%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP259-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:43:01 PM UTC 2026
% Result : Unsatisfiable 0.57s 0.50s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 23
% Syntax : Number of clauses : 142 ( 26 unt; 113 nHn; 119 RR)
% Number of literals : 290 ( 289 equ; 36 neg)
% Maximal clause size : 12 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_34,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_35,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_29,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
cnf(prove_this_30,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_32,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_31,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_33,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_27,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_26,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_28,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_16,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_11,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_20,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_15,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_9,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_36,negated_conjecture,
( multiply(X5,sk_c6) != sk_c7
| inverse(X5) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(X4) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(X3) != sk_c6
| multiply(X3,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
cnf(c_0_23,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_24,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_25,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_26,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_27,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_28,plain,
multiply(inverse(inverse(inverse(X1))),X1) = identity,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_28]),c_0_27]) ).
cnf(c_0_30,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_24,c_0_29]) ).
cnf(c_0_31,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c3) = sk_c6 ),
prove_this_34 ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c6 ),
prove_this_35 ).
cnf(c_0_33,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_23,c_0_30]) ).
cnf(c_0_34,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_27,c_0_29]) ).
cnf(c_0_35,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c8 ),
prove_this_29 ).
cnf(c_0_36,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c3,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_38,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c8 ),
prove_this_30 ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c3,sk_c6) = identity
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_30,c_0_32]) ).
cnf(c_0_40,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_33]),c_0_34]) ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c7,sk_c5) = identity
| multiply(sk_c3,sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_24,c_0_35]) ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c7,sk_c5) = identity
| multiply(sk_c3,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_36]) ).
cnf(c_0_43,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_37]) ).
cnf(c_0_44,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c6 ),
prove_this_32 ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c6 ),
prove_this_31 ).
cnf(c_0_46,negated_conjecture,
( identity = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_47,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_40]),c_0_29]) ).
cnf(c_0_48,negated_conjecture,
( identity = sk_c8
| multiply(sk_c7,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_49,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_24,c_0_43]) ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c6 ),
prove_this_33 ).
cnf(c_0_51,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c8 ),
prove_this_27 ).
cnf(c_0_52,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_44]) ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c8 ),
prove_this_26 ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c3,sk_c6) = identity
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_30,c_0_45]) ).
cnf(c_0_55,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c5),sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_26,c_0_46]) ).
cnf(c_0_56,negated_conjecture,
( identity = sk_c8
| inverse(sk_c5) = sk_c7 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_25]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c8 ),
prove_this_28 ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c3,sk_c6) = identity
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_30,c_0_50]) ).
cnf(c_0_59,negated_conjecture,
( multiply(sk_c8,sk_c4) = identity
| multiply(sk_c3,sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_24,c_0_51]) ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c8,sk_c4) = identity
| multiply(sk_c3,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_52]) ).
cnf(c_0_61,negated_conjecture,
( identity = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_62,negated_conjecture,
( identity = sk_c8
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_63,negated_conjecture,
( identity = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_64,negated_conjecture,
( identity = sk_c8
| multiply(sk_c8,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_65,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c7),sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_61]) ).
cnf(c_0_66,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c7),sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_26,c_0_62]) ).
cnf(c_0_67,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c4),sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_26,c_0_63]) ).
cnf(c_0_68,negated_conjecture,
( identity = sk_c8
| inverse(sk_c4) = sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_64]),c_0_49]),c_0_25]) ).
cnf(c_0_69,negated_conjecture,
( identity = sk_c8
| multiply(sk_c6,inverse(sk_c8)) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_65]),c_0_29]) ).
cnf(c_0_70,negated_conjecture,
( identity = sk_c8
| inverse(sk_c8) = sk_c4 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_64]),c_0_34]) ).
cnf(c_0_71,negated_conjecture,
( identity = sk_c8
| multiply(sk_c6,inverse(sk_c7)) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_66]),c_0_29]) ).
cnf(c_0_72,negated_conjecture,
( identity = sk_c8
| inverse(sk_c7) = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_48]),c_0_34]) ).
cnf(c_0_73,negated_conjecture,
( identity = sk_c8
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_74,negated_conjecture,
( identity = sk_c8
| multiply(sk_c6,sk_c4) = sk_c7 ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_75,negated_conjecture,
( identity = sk_c8
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_76,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c8),sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_73]) ).
cnf(c_0_77,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c6),sk_c7) = sk_c4 ),
inference(spm,[status(thm)],[c_0_26,c_0_74]) ).
cnf(c_0_78,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c6),sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_26,c_0_75]) ).
cnf(c_0_79,negated_conjecture,
( identity = sk_c8
| multiply(sk_c7,inverse(sk_c8)) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_76]),c_0_29]) ).
