3 ?4
+23854: Goal:
+23854: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23854: Order:
+23854: nrkbo
+23854: Leaf order:
+23854: c 2 0 2 2,2,2,2
+23854: a 3 0 3 1,2
+23854: b 3 0 3 1,2,2
+23854: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+23855: Facts:
+23855: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c10 ?2 ?3 ?4
+23855: Goal:
+23855: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23855: Order:
+23855: kbo
+23855: Leaf order:
+23855: c 2 0 2 2,2,2,2
+23855: a 3 0 3 1,2
+23855: b 3 0 3 1,2,2
+23855: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+23856: Facts:
+23856: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c10 ?2 ?3 ?4
+23856: Goal:
+23856: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23856: Order:
+23856: lpo
+23856: Leaf order:
+23856: c 2 0 2 2,2,2,2
+23856: a 3 0 3 1,2
+23856: b 3 0 3 1,2,2
+23856: nand 12 2 6 0,2
+% SZS status Timeout for BOO096-1.p
+NO CLASH, using fixed ground order
+23878: Facts:
+23878: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
+ [4, 3, 2] by c11 ?2 ?3 ?4
+23878: Goal:
+23878: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23878: Order:
+23878: nrkbo
+23878: Leaf order:
+23878: b 1 0 1 1,2,2
+23878: a 4 0 4 1,1,2
+23878: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+23879: Facts:
+23879: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
+ [4, 3, 2] by c11 ?2 ?3 ?4
+23879: Goal:
+23879: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23879: Order:
+23879: kbo
+23879: Leaf order:
+23879: b 1 0 1 1,2,2
+23879: a 4 0 4 1,1,2
+23879: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+23880: Facts:
+23880: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
+ [4, 3, 2] by c11 ?2 ?3 ?4
+23880: Goal:
+23880: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23880: Order:
+23880: lpo
+23880: Leaf order:
+23880: b 1 0 1 1,2,2
+23880: a 4 0 4 1,1,2
+23880: nand 9 2 3 0,2
+% SZS status Timeout for BOO097-1.p
+NO CLASH, using fixed ground order
+23905: Facts:
+23905: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
+ [4, 3, 2] by c11 ?2 ?3 ?4
+23905: Goal:
+23905: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23905: Order:
+23905: nrkbo
+23905: Leaf order:
+23905: c 2 0 2 2,2,2,2
+23905: a 3 0 3 1,2
+23905: b 3 0 3 1,2,2
+23905: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+23906: Facts:
+23906: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
+ [4, 3, 2] by c11 ?2 ?3 ?4
+23906: Goal:
+23906: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23906: Order:
+23906: kbo
+23906: Leaf order:
+23906: c 2 0 2 2,2,2,2
+23906: a 3 0 3 1,2
+23906: b 3 0 3 1,2,2
+23906: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+23907: Facts:
+23907: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4
+ [4, 3, 2] by c11 ?2 ?3 ?4
+23907: Goal:
+23907: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23907: Order:
+23907: lpo
+23907: Leaf order:
+23907: c 2 0 2 2,2,2,2
+23907: a 3 0 3 1,2
+23907: b 3 0 3 1,2,2
+23907: nand 12 2 6 0,2
+% SZS status Timeout for BOO098-1.p
+NO CLASH, using fixed ground order
+23950: Facts:
+23950: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c12 ?2 ?3 ?4
+23950: Goal:
+23950: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23950: Order:
+23950: kbo
+23950: Leaf order:
+23950: b 1 0 1 1,2,2
+23950: a 4 0 4 1,1,2
+23950: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+23951: Facts:
+23951: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c12 ?2 ?3 ?4
+23951: Goal:
+23951: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23951: Order:
+23951: lpo
+23951: Leaf order:
+23951: b 1 0 1 1,2,2
+23951: a 4 0 4 1,1,2
+23951: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+23949: Facts:
+23949: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c12 ?2 ?3 ?4
+23949: Goal:
+23949: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+23949: Order:
+23949: nrkbo
+23949: Leaf order:
+23949: b 1 0 1 1,2,2
+23949: a 4 0 4 1,1,2
+23949: nand 9 2 3 0,2
+% SZS status Timeout for BOO099-1.p
+NO CLASH, using fixed ground order
+23972: Facts:
+23972: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c12 ?2 ?3 ?4
+23972: Goal:
+23972: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23972: Order:
+23972: nrkbo
+23972: Leaf order:
+23972: c 2 0 2 2,2,2,2
+23972: a 3 0 3 1,2
+23972: b 3 0 3 1,2,2
+23972: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+23973: Facts:
+23973: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c12 ?2 ?3 ?4
+23973: Goal:
+23973: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23973: Order:
+23973: kbo
+23973: Leaf order:
+23973: c 2 0 2 2,2,2,2
+23973: a 3 0 3 1,2
+23973: b 3 0 3 1,2,2
+23973: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+23974: Facts:
+23974: Id : 2, {_}:
+ nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c12 ?2 ?3 ?4
+23974: Goal:
+23974: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+23974: Order:
+23974: lpo
+23974: Leaf order:
+23974: c 2 0 2 2,2,2,2
+23974: a 3 0 3 1,2
+23974: b 3 0 3 1,2,2
+23974: nand 12 2 6 0,2
+% SZS status Timeout for BOO100-1.p
+NO CLASH, using fixed ground order
+24933: Facts:
+24933: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c13 ?2 ?3 ?4
+24933: Goal:
+24933: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+24933: Order:
+24933: nrkbo
+24933: Leaf order:
+24933: b 1 0 1 1,2,2
+24933: a 4 0 4 1,1,2
+24933: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+24934: Facts:
+24934: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c13 ?2 ?3 ?4
+24934: Goal:
+24934: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+24934: Order:
+24934: kbo
+24934: Leaf order:
+24934: b 1 0 1 1,2,2
+24934: a 4 0 4 1,1,2
+24934: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+24935: Facts:
+24935: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c13 ?2 ?3 ?4
+24935: Goal:
+24935: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+24935: Order:
+24935: lpo
+24935: Leaf order:
+24935: b 1 0 1 1,2,2
+24935: a 4 0 4 1,1,2
+24935: nand 9 2 3 0,2
+% SZS status Timeout for BOO101-1.p
+NO CLASH, using fixed ground order
+24957: Facts:
+NO CLASH, using fixed ground order
+24958: Facts:
+24958: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c13 ?2 ?3 ?4
+24958: Goal:
+24958: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+24958: Order:
+24958: kbo
+24958: Leaf order:
+24958: c 2 0 2 2,2,2,2
+24958: a 3 0 3 1,2
+24958: b 3 0 3 1,2,2
+24958: nand 12 2 6 0,2
+24957: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c13 ?2 ?3 ?4
+24957: Goal:
+24957: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+24957: Order:
+24957: nrkbo
+24957: Leaf order:
+24957: c 2 0 2 2,2,2,2
+24957: a 3 0 3 1,2
+24957: b 3 0 3 1,2,2
+24957: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+24959: Facts:
+24959: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c13 ?2 ?3 ?4
+24959: Goal:
+24959: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+24959: Order:
+24959: lpo
+24959: Leaf order:
+24959: c 2 0 2 2,2,2,2
+24959: a 3 0 3 1,2
+24959: b 3 0 3 1,2,2
+24959: nand 12 2 6 0,2
+% SZS status Timeout for BOO102-1.p
+NO CLASH, using fixed ground order
+24983: Facts:
+24983: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c14 ?2 ?3 ?4
+24983: Goal:
+24983: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+24983: Order:
+24983: nrkbo
+24983: Leaf order:
+24983: b 1 0 1 1,2,2
+24983: a 4 0 4 1,1,2
+24983: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+24984: Facts:
+24984: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c14 ?2 ?3 ?4
+24984: Goal:
+24984: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+24984: Order:
+24984: kbo
+24984: Leaf order:
+24984: b 1 0 1 1,2,2
+24984: a 4 0 4 1,1,2
+24984: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+24985: Facts:
+24985: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c14 ?2 ?3 ?4
+24985: Goal:
+24985: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+24985: Order:
+24985: lpo
+24985: Leaf order:
+24985: b 1 0 1 1,2,2
+24985: a 4 0 4 1,1,2
+24985: nand 9 2 3 0,2
+% SZS status Timeout for BOO103-1.p
+NO CLASH, using fixed ground order
+25006: Facts:
+25006: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c14 ?2 ?3 ?4
+25006: Goal:
+25006: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+25006: Order:
+25006: nrkbo
+25006: Leaf order:
+25006: c 2 0 2 2,2,2,2
+25006: a 3 0 3 1,2
+25006: b 3 0 3 1,2,2
+25006: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+25007: Facts:
+25007: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c14 ?2 ?3 ?4
+25007: Goal:
+25007: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+25007: Order:
+25007: kbo
+25007: Leaf order:
+25007: c 2 0 2 2,2,2,2
+25007: a 3 0 3 1,2
+25007: b 3 0 3 1,2,2
+25007: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+25008: Facts:
+25008: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c14 ?2 ?3 ?4
+25008: Goal:
+25008: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+25008: Order:
+25008: lpo
+25008: Leaf order:
+25008: c 2 0 2 2,2,2,2
+25008: a 3 0 3 1,2
+25008: b 3 0 3 1,2,2
+25008: nand 12 2 6 0,2
+% SZS status Timeout for BOO104-1.p
+NO CLASH, using fixed ground order
+25030: Facts:
+25030: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c15 ?2 ?3 ?4
+25030: Goal:
+25030: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+25030: Order:
+25030: nrkbo
+25030: Leaf order:
+25030: b 1 0 1 1,2,2
+25030: a 4 0 4 1,1,2
+25030: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+25031: Facts:
+25031: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c15 ?2 ?3 ?4
+25031: Goal:
+25031: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+25031: Order:
+25031: kbo
+25031: Leaf order:
+25031: b 1 0 1 1,2,2
+25031: a 4 0 4 1,1,2
+25031: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+25032: Facts:
+25032: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c15 ?2 ?3 ?4
+25032: Goal:
+25032: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+25032: Order:
+25032: lpo
+25032: Leaf order:
+25032: b 1 0 1 1,2,2
+25032: a 4 0 4 1,1,2
+25032: nand 9 2 3 0,2
+% SZS status Timeout for BOO105-1.p
+NO CLASH, using fixed ground order
+25053: Facts:
+25053: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c15 ?2 ?3 ?4
+25053: Goal:
+25053: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+25053: Order:
+25053: nrkbo
+25053: Leaf order:
+25053: c 2 0 2 2,2,2,2
+25053: a 3 0 3 1,2
+25053: b 3 0 3 1,2,2
+25053: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+25054: Facts:
+25054: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c15 ?2 ?3 ?4
+25054: Goal:
+25054: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+25054: Order:
+25054: kbo
+25054: Leaf order:
+25054: c 2 0 2 2,2,2,2
+25054: a 3 0 3 1,2
+25054: b 3 0 3 1,2,2
+25054: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+25055: Facts:
+25055: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3
+ [4, 3, 2] by c15 ?2 ?3 ?4
+25055: Goal:
+25055: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+25055: Order:
+25055: lpo
+25055: Leaf order:
+25055: c 2 0 2 2,2,2,2
+25055: a 3 0 3 1,2
+25055: b 3 0 3 1,2,2
+25055: nand 12 2 6 0,2
+% SZS status Timeout for BOO106-1.p
+NO CLASH, using fixed ground order
+25082: Facts:
+25082: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c16 ?2 ?3 ?4
+25082: Goal:
+25082: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+25082: Order:
+25082: nrkbo
+25082: Leaf order:
+25082: b 1 0 1 1,2,2
+25082: a 4 0 4 1,1,2
+25082: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+25083: Facts:
+25083: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c16 ?2 ?3 ?4
+25083: Goal:
+25083: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+25083: Order:
+25083: kbo
+25083: Leaf order:
+25083: b 1 0 1 1,2,2
+25083: a 4 0 4 1,1,2
+25083: nand 9 2 3 0,2
+NO CLASH, using fixed ground order
+25084: Facts:
+25084: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c16 ?2 ?3 ?4
+25084: Goal:
+25084: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1
+25084: Order:
+25084: lpo
+25084: Leaf order:
+25084: b 1 0 1 1,2,2
+25084: a 4 0 4 1,1,2
+25084: nand 9 2 3 0,2
+% SZS status Timeout for BOO107-1.p
+NO CLASH, using fixed ground order
+25109: Facts:
+25109: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c16 ?2 ?3 ?4
+25109: Goal:
+25109: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+25109: Order:
+25109: nrkbo
+25109: Leaf order:
+25109: c 2 0 2 2,2,2,2
+25109: a 3 0 3 1,2
+25109: b 3 0 3 1,2,2
+25109: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+25110: Facts:
+25110: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c16 ?2 ?3 ?4
+25110: Goal:
+25110: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+25110: Order:
+25110: kbo
+25110: Leaf order:
+25110: c 2 0 2 2,2,2,2
+25110: a 3 0 3 1,2
+25110: b 3 0 3 1,2,2
+25110: nand 12 2 6 0,2
+NO CLASH, using fixed ground order
+25111: Facts:
+25111: Id : 2, {_}:
+ nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3
+ [4, 3, 2] by c16 ?2 ?3 ?4
+25111: Goal:
+25111: Id : 1, {_}:
+ nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a
+ [] by prove_meredith_2_basis_2
+25111: Order:
+25111: lpo
+25111: Leaf order:
+25111: c 2 0 2 2,2,2,2
+25111: a 3 0 3 1,2
+25111: b 3 0 3 1,2,2
+25111: nand 12 2 6 0,2
+% SZS status Timeout for BOO108-1.p
+CLASH, statistics insufficient
+25136: Facts:
+25136: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+25136: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+25136: Goal:
+25136: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+25136: Order:
+25136: nrkbo
+25136: Leaf order:
+25136: s 1 0 0
+25136: b 1 0 0
+25136: f 3 1 3 0,2,2
+25136: apply 14 2 3 0,2
+CLASH, statistics insufficient
+25137: Facts:
+25137: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+25137: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+25137: Goal:
+25137: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+25137: Order:
+25137: kbo
+25137: Leaf order:
+25137: s 1 0 0
+25137: b 1 0 0
+25137: f 3 1 3 0,2,2
+25137: apply 14 2 3 0,2
+CLASH, statistics insufficient
+25138: Facts:
+25138: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+25138: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+25138: Goal:
+25138: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+25138: Order:
+25138: lpo
+25138: Leaf order:
+25138: s 1 0 0
+25138: b 1 0 0
+25138: f 3 1 3 0,2,2
+25138: apply 14 2 3 0,2
+% SZS status Timeout for COL067-1.p
+CLASH, statistics insufficient
+25159: Facts:
+25159: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+25159: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+25159: Goal:
+25159: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
+25159: Order:
+25159: nrkbo
+25159: Leaf order:
+25159: s 1 0 0
+25159: b 1 0 0
+25159: combinator 1 0 1 1,3
+25159: apply 12 2 1 0,3
+CLASH, statistics insufficient
+25160: Facts:
+25160: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+25160: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+25160: Goal:
+25160: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
+25160: Order:
+25160: kbo
+25160: Leaf order:
+25160: s 1 0 0
+25160: b 1 0 0
+25160: combinator 1 0 1 1,3
+25160: apply 12 2 1 0,3
+CLASH, statistics insufficient
+25161: Facts:
+25161: Id : 2, {_}:
+ apply (apply (apply s ?3) ?4) ?5
+ =?=
+ apply (apply ?3 ?5) (apply ?4 ?5)
+ [5, 4, 3] by s_definition ?3 ?4 ?5
+25161: Id : 3, {_}:
+ apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9)
+ [9, 8, 7] by b_definition ?7 ?8 ?9
+25161: Goal:
+25161: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1
+25161: Order:
+25161: lpo
+25161: Leaf order:
+25161: s 1 0 0
+25161: b 1 0 0
+25161: combinator 1 0 1 1,3
+25161: apply 12 2 1 0,3
+% SZS status Timeout for COL068-1.p
+CLASH, statistics insufficient
+25183: Facts:
+25183: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+25183: Id : 3, {_}:
+ apply (apply l ?7) ?8 =?= apply ?7 (apply ?8 ?8)
+ [8, 7] by l_definition ?7 ?8
+25183: Goal:
+25183: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+25183: Order:
+25183: nrkbo
+25183: Leaf order:
+25183: b 1 0 0
+25183: l 1 0 0
+25183: f 3 1 3 0,2,2
+25183: apply 12 2 3 0,2
+CLASH, statistics insufficient
+25184: Facts:
+25184: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+25184: Id : 3, {_}:
+ apply (apply l ?7) ?8 =?= apply ?7 (apply ?8 ?8)
+ [8, 7] by l_definition ?7 ?8
+25184: Goal:
+25184: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+25184: Order:
+25184: kbo
+25184: Leaf order:
+25184: b 1 0 0
+25184: l 1 0 0
+25184: f 3 1 3 0,2,2
+25184: apply 12 2 3 0,2
+CLASH, statistics insufficient
+25185: Facts:
+25185: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by b_definition ?3 ?4 ?5
+25185: Id : 3, {_}:
+ apply (apply l ?7) ?8 =?= apply ?7 (apply ?8 ?8)
+ [8, 7] by l_definition ?7 ?8
+25185: Goal:
+25185: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by prove_fixed_point ?1
+25185: Order:
+25185: lpo
+25185: Leaf order:
+25185: b 1 0 0
+25185: l 1 0 0
+25185: f 3 1 3 0,2,2
+25185: apply 12 2 3 0,2
+% SZS status Timeout for COL069-1.p
+CLASH, statistics insufficient
+25251: Facts:
+25251: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by definition_B ?3 ?4 ?5
+25251: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by definition_M ?7
+25251: Goal:
+25251: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by strong_fixpoint ?1
+25251: Order:
+25251: nrkbo
+25251: Leaf order:
+25251: b 1 0 0
+25251: m 1 0 0
+25251: f 3 1 3 0,2,2
+25251: apply 10 2 3 0,2
+CLASH, statistics insufficient
+25252: Facts:
+25252: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by definition_B ?3 ?4 ?5
+25252: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by definition_M ?7
+25252: Goal:
+25252: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by strong_fixpoint ?1
+25252: Order:
+25252: kbo
+25252: Leaf order:
+25252: b 1 0 0
+25252: m 1 0 0
+25252: f 3 1 3 0,2,2
+25252: apply 10 2 3 0,2
+CLASH, statistics insufficient
+25253: Facts:
+25253: Id : 2, {_}:
+ apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5)
+ [5, 4, 3] by definition_B ?3 ?4 ?5
+25253: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by definition_M ?7
+25253: Goal:
+25253: Id : 1, {_}:
+ apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1))
+ [1] by strong_fixpoint ?1
+25253: Order:
+25253: lpo
+25253: Leaf order:
+25253: b 1 0 0
+25253: m 1 0 0
+25253: f 3 1 3 0,2,2
+25253: apply 10 2 3 0,2
+% SZS status Timeout for COL087-1.p
+NO CLASH, using fixed ground order
+25281: Facts:
+25281: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25281: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25281: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25281: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25281: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25281: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =?=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25281: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =?=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25281: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25281: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25281: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25281: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25281: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25281: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25281: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25281: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25281: Id : 17, {_}: least_upper_bound identity a =>= a [] by p08a_1
