%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP367-1 : 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 : n004.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 12:43:24 PM UTC 2026
% Result : Unsatisfiable 0.44s 0.49s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 21
% Syntax : Number of clauses : 128 ( 26 unt; 99 nHn; 105 RR)
% Number of literals : 257 ( 256 equ; 33 neg)
% Maximal clause size : 11 ( 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_29,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
cnf(prove_this_30,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_24,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_25,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_25) ).
cnf(prove_this_27,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_26,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_28,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_22,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_21,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_21) ).
cnf(prove_this_23,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_23) ).
cnf(prove_this_1,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_1) ).
cnf(prove_this_17,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_7,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_18,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_8,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_31,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
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
cnf(c_0_21,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_22,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_23,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_24,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_25,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_26,plain,
multiply(inverse(inverse(inverse(X1))),X1) = identity,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_26]),c_0_25]) ).
cnf(c_0_28,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_22,c_0_27]) ).
cnf(c_0_29,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c3) = sk_c6 ),
prove_this_29 ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c6 ),
prove_this_30 ).
cnf(c_0_31,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_21,c_0_28]) ).
cnf(c_0_32,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_25,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c8 ),
prove_this_24 ).
cnf(c_0_34,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c3,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c8 ),
prove_this_25 ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c3,sk_c6) = identity
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_28,c_0_30]) ).
cnf(c_0_38,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_31]),c_0_32]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c7,sk_c5) = identity
| multiply(sk_c3,sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_22,c_0_33]) ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c7,sk_c5) = identity
| multiply(sk_c3,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_22,c_0_34]) ).
cnf(c_0_41,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_35]) ).
cnf(c_0_42,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c6 ),
prove_this_27 ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c6 ),
prove_this_26 ).
cnf(c_0_44,negated_conjecture,
( identity = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_38]),c_0_27]) ).
cnf(c_0_46,negated_conjecture,
( identity = sk_c8
| multiply(sk_c7,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_22,c_0_41]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c6 ),
prove_this_28 ).
cnf(c_0_49,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c8 ),
prove_this_22 ).
cnf(c_0_50,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_42]) ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c8 ),
prove_this_21 ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c3,sk_c6) = identity
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_28,c_0_43]) ).
cnf(c_0_53,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c5),sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_24,c_0_44]) ).
cnf(c_0_54,negated_conjecture,
( identity = sk_c8
| inverse(sk_c5) = sk_c7 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_23]) ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c8 ),
prove_this_23 ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c3,sk_c6) = identity
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_28,c_0_48]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c8,sk_c4) = identity
| multiply(sk_c3,sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_22,c_0_49]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c8,sk_c4) = identity
| multiply(sk_c3,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_22,c_0_50]) ).
cnf(c_0_59,negated_conjecture,
( identity = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_60,negated_conjecture,
( identity = sk_c8
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_61,negated_conjecture,
( identity = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_62,negated_conjecture,
( identity = sk_c8
| multiply(sk_c8,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c7),sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_24,c_0_59]) ).
cnf(c_0_64,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c7),sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_24,c_0_60]) ).
cnf(c_0_65,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c4),sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_24,c_0_61]) ).
cnf(c_0_66,negated_conjecture,
( identity = sk_c8
| inverse(sk_c4) = sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_62]),c_0_47]),c_0_23]) ).
cnf(c_0_67,negated_conjecture,
( identity = sk_c8
| multiply(sk_c6,inverse(sk_c8)) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_63]),c_0_27]) ).
cnf(c_0_68,negated_conjecture,
( identity = sk_c8
| inverse(sk_c8) = sk_c4 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_62]),c_0_32]) ).
cnf(c_0_69,negated_conjecture,
( identity = sk_c8
| multiply(sk_c6,inverse(sk_c7)) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_64]),c_0_27]) ).
cnf(c_0_70,negated_conjecture,
( identity = sk_c8
| inverse(sk_c7) = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_46]),c_0_32]) ).
cnf(c_0_71,negated_conjecture,
( identity = sk_c8
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_72,negated_conjecture,
( identity = sk_c8
| multiply(sk_c6,sk_c4) = sk_c7 ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_73,negated_conjecture,
( identity = sk_c8
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_74,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c8),sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_24,c_0_71]) ).