cnf(c_0_80,negated_conjecture,
( sk_c5 = sk_c4
| identity = sk_c8 ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_81,negated_conjecture,
( identity = sk_c8
| multiply(sk_c7,sk_c4) = sk_c8 ),
inference(spm,[status(thm)],[c_0_79,c_0_70]) ).
cnf(c_0_82,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c6,sk_c8) = sk_c7 ),
prove_this_21 ).
cnf(c_0_83,negated_conjecture,
( sk_c5 = sk_c4
| inverse(sk_c8) = sk_c8 ),
inference(spm,[status(thm)],[c_0_49,c_0_80]) ).
cnf(c_0_84,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c7),sk_c8) = sk_c4 ),
inference(spm,[status(thm)],[c_0_26,c_0_81]) ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c6,multiply(sk_c8,X1)) = multiply(sk_c7,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_82]) ).
cnf(c_0_86,negated_conjecture,
( sk_c5 = sk_c4
| multiply(sk_c8,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_83]) ).
cnf(c_0_87,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c7 ),
prove_this_16 ).
cnf(c_0_88,negated_conjecture,
( identity = sk_c8
| multiply(sk_c5,sk_c8) = sk_c4 ),
inference(spm,[status(thm)],[c_0_84,c_0_72]) ).
cnf(c_0_89,negated_conjecture,
( sk_c5 = sk_c4
| multiply(X1,sk_c8) = X1 ),
inference(spm,[status(thm)],[c_0_34,c_0_80]) ).
cnf(c_0_90,negated_conjecture,
( sk_c5 = sk_c4
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_34])]) ).
cnf(c_0_91,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
prove_this_6 ).
cnf(c_0_92,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
prove_this_11 ).
cnf(c_0_93,negated_conjecture,
( multiply(sk_c2,sk_c7) = identity
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_30,c_0_87]) ).
cnf(c_0_94,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c5),sk_c4) = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_88]) ).
cnf(c_0_95,negated_conjecture,
( sk_c6 = sk_c7
| sk_c5 = sk_c4 ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_96,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
prove_this_1 ).
cnf(c_0_97,negated_conjecture,
( multiply(sk_c1,sk_c8) = identity
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_30,c_0_91]) ).
cnf(c_0_98,negated_conjecture,
( identity = sk_c8
| multiply(sk_c5,sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_65,c_0_72]) ).
cnf(c_0_99,negated_conjecture,
( identity = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_100,negated_conjecture,
( identity = sk_c8
| sk_c6 = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_24])]) ).
cnf(c_0_101,negated_conjecture,
( identity = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_102,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
prove_this_20 ).
cnf(c_0_103,negated_conjecture,
( sk_c8 = sk_c7
| identity = sk_c8 ),
inference(spm,[status(thm)],[c_0_46,c_0_98]) ).
cnf(c_0_104,negated_conjecture,
( identity = sk_c6
| multiply(inverse(sk_c7),sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_99]) ).
cnf(c_0_105,negated_conjecture,
( sk_c6 = sk_c7
| multiply(sk_c8,X1) = X1 ),
inference(spm,[status(thm)],[c_0_25,c_0_100]) ).
cnf(c_0_106,negated_conjecture,
( identity = sk_c7
| multiply(inverse(sk_c7),sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_101]) ).
cnf(c_0_107,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
prove_this_15 ).
cnf(c_0_108,negated_conjecture,
( multiply(sk_c2,sk_c7) = identity
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_30,c_0_102]) ).
cnf(c_0_109,negated_conjecture,
( sk_c8 = sk_c7
| inverse(sk_c8) = sk_c8 ),
inference(spm,[status(thm)],[c_0_49,c_0_103]) ).
cnf(c_0_110,negated_conjecture,
( identity = sk_c6
| multiply(sk_c6,inverse(sk_c8)) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_104]),c_0_29]) ).
cnf(c_0_111,negated_conjecture,
( sk_c6 = sk_c7
| inverse(sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_105]) ).
cnf(c_0_112,negated_conjecture,
( identity = sk_c7
| multiply(sk_c6,inverse(sk_c8)) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_106]),c_0_29]) ).
cnf(c_0_113,negated_conjecture,
( identity = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_114,negated_conjecture,
( sk_c8 = sk_c7
| multiply(sk_c8,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_109]) ).
cnf(c_0_115,negated_conjecture,
( sk_c6 = sk_c7
| identity = sk_c6 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_34])]) ).
cnf(c_0_116,negated_conjecture,
( sk_c6 = sk_c7
| identity = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_111]),c_0_34])]) ).