+25281: Id : 18, {_}: least_upper_bound identity b =>= b [] by p08a_2
+25281: Id : 19, {_}: least_upper_bound identity c =>= c [] by p08a_3
+25281: Goal:
+25281: Id : 1, {_}:
+ least_upper_bound (greatest_lower_bound a (multiply b c))
+ (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
+ =>=
+ multiply (greatest_lower_bound a b) (greatest_lower_bound a c)
+ [] by prove_p08a
+25281: Order:
+25281: nrkbo
+25281: Leaf order:
+25281: identity 5 0 0
+25281: b 5 0 3 1,2,1,2
+25281: c 5 0 3 2,2,1,2
+25281: a 7 0 5 1,1,2
+25281: inverse 1 1 0
+25281: least_upper_bound 17 2 1 0,2
+25281: greatest_lower_bound 18 2 5 0,1,2
+25281: multiply 21 2 3 0,2,1,2
+NO CLASH, using fixed ground order
+25282: Facts:
+25282: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25282: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25282: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25282: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25282: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25282: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25282: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25282: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25282: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25282: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25282: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25282: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =<=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25282: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =<=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25282: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =<=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25282: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =<=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25282: Id : 17, {_}: least_upper_bound identity a =>= a [] by p08a_1
+25282: Id : 18, {_}: least_upper_bound identity b =>= b [] by p08a_2
+25282: Id : 19, {_}: least_upper_bound identity c =>= c [] by p08a_3
+25282: Goal:
+25282: Id : 1, {_}:
+ least_upper_bound (greatest_lower_bound a (multiply b c))
+ (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
+ =>=
+ multiply (greatest_lower_bound a b) (greatest_lower_bound a c)
+ [] by prove_p08a
+25282: Order:
+25282: kbo
+25282: Leaf order:
+25282: identity 5 0 0
+25282: b 5 0 3 1,2,1,2
+25282: c 5 0 3 2,2,1,2
+25282: a 7 0 5 1,1,2
+25282: inverse 1 1 0
+25282: least_upper_bound 17 2 1 0,2
+25282: greatest_lower_bound 18 2 5 0,1,2
+25282: multiply 21 2 3 0,2,1,2
+NO CLASH, using fixed ground order
+25283: Facts:
+25283: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
+25283: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
+25283: Id : 4, {_}:
+ multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8)
+ [8, 7, 6] by associativity ?6 ?7 ?8
+25283: Id : 5, {_}:
+ greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
+ [11, 10] by symmetry_of_glb ?10 ?11
+25283: Id : 6, {_}:
+ least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
+ [14, 13] by symmetry_of_lub ?13 ?14
+25283: Id : 7, {_}:
+ greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
+ =<=
+ greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
+ [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
+25283: Id : 8, {_}:
+ least_upper_bound ?20 (least_upper_bound ?21 ?22)
+ =<=
+ least_upper_bound (least_upper_bound ?20 ?21) ?22
+ [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
+25283: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
+25283: Id : 10, {_}:
+ greatest_lower_bound ?26 ?26 =>= ?26
+ [26] by idempotence_of_gld ?26
+25283: Id : 11, {_}:
+ least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
+ [29, 28] by lub_absorbtion ?28 ?29
+25283: Id : 12, {_}:
+ greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
+ [32, 31] by glb_absorbtion ?31 ?32
+25283: Id : 13, {_}:
+ multiply ?34 (least_upper_bound ?35 ?36)
+ =>=
+ least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
+ [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
+25283: Id : 14, {_}:
+ multiply ?38 (greatest_lower_bound ?39 ?40)
+ =>=
+ greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
+ [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
+25283: Id : 15, {_}:
+ multiply (least_upper_bound ?42 ?43) ?44
+ =>=
+ least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
+ [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
+25283: Id : 16, {_}:
+ multiply (greatest_lower_bound ?46 ?47) ?48
+ =>=
+ greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
+ [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
+25283: Id : 17, {_}: least_upper_bound identity a =>= a [] by p08a_1
+25283: Id : 18, {_}: least_upper_bound identity b =>= b [] by p08a_2
+25283: Id : 19, {_}: least_upper_bound identity c =>= c [] by p08a_3
+25283: Goal:
+25283: Id : 1, {_}:
+ least_upper_bound (greatest_lower_bound a (multiply b c))
+ (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
+ =>=
+ multiply (greatest_lower_bound a b) (greatest_lower_bound a c)
+ [] by prove_p08a
+25283: Order:
+25283: lpo
+25283: Leaf order:
+25283: identity 5 0 0
+25283: b 5 0 3 1,2,1,2
+25283: c 5 0 3 2,2,1,2
+25283: a 7 0 5 1,1,2
+25283: inverse 1 1 0
+25283: least_upper_bound 17 2 1 0,2
+25283: greatest_lower_bound 18 2 5 0,1,2
+25283: multiply 21 2 3 0,2,1,2
+% SZS status Timeout for GRP177-1.p
+NO CLASH, using fixed ground order
+25304: Facts:
+25304: Id : 2, {_}:
+ f (f ?2 ?3) (f (f (f (f ?2 ?3) ?3) (f ?4 ?3)) (f (f ?3 ?3) ?5))
+ =>=
+ ?3
+ [5, 4, 3, 2] by oml_21C ?2 ?3 ?4 ?5
+25304: Goal:
+25304: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
+ [] by associativity
+25304: Order:
+25304: nrkbo
+25304: Leaf order:
+25304: a 3 0 3 1,2
+25304: c 3 0 3 2,1,2,2
+25304: b 4 0 4 1,1,2,2
+25304: f 17 2 8 0,2
+NO CLASH, using fixed ground order
+25305: Facts:
+25305: Id : 2, {_}:
+ f (f ?2 ?3) (f (f (f (f ?2 ?3) ?3) (f ?4 ?3)) (f (f ?3 ?3) ?5))
+ =>=
+ ?3
+ [5, 4, 3, 2] by oml_21C ?2 ?3 ?4 ?5
+25305: Goal:
+25305: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
+ [] by associativity
+25305: Order:
+25305: kbo
+25305: Leaf order:
+25305: a 3 0 3 1,2
+25305: c 3 0 3 2,1,2,2
+25305: b 4 0 4 1,1,2,2
+25305: f 17 2 8 0,2
+NO CLASH, using fixed ground order
+25306: Facts:
+25306: Id : 2, {_}:
+ f (f ?2 ?3) (f (f (f (f ?2 ?3) ?3) (f ?4 ?3)) (f (f ?3 ?3) ?5))
+ =>=
+ ?3
+ [5, 4, 3, 2] by oml_21C ?2 ?3 ?4 ?5
+25306: Goal:
+25306: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
+ [] by associativity
+25306: Order:
+25306: lpo
+25306: Leaf order:
+25306: a 3 0 3 1,2
+25306: c 3 0 3 2,1,2,2
+25306: b 4 0 4 1,1,2,2
+25306: f 17 2 8 0,2
+% SZS status Timeout for LAT071-1.p
+NO CLASH, using fixed ground order
+25332: Facts:
+25332: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
+ (f ?3 (f (f ?4 (f (f ?3 ?3) ?4)) ?4))
+ =>=
+ ?3
+ [5, 4, 3, 2] by oml_23A ?2 ?3 ?4 ?5
+25332: Goal:
+25332: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
+ [] by associativity
+25332: Order:
+25332: nrkbo
+25332: Leaf order:
+25332: a 3 0 3 1,2
+25332: c 3 0 3 2,1,2,2
+25332: b 4 0 4 1,1,2,2
+25332: f 18 2 8 0,2
+NO CLASH, using fixed ground order
+25333: Facts:
+25333: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
+ (f ?3 (f (f ?4 (f (f ?3 ?3) ?4)) ?4))
+ =>=
+ ?3
+ [5, 4, 3, 2] by oml_23A ?2 ?3 ?4 ?5
+25333: Goal:
+25333: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
+ [] by associativity
+25333: Order:
+25333: kbo
+25333: Leaf order:
+25333: a 3 0 3 1,2
+25333: c 3 0 3 2,1,2,2
+25333: b 4 0 4 1,1,2,2
+25333: f 18 2 8 0,2
+NO CLASH, using fixed ground order
+25334: Facts:
+25334: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
+ (f ?3 (f (f ?4 (f (f ?3 ?3) ?4)) ?4))
+ =>=
+ ?3
+ [5, 4, 3, 2] by oml_23A ?2 ?3 ?4 ?5
+25334: Goal:
+25334: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
+ [] by associativity
+25334: Order:
+25334: lpo
+25334: Leaf order:
+25334: a 3 0 3 1,2
+25334: c 3 0 3 2,1,2,2
+25334: b 4 0 4 1,1,2,2
+25334: f 18 2 8 0,2
+% SZS status Timeout for LAT072-1.p
+NO CLASH, using fixed ground order
+25355: Facts:
+25355: Id : 2, {_}:
+ f (f (f ?2 (f ?3 ?2)) ?2)
+ (f ?3 (f ?4 (f (f ?3 ?2) (f (f ?4 ?4) ?5))))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_23C ?2 ?3 ?4 ?5
+25355: Goal:
+25355: Id : 1, {_}:
+ f a (f b (f a (f c c))) =<= f a (f c (f a (f b b)))
+ [] by modularity
+25355: Order:
+25355: nrkbo
+25355: Leaf order:
+25355: b 3 0 3 1,2,2
+25355: c 3 0 3 1,2,2,2,2
+25355: a 4 0 4 1,2
+25355: f 18 2 8 0,2
+NO CLASH, using fixed ground order
+25356: Facts:
+25356: Id : 2, {_}:
+ f (f (f ?2 (f ?3 ?2)) ?2)
+ (f ?3 (f ?4 (f (f ?3 ?2) (f (f ?4 ?4) ?5))))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_23C ?2 ?3 ?4 ?5
+25356: Goal:
+25356: Id : 1, {_}:
+ f a (f b (f a (f c c))) =?= f a (f c (f a (f b b)))
+ [] by modularity
+25356: Order:
+25356: kbo
+25356: Leaf order:
+25356: b 3 0 3 1,2,2
+25356: c 3 0 3 1,2,2,2,2
+25356: a 4 0 4 1,2
+25356: f 18 2 8 0,2
+NO CLASH, using fixed ground order
+25357: Facts:
+25357: Id : 2, {_}:
+ f (f (f ?2 (f ?3 ?2)) ?2)
+ (f ?3 (f ?4 (f (f ?3 ?2) (f (f ?4 ?4) ?5))))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_23C ?2 ?3 ?4 ?5
+25357: Goal:
+25357: Id : 1, {_}:
+ f a (f b (f a (f c c))) =>= f a (f c (f a (f b b)))
+ [] by modularity
+25357: Order:
+25357: lpo
+25357: Leaf order:
+25357: b 3 0 3 1,2,2
+25357: c 3 0 3 1,2,2,2,2
+25357: a 4 0 4 1,2
+25357: f 18 2 8 0,2
+% SZS status Timeout for LAT073-1.p
+NO CLASH, using fixed ground order
+25379: Facts:
+NO CLASH, using fixed ground order
+25381: Facts:
+25381: Id : 2, {_}:
+ f (f ?2 ?3)
+ (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
+25381: Goal:
+25381: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
+ [] by associativity
+25381: Order:
+25381: lpo
+25381: Leaf order:
+25381: a 3 0 3 1,2
+25381: c 3 0 3 2,1,2,2
+25381: b 4 0 4 1,1,2,2
+25381: f 19 2 8 0,2
+NO CLASH, using fixed ground order
+25380: Facts:
+25380: Id : 2, {_}:
+ f (f ?2 ?3)
+ (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
+25380: Goal:
+25380: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
+ [] by associativity
+25380: Order:
+25380: kbo
+25380: Leaf order:
+25380: a 3 0 3 1,2
+25380: c 3 0 3 2,1,2,2
+25380: b 4 0 4 1,1,2,2
+25380: f 19 2 8 0,2
+25379: Id : 2, {_}:
+ f (f ?2 ?3)
+ (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
+25379: Goal:
+25379: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
+ [] by associativity
+25379: Order:
+25379: nrkbo
+25379: Leaf order:
+25379: a 3 0 3 1,2
+25379: c 3 0 3 2,1,2,2
+25379: b 4 0 4 1,1,2,2
+25379: f 19 2 8 0,2
+% SZS status Timeout for LAT074-1.p
+NO CLASH, using fixed ground order
+25407: Facts:
+25407: Id : 2, {_}:
+ f (f ?2 ?3)
+ (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
+25407: Goal:
+25407: Id : 1, {_}:
+ f a (f b (f a (f c c))) =<= f a (f c (f a (f b b)))
+ [] by modularity
+25407: Order:
+25407: nrkbo
+25407: Leaf order:
+25407: b 3 0 3 1,2,2
+25407: c 3 0 3 1,2,2,2,2
+25407: a 4 0 4 1,2
+25407: f 19 2 8 0,2
+NO CLASH, using fixed ground order
+25408: Facts:
+25408: Id : 2, {_}:
+ f (f ?2 ?3)
+ (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
+25408: Goal:
+25408: Id : 1, {_}:
+ f a (f b (f a (f c c))) =?= f a (f c (f a (f b b)))
+ [] by modularity
+25408: Order:
+25408: kbo
+25408: Leaf order:
+25408: b 3 0 3 1,2,2
+25408: c 3 0 3 1,2,2,2,2
+25408: a 4 0 4 1,2
+25408: f 19 2 8 0,2
+NO CLASH, using fixed ground order
+25409: Facts:
+25409: Id : 2, {_}:
+ f (f ?2 ?3)
+ (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5)))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5
+25409: Goal:
+25409: Id : 1, {_}:
+ f a (f b (f a (f c c))) =>= f a (f c (f a (f b b)))
+ [] by modularity
+25409: Order:
+25409: lpo
+25409: Leaf order:
+25409: b 3 0 3 1,2,2
+25409: c 3 0 3 1,2,2,2,2
+25409: a 4 0 4 1,2
+25409: f 19 2 8 0,2
+% SZS status Timeout for LAT075-1.p
+NO CLASH, using fixed ground order
+25460: Facts:
+25460: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
+ (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
+25460: Goal:
+25460: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
+ [] by associativity
+25460: Order:
+25460: nrkbo
+25460: Leaf order:
+25460: a 3 0 3 1,2
+25460: c 3 0 3 2,1,2,2
+25460: b 4 0 4 1,1,2,2
+25460: f 20 2 8 0,2
+NO CLASH, using fixed ground order
+25461: Facts:
+25461: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
+ (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
+25461: Goal:
+25461: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
+ [] by associativity
+25461: Order:
+25461: kbo
+25461: Leaf order:
+25461: a 3 0 3 1,2
+25461: c 3 0 3 2,1,2,2
+25461: b 4 0 4 1,1,2,2
+25461: f 20 2 8 0,2
+NO CLASH, using fixed ground order
+25462: Facts:
+25462: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
+ (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
+25462: Goal:
+25462: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
+ [] by associativity
+25462: Order:
+25462: lpo
+25462: Leaf order:
+25462: a 3 0 3 1,2
+25462: c 3 0 3 2,1,2,2
+25462: b 4 0 4 1,1,2,2
+25462: f 20 2 8 0,2
+% SZS status Timeout for LAT076-1.p
+NO CLASH, using fixed ground order
+25483: Facts:
+25483: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
+ (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
+25483: Goal:
+25483: Id : 1, {_}:
+ f a (f b (f a (f c c))) =<= f a (f c (f a (f b b)))
+ [] by modularity
+25483: Order:
+25483: nrkbo
+25483: Leaf order:
+25483: b 3 0 3 1,2,2
+25483: c 3 0 3 1,2,2,2,2
+25483: a 4 0 4 1,2
+25483: f 20 2 8 0,2
+NO CLASH, using fixed ground order
+25484: Facts:
+25484: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
+ (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
+25484: Goal:
+25484: Id : 1, {_}:
+ f a (f b (f a (f c c))) =?= f a (f c (f a (f b b)))
+ [] by modularity
+25484: Order:
+25484: kbo
+25484: Leaf order:
+25484: b 3 0 3 1,2,2
+25484: c 3 0 3 1,2,2,2,2
+25484: a 4 0 4 1,2
+25484: f 20 2 8 0,2
+NO CLASH, using fixed ground order
+25485: Facts:
+25485: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?4 ?3)) ?5)
+ (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5
+25485: Goal:
+25485: Id : 1, {_}:
+ f a (f b (f a (f c c))) =>= f a (f c (f a (f b b)))
+ [] by modularity
+25485: Order:
+25485: lpo
+25485: Leaf order:
+25485: b 3 0 3 1,2,2
+25485: c 3 0 3 1,2,2,2,2
+25485: a 4 0 4 1,2
+25485: f 20 2 8 0,2
+% SZS status Timeout for LAT077-1.p
+NO CLASH, using fixed ground order
+25507: Facts:
+25507: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
+ (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
+25507: Goal:
+25507: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
+ [] by associativity
+25507: Order:
+25507: nrkbo
+25507: Leaf order:
+25507: a 3 0 3 1,2
+25507: c 3 0 3 2,1,2,2
+25507: b 4 0 4 1,1,2,2
+25507: f 20 2 8 0,2
+NO CLASH, using fixed ground order
+25508: Facts:
+25508: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
+ (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
+25508: Goal:
+25508: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a))
+ [] by associativity
+25508: Order:
+25508: kbo
+25508: Leaf order:
+25508: a 3 0 3 1,2
+25508: c 3 0 3 2,1,2,2
+25508: b 4 0 4 1,1,2,2
+25508: f 20 2 8 0,2
+NO CLASH, using fixed ground order
+25509: Facts:
+25509: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
+ (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
+25509: Goal:
+25509: Id : 1, {_}:
+ f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a))
+ [] by associativity
+25509: Order:
+25509: lpo
+25509: Leaf order:
+25509: a 3 0 3 1,2
+25509: c 3 0 3 2,1,2,2
+25509: b 4 0 4 1,1,2,2
+25509: f 20 2 8 0,2
+% SZS status Timeout for LAT078-1.p
+NO CLASH, using fixed ground order
+25531: Facts:
+25531: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
+ (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
+25531: Goal:
+25531: Id : 1, {_}:
+ f a (f b (f a (f c c))) =<= f a (f c (f a (f b b)))
+ [] by modularity
+25531: Order:
+25531: nrkbo
+25531: Leaf order:
+25531: b 3 0 3 1,2,2
+25531: c 3 0 3 1,2,2,2,2
+25531: a 4 0 4 1,2
+25531: f 20 2 8 0,2
+NO CLASH, using fixed ground order
+25532: Facts:
+25532: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
+ (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
+25532: Goal:
+25532: Id : 1, {_}:
+ f a (f b (f a (f c c))) =?= f a (f c (f a (f b b)))
+ [] by modularity
+25532: Order:
+25532: kbo
+25532: Leaf order:
+25532: b 3 0 3 1,2,2
+25532: c 3 0 3 1,2,2,2,2
+25532: a 4 0 4 1,2
+25532: f 20 2 8 0,2
+NO CLASH, using fixed ground order
+25533: Facts:
+25533: Id : 2, {_}:
+ f (f (f (f ?2 ?3) (f ?3 ?4)) ?5)
+ (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4))
+ =>=
+ ?3
+ [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5
+25533: Goal:
+25533: Id : 1, {_}:
+ f a (f b (f a (f c c))) =>= f a (f c (f a (f b b)))
+ [] by modularity
+25533: Order:
+25533: lpo
+25533: Leaf order:
+25533: b 3 0 3 1,2,2
+25533: c 3 0 3 1,2,2,2,2
+25533: a 4 0 4 1,2
+25533: f 20 2 8 0,2
+% SZS status Timeout for LAT079-1.p
+NO CLASH, using fixed ground order
+25631: Facts:
+25631: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25631: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25631: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25631: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25631: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25631: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25631: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25631: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25631: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?28 (join ?26 (meet ?27 (join ?28 (meet ?26 ?27))))))
+ [28, 27, 26] by equation_H11 ?26 ?27 ?28
+25631: Goal:
+25631: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join a (meet b c))))
+ [] by prove_H10
+25631: Order:
+25631: nrkbo
+25631: Leaf order:
+25631: b 3 0 3 1,2,2
+25631: c 3 0 3 2,2,2,2
+25631: a 4 0 4 1,2
+25631: join 16 2 3 0,2,2
+25631: meet 20 2 5 0,2
+NO CLASH, using fixed ground order
+25633: Facts:
+25633: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25633: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25633: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25633: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25633: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25633: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25633: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25633: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25633: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =?=