cnf(c_0_75,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c6),sk_c7) = sk_c4 ),
inference(spm,[status(thm)],[c_0_24,c_0_72]) ).
cnf(c_0_76,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c6),sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_24,c_0_73]) ).
cnf(c_0_77,negated_conjecture,
( identity = sk_c8
| multiply(sk_c7,inverse(sk_c8)) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_74]),c_0_27]) ).
cnf(c_0_78,negated_conjecture,
( sk_c5 = sk_c4
| identity = sk_c8 ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_79,negated_conjecture,
( identity = sk_c8
| multiply(sk_c7,sk_c4) = sk_c8 ),
inference(spm,[status(thm)],[c_0_77,c_0_68]) ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c6,sk_c8) = sk_c7 ),
prove_this_1 ).
cnf(c_0_81,negated_conjecture,
( sk_c5 = sk_c4
| inverse(sk_c8) = sk_c8 ),
inference(spm,[status(thm)],[c_0_47,c_0_78]) ).
cnf(c_0_82,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c7),sk_c8) = sk_c4 ),
inference(spm,[status(thm)],[c_0_24,c_0_79]) ).
cnf(c_0_83,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_21,c_0_80]) ).
cnf(c_0_84,negated_conjecture,
( sk_c5 = sk_c4
| multiply(sk_c8,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_22,c_0_81]) ).
cnf(c_0_85,negated_conjecture,
( identity = sk_c8
| multiply(sk_c5,sk_c8) = sk_c4 ),
inference(spm,[status(thm)],[c_0_82,c_0_70]) ).
cnf(c_0_86,negated_conjecture,
( sk_c5 = sk_c4
| multiply(X1,sk_c8) = X1 ),
inference(spm,[status(thm)],[c_0_32,c_0_78]) ).
cnf(c_0_87,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_83,c_0_84]),c_0_32])]) ).
cnf(c_0_88,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c5),sk_c4) = sk_c8 ),
inference(spm,[status(thm)],[c_0_24,c_0_85]) ).
cnf(c_0_89,negated_conjecture,
( sk_c6 = sk_c7
| sk_c5 = sk_c4 ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_90,negated_conjecture,
( identity = sk_c8
| sk_c6 = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_22])]) ).
cnf(c_0_91,negated_conjecture,
( sk_c6 = sk_c7
| multiply(X1,sk_c8) = X1 ),
inference(spm,[status(thm)],[c_0_32,c_0_90]) ).
cnf(c_0_92,negated_conjecture,
( sk_c6 = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_80,c_0_91]) ).
cnf(c_0_93,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
prove_this_17 ).
cnf(c_0_94,negated_conjecture,
sk_c6 = sk_c7,
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_95,negated_conjecture,
( inverse(sk_c8) = sk_c1
| inverse(sk_c4) = sk_c8 ),
inference(spm,[status(thm)],[c_0_27,c_0_93]) ).
cnf(c_0_96,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c2 ),
prove_this_12 ).
cnf(c_0_97,negated_conjecture,
identity = sk_c8,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_94]),c_0_22])]) ).
cnf(c_0_98,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c2) = sk_c7 ),
prove_this_7 ).
cnf(c_0_99,negated_conjecture,
( inverse(sk_c8) = sk_c4
| inverse(sk_c8) = sk_c1 ),
inference(spm,[status(thm)],[c_0_27,c_0_95]) ).
cnf(c_0_100,negated_conjecture,
( inverse(sk_c8) = sk_c4
| multiply(sk_c1,sk_c8) = sk_c2 ),
inference(spm,[status(thm)],[c_0_27,c_0_96]) ).
cnf(c_0_101,plain,
multiply(X1,sk_c8) = X1,
inference(rw,[status(thm)],[c_0_32,c_0_97]) ).
cnf(c_0_102,negated_conjecture,
( inverse(sk_c8) = sk_c4
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(spm,[status(thm)],[c_0_27,c_0_98]) ).
cnf(c_0_103,plain,
multiply(sk_c8,X1) = X1,
inference(rw,[status(thm)],[c_0_23,c_0_97]) ).
cnf(c_0_104,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
prove_this_18 ).