cnf(c_0_117,negated_conjecture,
( identity = sk_c6
| multiply(inverse(sk_c5),sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_26,c_0_113]) ).
cnf(c_0_118,negated_conjecture,
( sk_c8 = sk_c7
| multiply(X1,sk_c8) = X1 ),
inference(spm,[status(thm)],[c_0_34,c_0_103]) ).
cnf(c_0_119,negated_conjecture,
( sk_c8 = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_114]),c_0_34])]) ).
cnf(c_0_120,negated_conjecture,
sk_c6 = sk_c7,
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_121,negated_conjecture,
( identity = sk_c6
| multiply(sk_c7,inverse(sk_c6)) = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_117]),c_0_29]) ).
cnf(c_0_122,negated_conjecture,
( sk_c6 = sk_c7
| sk_c8 = sk_c7 ),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_123,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
prove_this_9 ).
cnf(c_0_124,negated_conjecture,
identity = sk_c8,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_120]),c_0_24])]) ).
cnf(c_0_125,negated_conjecture,
( identity = sk_c5
| identity = sk_c7
| sk_c8 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_30]) ).
cnf(c_0_126,negated_conjecture,
( inverse(sk_c8) = sk_c1
| inverse(sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_29,c_0_123]) ).
cnf(c_0_127,plain,
inverse(sk_c8) = sk_c8,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_124]),c_0_124]) ).
cnf(c_0_128,negated_conjecture,
( sk_c5 = sk_c8
| sk_c8 = sk_c7
| identity = sk_c7 ),
inference(spm,[status(thm)],[c_0_103,c_0_125]) ).
cnf(c_0_129,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
prove_this_4 ).
cnf(c_0_130,plain,
multiply(X1,sk_c8) = X1,
inference(rw,[status(thm)],[c_0_34,c_0_124]) ).
cnf(c_0_131,negated_conjecture,
( sk_c1 = sk_c8
| inverse(sk_c5) = sk_c7 ),
inference(rw,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_132,negated_conjecture,
( sk_c8 = sk_c7
| sk_c5 = sk_c8 ),
inference(spm,[status(thm)],[c_0_103,c_0_128]) ).
cnf(c_0_133,negated_conjecture,
( sk_c1 = sk_c7
| inverse(sk_c5) = sk_c7 ),
inference(rw,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_134,negated_conjecture,
( sk_c8 = sk_c7
| sk_c1 = sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_127])]) ).
cnf(c_0_135,negated_conjecture,
( sk_c8 = sk_c7
| sk_c1 = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_132]),c_0_127])]) ).
cnf(c_0_136,negated_conjecture,
( multiply(X5,sk_c6) != sk_c7
| inverse(X5) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(X4) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(X3) != sk_c6
| multiply(X3,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7 ),
inference(fof_simplification,[status(thm)],[prove_this_36]) ).
cnf(c_0_137,negated_conjecture,
sk_c8 = sk_c7,
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_138,negated_conjecture,
( multiply(X5,sk_c6) != sk_c7
| inverse(X5) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(X4) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(X3) != sk_c6
| multiply(X3,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7 ),
c_0_136 ).
cnf(c_0_139,plain,
multiply(X1,sk_c7) = X1,
inference(rw,[status(thm)],[c_0_130,c_0_137]) ).
cnf(c_0_140,plain,
inverse(sk_c7) = sk_c7,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_127,c_0_137]),c_0_137]) ).
cnf(c_0_141,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_138,c_0_120]),c_0_120]),c_0_120]),c_0_120]),c_0_120]),c_0_120])]),c_0_130]),c_0_139]),c_0_139]),c_0_137]),c_0_139]),c_0_137]),c_0_139]),c_0_137]),c_0_139]),c_0_137]),c_0_137])])])])])])]),c_0_140])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP259-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.35 % Computer : n006.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8046.5625MB
% 0.12/0.35 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sun Sep 20 20:07:42 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.57/0.50 % Version: 3.5.1
% 0.57/0.50 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.57/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.57/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.57/0.50 % Starting new_bool_1 with 300s (1) cores
% 0.57/0.50 % Starting sh5l with 300s (1) cores
% 0.57/0.50 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1151804 completed with status 0
% 0.57/0.50 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.57/0.50 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.57/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.57/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.57/0.50 % No SInE strategy applied
% 0.57/0.50 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.57/0.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.57/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.57/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.57/0.50 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.57/0.50 % Starting new_bool_3 with 136s (1) cores
% 0.57/0.50 % Starting new_bool_1 with 136s (1) cores
% 0.57/0.50 % SubtermCWHack with pid 1151808 completed with status 0
% 0.57/0.50 % Result found by SubtermCWHack
% 0.57/0.50 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.57/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.57/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.57/0.50 % No SInE strategy applied
% 0.57/0.50 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.57/0.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.57/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.57/0.50 % Preprocessing time : 0.001 s
% 0.57/0.50
% 0.57/0.50 % Proof found!
