TSTP Solution File: GRP185-2 by Matita---1.0
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%------------------------------------------------------------------------------
% File : Matita---1.0
% Problem : GRP185-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% Computer : n008.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 10:29:30 EDT 2022
% Result : Unsatisfiable 3.34s 1.16s
% Output : CNFRefutation 3.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP185-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 07:22:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 7999: Facts:
% 0.13/0.35 7999: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
% 0.13/0.35 7999: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
% 0.13/0.35 7999: Id : 4, {_}:
% 0.13/0.35 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
% 0.13/0.35 [8, 7, 6] by associativity ?6 ?7 ?8
% 0.13/0.35 7999: Id : 5, {_}:
% 0.13/0.35 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
% 0.13/0.35 [11, 10] by symmetry_of_glb ?10 ?11
% 0.13/0.35 7999: Id : 6, {_}:
% 0.13/0.35 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
% 0.13/0.35 [14, 13] by symmetry_of_lub ?13 ?14
% 0.13/0.35 7999: Id : 7, {_}:
% 0.13/0.35 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
% 0.13/0.35 =?=
% 0.13/0.35 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
% 0.13/0.35 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
% 0.13/0.35 7999: Id : 8, {_}:
% 0.13/0.35 least_upper_bound ?20 (least_upper_bound ?21 ?22)
% 0.13/0.35 =?=
% 0.13/0.35 least_upper_bound (least_upper_bound ?20 ?21) ?22
% 0.13/0.35 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
% 0.13/0.35 7999: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
% 0.13/0.35 7999: Id : 10, {_}:
% 0.13/0.35 greatest_lower_bound ?26 ?26 =>= ?26
% 0.13/0.35 [26] by idempotence_of_gld ?26
% 0.13/0.35 7999: Id : 11, {_}:
% 0.13/0.35 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
% 0.13/0.35 [29, 28] by lub_absorbtion ?28 ?29
% 0.13/0.35 7999: Id : 12, {_}:
% 0.13/0.35 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
% 0.13/0.35 [32, 31] by glb_absorbtion ?31 ?32
% 0.13/0.35 7999: Id : 13, {_}:
% 0.13/0.35 multiply ?34 (least_upper_bound ?35 ?36)
% 0.13/0.35 =<=
% 0.13/0.35 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
% 0.13/0.35 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
% 0.13/0.35 7999: Id : 14, {_}:
% 0.13/0.35 multiply ?38 (greatest_lower_bound ?39 ?40)
% 0.13/0.35 =<=
% 0.13/0.35 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
% 0.13/0.35 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
% 0.13/0.35 7999: Id : 15, {_}:
% 0.13/0.35 multiply (least_upper_bound ?42 ?43) ?44
% 0.13/0.35 =<=
% 0.13/0.35 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
% 0.13/0.35 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
% 0.13/0.35 7999: Id : 16, {_}:
% 0.13/0.35 multiply (greatest_lower_bound ?46 ?47) ?48
% 0.13/0.35 =<=
% 0.13/0.35 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
% 0.13/0.35 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
% 0.13/0.35 7999: Id : 17, {_}: inverse identity =>= identity [] by p22a_1
% 0.13/0.35 7999: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
% 0.13/0.35 7999: Id : 19, {_}:
% 0.13/0.35 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
% 0.13/0.35 [54, 53] by p22a_3 ?53 ?54
% 0.13/0.35 7999: Goal:
% 0.13/0.35 7999: Id : 1, {_}:
% 0.13/0.35 least_upper_bound (least_upper_bound (multiply a b) identity)
% 0.13/0.35 (multiply (least_upper_bound a identity)
% 0.13/0.35 (least_upper_bound b identity))
% 0.13/0.35 =>=
% 0.13/0.35 multiply (least_upper_bound a identity)
% 0.13/0.35 (least_upper_bound b identity)
% 0.13/0.35 [] by prove_p22a
% 3.34/1.16 Statistics :
% 3.34/1.16 Max weight : 21
% 3.34/1.16 Found proof, 0.810405s
% 3.34/1.16 % SZS status Unsatisfiable for theBenchmark.p
% 3.34/1.16 % SZS output start CNFRefutation for theBenchmark.p
% 3.34/1.16 Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51
% 3.34/1.16 Id : 17, {_}: inverse identity =>= identity [] by p22a_1
% 3.34/1.16 Id : 426, {_}: inverse (multiply ?520 ?521) =?= multiply (inverse ?521) (inverse ?520) [521, 520] by p22a_3 ?520 ?521
% 3.34/1.16 Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
% 3.34/1.16 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
% 3.34/1.16 Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
% 3.34/1.16 Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
% 3.34/1.16 Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
% 3.34/1.16 Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
% 3.34/1.16 Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 Id : 427, {_}: inverse (multiply identity ?523) =<= multiply (inverse ?523) identity [523] by Super 426 with 17 at 2,3
% 3.34/1.16 Id : 481, {_}: inverse ?569 =<= multiply (inverse ?569) identity [569] by Demod 427 with 2 at 1,2
% 3.34/1.16 Id : 483, {_}: inverse (inverse ?572) =<= multiply ?572 identity [572] by Super 481 with 18 at 1,3
% 3.34/1.16 Id : 491, {_}: ?572 =<= multiply ?572 identity [572] by Demod 483 with 18 at 2
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 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
% 3.34/1.16 % SZS output end CNFRefutation for theBenchmark.p
% 3.34/1.16 8001: solved /export/starexec/sandbox/benchmark/theBenchmark.p in 0.814012 using lpo
%------------------------------------------------------------------------------