TSTP Solution File: GRP002-2 by Matita---1.0
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%------------------------------------------------------------------------------
% File : Matita---1.0
% Problem : GRP002-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:28:21 EDT 2022
% Result : Unsatisfiable 3.11s 1.16s
% Output : CNFRefutation 3.11s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP002-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 06:54:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.33 24191: Facts:
% 0.18/0.33 24191: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
% 0.18/0.33 24191: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
% 0.18/0.33 24191: Id : 4, {_}:
% 0.18/0.33 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
% 0.18/0.33 [8, 7, 6] by associativity ?6 ?7 ?8
% 0.18/0.33 24191: Id : 5, {_}: multiply ?10 identity =>= ?10 [10] by right_identity ?10
% 0.18/0.33 24191: Id : 6, {_}:
% 0.18/0.33 multiply ?12 (inverse ?12) =>= identity
% 0.18/0.33 [12] by right_inverse ?12
% 0.18/0.33 24191: Id : 7, {_}:
% 0.18/0.33 multiply ?14 (multiply ?14 ?14) =>= identity
% 0.18/0.33 [14] by x_cubed_is_identity ?14
% 0.18/0.33 24191: Id : 8, {_}: multiply a b =>= c [] by a_times_b_is_c
% 0.18/0.33 24191: Id : 9, {_}: multiply c (inverse a) =>= d [] by c_times_inverse_a_is_d
% 0.18/0.33 24191: Id : 10, {_}: multiply d (inverse b) =>= h [] by d_times_inverse_b_is_h
% 0.18/0.33 24191: Id : 11, {_}: multiply h b =>= j [] by h_times_b_is_j
% 0.18/0.33 24191: Id : 12, {_}: multiply j (inverse h) =>= k [] by j_times_inverse_h_is_k
% 0.18/0.33 24191: Goal:
% 0.18/0.33 24191: Id : 1, {_}:
% 0.18/0.33 multiply k (inverse b) =>= identity
% 0.18/0.33 [] by prove_k_times_inverse_b_is_e
% 3.11/1.16 Statistics :
% 3.11/1.16 Max weight : 17
% 3.11/1.16 Found proof, 0.823784s
% 3.11/1.16 % SZS status Unsatisfiable for theBenchmark.p
% 3.11/1.16 % SZS output start CNFRefutation for theBenchmark.p
% 3.11/1.16 Id : 12, {_}: multiply j (inverse h) =>= k [] by j_times_inverse_h_is_k
% 3.11/1.16 Id : 11, {_}: multiply h b =>= j [] by h_times_b_is_j
% 3.11/1.16 Id : 5, {_}: multiply ?10 identity =>= ?10 [10] by right_identity ?10
% 3.11/1.16 Id : 10, {_}: multiply d (inverse b) =>= h [] by d_times_inverse_b_is_h
% 3.11/1.16 Id : 6, {_}: multiply ?12 (inverse ?12) =>= identity [12] by right_inverse ?12
% 3.11/1.16 Id : 9, {_}: multiply c (inverse a) =>= d [] by c_times_inverse_a_is_d
% 3.11/1.16 Id : 8, {_}: multiply a b =>= c [] by a_times_b_is_c
% 3.11/1.16 Id : 7, {_}: multiply ?14 (multiply ?14 ?14) =>= identity [14] by x_cubed_is_identity ?14
% 3.11/1.16 Id : 4, {_}: multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
% 3.11/1.16 Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
% 3.11/1.16 Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