cnf(c_0_105,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c8) = sk_c4 ),
inference(spm,[status(thm)],[c_0_27,c_0_99]) ).
cnf(c_0_106,plain,
inverse(sk_c8) = sk_c8,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_97]),c_0_97]) ).
cnf(c_0_107,plain,
multiply(X1,inverse(X1)) = sk_c8,
inference(rw,[status(thm)],[c_0_28,c_0_97]) ).
cnf(c_0_108,negated_conjecture,
( sk_c2 = sk_c1
| inverse(sk_c8) = sk_c4 ),
inference(rw,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_109,negated_conjecture,
( sk_c2 = sk_c7
| inverse(sk_c8) = sk_c4 ),
inference(rw,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_110,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c2 ),
prove_this_13 ).
cnf(c_0_111,negated_conjecture,
( multiply(sk_c1,sk_c8) = identity
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_28,c_0_104]) ).
cnf(c_0_112,negated_conjecture,
( sk_c4 = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(rw,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_113,negated_conjecture,
( sk_c4 = sk_c8
| sk_c2 = sk_c1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_103]) ).
cnf(c_0_114,negated_conjecture,
( sk_c4 = sk_c8
| sk_c2 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_109]),c_0_103]) ).
cnf(c_0_115,negated_conjecture,
( identity = sk_c2
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_116,negated_conjecture,
( sk_c1 = sk_c8
| sk_c4 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_112]),c_0_106]) ).
cnf(c_0_117,negated_conjecture,
( sk_c1 = sk_c7
| sk_c4 = sk_c8 ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_118,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c8,sk_c2) = sk_c7 ),
prove_this_8 ).
cnf(c_0_119,negated_conjecture,
( sk_c2 = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(rw,[status(thm)],[c_0_115,c_0_97]) ).
cnf(c_0_120,negated_conjecture,
( sk_c4 = sk_c8
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_121,negated_conjecture,
( sk_c2 = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(rw,[status(thm)],[c_0_118,c_0_103]) ).
cnf(c_0_122,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
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(fof_simplification,[status(thm)],[prove_this_31]) ).
cnf(c_0_123,negated_conjecture,
( sk_c7 = sk_c8
| sk_c2 = sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_103])]) ).
cnf(c_0_124,negated_conjecture,
( sk_c7 = sk_c8
| sk_c2 = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_120]),c_0_103])]) ).
cnf(c_0_125,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
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7 ),
c_0_122 ).
cnf(c_0_126,negated_conjecture,
sk_c7 = sk_c8,
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_127,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[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(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(er,[status(thm)],[c_0_125]),c_0_94]),c_0_101]),c_0_101]),c_0_94]),c_0_94]),c_0_94]),c_0_101]),c_0_103]),c_0_94])])]),c_0_126]),c_0_101]),c_0_126]),c_0_126]),c_0_101]),c_0_126]),c_0_101]),c_0_126]),c_0_126]),c_0_126]),c_0_106])])])])]),c_0_106])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP367-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 20:10:05 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.44/0.49 % Version: 3.5.1
% 0.44/0.49 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.44/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.44/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.44/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.44/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.44/0.49 % Starting sh5l with 300s (1) cores
% 0.44/0.49 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1385232 completed with status 0
% 0.44/0.49 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.44/0.49 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.44/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.44/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.44/0.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.44/0.49 % No SInE strategy applied
% 0.44/0.49 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.44/0.49 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.44/0.49 % Starting SubtermCWHack with 136s (1) cores
% 0.44/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.44/0.49 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.44/0.49 % Starting new_bool_3 with 136s (1) cores
% 0.44/0.49 % Starting new_bool_1 with 136s (1) cores
% 0.44/0.49 % SubtermCWHack with pid 1385236 completed with status 0
% 0.44/0.49 % Result found by SubtermCWHack
% 0.44/0.49 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.44/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.44/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.44/0.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.44/0.49 % No SInE strategy applied
% 0.44/0.49 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.44/0.49 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.44/0.49 % Starting SubtermCWHack with 136s (1) cores
% 0.44/0.49 % Preprocessing time : 0.001 s
% 0.44/0.49
% 0.44/0.49 % Proof found!
