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