% 3.11/1.16 Id : 17, {_}: multiply (multiply ?28 ?29) ?30 =>= multiply ?28 (multiply ?29 ?30) [30, 29, 28] by associativity ?28 ?29 ?30
% 3.11/1.16 Id : 19, {_}: multiply identity ?35 =<= multiply (inverse ?36) (multiply ?36 ?35) [36, 35] by Super 17 with 3 at 1,2
% 3.11/1.16 Id : 23, {_}: ?35 =<= multiply (inverse ?36) (multiply ?36 ?35) [36, 35] by Demod 19 with 2 at 2
% 3.11/1.16 Id : 48, {_}: multiply identity ?79 =<= multiply ?80 (multiply (multiply ?80 ?80) ?79) [80, 79] by Super 4 with 7 at 1,2
% 3.11/1.16 Id : 57, {_}: ?79 =<= multiply ?80 (multiply (multiply ?80 ?80) ?79) [80, 79] by Demod 48 with 2 at 2
% 3.11/1.16 Id : 58, {_}: ?79 =<= multiply ?80 (multiply ?80 (multiply ?80 ?79)) [80, 79] by Demod 57 with 4 at 2,3
% 3.11/1.16 Id : 432, {_}: multiply ?431 (multiply ?431 ?432) =>= multiply (inverse ?431) ?432 [432, 431] by Super 23 with 58 at 2,3
% 3.11/1.16 Id : 49, {_}: identity =<= multiply ?82 (multiply ?83 (multiply (multiply ?82 ?83) (multiply ?82 ?83))) [83, 82] by Super 4 with 7 at 2
% 3.11/1.16 Id : 59, {_}: identity =<= multiply ?82 (multiply ?83 (multiply ?82 (multiply ?83 (multiply ?82 ?83)))) [83, 82] by Demod 49 with 4 at 2,2,3
% 3.11/1.16 Id : 13218, {_}: multiply ?8861 (multiply ?8861 ?8862) =>= multiply (inverse ?8861) ?8862 [8862, 8861] by Super 23 with 58 at 2,3
% 3.11/1.16 Id : 95, {_}: ?134 =<= multiply (inverse ?135) (multiply ?135 ?134) [135, 134] by Demod 19 with 2 at 2
% 3.11/1.16 Id : 98, {_}: ?141 =<= multiply (inverse (multiply ?142 ?143)) (multiply ?142 (multiply ?143 ?141)) [143, 142, 141] by Super 95 with 4 at 2,3
% 3.11/1.16 Id : 102, {_}: b =<= multiply (inverse a) c [] by Super 95 with 8 at 2,3
% 3.11/1.16 Id : 5825, {_}: multiply b ?4291 =<= multiply (inverse a) (multiply c ?4291) [4291] by Super 4 with 102 at 1,2
% 3.11/1.16 Id : 438, {_}: ?450 =<= multiply ?451 (multiply ?451 (multiply ?451 ?450)) [451, 450] by Demod 57 with 4 at 2,3
% 3.11/1.16 Id : 446, {_}: inverse a =<= multiply c (multiply c d) [] by Super 438 with 9 at 2,2,3
% 3.11/1.16 Id : 40, {_}: identity =<= multiply ?67 (multiply ?68 (inverse (multiply ?67 ?68))) [68, 67] by Super 4 with 6 at 2
% 3.11/1.16 Id : 447, {_}: inverse b =<= multiply d (multiply d h) [] by Super 438 with 10 at 2,2,3
% 3.11/1.16 Id : 674, {_}: identity =<= multiply d (multiply (multiply d h) (inverse (inverse b))) [] by Super 40 with 447 at 1,2,2,3
% 3.11/1.16 Id : 690, {_}: identity =<= multiply d (multiply d (multiply h (inverse (inverse b)))) [] by Demod 674 with 4 at 2,3
% 3.11/1.16 Id : 97, {_}: ?139 =<= multiply (inverse (inverse ?139)) identity [139] by Super 95 with 3 at 2,3
% 3.11/1.16 Id : 111, {_}: ?139 =<= inverse (inverse ?139) [139] by Demod 97 with 5 at 3
% 3.11/1.16 Id : 691, {_}: identity =<= multiply d (multiply d (multiply h b)) [] by Demod 690 with 111 at 2,2,2,3