% 0.57/0.50 % SZS status Unsatisfiable
% 0.57/0.50 % SZS output start CNFRefutation
% See solution above
% 0.57/0.50 % Parsed axioms : 39
% 0.57/0.50 % Removed by relevancy pruning/SinE : 0
% 0.57/0.50 % Initial clauses : 39
% 0.57/0.50 % Removed in clause preprocessing : 0
% 0.57/0.50 % Initial clauses in saturation : 39
% 0.57/0.50 % Processed clauses : 2024
% 0.57/0.50 % ...of these trivial : 91
% 0.57/0.50 % ...subsumed : 1410
% 0.57/0.50 % ...remaining for further processing : 523
% 0.57/0.50 % Other redundant clauses eliminated : 6
% 0.57/0.50 % Clauses deleted for lack of memory : 0
% 0.57/0.50 % Backward-subsumed : 19
% 0.57/0.50 % Backward-rewritten : 356
% 0.57/0.50 % Generated clauses : 8895
% 0.57/0.50 % ...of the previous two non-redundant : 8377
% 0.57/0.50 % ...aggressively subsumed : 0
% 0.57/0.50 % Contextual simplify-reflections : 0
% 0.57/0.50 % Paramodulations : 8889
% 0.57/0.50 % Factorizations : 4
% 0.57/0.50 % NegExts : 0
% 0.57/0.50 % Equation resolutions : 6
% 0.57/0.50 % Disequality decompositions : 0
% 0.57/0.50 % Total rewrite steps : 5248
% 0.57/0.50 % ...of those cached : 4788
% 0.57/0.50 % Propositional unsat checks : 0
% 0.57/0.50 % Propositional check models : 0
% 0.57/0.50 % Propositional check unsatisfiable : 0
% 0.57/0.50 % Propositional clauses : 0
% 0.57/0.50 % Propositional clauses after purity: 0
% 0.57/0.50 % Propositional unsat core size : 0
% 0.57/0.50 % Propositional preprocessing time : 0.000
% 0.57/0.50 % Propositional encoding time : 0.000
% 0.57/0.50 % Propositional solver time : 0.000
% 0.57/0.50 % Success case prop preproc time : 0.000
% 0.57/0.50 % Success case prop encoding time : 0.000
% 0.57/0.50 % Success case prop solver time : 0.000
% 0.57/0.50 % Current number of processed clauses : 147
% 0.57/0.50 % Positive orientable unit clauses : 20
% 0.57/0.50 % Positive unorientable unit clauses: 0
% 0.57/0.50 % Negative unit clauses : 0
% 0.57/0.50 % Non-unit-clauses : 127
% 0.57/0.50 % Current number of unprocessed clauses: 1825
% 0.57/0.50 % ...number of literals in the above : 4298
% 0.57/0.50 % Current number of archived formulas : 0
% 0.57/0.50 % Current number of archived clauses : 375
% 0.57/0.50 % Clause-clause subsumption calls (NU) : 8483
% 0.57/0.50 % Rec. Clause-clause subsumption calls : 8473
% 0.57/0.50 % Non-unit clause-clause subsumptions : 1420
% 0.57/0.50 % Unit Clause-clause subsumption calls : 267
% 0.57/0.50 % Rewrite failures with RHS unbound : 0
% 0.57/0.50 % BW rewrite match attempts : 43
% 0.57/0.50 % BW rewrite match successes : 23
% 0.57/0.50 % Condensation attempts : 0
% 0.57/0.50 % Condensation successes : 0
% 0.57/0.50 % Termbank termtop insertions : 70251
% 0.57/0.50 % Search garbage collected termcells : 33
% 0.57/0.50
% 0.57/0.50 % -------------------------------------------------
% 0.57/0.50 % User time : 0.074 s
% 0.57/0.50 % System time : 0.009 s
% 0.57/0.50 % Total time : 0.083 s
% 0.57/0.50 % Maximum resident set size: 3652 pages
% 0.57/0.50
% 0.57/0.50 % -------------------------------------------------
% 0.57/0.50 % User time : 0.332 s
% 0.57/0.50 % System time : 0.034 s
% 0.57/0.50 % Total time : 0.366 s
% 0.57/0.50 % Maximum resident set size: 4608 pages
% 0.57/0.50 % E exiting
%------------------------------------------------------------------------------