+ meet ?26
+ (join ?27
+ (meet ?28 (join ?26 (meet ?27 (join ?28 (meet ?26 ?27))))))
+ [28, 27, 26] by equation_H11 ?26 ?27 ?28
+25633: Goal:
+25633: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =>=
+ meet a (join b (meet c (join a (meet b c))))
+ [] by prove_H10
+25633: Order:
+25633: lpo
+25633: Leaf order:
+25633: b 3 0 3 1,2,2
+25633: c 3 0 3 2,2,2,2
+25633: a 4 0 4 1,2
+25633: join 16 2 3 0,2,2
+25633: meet 20 2 5 0,2
+NO CLASH, using fixed ground order
+25632: Facts:
+25632: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25632: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25632: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25632: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25632: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25632: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25632: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25632: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25632: Id : 10, {_}:
+ meet ?26 (join ?27 (meet ?26 ?28))
+ =<=
+ meet ?26
+ (join ?27
+ (meet ?28 (join ?26 (meet ?27 (join ?28 (meet ?26 ?27))))))
+ [28, 27, 26] by equation_H11 ?26 ?27 ?28
+25632: Goal:
+25632: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join b (meet c (join a (meet b c))))
+ [] by prove_H10
+25632: Order:
+25632: kbo
+25632: Leaf order:
+25632: b 3 0 3 1,2,2
+25632: c 3 0 3 2,2,2,2
+25632: a 4 0 4 1,2
+25632: join 16 2 3 0,2,2
+25632: meet 20 2 5 0,2
+% SZS status Timeout for LAT139-1.p
+NO CLASH, using fixed ground order
+25659: Facts:
+25659: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25659: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25659: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25659: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25659: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25659: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25659: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25659: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25659: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?26 (meet ?27 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H21 ?26 ?27 ?28
+25659: Goal:
+25659: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+25659: Order:
+25659: nrkbo
+25659: Leaf order:
+25659: b 3 0 3 1,2,2
+25659: c 3 0 3 2,2,2,2
+25659: a 6 0 6 1,2
+25659: join 17 2 4 0,2,2
+25659: meet 21 2 6 0,2
+NO CLASH, using fixed ground order
+25660: Facts:
+25660: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25660: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25660: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25660: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25660: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25660: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25660: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25660: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25660: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?26 (meet ?27 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H21 ?26 ?27 ?28
+25660: Goal:
+25660: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+25660: Order:
+25660: kbo
+25660: Leaf order:
+25660: b 3 0 3 1,2,2
+25660: c 3 0 3 2,2,2,2
+25660: a 6 0 6 1,2
+25660: join 17 2 4 0,2,2
+25660: meet 21 2 6 0,2
+NO CLASH, using fixed ground order
+25661: Facts:
+25661: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25661: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25661: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25661: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25661: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25661: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25661: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25661: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25661: Id : 10, {_}:
+ join (meet ?26 ?27) (meet ?26 ?28)
+ =<=
+ meet ?26
+ (join (meet ?27 (join ?26 (meet ?27 ?28)))
+ (meet ?28 (join ?26 ?27)))
+ [28, 27, 26] by equation_H21 ?26 ?27 ?28
+25661: Goal:
+25661: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+25661: Order:
+25661: lpo
+25661: Leaf order:
+25661: b 3 0 3 1,2,2
+25661: c 3 0 3 2,2,2,2
+25661: a 6 0 6 1,2
+25661: join 17 2 4 0,2,2
+25661: meet 21 2 6 0,2
+% SZS status Timeout for LAT141-1.p
+NO CLASH, using fixed ground order
+25683: Facts:
+25683: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25683: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25683: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25683: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25683: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25683: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25683: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25683: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25683: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ meet ?26 (join ?27 (meet (join ?26 ?27) (join ?28 (meet ?26 ?27))))
+ [28, 27, 26] by equation_H58 ?26 ?27 ?28
+25683: Goal:
+25683: Id : 1, {_}:
+ meet a (meet (join b c) (join b d))
+ =<=
+ meet a (join b (meet (join b d) (join c (meet a b))))
+ [] by prove_H59
+25683: Order:
+25683: nrkbo
+25683: Leaf order:
+25683: c 2 0 2 2,1,2,2
+25683: d 2 0 2 2,2,2,2
+25683: a 3 0 3 1,2
+25683: b 5 0 5 1,1,2,2
+25683: join 18 2 5 0,1,2,2
+25683: meet 18 2 5 0,2
+NO CLASH, using fixed ground order
+25684: Facts:
+25684: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25684: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25684: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25684: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25684: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25684: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25684: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25684: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25684: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ meet ?26 (join ?27 (meet (join ?26 ?27) (join ?28 (meet ?26 ?27))))
+ [28, 27, 26] by equation_H58 ?26 ?27 ?28
+25684: Goal:
+25684: Id : 1, {_}:
+ meet a (meet (join b c) (join b d))
+ =<=
+ meet a (join b (meet (join b d) (join c (meet a b))))
+ [] by prove_H59
+25684: Order:
+25684: kbo
+25684: Leaf order:
+25684: c 2 0 2 2,1,2,2
+25684: d 2 0 2 2,2,2,2
+25684: a 3 0 3 1,2
+25684: b 5 0 5 1,1,2,2
+25684: join 18 2 5 0,1,2,2
+25684: meet 18 2 5 0,2
+NO CLASH, using fixed ground order
+25685: Facts:
+25685: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25685: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25685: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25685: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25685: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25685: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25685: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25685: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25685: Id : 10, {_}:
+ meet ?26 (join ?27 ?28)
+ =<=
+ meet ?26 (join ?27 (meet (join ?26 ?27) (join ?28 (meet ?26 ?27))))
+ [28, 27, 26] by equation_H58 ?26 ?27 ?28
+25685: Goal:
+25685: Id : 1, {_}:
+ meet a (meet (join b c) (join b d))
+ =<=
+ meet a (join b (meet (join b d) (join c (meet a b))))
+ [] by prove_H59
+25685: Order:
+25685: lpo
+25685: Leaf order:
+25685: c 2 0 2 2,1,2,2
+25685: d 2 0 2 2,2,2,2
+25685: a 3 0 3 1,2
+25685: b 5 0 5 1,1,2,2
+25685: join 18 2 5 0,1,2,2
+25685: meet 18 2 5 0,2
+% SZS status Timeout for LAT161-1.p
+NO CLASH, using fixed ground order
+25706: Facts:
+25706: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25706: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25706: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25706: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25706: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25706: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25706: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25706: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+NO CLASH, using fixed ground order
+25707: Facts:
+25707: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25707: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25707: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25707: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25707: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25707: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25707: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25707: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25707: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
+ [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
+25707: Goal:
+25707: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+25707: Order:
+25707: kbo
+25707: Leaf order:
+25707: b 3 0 3 1,2,2
+25707: c 3 0 3 2,2,2,2
+25707: a 6 0 6 1,2
+25707: join 19 2 4 0,2,2
+25707: meet 19 2 6 0,2
+NO CLASH, using fixed ground order
+25708: Facts:
+25708: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2
+25708: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4
+25708: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7
+25708: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10
+25708: Id : 6, {_}:
+ meet ?12 ?13 =?= meet ?13 ?12
+ [13, 12] by commutativity_of_meet ?12 ?13
+25708: Id : 7, {_}:
+ join ?15 ?16 =?= join ?16 ?15
+ [16, 15] by commutativity_of_join ?15 ?16
+25708: Id : 8, {_}:
+ meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20)
+ [20, 19, 18] by associativity_of_meet ?18 ?19 ?20
+25708: Id : 9, {_}:
+ join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24)
+ [24, 23, 22] by associativity_of_join ?22 ?23 ?24
+25708: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
+ [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
+25708: Goal:
+25708: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+25708: Order:
+25708: lpo
+25708: Leaf order:
+25708: b 3 0 3 1,2,2
+25708: c 3 0 3 2,2,2,2
+25708: a 6 0 6 1,2
+25708: join 19 2 4 0,2,2
+25708: meet 19 2 6 0,2
+25706: Id : 10, {_}:
+ join ?26 (meet ?27 (join ?28 (meet ?26 ?29)))
+ =<=
+ join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29))
+ [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29
+25706: Goal:
+25706: Id : 1, {_}:
+ meet a (join b (meet a c))
+ =<=
+ meet a (join (meet a (join b (meet a c))) (meet c (join a b)))
+ [] by prove_H6
+25706: Order:
+25706: nrkbo
+25706: Leaf order:
+25706: b 3 0 3 1,2,2
+25706: c 3 0 3 2,2,2,2
+25706: a 6 0 6 1,2
+25706: join 19 2 4 0,2,2
+25706: meet 19 2 6 0,2
+% SZS status Timeout for LAT177-1.p
+NO CLASH, using fixed ground order
+25759: Facts:
+25759: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutative_addition ?2 ?3
+25759: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associative_addition ?5 ?6 ?7
+25759: Id : 4, {_}: add ?9 additive_identity =>= ?9 [9] by right_identity ?9
+25759: Id : 5, {_}: add additive_identity ?11 =>= ?11 [11] by left_identity ?11
+25759: Id : 6, {_}:
+ add ?13 (additive_inverse ?13) =>= additive_identity
+ [13] by right_additive_inverse ?13
+25759: Id : 7, {_}:
+ add (additive_inverse ?15) ?15 =>= additive_identity
+ [15] by left_additive_inverse ?15
+25759: Id : 8, {_}:
+ additive_inverse additive_identity =>= additive_identity
+ [] by additive_inverse_identity
+25759: Id : 9, {_}:
+ add ?18 (add (additive_inverse ?18) ?19) =>= ?19
+ [19, 18] by property_of_inverse_and_add ?18 ?19
+25759: Id : 10, {_}:
+ additive_inverse (add ?21 ?22)
+ =<=
+ add (additive_inverse ?21) (additive_inverse ?22)
+ [22, 21] by distribute_additive_inverse ?21 ?22
+25759: Id : 11, {_}:
+ additive_inverse (additive_inverse ?24) =>= ?24
+ [24] by additive_inverse_additive_inverse ?24
+25759: Id : 12, {_}:
+ multiply ?26 additive_identity =>= additive_identity
+ [26] by multiply_additive_id1 ?26
+25759: Id : 13, {_}:
+ multiply additive_identity ?28 =>= additive_identity
+ [28] by multiply_additive_id2 ?28
+25759: Id : 14, {_}:
+ multiply (additive_inverse ?30) (additive_inverse ?31)
+ =>=
+ multiply ?30 ?31
+ [31, 30] by product_of_inverse ?30 ?31
+25759: Id : 15, {_}:
+ multiply ?33 (additive_inverse ?34)
+ =>=
+ additive_inverse (multiply ?33 ?34)
+ [34, 33] by multiply_additive_inverse1 ?33 ?34
+25759: Id : 16, {_}:
+ multiply (additive_inverse ?36) ?37
+ =>=
+ additive_inverse (multiply ?36 ?37)
+ [37, 36] by multiply_additive_inverse2 ?36 ?37
+25759: Id : 17, {_}:
+ multiply ?39 (add ?40 ?41)
+ =<=
+ add (multiply ?39 ?40) (multiply ?39 ?41)
+ [41, 40, 39] by distribute1 ?39 ?40 ?41
+25759: Id : 18, {_}:
+ multiply (add ?43 ?44) ?45
+ =<=
+ add (multiply ?43 ?45) (multiply ?44 ?45)
+ [45, 44, 43] by distribute2 ?43 ?44 ?45
+25759: Id : 19, {_}:
+ multiply (multiply ?47 ?48) ?48 =?= multiply ?47 (multiply ?48 ?48)
+ [48, 47] by right_alternative ?47 ?48
+25759: Id : 20, {_}:
+ associator ?50 ?51 ?52
+ =<=
+ add (multiply (multiply ?50 ?51) ?52)
+ (additive_inverse (multiply ?50 (multiply ?51 ?52)))
+ [52, 51, 50] by associator ?50 ?51 ?52
+25759: Id : 21, {_}:
+ commutator ?54 ?55
+ =<=
+ add (multiply ?55 ?54) (additive_inverse (multiply ?54 ?55))
+ [55, 54] by commutator ?54 ?55
+25759: Id : 22, {_}:
+ multiply (multiply (associator ?57 ?57 ?58) ?57)
+ (associator ?57 ?57 ?58)
+ =>=
+ additive_identity
+ [58, 57] by middle_associator ?57 ?58
+25759: Id : 23, {_}:
+ multiply (multiply ?60 ?60) ?61 =?= multiply ?60 (multiply ?60 ?61)
+ [61, 60] by left_alternative ?60 ?61
+25759: Id : 24, {_}:
+ s ?63 ?64 ?65 ?66
+ =<=
+ add
+ (add (associator (multiply ?63 ?64) ?65 ?66)
+ (additive_inverse (multiply ?64 (associator ?63 ?65 ?66))))
+ (additive_inverse (multiply (associator ?64 ?65 ?66) ?63))
+ [66, 65, 64, 63] by defines_s ?63 ?64 ?65 ?66
+25759: Id : 25, {_}:
+ multiply ?68 (multiply ?69 (multiply ?70 ?69))
+ =?=
+ multiply (multiply (multiply ?68 ?69) ?70) ?69
+ [70, 69, 68] by right_moufang ?68 ?69 ?70
+25759: Id : 26, {_}:
+ multiply (multiply ?72 (multiply ?73 ?72)) ?74
+ =?=
+ multiply ?72 (multiply ?73 (multiply ?72 ?74))
+ [74, 73, 72] by left_moufang ?72 ?73 ?74
+25759: Id : 27, {_}:
+ multiply (multiply ?76 ?77) (multiply ?78 ?76)
+ =?=
+ multiply (multiply ?76 (multiply ?77 ?78)) ?76
+ [78, 77, 76] by middle_moufang ?76 ?77 ?78
+25759: Goal:
+25759: Id : 1, {_}:
+ s a b c d =<= additive_inverse (s b a c d)
+ [] by prove_skew_symmetry
+25759: Order:
+25759: nrkbo
+25759: Leaf order:
+25759: a 2 0 2 1,2
+25759: b 2 0 2 2,2
+25759: c 2 0 2 3,2
+25759: d 2 0 2 4,2
+25759: additive_identity 11 0 0
+25759: additive_inverse 20 1 1 0,3
+25759: commutator 1 2 0
+25759: add 22 2 0
+25759: multiply 51 2 0
+25759: associator 6 3 0
+25759: s 3 4 2 0,2
+NO CLASH, using fixed ground order
+25760: Facts:
+25760: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutative_addition ?2 ?3
+25760: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associative_addition ?5 ?6 ?7
+25760: Id : 4, {_}: add ?9 additive_identity =>= ?9 [9] by right_identity ?9
+25760: Id : 5, {_}: add additive_identity ?11 =>= ?11 [11] by left_identity ?11
+25760: Id : 6, {_}:
+ add ?13 (additive_inverse ?13) =>= additive_identity
+ [13] by right_additive_inverse ?13
+25760: Id : 7, {_}:
+ add (additive_inverse ?15) ?15 =>= additive_identity
+ [15] by left_additive_inverse ?15
+25760: Id : 8, {_}:
+ additive_inverse additive_identity =>= additive_identity
+ [] by additive_inverse_identity
+25760: Id : 9, {_}:
+ add ?18 (add (additive_inverse ?18) ?19) =>= ?19
+ [19, 18] by property_of_inverse_and_add ?18 ?19
+25760: Id : 10, {_}:
+ additive_inverse (add ?21 ?22)
+ =<=
+ add (additive_inverse ?21) (additive_inverse ?22)
+ [22, 21] by distribute_additive_inverse ?21 ?22
+25760: Id : 11, {_}:
+ additive_inverse (additive_inverse ?24) =>= ?24
+ [24] by additive_inverse_additive_inverse ?24
+25760: Id : 12, {_}:
+ multiply ?26 additive_identity =>= additive_identity
+ [26] by multiply_additive_id1 ?26
+25760: Id : 13, {_}:
+ multiply additive_identity ?28 =>= additive_identity
+ [28] by multiply_additive_id2 ?28
+25760: Id : 14, {_}:
+ multiply (additive_inverse ?30) (additive_inverse ?31)
+ =>=
+ multiply ?30 ?31
+ [31, 30] by product_of_inverse ?30 ?31
+25760: Id : 15, {_}:
+ multiply ?33 (additive_inverse ?34)
+ =>=
+ additive_inverse (multiply ?33 ?34)
+ [34, 33] by multiply_additive_inverse1 ?33 ?34
+25760: Id : 16, {_}:
+ multiply (additive_inverse ?36) ?37
+ =>=
+ additive_inverse (multiply ?36 ?37)
+ [37, 36] by multiply_additive_inverse2 ?36 ?37
+25760: Id : 17, {_}:
+ multiply ?39 (add ?40 ?41)
+ =<=
+ add (multiply ?39 ?40) (multiply ?39 ?41)
+ [41, 40, 39] by distribute1 ?39 ?40 ?41
+25760: Id : 18, {_}:
+ multiply (add ?43 ?44) ?45
+ =<=
+ add (multiply ?43 ?45) (multiply ?44 ?45)
+ [45, 44, 43] by distribute2 ?43 ?44 ?45
+25760: Id : 19, {_}:
+ multiply (multiply ?47 ?48) ?48 =>= multiply ?47 (multiply ?48 ?48)
+ [48, 47] by right_alternative ?47 ?48
+25760: Id : 20, {_}:
+ associator ?50 ?51 ?52
+ =<=
+ add (multiply (multiply ?50 ?51) ?52)
+ (additive_inverse (multiply ?50 (multiply ?51 ?52)))
+ [52, 51, 50] by associator ?50 ?51 ?52
+25760: Id : 21, {_}:
+ commutator ?54 ?55
+ =<=
+ add (multiply ?55 ?54) (additive_inverse (multiply ?54 ?55))
+ [55, 54] by commutator ?54 ?55
+25760: Id : 22, {_}:
+ multiply (multiply (associator ?57 ?57 ?58) ?57)
+ (associator ?57 ?57 ?58)
+ =>=
+ additive_identity
+ [58, 57] by middle_associator ?57 ?58
+25760: Id : 23, {_}:
+ multiply (multiply ?60 ?60) ?61 =>= multiply ?60 (multiply ?60 ?61)
+ [61, 60] by left_alternative ?60 ?61
+25760: Id : 24, {_}:
+ s ?63 ?64 ?65 ?66
+ =<=
+ add
+ (add (associator (multiply ?63 ?64) ?65 ?66)
+ (additive_inverse (multiply ?64 (associator ?63 ?65 ?66))))
+ (additive_inverse (multiply (associator ?64 ?65 ?66) ?63))
+ [66, 65, 64, 63] by defines_s ?63 ?64 ?65 ?66
+25760: Id : 25, {_}:
+ multiply ?68 (multiply ?69 (multiply ?70 ?69))
+ =<=
+ multiply (multiply (multiply ?68 ?69) ?70) ?69
+ [70, 69, 68] by right_moufang ?68 ?69 ?70
+25760: Id : 26, {_}:
+ multiply (multiply ?72 (multiply ?73 ?72)) ?74
+ =>=
+ multiply ?72 (multiply ?73 (multiply ?72 ?74))
+ [74, 73, 72] by left_moufang ?72 ?73 ?74
+25760: Id : 27, {_}:
+ multiply (multiply ?76 ?77) (multiply ?78 ?76)
+ =<=
+ multiply (multiply ?76 (multiply ?77 ?78)) ?76
+ [78, 77, 76] by middle_moufang ?76 ?77 ?78
+25760: Goal:
+25760: Id : 1, {_}:
+ s a b c d =<= additive_inverse (s b a c d)
+ [] by prove_skew_symmetry
+25760: Order:
+25760: kbo
+25760: Leaf order:
+25760: a 2 0 2 1,2
+25760: b 2 0 2 2,2
+25760: c 2 0 2 3,2
+25760: d 2 0 2 4,2
+25760: additive_identity 11 0 0
+25760: additive_inverse 20 1 1 0,3
+25760: commutator 1 2 0
+25760: add 22 2 0
+25760: multiply 51 2 0
+25760: associator 6 3 0
+25760: s 3 4 2 0,2
+NO CLASH, using fixed ground order
+25761: Facts:
+25761: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutative_addition ?2 ?3
+25761: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associative_addition ?5 ?6 ?7
+25761: Id : 4, {_}: add ?9 additive_identity =>= ?9 [9] by right_identity ?9
+25761: Id : 5, {_}: add additive_identity ?11 =>= ?11 [11] by left_identity ?11