% 3.11/1.16 Id : 692, {_}: identity =<= multiply d (multiply d j) [] by Demod 691 with 11 at 2,2,3
% 3.11/1.16 Id : 1020, {_}: j =<= multiply d identity [] by Super 58 with 692 at 2,3
% 3.11/1.16 Id : 1041, {_}: j =<= d [] by Demod 1020 with 5 at 3
% 3.11/1.16 Id : 1057, {_}: inverse a =<= multiply c (multiply c j) [] by Demod 446 with 1041 at 2,2,3
% 3.11/1.16 Id : 5839, {_}: multiply b (multiply c j) =<= multiply (inverse a) (inverse a) [] by Super 5825 with 1057 at 2,3
% 3.11/1.16 Id : 101, {_}: multiply ?149 ?149 =?= multiply (inverse ?149) identity [149] by Super 95 with 7 at 2,3
% 3.11/1.16 Id : 114, {_}: multiply ?149 ?149 =>= inverse ?149 [149] by Demod 101 with 5 at 3
% 3.11/1.16 Id : 5914, {_}: multiply b (multiply c j) =>= inverse (inverse a) [] by Demod 5839 with 114 at 3
% 3.11/1.16 Id : 5915, {_}: multiply b (multiply c j) =>= a [] by Demod 5914 with 111 at 3
% 3.11/1.16 Id : 6121, {_}: j =<= multiply (inverse (multiply b c)) a [] by Super 98 with 5915 at 2,3
% 3.11/1.16 Id : 13357, {_}: multiply (inverse (multiply b c)) j =<= multiply (inverse (inverse (multiply b c))) a [] by Super 13218 with 6121 at 2,2
% 3.11/1.16 Id : 13715, {_}: multiply (inverse (multiply b c)) j =>= multiply (multiply b c) a [] by Demod 13357 with 111 at 1,3
% 3.11/1.16 Id : 13716, {_}: multiply (inverse (multiply b c)) j =>= multiply b (multiply c a) [] by Demod 13715 with 4 at 3
% 3.11/1.16 Id : 103, {_}: inverse a =<= multiply (inverse c) d [] by Super 95 with 9 at 2,3
% 3.11/1.16 Id : 264, {_}: multiply (inverse a) ?282 =<= multiply (inverse c) (multiply d ?282) [282] by Super 4 with 103 at 1,2
% 3.11/1.16 Id : 9891, {_}: multiply (inverse a) ?6910 =<= multiply (inverse c) (multiply j ?6910) [6910] by Demod 264 with 1041 at 1,2,3
% 3.11/1.16 Id : 1060, {_}: multiply j (inverse b) =>= h [] by Demod 10 with 1041 at 1,2
% 3.11/1.16 Id : 9899, {_}: multiply (inverse a) (inverse b) =>= multiply (inverse c) h [] by Super 9891 with 1060 at 2,3
% 3.11/1.16 Id : 1161, {_}: multiply c ?920 =<= multiply a (multiply b ?920) [920] by Super 4 with 8 at 1,2
% 3.11/1.16 Id : 1165, {_}: multiply c (inverse b) =>= multiply a identity [] by Super 1161 with 6 at 2,3
% 3.11/1.16 Id : 1203, {_}: multiply c (inverse b) =>= a [] by Demod 1165 with 5 at 3
% 3.11/1.16 Id : 1237, {_}: inverse b =<= multiply c (multiply c a) [] by Super 58 with 1203 at 2,2,3
% 3.11/1.16 Id : 5840, {_}: multiply b (multiply c a) =<= multiply (inverse a) (inverse b) [] by Super 5825 with 1237 at 2,3
% 3.11/1.16 Id : 9996, {_}: multiply b (multiply c a) =>= multiply (inverse c) h [] by Demod 9899 with 5840 at 2
% 3.11/1.16 Id : 13717, {_}: multiply (inverse (multiply b c)) j =>= multiply (inverse c) h [] by Demod 13716 with 9996 at 3
% 3.11/1.16 Id : 15999, {_}: j =<= multiply (inverse (inverse (multiply b c))) (multiply (inverse c) h) [] by Super 23 with 13717 at 2,3