% 0.44/0.49 % SZS status Unsatisfiable
% 0.44/0.49 % SZS output start CNFRefutation
% See solution above
% 0.44/0.49 % Parsed axioms : 34
% 0.44/0.49 % Removed by relevancy pruning/SinE : 0
% 0.44/0.49 % Initial clauses : 34
% 0.44/0.49 % Removed in clause preprocessing : 0
% 0.44/0.49 % Initial clauses in saturation : 34
% 0.44/0.49 % Processed clauses : 2178
% 0.44/0.49 % ...of these trivial : 71
% 0.44/0.49 % ...subsumed : 1561
% 0.44/0.49 % ...remaining for further processing : 546
% 0.44/0.49 % Other redundant clauses eliminated : 5
% 0.44/0.49 % Clauses deleted for lack of memory : 0
% 0.44/0.49 % Backward-subsumed : 16
% 0.44/0.49 % Backward-rewritten : 336
% 0.44/0.49 % Generated clauses : 9371
% 0.44/0.49 % ...of the previous two non-redundant : 8864
% 0.44/0.49 % ...aggressively subsumed : 0
% 0.44/0.49 % Contextual simplify-reflections : 0
% 0.44/0.49 % Paramodulations : 9364
% 0.44/0.49 % Factorizations : 4
% 0.44/0.49 % NegExts : 0
% 0.44/0.49 % Equation resolutions : 5
% 0.44/0.49 % Disequality decompositions : 0
% 0.44/0.49 % Total rewrite steps : 5310
% 0.44/0.49 % ...of those cached : 4863
% 0.44/0.49 % Propositional unsat checks : 0
% 0.44/0.49 % Propositional check models : 0
% 0.44/0.49 % Propositional check unsatisfiable : 0
% 0.44/0.49 % Propositional clauses : 0
% 0.44/0.49 % Propositional clauses after purity: 0
% 0.44/0.49 % Propositional unsat core size : 0
% 0.44/0.49 % Propositional preprocessing time : 0.000
% 0.44/0.49 % Propositional encoding time : 0.000
% 0.44/0.49 % Propositional solver time : 0.000
% 0.44/0.49 % Success case prop preproc time : 0.000
% 0.44/0.49 % Success case prop encoding time : 0.000
% 0.44/0.49 % Success case prop solver time : 0.000
% 0.44/0.49 % Current number of processed clauses : 191
% 0.44/0.49 % Positive orientable unit clauses : 20
% 0.44/0.49 % Positive unorientable unit clauses: 0
% 0.44/0.49 % Negative unit clauses : 0
% 0.44/0.49 % Non-unit-clauses : 171
% 0.44/0.49 % Current number of unprocessed clauses: 2854
% 0.44/0.49 % ...number of literals in the above : 7007
% 0.44/0.49 % Current number of archived formulas : 0
% 0.44/0.49 % Current number of archived clauses : 352
% 0.44/0.49 % Clause-clause subsumption calls (NU) : 8082
% 0.44/0.49 % Rec. Clause-clause subsumption calls : 8067
% 0.44/0.49 % Non-unit clause-clause subsumptions : 1568
% 0.44/0.49 % Unit Clause-clause subsumption calls : 209
% 0.44/0.49 % Rewrite failures with RHS unbound : 0
% 0.44/0.49 % BW rewrite match attempts : 34
% 0.44/0.49 % BW rewrite match successes : 21
% 0.44/0.49 % Condensation attempts : 0
% 0.44/0.49 % Condensation successes : 0
% 0.44/0.49 % Termbank termtop insertions : 66962
% 0.44/0.49 % Search garbage collected termcells : 30
% 0.44/0.49
% 0.44/0.49 % -------------------------------------------------
% 0.44/0.49 % User time : 0.050 s
% 0.44/0.49 % System time : 0.008 s
% 0.44/0.49 % Total time : 0.058 s
% 0.44/0.49 % Maximum resident set size: 3360 pages
% 0.44/0.49
% 0.44/0.49 % -------------------------------------------------
% 0.44/0.49 % User time : 0.222 s
% 0.44/0.49 % System time : 0.026 s
% 0.44/0.49 % Total time : 0.248 s
% 0.44/0.49 % Maximum resident set size: 4608 pages
% 0.44/0.49 % E exiting
%------------------------------------------------------------------------------