%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP220-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:39:00 PM UTC 2026
% Result : Unsatisfiable 9.90s 1.78s
% Output : CNFRefutation 9.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 21
% Syntax : Number of clauses : 119 ( 35 unt; 74 nHn; 87 RR)
% Number of literals : 295 ( 294 equ; 113 neg)
% Maximal clause size : 17 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 107 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(prove_this_19,negated_conjecture,
( inverse(sk_c12) = sk_c11
| multiply(sk_c2,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_28,negated_conjecture,
( inverse(sk_c12) = sk_c11
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_55,negated_conjecture,
( inverse(sk_c12) = sk_c11
| multiply(sk_c4,sk_c12) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_55) ).
cnf(prove_this_64,negated_conjecture,
( inverse(sk_c12) = sk_c11
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_64) ).
cnf(prove_this_46,negated_conjecture,
( inverse(sk_c12) = sk_c11
| multiply(sk_c12,sk_c5) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
cnf(prove_this_68,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_68) ).
cnf(prove_this_58,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c12
| multiply(sk_c4,sk_c12) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_58) ).
cnf(prove_this_59,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c4,sk_c12) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_59) ).
cnf(prove_this_67,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c12
| inverse(sk_c4) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_67) ).
cnf(prove_this_50,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c12,sk_c5) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_50) ).
cnf(prove_this_49,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c12
| multiply(sk_c12,sk_c5) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_49) ).
cnf(prove_this_32,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_31,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c12
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_20,negated_conjecture,
( inverse(sk_c6) = sk_c12
| multiply(sk_c2,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_12,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c12
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_73,negated_conjecture,
( multiply(X9,X8) != X10
| inverse(X10) != X8
| inverse(X9) != X10
| multiply(X8,sk_c11) != sk_c12
| inverse(X7) != X8
| multiply(X7,X8) != sk_c12
| multiply(X6,sk_c11) != sk_c12
| inverse(X6) != sk_c12
| inverse(sk_c12) != sk_c11
| inverse(X5) != sk_c12
| multiply(X5,sk_c12) != X4
| multiply(sk_c12,X4) != sk_c11
| multiply(X3,sk_c12) != sk_c11
| inverse(X2) != X3
| multiply(X2,X3) != sk_c11
| multiply(X1,sk_c11) != sk_c12
| inverse(X1) != sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_73) ).
cnf(prove_this_5,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c12
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(c_0_21,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_22,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_23,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
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,negated_conjecture,
( inverse(sk_c12) = sk_c11
| multiply(sk_c2,sk_c3) = sk_c11 ),
prove_this_19 ).
cnf(c_0_26,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_27,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_24]) ).
cnf(c_0_28,negated_conjecture,
( sk_c11 = inverse(sk_c12)
| multiply(inverse(sk_c2),sk_c11) = sk_c3 ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( inverse(sk_c12) = sk_c11
| inverse(sk_c2) = sk_c3 ),
prove_this_28 ).
cnf(c_0_30,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,negated_conjecture,
( sk_c11 = inverse(sk_c12)
| multiply(sk_c3,sk_c11) = sk_c3 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
( inverse(sk_c12) = sk_c11
| multiply(sk_c4,sk_c12) = sk_c5 ),
prove_this_55 ).
cnf(c_0_33,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_30]),c_0_30]) ).
cnf(c_0_34,negated_conjecture,
( inverse(sk_c12) = sk_c11
| inverse(sk_c4) = sk_c12 ),
prove_this_64 ).
cnf(c_0_35,negated_conjecture,
( inverse(sk_c12) = sk_c11
| multiply(sk_c12,sk_c5) = sk_c11 ),
prove_this_46 ).
cnf(c_0_36,negated_conjecture,
( identity = sk_c11
| sk_c11 = inverse(sk_c12) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_31]),c_0_22]) ).
cnf(c_0_37,negated_conjecture,
( sk_c11 = inverse(sk_c12)
| multiply(sk_c4,multiply(sk_c12,X1)) = multiply(sk_c5,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_32]) ).
cnf(c_0_38,negated_conjecture,
( sk_c4 = inverse(sk_c12)
| sk_c11 = inverse(sk_c12) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_22,c_0_33]) ).
cnf(c_0_40,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c4) = sk_c12 ),
prove_this_68 ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c12
| multiply(sk_c4,sk_c12) = sk_c5 ),
prove_this_58 ).
cnf(c_0_42,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c4,sk_c12) = sk_c5 ),
prove_this_59 ).
cnf(c_0_43,negated_conjecture,
( sk_c11 = inverse(sk_c12)
| multiply(inverse(sk_c12),sk_c11) = sk_c5 ),
inference(spm,[status(thm)],[c_0_24,c_0_35]) ).
cnf(c_0_44,negated_conjecture,
( multiply(X1,sk_c11) = X1
| sk_c11 = inverse(sk_c12) ),
inference(spm,[status(thm)],[c_0_30,c_0_36]) ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c5,X1) = X1
| sk_c11 = inverse(sk_c12) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_24]) ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c12
| inverse(sk_c4) = sk_c12 ),
prove_this_67 ).