+25761: Id : 6, {_}:
+ add ?13 (additive_inverse ?13) =>= additive_identity
+ [13] by right_additive_inverse ?13
+25761: Id : 7, {_}:
+ add (additive_inverse ?15) ?15 =>= additive_identity
+ [15] by left_additive_inverse ?15
+25761: Id : 8, {_}:
+ additive_inverse additive_identity =>= additive_identity
+ [] by additive_inverse_identity
+25761: Id : 9, {_}:
+ add ?18 (add (additive_inverse ?18) ?19) =>= ?19
+ [19, 18] by property_of_inverse_and_add ?18 ?19
+25761: Id : 10, {_}:
+ additive_inverse (add ?21 ?22)
+ =<=
+ add (additive_inverse ?21) (additive_inverse ?22)
+ [22, 21] by distribute_additive_inverse ?21 ?22
+25761: Id : 11, {_}:
+ additive_inverse (additive_inverse ?24) =>= ?24
+ [24] by additive_inverse_additive_inverse ?24
+25761: Id : 12, {_}:
+ multiply ?26 additive_identity =>= additive_identity
+ [26] by multiply_additive_id1 ?26
+25761: Id : 13, {_}:
+ multiply additive_identity ?28 =>= additive_identity
+ [28] by multiply_additive_id2 ?28
+25761: Id : 14, {_}:
+ multiply (additive_inverse ?30) (additive_inverse ?31)
+ =>=
+ multiply ?30 ?31
+ [31, 30] by product_of_inverse ?30 ?31
+25761: Id : 15, {_}:
+ multiply ?33 (additive_inverse ?34)
+ =>=
+ additive_inverse (multiply ?33 ?34)
+ [34, 33] by multiply_additive_inverse1 ?33 ?34
+25761: Id : 16, {_}:
+ multiply (additive_inverse ?36) ?37
+ =>=
+ additive_inverse (multiply ?36 ?37)
+ [37, 36] by multiply_additive_inverse2 ?36 ?37
+25761: Id : 17, {_}:
+ multiply ?39 (add ?40 ?41)
+ =>=
+ add (multiply ?39 ?40) (multiply ?39 ?41)
+ [41, 40, 39] by distribute1 ?39 ?40 ?41
+25761: Id : 18, {_}:
+ multiply (add ?43 ?44) ?45
+ =>=
+ add (multiply ?43 ?45) (multiply ?44 ?45)
+ [45, 44, 43] by distribute2 ?43 ?44 ?45
+25761: Id : 19, {_}:
+ multiply (multiply ?47 ?48) ?48 =>= multiply ?47 (multiply ?48 ?48)
+ [48, 47] by right_alternative ?47 ?48
+25761: Id : 20, {_}:
+ associator ?50 ?51 ?52
+ =>=
+ add (multiply (multiply ?50 ?51) ?52)
+ (additive_inverse (multiply ?50 (multiply ?51 ?52)))
+ [52, 51, 50] by associator ?50 ?51 ?52
+25761: Id : 21, {_}:
+ commutator ?54 ?55
+ =<=
+ add (multiply ?55 ?54) (additive_inverse (multiply ?54 ?55))
+ [55, 54] by commutator ?54 ?55
+25761: Id : 22, {_}:
+ multiply (multiply (associator ?57 ?57 ?58) ?57)
+ (associator ?57 ?57 ?58)
+ =>=
+ additive_identity
+ [58, 57] by middle_associator ?57 ?58
+25761: Id : 23, {_}:
+ multiply (multiply ?60 ?60) ?61 =>= multiply ?60 (multiply ?60 ?61)
+ [61, 60] by left_alternative ?60 ?61
+25761: Id : 24, {_}:
+ s ?63 ?64 ?65 ?66
+ =>=
+ add
+ (add (associator (multiply ?63 ?64) ?65 ?66)
+ (additive_inverse (multiply ?64 (associator ?63 ?65 ?66))))
+ (additive_inverse (multiply (associator ?64 ?65 ?66) ?63))
+ [66, 65, 64, 63] by defines_s ?63 ?64 ?65 ?66
+25761: Id : 25, {_}:
+ multiply ?68 (multiply ?69 (multiply ?70 ?69))
+ =<=
+ multiply (multiply (multiply ?68 ?69) ?70) ?69
+ [70, 69, 68] by right_moufang ?68 ?69 ?70
+25761: Id : 26, {_}:
+ multiply (multiply ?72 (multiply ?73 ?72)) ?74
+ =>=
+ multiply ?72 (multiply ?73 (multiply ?72 ?74))
+ [74, 73, 72] by left_moufang ?72 ?73 ?74
+25761: Id : 27, {_}:
+ multiply (multiply ?76 ?77) (multiply ?78 ?76)
+ =<=
+ multiply (multiply ?76 (multiply ?77 ?78)) ?76
+ [78, 77, 76] by middle_moufang ?76 ?77 ?78
+25761: Goal:
+25761: Id : 1, {_}:
+ s a b c d =<= additive_inverse (s b a c d)
+ [] by prove_skew_symmetry
+25761: Order:
+25761: lpo
+25761: Leaf order:
+25761: a 2 0 2 1,2
+25761: b 2 0 2 2,2
+25761: c 2 0 2 3,2
+25761: d 2 0 2 4,2
+25761: additive_identity 11 0 0
+25761: additive_inverse 20 1 1 0,3
+25761: commutator 1 2 0
+25761: add 22 2 0
+25761: multiply 51 2 0
+25761: associator 6 3 0
+25761: s 3 4 2 0,2
+% SZS status Timeout for RNG010-5.p
+NO CLASH, using fixed ground order
+25787: Facts:
+25787: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25787: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25787: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25787: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25787: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25787: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25787: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25787: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25787: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25787: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25787: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25787: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25787: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25787: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25787: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25787: Id : 17, {_}:
+ s ?44 ?45 ?46 ?47
+ =<=
+ add
+ (add (associator (multiply ?44 ?45) ?46 ?47)
+ (additive_inverse (multiply ?45 (associator ?44 ?46 ?47))))
+ (additive_inverse (multiply (associator ?45 ?46 ?47) ?44))
+ [47, 46, 45, 44] by defines_s ?44 ?45 ?46 ?47
+25787: Id : 18, {_}:
+ multiply ?49 (multiply ?50 (multiply ?51 ?50))
+ =?=
+ multiply (multiply (multiply ?49 ?50) ?51) ?50
+ [51, 50, 49] by right_moufang ?49 ?50 ?51
+25787: Id : 19, {_}:
+ multiply (multiply ?53 (multiply ?54 ?53)) ?55
+ =?=
+ multiply ?53 (multiply ?54 (multiply ?53 ?55))
+ [55, 54, 53] by left_moufang ?53 ?54 ?55
+25787: Id : 20, {_}:
+ multiply (multiply ?57 ?58) (multiply ?59 ?57)
+ =?=
+ multiply (multiply ?57 (multiply ?58 ?59)) ?57
+ [59, 58, 57] by middle_moufang ?57 ?58 ?59
+25787: Goal:
+25787: Id : 1, {_}:
+ s a b c d =<= additive_inverse (s b a c d)
+ [] by prove_skew_symmetry
+25787: Order:
+25787: nrkbo
+25787: Leaf order:
+25787: a 2 0 2 1,2
+25787: b 2 0 2 2,2
+25787: c 2 0 2 3,2
+25787: d 2 0 2 4,2
+25787: additive_identity 8 0 0
+25787: additive_inverse 9 1 1 0,3
+25787: commutator 1 2 0
+25787: add 18 2 0
+25787: multiply 43 2 0
+25787: associator 4 3 0
+25787: s 3 4 2 0,2
+NO CLASH, using fixed ground order
+25788: Facts:
+25788: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25788: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25788: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25788: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25788: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25788: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25788: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25788: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25788: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25788: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25788: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25788: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25788: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25788: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25788: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25788: Id : 17, {_}:
+ s ?44 ?45 ?46 ?47
+ =<=
+ add
+ (add (associator (multiply ?44 ?45) ?46 ?47)
+ (additive_inverse (multiply ?45 (associator ?44 ?46 ?47))))
+ (additive_inverse (multiply (associator ?45 ?46 ?47) ?44))
+ [47, 46, 45, 44] by defines_s ?44 ?45 ?46 ?47
+25788: Id : 18, {_}:
+ multiply ?49 (multiply ?50 (multiply ?51 ?50))
+ =<=
+ multiply (multiply (multiply ?49 ?50) ?51) ?50
+ [51, 50, 49] by right_moufang ?49 ?50 ?51
+25788: Id : 19, {_}:
+ multiply (multiply ?53 (multiply ?54 ?53)) ?55
+ =>=
+ multiply ?53 (multiply ?54 (multiply ?53 ?55))
+ [55, 54, 53] by left_moufang ?53 ?54 ?55
+25788: Id : 20, {_}:
+ multiply (multiply ?57 ?58) (multiply ?59 ?57)
+ =<=
+ multiply (multiply ?57 (multiply ?58 ?59)) ?57
+ [59, 58, 57] by middle_moufang ?57 ?58 ?59
+25788: Goal:
+25788: Id : 1, {_}:
+ s a b c d =<= additive_inverse (s b a c d)
+ [] by prove_skew_symmetry
+25788: Order:
+25788: kbo
+25788: Leaf order:
+25788: a 2 0 2 1,2
+25788: b 2 0 2 2,2
+25788: c 2 0 2 3,2
+25788: d 2 0 2 4,2
+25788: additive_identity 8 0 0
+25788: additive_inverse 9 1 1 0,3
+25788: commutator 1 2 0
+25788: add 18 2 0
+25788: multiply 43 2 0
+25788: associator 4 3 0
+25788: s 3 4 2 0,2
+NO CLASH, using fixed ground order
+25789: Facts:
+25789: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25789: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25789: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25789: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25789: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25789: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25789: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25789: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25789: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25789: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25789: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25789: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25789: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25789: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25789: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25789: Id : 17, {_}:
+ s ?44 ?45 ?46 ?47
+ =>=
+ add
+ (add (associator (multiply ?44 ?45) ?46 ?47)
+ (additive_inverse (multiply ?45 (associator ?44 ?46 ?47))))
+ (additive_inverse (multiply (associator ?45 ?46 ?47) ?44))
+ [47, 46, 45, 44] by defines_s ?44 ?45 ?46 ?47
+25789: Id : 18, {_}:
+ multiply ?49 (multiply ?50 (multiply ?51 ?50))
+ =<=
+ multiply (multiply (multiply ?49 ?50) ?51) ?50
+ [51, 50, 49] by right_moufang ?49 ?50 ?51
+25789: Id : 19, {_}:
+ multiply (multiply ?53 (multiply ?54 ?53)) ?55
+ =>=
+ multiply ?53 (multiply ?54 (multiply ?53 ?55))
+ [55, 54, 53] by left_moufang ?53 ?54 ?55
+25789: Id : 20, {_}:
+ multiply (multiply ?57 ?58) (multiply ?59 ?57)
+ =<=
+ multiply (multiply ?57 (multiply ?58 ?59)) ?57
+ [59, 58, 57] by middle_moufang ?57 ?58 ?59
+25789: Goal:
+25789: Id : 1, {_}:
+ s a b c d =<= additive_inverse (s b a c d)
+ [] by prove_skew_symmetry
+25789: Order:
+25789: lpo
+25789: Leaf order:
+25789: a 2 0 2 1,2
+25789: b 2 0 2 2,2
+25789: c 2 0 2 3,2
+25789: d 2 0 2 4,2
+25789: additive_identity 8 0 0
+25789: additive_inverse 9 1 1 0,3
+25789: commutator 1 2 0
+25789: add 18 2 0
+25789: multiply 43 2 0
+25789: associator 4 3 0
+25789: s 3 4 2 0,2
+% SZS status Timeout for RNG010-6.p
+NO CLASH, using fixed ground order
+25814: Facts:
+25814: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25814: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25814: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25814: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25814: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25814: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25814: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25814: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25814: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25814: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25814: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25814: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25814: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25814: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25814: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25814: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+25814: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+25814: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+25814: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+25814: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+25814: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+25814: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+25814: Id : 24, {_}:
+ s ?69 ?70 ?71 ?72
+ =<=
+ add
+ (add (associator (multiply ?69 ?70) ?71 ?72)
+ (additive_inverse (multiply ?70 (associator ?69 ?71 ?72))))
+ (additive_inverse (multiply (associator ?70 ?71 ?72) ?69))
+ [72, 71, 70, 69] by defines_s ?69 ?70 ?71 ?72
+25814: Id : 25, {_}:
+ multiply ?74 (multiply ?75 (multiply ?76 ?75))
+ =?=
+ multiply (multiply (multiply ?74 ?75) ?76) ?75
+ [76, 75, 74] by right_moufang ?74 ?75 ?76
+25814: Id : 26, {_}:
+ multiply (multiply ?78 (multiply ?79 ?78)) ?80
+ =?=
+ multiply ?78 (multiply ?79 (multiply ?78 ?80))
+ [80, 79, 78] by left_moufang ?78 ?79 ?80
+25814: Id : 27, {_}:
+ multiply (multiply ?82 ?83) (multiply ?84 ?82)
+ =?=
+ multiply (multiply ?82 (multiply ?83 ?84)) ?82
+ [84, 83, 82] by middle_moufang ?82 ?83 ?84
+25814: Goal:
+25814: Id : 1, {_}:
+ s a b c d =<= additive_inverse (s b a c d)
+ [] by prove_skew_symmetry
+25814: Order:
+25814: nrkbo
+25814: Leaf order:
+25814: a 2 0 2 1,2
+25814: b 2 0 2 2,2
+25814: c 2 0 2 3,2
+25814: d 2 0 2 4,2
+25814: additive_identity 8 0 0
+25814: additive_inverse 25 1 1 0,3
+25814: commutator 1 2 0
+25814: add 26 2 0
+25814: multiply 61 2 0
+25814: associator 4 3 0
+25814: s 3 4 2 0,2
+NO CLASH, using fixed ground order
+25815: Facts:
+NO CLASH, using fixed ground order
+25816: Facts:
+25816: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25816: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25816: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25816: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25816: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25816: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25816: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25816: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25816: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25816: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25816: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25816: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25816: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25816: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25816: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25816: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+25816: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+25816: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+25816: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =>=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+25816: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =>=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+25816: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =>=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+25816: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =>=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+25816: Id : 24, {_}:
+ s ?69 ?70 ?71 ?72
+ =>=
+ add
+ (add (associator (multiply ?69 ?70) ?71 ?72)
+ (additive_inverse (multiply ?70 (associator ?69 ?71 ?72))))
+ (additive_inverse (multiply (associator ?70 ?71 ?72) ?69))
+ [72, 71, 70, 69] by defines_s ?69 ?70 ?71 ?72
+25816: Id : 25, {_}:
+ multiply ?74 (multiply ?75 (multiply ?76 ?75))
+ =<=
+ multiply (multiply (multiply ?74 ?75) ?76) ?75
+ [76, 75, 74] by right_moufang ?74 ?75 ?76
+25816: Id : 26, {_}:
+ multiply (multiply ?78 (multiply ?79 ?78)) ?80
+ =>=
+ multiply ?78 (multiply ?79 (multiply ?78 ?80))
+ [80, 79, 78] by left_moufang ?78 ?79 ?80
+25816: Id : 27, {_}:
+ multiply (multiply ?82 ?83) (multiply ?84 ?82)
+ =<=
+ multiply (multiply ?82 (multiply ?83 ?84)) ?82
+ [84, 83, 82] by middle_moufang ?82 ?83 ?84
+25816: Goal:
+25816: Id : 1, {_}:
+ s a b c d =<= additive_inverse (s b a c d)
+ [] by prove_skew_symmetry
+25816: Order:
+25816: lpo
+25816: Leaf order:
+25816: a 2 0 2 1,2
+25816: b 2 0 2 2,2
+25816: c 2 0 2 3,2
+25816: d 2 0 2 4,2
+25816: additive_identity 8 0 0
+25816: additive_inverse 25 1 1 0,3
+25816: commutator 1 2 0
+25816: add 26 2 0
+25816: multiply 61 2 0
+25816: associator 4 3 0
+25816: s 3 4 2 0,2
+25815: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+25815: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+25815: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+25815: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+25815: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+25815: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+25815: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+25815: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+25815: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+25815: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+25815: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+25815: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25815: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+25815: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+25815: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+25815: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+25815: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+25815: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+25815: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+25815: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+25815: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+25815: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+25815: Id : 24, {_}:
+ s ?69 ?70 ?71 ?72
+ =<=
+ add
+ (add (associator (multiply ?69 ?70) ?71 ?72)
+ (additive_inverse (multiply ?70 (associator ?69 ?71 ?72))))
+ (additive_inverse (multiply (associator ?70 ?71 ?72) ?69))
+ [72, 71, 70, 69] by defines_s ?69 ?70 ?71 ?72
+25815: Id : 25, {_}:
+ multiply ?74 (multiply ?75 (multiply ?76 ?75))
+ =<=
+ multiply (multiply (multiply ?74 ?75) ?76) ?75
+ [76, 75, 74] by right_moufang ?74 ?75 ?76
+25815: Id : 26, {_}:
+ multiply (multiply ?78 (multiply ?79 ?78)) ?80
+ =>=
+ multiply ?78 (multiply ?79 (multiply ?78 ?80))
+ [80, 79, 78] by left_moufang ?78 ?79 ?80
+25815: Id : 27, {_}:
+ multiply (multiply ?82 ?83) (multiply ?84 ?82)
+ =<=
+ multiply (multiply ?82 (multiply ?83 ?84)) ?82
+ [84, 83, 82] by middle_moufang ?82 ?83 ?84
+25815: Goal:
+25815: Id : 1, {_}:
+ s a b c d =<= additive_inverse (s b a c d)
+ [] by prove_skew_symmetry
+25815: Order:
+25815: kbo
+25815: Leaf order:
+25815: a 2 0 2 1,2
+25815: b 2 0 2 2,2
+25815: c 2 0 2 3,2
+25815: d 2 0 2 4,2
+25815: additive_identity 8 0 0
+25815: additive_inverse 25 1 1 0,3
+25815: commutator 1 2 0
+25815: add 26 2 0
+25815: multiply 61 2 0
+25815: associator 4 3 0
+25815: s 3 4 2 0,2
+% SZS status Timeout for RNG010-7.p
+NO CLASH, using fixed ground order
+25837: Facts:
+25837: Id : 2, {_}:
+ add ?2 ?3 =?= add ?3 ?2
+ [3, 2] by commutativity_for_addition ?2 ?3
+25837: Id : 3, {_}:
+ add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7
+ [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
+25837: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
+25837: Id : 5, {_}:
+ add ?11 additive_identity =>= ?11
+ [11] by right_additive_identity ?11
+25837: Id : 6, {_}:
+ multiply additive_identity ?13 =>= additive_identity
+ [13] by left_multiplicative_zero ?13
+25837: Id : 7, {_}:
+ multiply ?15 additive_identity =>= additive_identity
+ [15] by right_multiplicative_zero ?15
+25837: Id : 8, {_}:
+ add (additive_inverse ?17) ?17 =>= additive_identity
+ [17] by left_additive_inverse ?17
+25837: Id : 9, {_}:
+ add ?19 (additive_inverse ?19) =>= additive_identity
+ [19] by right_additive_inverse ?19