% 3.11/1.16 Id : 16017, {_}: j =<= multiply (multiply b c) (multiply (inverse c) h) [] by Demod 15999 with 111 at 1,3
% 3.11/1.16 Id : 16018, {_}: j =<= multiply b (multiply c (multiply (inverse c) h)) [] by Demod 16017 with 4 at 3
% 3.11/1.16 Id : 39, {_}: multiply identity ?64 =<= multiply ?65 (multiply (inverse ?65) ?64) [65, 64] by Super 4 with 6 at 1,2
% 3.11/1.16 Id : 46, {_}: ?64 =<= multiply ?65 (multiply (inverse ?65) ?64) [65, 64] by Demod 39 with 2 at 2
% 3.11/1.16 Id : 16019, {_}: j =<= multiply b h [] by Demod 16018 with 46 at 2,3
% 3.11/1.16 Id : 16059, {_}: multiply b j =<= multiply (inverse b) h [] by Super 432 with 16019 at 2,2
% 3.11/1.16 Id : 104, {_}: inverse b =<= multiply (inverse d) h [] by Super 95 with 10 at 2,3
% 3.11/1.16 Id : 321, {_}: multiply (inverse b) ?344 =<= multiply (inverse d) (multiply h ?344) [344] by Super 4 with 104 at 1,2
% 3.11/1.16 Id : 10422, {_}: multiply (inverse b) ?7217 =<= multiply (inverse j) (multiply h ?7217) [7217] by Demod 321 with 1041 at 1,1,3
% 3.11/1.16 Id : 10428, {_}: multiply (inverse b) h =<= multiply (inverse j) (inverse h) [] by Super 10422 with 114 at 2,3
% 3.11/1.16 Id : 449, {_}: inverse h =<= multiply j (multiply j k) [] by Super 438 with 12 at 2,2,3
% 3.11/1.16 Id : 940, {_}: multiply j k =<= multiply (inverse j) (inverse h) [] by Super 23 with 449 at 2,3
% 3.11/1.16 Id : 10520, {_}: multiply (inverse b) h =>= multiply j k [] by Demod 10428 with 940 at 3
% 3.11/1.16 Id : 16066, {_}: multiply b j =>= multiply j k [] by Demod 16059 with 10520 at 3
% 3.11/1.16 Id : 16491, {_}: identity =<= multiply b (multiply j (multiply b (multiply j (multiply j k)))) [] by Super 59 with 16066 at 2,2,2,2,3
% 3.11/1.16 Id : 16527, {_}: identity =<= multiply b (multiply j (multiply b (multiply (inverse j) k))) [] by Demod 16491 with 432 at 2,2,2,3
% 3.11/1.16 Id : 106, {_}: inverse h =<= multiply (inverse j) k [] by Super 95 with 12 at 2,3
% 3.11/1.16 Id : 16528, {_}: identity =<= multiply b (multiply j (multiply b (inverse h))) [] by Demod 16527 with 106 at 2,2,2,3
% 3.11/1.16 Id : 2869, {_}: multiply k ?1975 =<= multiply j (multiply (inverse h) ?1975) [1975] by Super 4 with 12 at 1,2
% 3.11/1.16 Id : 105, {_}: b =<= multiply (inverse h) j [] by Super 95 with 11 at 2,3
% 3.11/1.16 Id : 2883, {_}: multiply k j =>= multiply j b [] by Super 2869 with 105 at 2,3
% 3.11/1.16 Id : 2939, {_}: multiply (multiply j b) ?2013 =>= multiply k (multiply j ?2013) [2013] by Super 4 with 2883 at 1,2
% 3.11/1.16 Id : 3900, {_}: multiply j (multiply b ?2890) =<= multiply k (multiply j ?2890) [2890] by Demod 2939 with 4 at 2
% 3.11/1.16 Id : 3905, {_}: multiply j (multiply b (inverse h)) =>= multiply k k [] by Super 3900 with 12 at 2,3
% 3.11/1.16 Id : 3960, {_}: multiply j (multiply b (inverse h)) =>= inverse k [] by Demod 3905 with 114 at 3