+25837: Id : 10, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+25837: Id : 11, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+25837: Id : 12, {_}:
+ additive_inverse (additive_inverse ?29) =>= ?29
+ [29] by additive_inverse_additive_inverse ?29
+25837: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25837: Id : 14, {_}:
+ associator ?34 ?35 ?36
+ =<=
+ add (multiply (multiply ?34 ?35) ?36)
+ (additive_inverse (multiply ?34 (multiply ?35 ?36)))
+ [36, 35, 34] by associator ?34 ?35 ?36
+25837: Id : 15, {_}:
+ commutator ?38 ?39
+ =<=
+ add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
+ [39, 38] by commutator ?38 ?39
+25837: Goal:
+25837: Id : 1, {_}:
+ add
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ =>=
+ additive_identity
+ [] by prove_conjecture_1
+25837: Order:
+25837: nrkbo
+25837: Leaf order:
+25837: y 6 0 6 3,1,1,2
+25837: additive_identity 9 0 1 3
+25837: x 12 0 12 1,1,1,2
+25837: additive_inverse 6 1 0
+25837: commutator 1 2 0
+25837: add 17 2 1 0,2
+25837: multiply 22 2 4 0,1,2
+25837: associator 7 3 6 0,1,1,2
+NO CLASH, using fixed ground order
+25838: Facts:
+25838: Id : 2, {_}:
+ add ?2 ?3 =?= add ?3 ?2
+ [3, 2] by commutativity_for_addition ?2 ?3
+25838: Id : 3, {_}:
+ add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
+ [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
+25838: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
+25838: Id : 5, {_}:
+ add ?11 additive_identity =>= ?11
+ [11] by right_additive_identity ?11
+25838: Id : 6, {_}:
+ multiply additive_identity ?13 =>= additive_identity
+ [13] by left_multiplicative_zero ?13
+25838: Id : 7, {_}:
+ multiply ?15 additive_identity =>= additive_identity
+ [15] by right_multiplicative_zero ?15
+25838: Id : 8, {_}:
+ add (additive_inverse ?17) ?17 =>= additive_identity
+ [17] by left_additive_inverse ?17
+25838: Id : 9, {_}:
+ add ?19 (additive_inverse ?19) =>= additive_identity
+ [19] by right_additive_inverse ?19
+25838: Id : 10, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+25838: Id : 11, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+25838: Id : 12, {_}:
+ additive_inverse (additive_inverse ?29) =>= ?29
+ [29] by additive_inverse_additive_inverse ?29
+25838: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25838: Id : 14, {_}:
+ associator ?34 ?35 ?36
+ =<=
+ add (multiply (multiply ?34 ?35) ?36)
+ (additive_inverse (multiply ?34 (multiply ?35 ?36)))
+ [36, 35, 34] by associator ?34 ?35 ?36
+25838: Id : 15, {_}:
+ commutator ?38 ?39
+ =<=
+ add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
+ [39, 38] by commutator ?38 ?39
+25838: Goal:
+25838: Id : 1, {_}:
+ add
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ =>=
+ additive_identity
+ [] by prove_conjecture_1
+25838: Order:
+25838: kbo
+25838: Leaf order:
+25838: y 6 0 6 3,1,1,2
+25838: additive_identity 9 0 1 3
+25838: x 12 0 12 1,1,1,2
+25838: additive_inverse 6 1 0
+25838: commutator 1 2 0
+25838: add 17 2 1 0,2
+25838: multiply 22 2 4 0,1,2
+25838: associator 7 3 6 0,1,1,2
+NO CLASH, using fixed ground order
+25839: Facts:
+25839: Id : 2, {_}:
+ add ?2 ?3 =?= add ?3 ?2
+ [3, 2] by commutativity_for_addition ?2 ?3
+25839: Id : 3, {_}:
+ add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
+ [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
+25839: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
+25839: Id : 5, {_}:
+ add ?11 additive_identity =>= ?11
+ [11] by right_additive_identity ?11
+25839: Id : 6, {_}:
+ multiply additive_identity ?13 =>= additive_identity
+ [13] by left_multiplicative_zero ?13
+25839: Id : 7, {_}:
+ multiply ?15 additive_identity =>= additive_identity
+ [15] by right_multiplicative_zero ?15
+25839: Id : 8, {_}:
+ add (additive_inverse ?17) ?17 =>= additive_identity
+ [17] by left_additive_inverse ?17
+25839: Id : 9, {_}:
+ add ?19 (additive_inverse ?19) =>= additive_identity
+ [19] by right_additive_inverse ?19
+25839: Id : 10, {_}:
+ multiply ?21 (add ?22 ?23)
+ =>=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+25839: Id : 11, {_}:
+ multiply (add ?25 ?26) ?27
+ =>=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+25839: Id : 12, {_}:
+ additive_inverse (additive_inverse ?29) =>= ?29
+ [29] by additive_inverse_additive_inverse ?29
+25839: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25839: Id : 14, {_}:
+ associator ?34 ?35 ?36
+ =>=
+ add (multiply (multiply ?34 ?35) ?36)
+ (additive_inverse (multiply ?34 (multiply ?35 ?36)))
+ [36, 35, 34] by associator ?34 ?35 ?36
+25839: Id : 15, {_}:
+ commutator ?38 ?39
+ =<=
+ add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
+ [39, 38] by commutator ?38 ?39
+25839: Goal:
+25839: Id : 1, {_}:
+ add
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ =>=
+ additive_identity
+ [] by prove_conjecture_1
+25839: Order:
+25839: lpo
+25839: Leaf order:
+25839: y 6 0 6 3,1,1,2
+25839: additive_identity 9 0 1 3
+25839: x 12 0 12 1,1,1,2
+25839: additive_inverse 6 1 0
+25839: commutator 1 2 0
+25839: add 17 2 1 0,2
+25839: multiply 22 2 4 0,1,2
+25839: associator 7 3 6 0,1,1,2
+% SZS status Timeout for RNG030-6.p
+NO CLASH, using fixed ground order
+25861: Facts:
+25861: Id : 2, {_}:
+ multiply (additive_inverse ?2) (additive_inverse ?3)
+ =>=
+ multiply ?2 ?3
+ [3, 2] by product_of_inverses ?2 ?3
+25861: Id : 3, {_}:
+ multiply (additive_inverse ?5) ?6
+ =>=
+ additive_inverse (multiply ?5 ?6)
+ [6, 5] by inverse_product1 ?5 ?6
+25861: Id : 4, {_}:
+ multiply ?8 (additive_inverse ?9)
+ =>=
+ additive_inverse (multiply ?8 ?9)
+ [9, 8] by inverse_product2 ?8 ?9
+25861: Id : 5, {_}:
+ multiply ?11 (add ?12 (additive_inverse ?13))
+ =<=
+ add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
+ [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
+25861: Id : 6, {_}:
+ multiply (add ?15 (additive_inverse ?16)) ?17
+ =<=
+ add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
+ [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
+25861: Id : 7, {_}:
+ multiply (additive_inverse ?19) (add ?20 ?21)
+ =<=
+ add (additive_inverse (multiply ?19 ?20))
+ (additive_inverse (multiply ?19 ?21))
+ [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
+25861: Id : 8, {_}:
+ multiply (add ?23 ?24) (additive_inverse ?25)
+ =<=
+ add (additive_inverse (multiply ?23 ?25))
+ (additive_inverse (multiply ?24 ?25))
+ [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
+25861: Id : 9, {_}:
+ add ?27 ?28 =?= add ?28 ?27
+ [28, 27] by commutativity_for_addition ?27 ?28
+25861: Id : 10, {_}:
+ add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32
+ [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
+25861: Id : 11, {_}:
+ add additive_identity ?34 =>= ?34
+ [34] by left_additive_identity ?34
+25861: Id : 12, {_}:
+ add ?36 additive_identity =>= ?36
+ [36] by right_additive_identity ?36
+25861: Id : 13, {_}:
+ multiply additive_identity ?38 =>= additive_identity
+ [38] by left_multiplicative_zero ?38
+25861: Id : 14, {_}:
+ multiply ?40 additive_identity =>= additive_identity
+ [40] by right_multiplicative_zero ?40
+25861: Id : 15, {_}:
+ add (additive_inverse ?42) ?42 =>= additive_identity
+ [42] by left_additive_inverse ?42
+25861: Id : 16, {_}:
+ add ?44 (additive_inverse ?44) =>= additive_identity
+ [44] by right_additive_inverse ?44
+25861: Id : 17, {_}:
+ multiply ?46 (add ?47 ?48)
+ =<=
+ add (multiply ?46 ?47) (multiply ?46 ?48)
+ [48, 47, 46] by distribute1 ?46 ?47 ?48
+25861: Id : 18, {_}:
+ multiply (add ?50 ?51) ?52
+ =<=
+ add (multiply ?50 ?52) (multiply ?51 ?52)
+ [52, 51, 50] by distribute2 ?50 ?51 ?52
+25861: Id : 19, {_}:
+ additive_inverse (additive_inverse ?54) =>= ?54
+ [54] by additive_inverse_additive_inverse ?54
+25861: Id : 20, {_}:
+ multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57)
+ [57, 56] by right_alternative ?56 ?57
+25861: Id : 21, {_}:
+ associator ?59 ?60 ?61
+ =<=
+ add (multiply (multiply ?59 ?60) ?61)
+ (additive_inverse (multiply ?59 (multiply ?60 ?61)))
+ [61, 60, 59] by associator ?59 ?60 ?61
+25861: Id : 22, {_}:
+ commutator ?63 ?64
+ =<=
+ add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
+ [64, 63] by commutator ?63 ?64
+25861: Goal:
+25861: Id : 1, {_}:
+ add
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ =>=
+ additive_identity
+ [] by prove_conjecture_1
+25861: Order:
+25861: nrkbo
+25861: Leaf order:
+25861: y 6 0 6 3,1,1,2
+25861: additive_identity 9 0 1 3
+25861: x 12 0 12 1,1,1,2
+25861: additive_inverse 22 1 0
+25861: commutator 1 2 0
+25861: add 25 2 1 0,2
+25861: multiply 40 2 4 0,1,2add
+25861: associator 7 3 6 0,1,1,2
+NO CLASH, using fixed ground order
+25862: Facts:
+NO CLASH, using fixed ground order
+25863: Facts:
+25863: Id : 2, {_}:
+ multiply (additive_inverse ?2) (additive_inverse ?3)
+ =>=
+ multiply ?2 ?3
+ [3, 2] by product_of_inverses ?2 ?3
+25863: Id : 3, {_}:
+ multiply (additive_inverse ?5) ?6
+ =>=
+ additive_inverse (multiply ?5 ?6)
+ [6, 5] by inverse_product1 ?5 ?6
+25863: Id : 4, {_}:
+ multiply ?8 (additive_inverse ?9)
+ =>=
+ additive_inverse (multiply ?8 ?9)
+ [9, 8] by inverse_product2 ?8 ?9
+25863: Id : 5, {_}:
+ multiply ?11 (add ?12 (additive_inverse ?13))
+ =>=
+ add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
+ [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
+25863: Id : 6, {_}:
+ multiply (add ?15 (additive_inverse ?16)) ?17
+ =>=
+ add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
+ [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
+25863: Id : 7, {_}:
+ multiply (additive_inverse ?19) (add ?20 ?21)
+ =>=
+ add (additive_inverse (multiply ?19 ?20))
+ (additive_inverse (multiply ?19 ?21))
+ [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
+25863: Id : 8, {_}:
+ multiply (add ?23 ?24) (additive_inverse ?25)
+ =>=
+ add (additive_inverse (multiply ?23 ?25))
+ (additive_inverse (multiply ?24 ?25))
+ [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
+25863: Id : 9, {_}:
+ add ?27 ?28 =?= add ?28 ?27
+ [28, 27] by commutativity_for_addition ?27 ?28
+25863: Id : 10, {_}:
+ add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
+ [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
+25863: Id : 11, {_}:
+ add additive_identity ?34 =>= ?34
+ [34] by left_additive_identity ?34
+25863: Id : 12, {_}:
+ add ?36 additive_identity =>= ?36
+ [36] by right_additive_identity ?36
+25863: Id : 13, {_}:
+ multiply additive_identity ?38 =>= additive_identity
+ [38] by left_multiplicative_zero ?38
+25863: Id : 14, {_}:
+ multiply ?40 additive_identity =>= additive_identity
+ [40] by right_multiplicative_zero ?40
+25863: Id : 15, {_}:
+ add (additive_inverse ?42) ?42 =>= additive_identity
+ [42] by left_additive_inverse ?42
+25863: Id : 16, {_}:
+ add ?44 (additive_inverse ?44) =>= additive_identity
+ [44] by right_additive_inverse ?44
+25863: Id : 17, {_}:
+ multiply ?46 (add ?47 ?48)
+ =>=
+ add (multiply ?46 ?47) (multiply ?46 ?48)
+ [48, 47, 46] by distribute1 ?46 ?47 ?48
+25863: Id : 18, {_}:
+ multiply (add ?50 ?51) ?52
+ =>=
+ add (multiply ?50 ?52) (multiply ?51 ?52)
+ [52, 51, 50] by distribute2 ?50 ?51 ?52
+25863: Id : 19, {_}:
+ additive_inverse (additive_inverse ?54) =>= ?54
+ [54] by additive_inverse_additive_inverse ?54
+25863: Id : 20, {_}:
+ multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
+ [57, 56] by right_alternative ?56 ?57
+25863: Id : 21, {_}:
+ associator ?59 ?60 ?61
+ =>=
+ add (multiply (multiply ?59 ?60) ?61)
+ (additive_inverse (multiply ?59 (multiply ?60 ?61)))
+ [61, 60, 59] by associator ?59 ?60 ?61
+25863: Id : 22, {_}:
+ commutator ?63 ?64
+ =<=
+ add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
+ [64, 63] by commutator ?63 ?64
+25863: Goal:
+25863: Id : 1, {_}:
+ add
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ =>=
+ additive_identity
+ [] by prove_conjecture_1
+25863: Order:
+25863: lpo
+25863: Leaf order:
+25863: y 6 0 6 3,1,1,2
+25863: additive_identity 9 0 1 3
+25863: x 12 0 12 1,1,1,2
+25863: additive_inverse 22 1 0
+25863: commutator 1 2 0
+25863: add 25 2 1 0,2
+25863: multiply 40 2 4 0,1,2add
+25863: associator 7 3 6 0,1,1,2
+25862: Id : 2, {_}:
+ multiply (additive_inverse ?2) (additive_inverse ?3)
+ =>=
+ multiply ?2 ?3
+ [3, 2] by product_of_inverses ?2 ?3
+25862: Id : 3, {_}:
+ multiply (additive_inverse ?5) ?6
+ =>=
+ additive_inverse (multiply ?5 ?6)
+ [6, 5] by inverse_product1 ?5 ?6
+25862: Id : 4, {_}:
+ multiply ?8 (additive_inverse ?9)
+ =>=
+ additive_inverse (multiply ?8 ?9)
+ [9, 8] by inverse_product2 ?8 ?9
+25862: Id : 5, {_}:
+ multiply ?11 (add ?12 (additive_inverse ?13))
+ =<=
+ add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
+ [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
+25862: Id : 6, {_}:
+ multiply (add ?15 (additive_inverse ?16)) ?17
+ =<=
+ add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
+ [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
+25862: Id : 7, {_}:
+ multiply (additive_inverse ?19) (add ?20 ?21)
+ =<=
+ add (additive_inverse (multiply ?19 ?20))
+ (additive_inverse (multiply ?19 ?21))
+ [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
+25862: Id : 8, {_}:
+ multiply (add ?23 ?24) (additive_inverse ?25)
+ =<=
+ add (additive_inverse (multiply ?23 ?25))
+ (additive_inverse (multiply ?24 ?25))
+ [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
+25862: Id : 9, {_}:
+ add ?27 ?28 =?= add ?28 ?27
+ [28, 27] by commutativity_for_addition ?27 ?28
+25862: Id : 10, {_}:
+ add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
+ [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
+25862: Id : 11, {_}:
+ add additive_identity ?34 =>= ?34
+ [34] by left_additive_identity ?34
+25862: Id : 12, {_}:
+ add ?36 additive_identity =>= ?36
+ [36] by right_additive_identity ?36
+25862: Id : 13, {_}:
+ multiply additive_identity ?38 =>= additive_identity
+ [38] by left_multiplicative_zero ?38
+25862: Id : 14, {_}:
+ multiply ?40 additive_identity =>= additive_identity
+ [40] by right_multiplicative_zero ?40
+25862: Id : 15, {_}:
+ add (additive_inverse ?42) ?42 =>= additive_identity
+ [42] by left_additive_inverse ?42
+25862: Id : 16, {_}:
+ add ?44 (additive_inverse ?44) =>= additive_identity
+ [44] by right_additive_inverse ?44
+25862: Id : 17, {_}:
+ multiply ?46 (add ?47 ?48)
+ =<=
+ add (multiply ?46 ?47) (multiply ?46 ?48)
+ [48, 47, 46] by distribute1 ?46 ?47 ?48
+25862: Id : 18, {_}:
+ multiply (add ?50 ?51) ?52
+ =<=
+ add (multiply ?50 ?52) (multiply ?51 ?52)
+ [52, 51, 50] by distribute2 ?50 ?51 ?52
+25862: Id : 19, {_}:
+ additive_inverse (additive_inverse ?54) =>= ?54
+ [54] by additive_inverse_additive_inverse ?54
+25862: Id : 20, {_}:
+ multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
+ [57, 56] by right_alternative ?56 ?57
+25862: Id : 21, {_}:
+ associator ?59 ?60 ?61
+ =<=
+ add (multiply (multiply ?59 ?60) ?61)
+ (additive_inverse (multiply ?59 (multiply ?60 ?61)))
+ [61, 60, 59] by associator ?59 ?60 ?61
+25862: Id : 22, {_}:
+ commutator ?63 ?64
+ =<=
+ add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
+ [64, 63] by commutator ?63 ?64
+25862: Goal:
+25862: Id : 1, {_}:
+ add
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ =>=
+ additive_identity
+ [] by prove_conjecture_1
+25862: Order:
+25862: kbo
+25862: Leaf order:
+25862: y 6 0 6 3,1,1,2
+25862: additive_identity 9 0 1 3
+25862: x 12 0 12 1,1,1,2
+25862: additive_inverse 22 1 0
+25862: commutator 1 2 0
+25862: add 25 2 1 0,2
+25862: multiply 40 2 4 0,1,2add
+25862: associator 7 3 6 0,1,1,2
+% SZS status Timeout for RNG030-7.p
+NO CLASH, using fixed ground order
+25886: Facts:
+25886: Id : 2, {_}:
+ add ?2 ?3 =?= add ?3 ?2
+ [3, 2] by commutativity_for_addition ?2 ?3
+25886: Id : 3, {_}:
+ add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7
+ [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
+25886: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
+25886: Id : 5, {_}:
+ add ?11 additive_identity =>= ?11
+ [11] by right_additive_identity ?11
+25886: Id : 6, {_}:
+ multiply additive_identity ?13 =>= additive_identity
+ [13] by left_multiplicative_zero ?13
+25886: Id : 7, {_}:
+ multiply ?15 additive_identity =>= additive_identity
+ [15] by right_multiplicative_zero ?15
+25886: Id : 8, {_}:
+ add (additive_inverse ?17) ?17 =>= additive_identity
+ [17] by left_additive_inverse ?17
+25886: Id : 9, {_}:
+ add ?19 (additive_inverse ?19) =>= additive_identity
+ [19] by right_additive_inverse ?19
+25886: Id : 10, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+25886: Id : 11, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+25886: Id : 12, {_}:
+ additive_inverse (additive_inverse ?29) =>= ?29
+ [29] by additive_inverse_additive_inverse ?29
+25886: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25886: Id : 14, {_}:
+ associator ?34 ?35 ?36
+ =<=
+ add (multiply (multiply ?34 ?35) ?36)
+ (additive_inverse (multiply ?34 (multiply ?35 ?36)))
+ [36, 35, 34] by associator ?34 ?35 ?36
+25886: Id : 15, {_}:
+ commutator ?38 ?39
+ =<=
+ add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
+ [39, 38] by commutator ?38 ?39
+25886: Goal:
+25886: Id : 1, {_}:
+ add
+ (add
+ (add
+ (add
+ (add
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ =>=
+ additive_identity
+ [] by prove_conjecture_3
+25886: Order:
+25886: nrkbo
+25886: Leaf order:
+25886: additive_identity 9 0 1 3
+25886: y 18 0 18 3,1,1,1,1,1,1,2
+25886: x 36 0 36 1,1,1,1,1,1,1,2
+25886: additive_inverse 6 1 0
+25886: commutator 1 2 0
+25886: add 21 2 5 0,2
+25886: multiply 30 2 12 0,1,1,1,1,1,2
+25886: associator 19 3 18 0,1,1,1,1,1,1,2
+NO CLASH, using fixed ground order
+25887: Facts:
+25887: Id : 2, {_}:
+ add ?2 ?3 =?= add ?3 ?2
+ [3, 2] by commutativity_for_addition ?2 ?3
+25887: Id : 3, {_}:
+ add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
+ [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
+25887: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
+25887: Id : 5, {_}:
+ add ?11 additive_identity =>= ?11
+ [11] by right_additive_identity ?11
+25887: Id : 6, {_}:
+ multiply additive_identity ?13 =>= additive_identity
+ [13] by left_multiplicative_zero ?13
+25887: Id : 7, {_}:
+ multiply ?15 additive_identity =>= additive_identity
+ [15] by right_multiplicative_zero ?15
+25887: Id : 8, {_}:
+ add (additive_inverse ?17) ?17 =>= additive_identity
+ [17] by left_additive_inverse ?17
+25887: Id : 9, {_}:
+ add ?19 (additive_inverse ?19) =>= additive_identity
+ [19] by right_additive_inverse ?19
+25887: Id : 10, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+25887: Id : 11, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+25887: Id : 12, {_}:
+ additive_inverse (additive_inverse ?29) =>= ?29
+ [29] by additive_inverse_additive_inverse ?29
+25887: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25887: Id : 14, {_}:
+ associator ?34 ?35 ?36
+ =<=
+ add (multiply (multiply ?34 ?35) ?36)
+ (additive_inverse (multiply ?34 (multiply ?35 ?36)))
+ [36, 35, 34] by associator ?34 ?35 ?36
+25887: Id : 15, {_}:
+ commutator ?38 ?39
+ =<=
+ add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
+ [39, 38] by commutator ?38 ?39
+25887: Goal:
+25887: Id : 1, {_}:
+ add
+ (add
+ (add
+ (add
+ (add
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ =>=
+ additive_identity
+ [] by prove_conjecture_3
+25887: Order:
+25887: kbo
+25887: Leaf order:
+25887: additive_identity 9 0 1 3
+25887: y 18 0 18 3,1,1,1,1,1,1,2
+25887: x 36 0 36 1,1,1,1,1,1,1,2
+25887: additive_inverse 6 1 0
+25887: commutator 1 2 0
+25887: add 21 2 5 0,2
+25887: multiply 30 2 12 0,1,1,1,1,1,2
+25887: associator 19 3 18 0,1,1,1,1,1,1,2
+NO CLASH, using fixed ground order
+25888: Facts:
+25888: Id : 2, {_}:
+ add ?2 ?3 =?= add ?3 ?2
+ [3, 2] by commutativity_for_addition ?2 ?3
+25888: Id : 3, {_}:
+ add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7
+ [7, 6, 5] by associativity_for_addition ?5 ?6 ?7
+25888: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9
+25888: Id : 5, {_}:
+ add ?11 additive_identity =>= ?11
+ [11] by right_additive_identity ?11
+25888: Id : 6, {_}:
+ multiply additive_identity ?13 =>= additive_identity
+ [13] by left_multiplicative_zero ?13
+25888: Id : 7, {_}:
+ multiply ?15 additive_identity =>= additive_identity
+ [15] by right_multiplicative_zero ?15
+25888: Id : 8, {_}:
+ add (additive_inverse ?17) ?17 =>= additive_identity
+ [17] by left_additive_inverse ?17
+25888: Id : 9, {_}:
+ add ?19 (additive_inverse ?19) =>= additive_identity
+ [19] by right_additive_inverse ?19
+25888: Id : 10, {_}:
+ multiply ?21 (add ?22 ?23)
+ =>=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+25888: Id : 11, {_}:
+ multiply (add ?25 ?26) ?27
+ =>=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+25888: Id : 12, {_}:
+ additive_inverse (additive_inverse ?29) =>= ?29
+ [29] by additive_inverse_additive_inverse ?29
+25888: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+25888: Id : 14, {_}:
+ associator ?34 ?35 ?36
+ =>=
+ add (multiply (multiply ?34 ?35) ?36)
+ (additive_inverse (multiply ?34 (multiply ?35 ?36)))
+ [36, 35, 34] by associator ?34 ?35 ?36
+25888: Id : 15, {_}:
+ commutator ?38 ?39
+ =<=
+ add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39))
+ [39, 38] by commutator ?38 ?39
+25888: Goal:
+25888: Id : 1, {_}:
+ add
+ (add
+ (add
+ (add
+ (add
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ =>=
+ additive_identity
+ [] by prove_conjecture_3
+25888: Order:
+25888: lpo
+25888: Leaf order:
+25888: additive_identity 9 0 1 3
+25888: y 18 0 18 3,1,1,1,1,1,1,2
+25888: x 36 0 36 1,1,1,1,1,1,1,2
+25888: additive_inverse 6 1 0
+25888: commutator 1 2 0
+25888: add 21 2 5 0,2
+25888: multiply 30 2 12 0,1,1,1,1,1,2
+25888: associator 19 3 18 0,1,1,1,1,1,1,2
+% SZS status Timeout for RNG032-6.p
+NO CLASH, using fixed ground order
+25915: Facts:
+25915: Id : 2, {_}:
+ multiply (additive_inverse ?2) (additive_inverse ?3)
+ =>=
+ multiply ?2 ?3
+ [3, 2] by product_of_inverses ?2 ?3
+25915: Id : 3, {_}:
+ multiply (additive_inverse ?5) ?6
+ =>=
+ additive_inverse (multiply ?5 ?6)
+ [6, 5] by inverse_product1 ?5 ?6
+25915: Id : 4, {_}:
+ multiply ?8 (additive_inverse ?9)
+ =>=
+ additive_inverse (multiply ?8 ?9)
+ [9, 8] by inverse_product2 ?8 ?9
+25915: Id : 5, {_}:
+ multiply ?11 (add ?12 (additive_inverse ?13))
+ =<=
+ add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
+ [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
+25915: Id : 6, {_}:
+ multiply (add ?15 (additive_inverse ?16)) ?17
+ =<=
+ add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
+ [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
+25915: Id : 7, {_}:
+ multiply (additive_inverse ?19) (add ?20 ?21)
+ =<=
+ add (additive_inverse (multiply ?19 ?20))
+ (additive_inverse (multiply ?19 ?21))
+ [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
+25915: Id : 8, {_}:
+ multiply (add ?23 ?24) (additive_inverse ?25)
+ =<=
+ add (additive_inverse (multiply ?23 ?25))
+ (additive_inverse (multiply ?24 ?25))
+ [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
+25915: Id : 9, {_}:
+ add ?27 ?28 =?= add ?28 ?27
+ [28, 27] by commutativity_for_addition ?27 ?28
+25915: Id : 10, {_}:
+ add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32
+ [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
+25915: Id : 11, {_}:
+ add additive_identity ?34 =>= ?34
+ [34] by left_additive_identity ?34
+25915: Id : 12, {_}:
+ add ?36 additive_identity =>= ?36
+ [36] by right_additive_identity ?36
+25915: Id : 13, {_}:
+ multiply additive_identity ?38 =>= additive_identity
+ [38] by left_multiplicative_zero ?38
+25915: Id : 14, {_}:
+ multiply ?40 additive_identity =>= additive_identity
+ [40] by right_multiplicative_zero ?40
+25915: Id : 15, {_}:
+ add (additive_inverse ?42) ?42 =>= additive_identity
+ [42] by left_additive_inverse ?42
+25915: Id : 16, {_}:
+ add ?44 (additive_inverse ?44) =>= additive_identity
+ [44] by right_additive_inverse ?44
+25915: Id : 17, {_}:
+ multiply ?46 (add ?47 ?48)
+ =<=
+ add (multiply ?46 ?47) (multiply ?46 ?48)
+ [48, 47, 46] by distribute1 ?46 ?47 ?48
+25915: Id : 18, {_}:
+ multiply (add ?50 ?51) ?52
+ =<=
+ add (multiply ?50 ?52) (multiply ?51 ?52)
+ [52, 51, 50] by distribute2 ?50 ?51 ?52
+25915: Id : 19, {_}:
+ additive_inverse (additive_inverse ?54) =>= ?54
+ [54] by additive_inverse_additive_inverse ?54
+25915: Id : 20, {_}:
+ multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57)
+ [57, 56] by right_alternative ?56 ?57
+25915: Id : 21, {_}:
+ associator ?59 ?60 ?61
+ =<=
+ add (multiply (multiply ?59 ?60) ?61)
+ (additive_inverse (multiply ?59 (multiply ?60 ?61)))
+ [61, 60, 59] by associator ?59 ?60 ?61
+25915: Id : 22, {_}:
+ commutator ?63 ?64
+ =<=
+ add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
+ [64, 63] by commutator ?63 ?64
+25915: Goal:
+25915: Id : 1, {_}:
+ add
+ (add
+ (add
+ (add
+ (add
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ =>=
+ additive_identity
+ [] by prove_conjecture_3
+25915: Order:
+25915: nrkbo
+25915: Leaf order:
+25915: additive_identity 9 0 1 3
+25915: y 18 0 18 3,1,1,1,1,1,1,2
+25915: x 36 0 36 1,1,1,1,1,1,1,2
+25915: additive_inverse 22 1 0
+25915: commutator 1 2 0
+25915: add 29 2 5 0,2
+25915: multiply 48 2 12 0,1,1,1,1,1,2add
+25915: associator 19 3 18 0,1,1,1,1,1,1,2
+NO CLASH, using fixed ground order
+25916: Facts:
+25916: Id : 2, {_}:
+ multiply (additive_inverse ?2) (additive_inverse ?3)
+ =>=
+ multiply ?2 ?3
+ [3, 2] by product_of_inverses ?2 ?3
+25916: Id : 3, {_}:
+ multiply (additive_inverse ?5) ?6
+ =>=
+ additive_inverse (multiply ?5 ?6)
+ [6, 5] by inverse_product1 ?5 ?6
+25916: Id : 4, {_}:
+ multiply ?8 (additive_inverse ?9)
+ =>=
+ additive_inverse (multiply ?8 ?9)
+ [9, 8] by inverse_product2 ?8 ?9
+25916: Id : 5, {_}:
+ multiply ?11 (add ?12 (additive_inverse ?13))
+ =<=
+ add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
+ [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
+25916: Id : 6, {_}:
+ multiply (add ?15 (additive_inverse ?16)) ?17
+ =<=
+ add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
+ [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
+25916: Id : 7, {_}:
+ multiply (additive_inverse ?19) (add ?20 ?21)
+ =<=
+ add (additive_inverse (multiply ?19 ?20))
+ (additive_inverse (multiply ?19 ?21))
+ [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
+25916: Id : 8, {_}:
+ multiply (add ?23 ?24) (additive_inverse ?25)
+ =<=
+ add (additive_inverse (multiply ?23 ?25))
+ (additive_inverse (multiply ?24 ?25))
+ [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
+25916: Id : 9, {_}:
+ add ?27 ?28 =?= add ?28 ?27
+ [28, 27] by commutativity_for_addition ?27 ?28
+25916: Id : 10, {_}:
+ add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
+ [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
+25916: Id : 11, {_}:
+ add additive_identity ?34 =>= ?34
+ [34] by left_additive_identity ?34
+25916: Id : 12, {_}:
+ add ?36 additive_identity =>= ?36
+ [36] by right_additive_identity ?36
+25916: Id : 13, {_}:
+ multiply additive_identity ?38 =>= additive_identity
+ [38] by left_multiplicative_zero ?38
+25916: Id : 14, {_}:
+ multiply ?40 additive_identity =>= additive_identity
+ [40] by right_multiplicative_zero ?40
+25916: Id : 15, {_}:
+ add (additive_inverse ?42) ?42 =>= additive_identity
+ [42] by left_additive_inverse ?42
+25916: Id : 16, {_}:
+ add ?44 (additive_inverse ?44) =>= additive_identity
+ [44] by right_additive_inverse ?44
+25916: Id : 17, {_}:
+ multiply ?46 (add ?47 ?48)
+ =<=
+ add (multiply ?46 ?47) (multiply ?46 ?48)
+ [48, 47, 46] by distribute1 ?46 ?47 ?48
+25916: Id : 18, {_}:
+ multiply (add ?50 ?51) ?52
+ =<=
+ add (multiply ?50 ?52) (multiply ?51 ?52)
+ [52, 51, 50] by distribute2 ?50 ?51 ?52
+25916: Id : 19, {_}:
+ additive_inverse (additive_inverse ?54) =>= ?54
+ [54] by additive_inverse_additive_inverse ?54
+25916: Id : 20, {_}:
+ multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
+ [57, 56] by right_alternative ?56 ?57
+25916: Id : 21, {_}:
+ associator ?59 ?60 ?61
+ =<=
+ add (multiply (multiply ?59 ?60) ?61)
+ (additive_inverse (multiply ?59 (multiply ?60 ?61)))
+ [61, 60, 59] by associator ?59 ?60 ?61
+25916: Id : 22, {_}:
+ commutator ?63 ?64
+ =<=
+ add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
+ [64, 63] by commutator ?63 ?64
+25916: Goal:
+25916: Id : 1, {_}:
+ add
+ (add
+ (add
+ (add
+ (add
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ =>=
+ additive_identity
+ [] by prove_conjecture_3
+25916: Order:
+25916: kbo
+25916: Leaf order:
+25916: additive_identity 9 0 1 3
+25916: y 18 0 18 3,1,1,1,1,1,1,2
+25916: x 36 0 36 1,1,1,1,1,1,1,2
+25916: additive_inverse 22 1 0
+25916: commutator 1 2 0
+25916: add 29 2 5 0,2
+25916: multiply 48 2 12 0,1,1,1,1,1,2add
+25916: associator 19 3 18 0,1,1,1,1,1,1,2
+NO CLASH, using fixed ground order
+25917: Facts:
+25917: Id : 2, {_}:
+ multiply (additive_inverse ?2) (additive_inverse ?3)
+ =>=
+ multiply ?2 ?3
+ [3, 2] by product_of_inverses ?2 ?3
+25917: Id : 3, {_}:
+ multiply (additive_inverse ?5) ?6
+ =>=
+ additive_inverse (multiply ?5 ?6)
+ [6, 5] by inverse_product1 ?5 ?6
+25917: Id : 4, {_}:
+ multiply ?8 (additive_inverse ?9)
+ =>=
+ additive_inverse (multiply ?8 ?9)
+ [9, 8] by inverse_product2 ?8 ?9
+25917: Id : 5, {_}:
+ multiply ?11 (add ?12 (additive_inverse ?13))
+ =>=
+ add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13))
+ [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13
+25917: Id : 6, {_}:
+ multiply (add ?15 (additive_inverse ?16)) ?17
+ =>=
+ add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17))
+ [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17
+25917: Id : 7, {_}:
+ multiply (additive_inverse ?19) (add ?20 ?21)
+ =>=
+ add (additive_inverse (multiply ?19 ?20))
+ (additive_inverse (multiply ?19 ?21))
+ [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21
+25917: Id : 8, {_}:
+ multiply (add ?23 ?24) (additive_inverse ?25)
+ =>=
+ add (additive_inverse (multiply ?23 ?25))
+ (additive_inverse (multiply ?24 ?25))
+ [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25
+25917: Id : 9, {_}:
+ add ?27 ?28 =?= add ?28 ?27
+ [28, 27] by commutativity_for_addition ?27 ?28
+25917: Id : 10, {_}:
+ add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32
+ [32, 31, 30] by associativity_for_addition ?30 ?31 ?32
+25917: Id : 11, {_}:
+ add additive_identity ?34 =>= ?34
+ [34] by left_additive_identity ?34
+25917: Id : 12, {_}:
+ add ?36 additive_identity =>= ?36
+ [36] by right_additive_identity ?36
+25917: Id : 13, {_}:
+ multiply additive_identity ?38 =>= additive_identity
+ [38] by left_multiplicative_zero ?38
+25917: Id : 14, {_}:
+ multiply ?40 additive_identity =>= additive_identity
+ [40] by right_multiplicative_zero ?40
+25917: Id : 15, {_}:
+ add (additive_inverse ?42) ?42 =>= additive_identity
+ [42] by left_additive_inverse ?42
+25917: Id : 16, {_}:
+ add ?44 (additive_inverse ?44) =>= additive_identity
+ [44] by right_additive_inverse ?44
+25917: Id : 17, {_}:
+ multiply ?46 (add ?47 ?48)
+ =>=
+ add (multiply ?46 ?47) (multiply ?46 ?48)
+ [48, 47, 46] by distribute1 ?46 ?47 ?48
+25917: Id : 18, {_}:
+ multiply (add ?50 ?51) ?52
+ =>=
+ add (multiply ?50 ?52) (multiply ?51 ?52)
+ [52, 51, 50] by distribute2 ?50 ?51 ?52
+25917: Id : 19, {_}:
+ additive_inverse (additive_inverse ?54) =>= ?54
+ [54] by additive_inverse_additive_inverse ?54
+25917: Id : 20, {_}:
+ multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57)
+ [57, 56] by right_alternative ?56 ?57
+25917: Id : 21, {_}:
+ associator ?59 ?60 ?61
+ =>=
+ add (multiply (multiply ?59 ?60) ?61)
+ (additive_inverse (multiply ?59 (multiply ?60 ?61)))
+ [61, 60, 59] by associator ?59 ?60 ?61
+25917: Id : 22, {_}:
+ commutator ?63 ?64
+ =<=
+ add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64))
+ [64, 63] by commutator ?63 ?64
+25917: Goal:
+25917: Id : 1, {_}:
+ add
+ (add
+ (add
+ (add
+ (add
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y))))
+ (multiply (associator x x y)
+ (multiply (associator x x y) (associator x x y)))
+ =>=
+ additive_identity
+ [] by prove_conjecture_3
+25917: Order:
+25917: lpo
+25917: Leaf order:
+25917: additive_identity 9 0 1 3
+25917: y 18 0 18 3,1,1,1,1,1,1,2
+25917: x 36 0 36 1,1,1,1,1,1,1,2
+25917: additive_inverse 22 1 0
+25917: commutator 1 2 0
+25917: add 29 2 5 0,2
+25917: multiply 48 2 12 0,1,1,1,1,1,2add
+25917: associator 19 3 18 0,1,1,1,1,1,1,2
+% SZS status Timeout for RNG032-7.p
+NO CLASH, using fixed ground order
+26009: Facts:
+26009: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+26009: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+26009: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+26009: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+26009: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+26009: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+26009: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+26009: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+26009: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+26009: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+26009: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+NO CLASH, using fixed ground order
+26010: Facts:
+26010: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+26010: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+26010: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+26010: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+26010: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+26010: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+26010: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+26010: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+26010: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+26010: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+26010: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+26010: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+26010: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+26010: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+26010: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+26010: Goal:
+26010: Id : 1, {_}:
+ add (associator (multiply x y) z w) (associator x y (commutator z w))
+ =>=
+ add (multiply x (associator y z w)) (multiply (associator x z w) y)
+ [] by prove_challenge
+26010: Order:
+26010: lpo
+26010: Leaf order:
+26010: x 4 0 4 1,1,1,2
+26010: y 4 0 4 2,1,1,2
+26010: z 4 0 4 2,1,2
+26010: w 4 0 4 3,1,2
+26010: additive_identity 8 0 0
+26010: additive_inverse 6 1 0
+26010: commutator 2 2 1 0,3,2,2
+26010: add 18 2 2 0,2
+26010: multiply 25 2 3 0,1,1,2
+26010: associator 5 3 4 0,1,2
+26009: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+26009: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+26009: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+26009: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+26009: Goal:
+26009: Id : 1, {_}:
+ add (associator (multiply x y) z w) (associator x y (commutator z w))
+ =>=
+ add (multiply x (associator y z w)) (multiply (associator x z w) y)
+ [] by prove_challenge
+26009: Order:
+26009: kbo
+26009: Leaf order:
+26009: x 4 0 4 1,1,1,2
+26009: y 4 0 4 2,1,1,2
+26009: z 4 0 4 2,1,2
+26009: w 4 0 4 3,1,2
+26009: additive_identity 8 0 0
+26009: additive_inverse 6 1 0
+26009: commutator 2 2 1 0,3,2,2
+26009: add 18 2 2 0,2
+26009: multiply 25 2 3 0,1,1,2
+26009: associator 5 3 4 0,1,2
+NO CLASH, using fixed ground order
+26008: Facts:
+26008: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+26008: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+26008: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+26008: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+26008: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+26008: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+26008: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+26008: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+26008: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+26008: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+26008: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+26008: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+26008: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+26008: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+26008: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+26008: Goal:
+26008: Id : 1, {_}:
+ add (associator (multiply x y) z w) (associator x y (commutator z w))
+ =>=
+ add (multiply x (associator y z w)) (multiply (associator x z w) y)
+ [] by prove_challenge
+26008: Order:
+26008: nrkbo
+26008: Leaf order:
+26008: x 4 0 4 1,1,1,2
+26008: y 4 0 4 2,1,1,2
+26008: z 4 0 4 2,1,2
+26008: w 4 0 4 3,1,2
+26008: additive_identity 8 0 0
+26008: additive_inverse 6 1 0
+26008: commutator 2 2 1 0,3,2,2
+26008: add 18 2 2 0,2
+26008: multiply 25 2 3 0,1,1,2
+26008: associator 5 3 4 0,1,2
+% SZS status Timeout for RNG033-6.p
+NO CLASH, using fixed ground order
+26035: Facts:
+26035: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+26035: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+26035: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+26035: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+26035: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+26035: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+26035: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+26035: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+26035: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+26035: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+26035: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+26035: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+26035: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+26035: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+26035: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+26035: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+26035: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+26035: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+26035: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+26035: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+26035: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+26035: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+26035: Goal:
+26035: Id : 1, {_}:
+ add (associator (multiply x y) z w) (associator x y (commutator z w))
+ =>=
+ add (multiply x (associator y z w)) (multiply (associator x z w) y)
+ [] by prove_challenge
+26035: Order:
+26035: nrkbo
+26035: Leaf order:
+26035: x 4 0 4 1,1,1,2
+26035: y 4 0 4 2,1,1,2
+26035: z 4 0 4 2,1,2
+26035: w 4 0 4 3,1,2
+26035: additive_identity 8 0 0
+26035: additive_inverse 22 1 0
+26035: commutator 2 2 1 0,3,2,2
+26035: add 26 2 2 0,2
+26035: multiply 43 2 3 0,1,1,2
+26035: associator 5 3 4 0,1,2
+NO CLASH, using fixed ground order
+26036: Facts:
+26036: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+26036: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+26036: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+26036: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+26036: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+26036: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+26036: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+26036: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+26036: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+26036: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+26036: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+26036: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+26036: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+26036: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+26036: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+26036: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+26036: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+26036: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+26036: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+26036: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+26036: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+26036: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+26036: Goal:
+26036: Id : 1, {_}:
+ add (associator (multiply x y) z w) (associator x y (commutator z w))
+ =>=
+ add (multiply x (associator y z w)) (multiply (associator x z w) y)
+ [] by prove_challenge
+26036: Order:
+26036: kbo
+26036: Leaf order:
+26036: x 4 0 4 1,1,1,2
+26036: y 4 0 4 2,1,1,2
+26036: z 4 0 4 2,1,2
+26036: w 4 0 4 3,1,2
+26036: additive_identity 8 0 0
+26036: additive_inverse 22 1 0
+26036: commutator 2 2 1 0,3,2,2
+26036: add 26 2 2 0,2
+26036: multiply 43 2 3 0,1,1,2
+26036: associator 5 3 4 0,1,2
+NO CLASH, using fixed ground order
+26037: Facts:
+26037: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+26037: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+26037: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+26037: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+26037: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+26037: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+26037: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+26037: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+26037: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+26037: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+26037: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+26037: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+26037: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+26037: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+26037: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+26037: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+26037: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+26037: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+26037: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =>=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+26037: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =>=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+26037: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =>=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+26037: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =>=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+26037: Goal:
+26037: Id : 1, {_}:
+ add (associator (multiply x y) z w) (associator x y (commutator z w))
+ =>=
+ add (multiply x (associator y z w)) (multiply (associator x z w) y)
+ [] by prove_challenge
+26037: Order:
+26037: lpo
+26037: Leaf order:
+26037: x 4 0 4 1,1,1,2
+26037: y 4 0 4 2,1,1,2
+26037: z 4 0 4 2,1,2
+26037: w 4 0 4 3,1,2
+26037: additive_identity 8 0 0
+26037: additive_inverse 22 1 0
+26037: commutator 2 2 1 0,3,2,2
+26037: add 26 2 2 0,2
+26037: multiply 43 2 3 0,1,1,2
+26037: associator 5 3 4 0,1,2
+% SZS status Timeout for RNG033-7.p
+NO CLASH, using fixed ground order
+26058: Facts:
+26058: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+26058: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+26058: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+26058: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+26058: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+26058: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+26058: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+26058: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+26058: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+26058: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+26058: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+26058: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+26058: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+26058: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+26058: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+26058: Id : 17, {_}:
+ multiply ?44 (multiply ?45 (multiply ?46 ?45))
+ =?=
+ multiply (multiply (multiply ?44 ?45) ?46) ?45
+ [46, 45, 44] by right_moufang ?44 ?45 ?46
+26058: Goal:
+26058: Id : 1, {_}:
+ add (associator (multiply x y) z w) (associator x y (commutator z w))
+ =>=
+ add (multiply x (associator y z w)) (multiply (associator x z w) y)
+ [] by prove_challenge
+26058: Order:
+26058: nrkbo
+26058: Leaf order:
+26058: x 4 0 4 1,1,1,2
+26058: y 4 0 4 2,1,1,2
+26058: z 4 0 4 2,1,2
+26058: w 4 0 4 3,1,2
+26058: additive_identity 8 0 0
+26058: additive_inverse 6 1 0
+26058: commutator 2 2 1 0,3,2,2
+26058: add 18 2 2 0,2
+26058: multiply 31 2 3 0,1,1,2
+26058: associator 5 3 4 0,1,2
+NO CLASH, using fixed ground order
+26059: Facts:
+26059: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+26059: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+26059: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+26059: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+26059: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+26059: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+26059: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+26059: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+26059: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+26059: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+26059: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+26059: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+26059: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+26059: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+26059: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+26059: Id : 17, {_}:
+ multiply ?44 (multiply ?45 (multiply ?46 ?45))
+ =<=
+ multiply (multiply (multiply ?44 ?45) ?46) ?45
+ [46, 45, 44] by right_moufang ?44 ?45 ?46
+26059: Goal:
+26059: Id : 1, {_}:
+ add (associator (multiply x y) z w) (associator x y (commutator z w))
+ =>=
+ add (multiply x (associator y z w)) (multiply (associator x z w) y)
+ [] by prove_challenge
+26059: Order:
+26059: kbo
+26059: Leaf order:
+26059: x 4 0 4 1,1,1,2
+26059: y 4 0 4 2,1,1,2
+26059: z 4 0 4 2,1,2
+26059: w 4 0 4 3,1,2
+26059: additive_identity 8 0 0
+26059: additive_inverse 6 1 0
+26059: commutator 2 2 1 0,3,2,2
+26059: add 18 2 2 0,2
+26059: multiply 31 2 3 0,1,1,2
+26059: associator 5 3 4 0,1,2
+NO CLASH, using fixed ground order
+26060: Facts:
+26060: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+26060: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+26060: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+26060: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+26060: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+26060: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+26060: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+26060: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+26060: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+26060: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+26060: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+26060: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+26060: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+26060: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+26060: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+26060: Id : 17, {_}:
+ multiply ?44 (multiply ?45 (multiply ?46 ?45))
+ =<=
+ multiply (multiply (multiply ?44 ?45) ?46) ?45
+ [46, 45, 44] by right_moufang ?44 ?45 ?46
+26060: Goal:
+26060: Id : 1, {_}:
+ add (associator (multiply x y) z w) (associator x y (commutator z w))
+ =>=
+ add (multiply x (associator y z w)) (multiply (associator x z w) y)
+ [] by prove_challenge
+26060: Order:
+26060: lpo
+26060: Leaf order:
+26060: x 4 0 4 1,1,1,2
+26060: y 4 0 4 2,1,1,2
+26060: z 4 0 4 2,1,2
+26060: w 4 0 4 3,1,2
+26060: additive_identity 8 0 0
+26060: additive_inverse 6 1 0
+26060: commutator 2 2 1 0,3,2,2
+26060: add 18 2 2 0,2
+26060: multiply 31 2 3 0,1,1,2
+26060: associator 5 3 4 0,1,2
+% SZS status Timeout for RNG033-8.p
+NO CLASH, using fixed ground order
+26087: Facts:
+26087: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+26087: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+26087: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+26087: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+26087: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+26087: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+26087: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+26087: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+26087: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+26087: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+26087: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+26087: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+26087: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+26087: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+26087: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+26087: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+26087: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+26087: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+26087: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+26087: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+26087: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+26087: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+26087: Id : 24, {_}:
+ multiply ?69 (multiply ?70 (multiply ?71 ?70))
+ =?=
+ multiply (multiply (multiply ?69 ?70) ?71) ?70
+ [71, 70, 69] by right_moufang ?69 ?70 ?71
+26087: Goal:
+26087: Id : 1, {_}:
+ add (associator (multiply x y) z w) (associator x y (commutator z w))
+ =>=
+ add (multiply x (associator y z w)) (multiply (associator x z w) y)
+ [] by prove_challenge
+26087: Order:
+26087: nrkbo
+26087: Leaf order:
+26087: x 4 0 4 1,1,1,2
+26087: y 4 0 4 2,1,1,2
+26087: z 4 0 4 2,1,2
+26087: w 4 0 4 3,1,2
+26087: additive_identity 8 0 0
+26087: additive_inverse 22 1 0
+26087: commutator 2 2 1 0,3,2,2
+26087: add 26 2 2 0,2
+26087: multiply 49 2 3 0,1,1,2
+26087: associator 5 3 4 0,1,2
+NO CLASH, using fixed ground order
+26089: Facts:
+26089: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+26089: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+26089: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+26089: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+26089: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+26089: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+26089: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+26089: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =>=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+26089: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =>=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+26089: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+26089: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+26089: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+26089: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+26089: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =>=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+26089: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+26089: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+26089: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+26089: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+26089: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =>=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+26089: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =>=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+26089: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =>=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+26089: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =>=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+26089: Id : 24, {_}:
+ multiply ?69 (multiply ?70 (multiply ?71 ?70))
+ =<=
+ multiply (multiply (multiply ?69 ?70) ?71) ?70
+ [71, 70, 69] by right_moufang ?69 ?70 ?71
+26089: Goal:
+26089: Id : 1, {_}:
+ add (associator (multiply x y) z w) (associator x y (commutator z w))
+ =>=
+ add (multiply x (associator y z w)) (multiply (associator x z w) y)
+ [] by prove_challenge
+26089: Order:
+26089: lpo
+26089: Leaf order:
+26089: x 4 0 4 1,1,1,2
+26089: y 4 0 4 2,1,1,2
+26089: z 4 0 4 2,1,2
+26089: w 4 0 4 3,1,2
+26089: additive_identity 8 0 0
+26089: additive_inverse 22 1 0
+26089: commutator 2 2 1 0,3,2,2
+26089: add 26 2 2 0,2
+26089: multiply 49 2 3 0,1,1,2
+26089: associator 5 3 4 0,1,2
+NO CLASH, using fixed ground order
+26088: Facts:
+26088: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+26088: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+26088: Id : 4, {_}:
+ multiply additive_identity ?6 =>= additive_identity
+ [6] by left_multiplicative_zero ?6
+26088: Id : 5, {_}:
+ multiply ?8 additive_identity =>= additive_identity
+ [8] by right_multiplicative_zero ?8
+26088: Id : 6, {_}:
+ add (additive_inverse ?10) ?10 =>= additive_identity
+ [10] by left_additive_inverse ?10
+26088: Id : 7, {_}:
+ add ?12 (additive_inverse ?12) =>= additive_identity
+ [12] by right_additive_inverse ?12
+26088: Id : 8, {_}:
+ additive_inverse (additive_inverse ?14) =>= ?14
+ [14] by additive_inverse_additive_inverse ?14
+26088: Id : 9, {_}:
+ multiply ?16 (add ?17 ?18)
+ =<=
+ add (multiply ?16 ?17) (multiply ?16 ?18)
+ [18, 17, 16] by distribute1 ?16 ?17 ?18
+26088: Id : 10, {_}:
+ multiply (add ?20 ?21) ?22
+ =<=
+ add (multiply ?20 ?22) (multiply ?21 ?22)
+ [22, 21, 20] by distribute2 ?20 ?21 ?22
+26088: Id : 11, {_}:
+ add ?24 ?25 =?= add ?25 ?24
+ [25, 24] by commutativity_for_addition ?24 ?25
+26088: Id : 12, {_}:
+ add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29
+ [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
+26088: Id : 13, {_}:
+ multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32)
+ [32, 31] by right_alternative ?31 ?32
+26088: Id : 14, {_}:
+ multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35)
+ [35, 34] by left_alternative ?34 ?35
+26088: Id : 15, {_}:
+ associator ?37 ?38 ?39
+ =<=
+ add (multiply (multiply ?37 ?38) ?39)
+ (additive_inverse (multiply ?37 (multiply ?38 ?39)))
+ [39, 38, 37] by associator ?37 ?38 ?39
+26088: Id : 16, {_}:
+ commutator ?41 ?42
+ =<=
+ add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
+ [42, 41] by commutator ?41 ?42
+26088: Id : 17, {_}:
+ multiply (additive_inverse ?44) (additive_inverse ?45)
+ =>=
+ multiply ?44 ?45
+ [45, 44] by product_of_inverses ?44 ?45
+26088: Id : 18, {_}:
+ multiply (additive_inverse ?47) ?48
+ =>=
+ additive_inverse (multiply ?47 ?48)
+ [48, 47] by inverse_product1 ?47 ?48
+26088: Id : 19, {_}:
+ multiply ?50 (additive_inverse ?51)
+ =>=
+ additive_inverse (multiply ?50 ?51)
+ [51, 50] by inverse_product2 ?50 ?51
+26088: Id : 20, {_}:
+ multiply ?53 (add ?54 (additive_inverse ?55))
+ =<=
+ add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
+ [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
+26088: Id : 21, {_}:
+ multiply (add ?57 (additive_inverse ?58)) ?59
+ =<=
+ add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
+ [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
+26088: Id : 22, {_}:
+ multiply (additive_inverse ?61) (add ?62 ?63)
+ =<=
+ add (additive_inverse (multiply ?61 ?62))
+ (additive_inverse (multiply ?61 ?63))
+ [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
+26088: Id : 23, {_}:
+ multiply (add ?65 ?66) (additive_inverse ?67)
+ =<=
+ add (additive_inverse (multiply ?65 ?67))
+ (additive_inverse (multiply ?66 ?67))
+ [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
+26088: Id : 24, {_}:
+ multiply ?69 (multiply ?70 (multiply ?71 ?70))
+ =<=
+ multiply (multiply (multiply ?69 ?70) ?71) ?70
+ [71, 70, 69] by right_moufang ?69 ?70 ?71
+26088: Goal:
+26088: Id : 1, {_}:
+ add (associator (multiply x y) z w) (associator x y (commutator z w))
+ =>=
+ add (multiply x (associator y z w)) (multiply (associator x z w) y)
+ [] by prove_challenge
+26088: Order:
+26088: kbo
+26088: Leaf order:
+26088: x 4 0 4 1,1,1,2
+26088: y 4 0 4 2,1,1,2
+26088: z 4 0 4 2,1,2
+26088: w 4 0 4 3,1,2
+26088: additive_identity 8 0 0
+26088: additive_inverse 22 1 0
+26088: commutator 2 2 1 0,3,2,2
+26088: add 26 2 2 0,2
+26088: multiply 49 2 3 0,1,1,2
+26088: associator 5 3 4 0,1,2
+% SZS status Timeout for RNG033-9.p
+NO CLASH, using fixed ground order
+NO CLASH, using fixed ground order
+26115: Facts:
+26115: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+26116: Facts:
+26116: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+26116: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+26116: Id : 4, {_}:
+ add (additive_inverse ?6) ?6 =>= additive_identity
+ [6] by left_additive_inverse ?6
+26116: Id : 5, {_}:
+ add ?8 (additive_inverse ?8) =>= additive_identity
+ [8] by right_additive_inverse ?8
+26116: Id : 6, {_}:
+ add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
+ [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
+26116: Id : 7, {_}:
+ add ?14 ?15 =?= add ?15 ?14
+ [15, 14] by commutativity_for_addition ?14 ?15
+26116: Id : 8, {_}:
+ multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
+ [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