% 3.11/1.16 Id : 16529, {_}: identity =<= multiply b (inverse k) [] by Demod 16528 with 3960 at 2,3
% 3.11/1.16 Id : 16774, {_}: multiply b identity =<= multiply (inverse b) (inverse k) [] by Super 432 with 16529 at 2,2
% 3.11/1.16 Id : 16815, {_}: b =<= multiply (inverse b) (inverse k) [] by Demod 16774 with 5 at 2
% 3.11/1.16 Id : 3906, {_}: multiply j (multiply b j) =>= multiply k (inverse j) [] by Super 3900 with 114 at 2,3
% 3.11/1.16 Id : 13245, {_}: multiply j (multiply k (inverse j)) =<= multiply (inverse j) (multiply b j) [] by Super 13218 with 3906 at 2,2
% 3.11/1.16 Id : 10400, {_}: multiply (inverse b) ?344 =<= multiply (inverse j) (multiply h ?344) [344] by Demod 321 with 1041 at 1,1,3
% 3.11/1.16 Id : 165, {_}: multiply ?202 (inverse (multiply ?203 ?202)) =>= multiply (inverse ?203) identity [203, 202] by Super 23 with 40 at 2,3
% 3.11/1.16 Id : 187, {_}: multiply ?202 (inverse (multiply ?203 ?202)) =>= inverse ?203 [203, 202] by Demod 165 with 5 at 3
% 3.11/1.16 Id : 10576, {_}: h =<= multiply b (multiply j k) [] by Super 46 with 10520 at 2,3
% 3.11/1.16 Id : 10621, {_}: k =<= multiply (inverse (multiply b j)) h [] by Super 98 with 10576 at 2,3
% 3.11/1.16 Id : 11059, {_}: multiply h (inverse k) =<= inverse (inverse (multiply b j)) [] by Super 187 with 10621 at 1,2,2
% 3.11/1.16 Id : 11073, {_}: multiply h (inverse k) =>= multiply b j [] by Demod 11059 with 111 at 3
% 3.11/1.16 Id : 11103, {_}: multiply (inverse b) (inverse k) =<= multiply (inverse j) (multiply b j) [] by Super 10400 with 11073 at 2,3
% 3.11/1.16 Id : 13526, {_}: multiply j (multiply k (inverse j)) =>= multiply (inverse b) (inverse k) [] by Demod 13245 with 11103 at 3
% 3.11/1.16 Id : 16472, {_}: multiply j (multiply j k) =>= multiply k (inverse j) [] by Demod 3906 with 16066 at 2,2
% 3.11/1.16 Id : 16475, {_}: multiply (inverse j) k =>= multiply k (inverse j) [] by Demod 16472 with 432 at 2
% 3.11/1.16 Id : 16476, {_}: inverse h =<= multiply k (inverse j) [] by Demod 16475 with 106 at 2
% 3.11/1.16 Id : 16479, {_}: multiply j (inverse h) =<= multiply (inverse b) (inverse k) [] by Demod 13526 with 16476 at 2,2
% 3.11/1.16 Id : 16480, {_}: k =<= multiply (inverse b) (inverse k) [] by Demod 16479 with 12 at 2
% 3.11/1.16 Id : 16816, {_}: b =<= k [] by Demod 16815 with 16480 at 3
% 3.11/1.16 Id : 17039, {_}: identity =?= identity [] by Demod 17038 with 6 at 2
% 3.11/1.16 Id : 17038, {_}: multiply b (inverse b) =>= identity [] by Demod 1 with 16816 at 1,2
% 3.11/1.16 Id : 1, {_}: multiply k (inverse b) =>= identity [] by prove_k_times_inverse_b_is_e
% 3.11/1.16 % SZS output end CNFRefutation for theBenchmark.p
% 3.11/1.16 24192: solved /export/starexec/sandbox/benchmark/theBenchmark.p in 0.826945 using kbo
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