+26116: Id : 9, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+26115: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+26116: Id : 10, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+26115: Id : 4, {_}:
+ add (additive_inverse ?6) ?6 =>= additive_identity
+ [6] by left_additive_inverse ?6
+26115: Id : 5, {_}:
+ add ?8 (additive_inverse ?8) =>= additive_identity
+ [8] by right_additive_inverse ?8
+26115: Id : 6, {_}:
+ add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12
+ [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
+26115: Id : 7, {_}:
+ add ?14 ?15 =?= add ?15 ?14
+ [15, 14] by commutativity_for_addition ?14 ?15
+26115: Id : 8, {_}:
+ multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19
+ [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
+26115: Id : 9, {_}:
+ multiply ?21 (add ?22 ?23)
+ =<=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+26115: Id : 10, {_}:
+ multiply (add ?25 ?26) ?27
+ =<=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+26115: Id : 11, {_}:
+ multiply ?29 (multiply ?29 (multiply ?29 (multiply ?29 ?29))) =>= ?29
+ [29] by x_fifthed_is_x ?29
+26115: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
+26115: Goal:
+NO CLASH, using fixed ground order
+26117: Facts:
+26117: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
+26117: Id : 3, {_}:
+ add ?4 additive_identity =>= ?4
+ [4] by right_additive_identity ?4
+26117: Id : 4, {_}:
+ add (additive_inverse ?6) ?6 =>= additive_identity
+ [6] by left_additive_inverse ?6
+26117: Id : 5, {_}:
+ add ?8 (additive_inverse ?8) =>= additive_identity
+ [8] by right_additive_inverse ?8
+26117: Id : 6, {_}:
+ add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12
+ [12, 11, 10] by associativity_for_addition ?10 ?11 ?12
+26117: Id : 7, {_}:
+ add ?14 ?15 =?= add ?15 ?14
+ [15, 14] by commutativity_for_addition ?14 ?15
+26117: Id : 8, {_}:
+ multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19
+ [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19
+26117: Id : 9, {_}:
+ multiply ?21 (add ?22 ?23)
+ =>=
+ add (multiply ?21 ?22) (multiply ?21 ?23)
+ [23, 22, 21] by distribute1 ?21 ?22 ?23
+26117: Id : 10, {_}:
+ multiply (add ?25 ?26) ?27
+ =>=
+ add (multiply ?25 ?27) (multiply ?26 ?27)
+ [27, 26, 25] by distribute2 ?25 ?26 ?27
+26117: Id : 11, {_}:
+ multiply ?29 (multiply ?29 (multiply ?29 (multiply ?29 ?29))) =>= ?29
+ [29] by x_fifthed_is_x ?29
+26117: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
+26117: Goal:
+26117: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
+26117: Order:
+26117: lpo
+26117: Leaf order:
+26117: b 2 0 1 1,2
+26117: a 2 0 1 2,2
+26117: c 2 0 1 3
+26117: additive_identity 4 0 0
+26117: additive_inverse 2 1 0
+26117: add 14 2 0
+26117: multiply 16 2 1 0,2
+26116: Id : 11, {_}:
+ multiply ?29 (multiply ?29 (multiply ?29 (multiply ?29 ?29))) =>= ?29
+ [29] by x_fifthed_is_x ?29
+26116: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c
+26116: Goal:
+26116: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
+26116: Order:
+26116: kbo
+26116: Leaf order:
+26116: b 2 0 1 1,2
+26116: a 2 0 1 2,2
+26116: c 2 0 1 3
+26116: additive_identity 4 0 0
+26116: additive_inverse 2 1 0
+26116: add 14 2 0
+26116: multiply 16 2 1 0,2
+26115: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
+26115: Order:
+26115: nrkbo
+26115: Leaf order:
+26115: b 2 0 1 1,2
+26115: a 2 0 1 2,2
+26115: c 2 0 1 3
+26115: additive_identity 4 0 0
+26115: additive_inverse 2 1 0
+26115: add 14 2 0
+26115: multiply 16 2 1 0,2
+% SZS status Timeout for RNG036-7.p
+NO CLASH, using fixed ground order
+26159: Facts:
+26159: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+26159: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+26159: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+26159: Goal:
+26159: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+26159: Order:
+26159: nrkbo
+26159: Leaf order:
+26159: a 2 0 2 1,1,1,2
+26159: b 3 0 3 1,2,1,1,2
+26159: negate 9 1 5 0,1,2
+26159: add 12 2 3 0,2
+NO CLASH, using fixed ground order
+26160: Facts:
+26160: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+26160: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+26160: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+26160: Goal:
+26160: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+26160: Order:
+26160: kbo
+26160: Leaf order:
+26160: a 2 0 2 1,1,1,2
+26160: b 3 0 3 1,2,1,1,2
+26160: negate 9 1 5 0,1,2
+26160: add 12 2 3 0,2
+NO CLASH, using fixed ground order
+26161: Facts:
+26161: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+26161: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+26161: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+26161: Goal:
+26161: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+26161: Order:
+26161: lpo
+26161: Leaf order:
+26161: a 2 0 2 1,1,1,2
+26161: b 3 0 3 1,2,1,1,2
+26161: negate 9 1 5 0,1,2
+26161: add 12 2 3 0,2
+% SZS status Timeout for ROB001-1.p
+NO CLASH, using fixed ground order
+26183: Facts:
+26183: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+26183: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+26183: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+26183: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
+26183: Goal:
+26183: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+26183: Order:
+26183: nrkbo
+26183: Leaf order:
+26183: a 3 0 2 1,1,1,2
+26183: b 5 0 3 1,2,1,1,2
+26183: negate 11 1 5 0,1,2
+26183: add 13 2 3 0,2
+NO CLASH, using fixed ground order
+26184: Facts:
+26184: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+26184: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+26184: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+26184: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
+26184: Goal:
+26184: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+26184: Order:
+26184: kbo
+26184: Leaf order:
+26184: a 3 0 2 1,1,1,2
+26184: b 5 0 3 1,2,1,1,2
+26184: negate 11 1 5 0,1,2
+26184: add 13 2 3 0,2
+NO CLASH, using fixed ground order
+26185: Facts:
+26185: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+26185: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+26185: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+26185: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
+26185: Goal:
+26185: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+26185: Order:
+26185: lpo
+26185: Leaf order:
+26185: a 3 0 2 1,1,1,2
+26185: b 5 0 3 1,2,1,1,2
+26185: negate 11 1 5 0,1,2
+26185: add 13 2 3 0,2
+% SZS status Timeout for ROB007-1.p
+NO CLASH, using fixed ground order
+26215: Facts:
+26215: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
+26215: Id : 3, {_}:
+ add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8)
+ [8, 7, 6] by associativity_of_add ?6 ?7 ?8
+26215: Id : 4, {_}:
+ negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
+ =>=
+ ?10
+ [11, 10] by robbins_axiom ?10 ?11
+26215: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
+26215: Goal:
+26215: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
+26215: Order:
+26215: nrkbo
+26215: Leaf order:
+26215: a 1 0 0
+26215: b 2 0 0
+26215: negate 6 1 0
+26215: add 11 2 1 0,2
+NO CLASH, using fixed ground order
+26216: Facts:
+26216: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
+26216: Id : 3, {_}:
+ add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
+ [8, 7, 6] by associativity_of_add ?6 ?7 ?8
+26216: Id : 4, {_}:
+ negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
+ =>=
+ ?10
+ [11, 10] by robbins_axiom ?10 ?11
+26216: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
+26216: Goal:
+26216: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
+26216: Order:
+26216: kbo
+26216: Leaf order:
+26216: a 1 0 0
+26216: b 2 0 0
+26216: negate 6 1 0
+26216: add 11 2 1 0,2
+NO CLASH, using fixed ground order
+26217: Facts:
+26217: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
+26217: Id : 3, {_}:
+ add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
+ [8, 7, 6] by associativity_of_add ?6 ?7 ?8
+26217: Id : 4, {_}:
+ negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
+ =>=
+ ?10
+ [11, 10] by robbins_axiom ?10 ?11
+26217: Id : 5, {_}: negate (add a b) =>= negate b [] by condition
+26217: Goal:
+26217: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
+26217: Order:
+26217: lpo
+26217: Leaf order:
+26217: a 1 0 0
+26217: b 2 0 0
+26217: negate 6 1 0
+26217: add 11 2 1 0,2
+% SZS status Timeout for ROB007-2.p
+NO CLASH, using fixed ground order
+26249: Facts:
+26249: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+26249: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+26249: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+26249: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
+26249: Goal:
+26249: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+26249: Order:
+26249: nrkbo
+26249: Leaf order:
+26249: a 3 0 2 1,1,1,2
+26249: b 5 0 3 1,2,1,1,2
+26249: negate 11 1 5 0,1,2
+26249: add 13 2 3 0,2
+NO CLASH, using fixed ground order
+26250: Facts:
+26250: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+26250: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+26250: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+26250: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
+26250: Goal:
+26250: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+26250: Order:
+26250: kbo
+26250: Leaf order:
+26250: a 3 0 2 1,1,1,2
+26250: b 5 0 3 1,2,1,1,2
+26250: negate 11 1 5 0,1,2
+26250: add 13 2 3 0,2
+NO CLASH, using fixed ground order
+26251: Facts:
+26251: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+26251: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+26251: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+26251: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
+26251: Goal:
+26251: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+26251: Order:
+26251: lpo
+26251: Leaf order:
+26251: a 3 0 2 1,1,1,2
+26251: b 5 0 3 1,2,1,1,2
+26251: negate 11 1 5 0,1,2
+26251: add 13 2 3 0,2
+% SZS status Timeout for ROB020-1.p
+NO CLASH, using fixed ground order
+26275: Facts:
+26275: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
+26275: Id : 3, {_}:
+ add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8)
+ [8, 7, 6] by associativity_of_add ?6 ?7 ?8
+26275: Id : 4, {_}:
+ negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
+ =>=
+ ?10
+ [11, 10] by robbins_axiom ?10 ?11
+26275: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
+26275: Goal:
+26275: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
+26275: Order:
+26275: nrkbo
+26275: Leaf order:
+26275: a 1 0 0
+26275: b 2 0 0
+26275: negate 6 1 0
+26275: add 11 2 1 0,2
+NO CLASH, using fixed ground order
+26276: Facts:
+26276: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
+26276: Id : 3, {_}:
+ add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
+ [8, 7, 6] by associativity_of_add ?6 ?7 ?8
+26276: Id : 4, {_}:
+ negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
+ =>=
+ ?10
+ [11, 10] by robbins_axiom ?10 ?11
+26276: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
+26276: Goal:
+26276: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
+26276: Order:
+26276: kbo
+26276: Leaf order:
+26276: a 1 0 0
+26276: b 2 0 0
+26276: negate 6 1 0
+26276: add 11 2 1 0,2
+NO CLASH, using fixed ground order
+26277: Facts:
+26277: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4
+26277: Id : 3, {_}:
+ add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8)
+ [8, 7, 6] by associativity_of_add ?6 ?7 ?8
+26277: Id : 4, {_}:
+ negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11))))
+ =>=
+ ?10
+ [11, 10] by robbins_axiom ?10 ?11
+26277: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1
+26277: Goal:
+26277: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1
+26277: Order:
+26277: lpo
+26277: Leaf order:
+26277: a 1 0 0
+26277: b 2 0 0
+26277: negate 6 1 0
+26277: add 11 2 1 0,2
+% SZS status Timeout for ROB020-2.p
+NO CLASH, using fixed ground order
+26303: Facts:
+26303: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+26303: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+26303: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+26303: Id : 5, {_}:
+ negate (add (negate (add a (add a b))) (negate (add a (negate b))))
+ =>=
+ a
+ [] by the_condition
+26303: Goal:
+26303: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+26303: Order:
+26303: nrkbo
+26303: Leaf order:
+26303: b 5 0 3 1,2,1,1,2
+26303: a 6 0 2 1,1,1,2
+26303: negate 13 1 5 0,1,2
+26303: add 16 2 3 0,2
+NO CLASH, using fixed ground order
+26304: Facts:
+26304: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+26304: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+26304: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+26304: Id : 5, {_}:
+ negate (add (negate (add a (add a b))) (negate (add a (negate b))))
+ =>=
+ a
+ [] by the_condition
+26304: Goal:
+26304: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+26304: Order:
+26304: kbo
+26304: Leaf order:
+26304: b 5 0 3 1,2,1,1,2
+26304: a 6 0 2 1,1,1,2
+26304: negate 13 1 5 0,1,2
+26304: add 16 2 3 0,2
+NO CLASH, using fixed ground order
+26305: Facts:
+26305: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+26305: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+26305: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+26305: Id : 5, {_}:
+ negate (add (negate (add a (add a b))) (negate (add a (negate b))))
+ =>=
+ a
+ [] by the_condition
+26305: Goal:
+26305: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+26305: Order:
+26305: lpo
+26305: Leaf order:
+26305: b 5 0 3 1,2,1,1,2
+26305: a 6 0 2 1,1,1,2
+26305: negate 13 1 5 0,1,2
+26305: add 16 2 3 0,2
+% SZS status Timeout for ROB024-1.p
+NO CLASH, using fixed ground order
+26392: Facts:
+26392: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+26392: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+26392: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+26392: Id : 5, {_}: negate (negate c) =>= c [] by double_negation
+26392: Goal:
+26392: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+26392: Order:
+26392: nrkbo
+26392: Leaf order:
+26392: c 2 0 0
+26392: a 2 0 2 1,1,1,2
+26392: b 3 0 3 1,2,1,1,2
+26392: negate 11 1 5 0,1,2
+26392: add 12 2 3 0,2
+NO CLASH, using fixed ground order
+26393: Facts:
+26393: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+26393: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+26393: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+26393: Id : 5, {_}: negate (negate c) =>= c [] by double_negation
+26393: Goal:
+26393: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+26393: Order:
+26393: kbo
+26393: Leaf order:
+26393: c 2 0 0
+26393: a 2 0 2 1,1,1,2
+26393: b 3 0 3 1,2,1,1,2
+26393: negate 11 1 5 0,1,2
+26393: add 12 2 3 0,2
+NO CLASH, using fixed ground order
+26394: Facts:
+26394: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
+26394: Id : 3, {_}:
+ add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7)
+ [7, 6, 5] by associativity_of_add ?5 ?6 ?7
+26394: Id : 4, {_}:
+ negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10))))
+ =>=
+ ?9
+ [10, 9] by robbins_axiom ?9 ?10
+26394: Id : 5, {_}: negate (negate c) =>= c [] by double_negation
+26394: Goal:
+26394: Id : 1, {_}:
+ add (negate (add a (negate b))) (negate (add (negate a) (negate b)))
+ =>=
+ b
+ [] by prove_huntingtons_axiom
+26394: Order:
+26394: lpo
+26394: Leaf order:
+26394: c 2 0 0
+26394: a 2 0 2 1,1,1,2
+26394: b 3 0 3 1,2,1,1,2
+26394: negate 11 1 5 0,1,2
+26394: add 12 2 3 0,2
+% SZS status Timeout for ROB027-1.p
+NO CLASH, using fixed ground order
+26415: Facts:
+26415: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
+26415: Id : 3, {_}:
+ add (add ?7 ?8) ?9 =?= add ?7 (add ?8 ?9)
+ [9, 8, 7] by associativity_of_add ?7 ?8 ?9
+26415: Id : 4, {_}:
+ negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
+ =>=
+ ?11
+ [12, 11] by robbins_axiom ?11 ?12
+26415: Goal:
+26415: Id : 1, {_}:
+ negate (add ?1 ?2) =>= negate ?2
+ [2, 1] by prove_absorption_within_negation ?1 ?2
+26415: Order:
+26415: nrkbo
+26415: Leaf order:
+26415: negate 6 1 2 0,2
+26415: add 10 2 1 0,1,2
+NO CLASH, using fixed ground order
+26416: Facts:
+26416: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
+26416: Id : 3, {_}:
+ add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9)
+ [9, 8, 7] by associativity_of_add ?7 ?8 ?9
+26416: Id : 4, {_}:
+ negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
+ =>=
+ ?11
+ [12, 11] by robbins_axiom ?11 ?12
+26416: Goal:
+26416: Id : 1, {_}:
+ negate (add ?1 ?2) =>= negate ?2
+ [2, 1] by prove_absorption_within_negation ?1 ?2
+26416: Order:
+26416: kbo
+26416: Leaf order:
+26416: negate 6 1 2 0,2
+26416: add 10 2 1 0,1,2
+NO CLASH, using fixed ground order
+26417: Facts:
+26417: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
+26417: Id : 3, {_}:
+ add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9)
+ [9, 8, 7] by associativity_of_add ?7 ?8 ?9
+26417: Id : 4, {_}:
+ negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
+ =>=
+ ?11
+ [12, 11] by robbins_axiom ?11 ?12
+26417: Goal:
+26417: Id : 1, {_}:
+ negate (add ?1 ?2) =>= negate ?2
+ [2, 1] by prove_absorption_within_negation ?1 ?2
+26417: Order:
+26417: lpo
+26417: Leaf order:
+26417: negate 6 1 2 0,2
+26417: add 10 2 1 0,1,2
+% SZS status Timeout for ROB031-1.p
+NO CLASH, using fixed ground order
+26440: Facts:
+26440: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
+26440: Id : 3, {_}:
+ add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9)
+ [9, 8, 7] by associativity_of_add ?7 ?8 ?9
+26440: Id : 4, {_}:
+ negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
+ =>=
+ ?11
+ [12, 11] by robbins_axiom ?11 ?12
+26440: Goal:
+26440: Id : 1, {_}: add ?1 ?2 =>= ?2 [2, 1] by prove_absorbtion ?1 ?2
+26440: Order:
+26440: kbo
+26440: Leaf order:
+26440: negate 4 1 0
+26440: add 10 2 1 0,2
+NO CLASH, using fixed ground order
+26441: Facts:
+26441: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
+26441: Id : 3, {_}:
+ add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9)
+ [9, 8, 7] by associativity_of_add ?7 ?8 ?9
+26441: Id : 4, {_}:
+ negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
+ =>=
+ ?11
+ [12, 11] by robbins_axiom ?11 ?12
+26441: Goal:
+26441: Id : 1, {_}: add ?1 ?2 =>= ?2 [2, 1] by prove_absorbtion ?1 ?2
+26441: Order:
+26441: lpo
+26441: Leaf order:
+26441: negate 4 1 0
+26441: add 10 2 1 0,2
+NO CLASH, using fixed ground order
+26439: Facts:
+26439: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5
+26439: Id : 3, {_}:
+ add (add ?7 ?8) ?9 =?= add ?7 (add ?8 ?9)
+ [9, 8, 7] by associativity_of_add ?7 ?8 ?9
+26439: Id : 4, {_}:
+ negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12))))
+ =>=
+ ?11
+ [12, 11] by robbins_axiom ?11 ?12
+26439: Goal:
+26439: Id : 1, {_}: add ?1 ?2 =>= ?2 [2, 1] by prove_absorbtion ?1 ?2
+26439: Order:
+26439: nrkbo
+26439: Leaf order:
+26439: negate 4 1 0
+26439: add 10 2 1 0,2
+% SZS status Timeout for ROB032-1.p
projects / helm.git / commitdiff