cnf(c_0_47,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c7,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c5
| multiply(sk_c7,multiply(sk_c10,X1)) = multiply(sk_c12,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_41]) ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c10,sk_c7) = identity
| multiply(sk_c4,sk_c12) = sk_c5 ),
inference(spm,[status(thm)],[c_0_22,c_0_42]) ).
cnf(c_0_50,negated_conjecture,
( sk_c5 = inverse(sk_c12)
| sk_c11 = inverse(sk_c12) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_51,negated_conjecture,
( sk_c5 = sk_c11
| sk_c11 = inverse(sk_c12) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_52,negated_conjecture,
( identity = sk_c12
| inverse(sk_c4) = sk_c12 ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_53,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_23,c_0_39]) ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c12,sk_c7) = sk_c7
| multiply(sk_c4,sk_c12) = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_30]) ).
cnf(c_0_55,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_39]) ).
cnf(c_0_56,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c12,sk_c5) = sk_c11 ),
prove_this_50 ).
cnf(c_0_57,negated_conjecture,
sk_c11 = inverse(sk_c12),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_58,negated_conjecture,
( identity = sk_c12
| multiply(sk_c4,sk_c12) = identity ),
inference(spm,[status(thm)],[c_0_39,c_0_52]) ).
cnf(c_0_59,negated_conjecture,
( identity = sk_c12
| multiply(sk_c4,sk_c12) = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c12
| multiply(sk_c12,sk_c5) = sk_c11 ),
prove_this_49 ).
cnf(c_0_61,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c12,sk_c5) = inverse(sk_c12) ),
inference(rw,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_62,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_63,negated_conjecture,
( identity = sk_c5
| identity = sk_c12 ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c12
| multiply(sk_c12,sk_c5) = inverse(sk_c12) ),
inference(rw,[status(thm)],[c_0_60,c_0_57]) ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c7,sk_c10) = identity
| multiply(sk_c12,sk_c5) = inverse(sk_c12) ),
inference(spm,[status(thm)],[c_0_39,c_0_61]) ).
cnf(c_0_66,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_62]) ).
cnf(c_0_67,negated_conjecture,
( identity = sk_c12
| multiply(X1,sk_c5) = X1 ),
inference(spm,[status(thm)],[c_0_30,c_0_63]) ).
cnf(c_0_68,negated_conjecture,
( identity = sk_c12
| multiply(sk_c12,sk_c5) = inverse(sk_c12) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_69,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_22,c_0_66]) ).
cnf(c_0_70,negated_conjecture,
( identity = sk_c12
| inverse(sk_c12) = sk_c12 ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_71,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c2) = sk_c3 ),
prove_this_32 ).
cnf(c_0_72,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_22,c_0_22]) ).
cnf(c_0_73,negated_conjecture,
inverse(sk_c12) = sk_c12,
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_74,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c12
| inverse(sk_c2) = sk_c3 ),
prove_this_31 ).
cnf(c_0_75,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c7,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_39,c_0_71]) ).
cnf(c_0_76,negated_conjecture,
( inverse(sk_c6) = sk_c12
| multiply(sk_c2,sk_c3) = sk_c11 ),
prove_this_20 ).
cnf(c_0_77,negated_conjecture,
multiply(inverse(X1),X1) = multiply(sk_c12,sk_c12),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c12
| multiply(sk_c1,sk_c11) = sk_c12 ),
prove_this_12 ).
cnf(c_0_79,negated_conjecture,
( multiply(X9,X8) != X10
| inverse(X10) != X8
| inverse(X9) != X10
| multiply(X8,sk_c11) != sk_c12
| inverse(X7) != X8
| multiply(X7,X8) != sk_c12
| multiply(X6,sk_c11) != sk_c12
| inverse(X6) != sk_c12
| inverse(sk_c12) != sk_c11
| inverse(X5) != sk_c12
| multiply(X5,sk_c12) != X4
| multiply(sk_c12,X4) != sk_c11
| multiply(X3,sk_c12) != sk_c11
| inverse(X2) != X3
| multiply(X2,X3) != sk_c11
| multiply(X1,sk_c11) != sk_c12
| inverse(X1) != sk_c12 ),
inference(fof_simplification,[status(thm)],[prove_this_73]) ).
cnf(c_0_80,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c12 ),
prove_this_5 ).
cnf(c_0_81,negated_conjecture,
( identity = sk_c12
| inverse(sk_c2) = sk_c3 ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_82,negated_conjecture,
( inverse(sk_c6) = sk_c12
| multiply(sk_c2,sk_c3) = inverse(sk_c12) ),
inference(rw,[status(thm)],[c_0_76,c_0_57]) ).
cnf(c_0_83,plain,
identity = multiply(sk_c12,sk_c12),
inference(rw,[status(thm)],[c_0_22,c_0_77]) ).
cnf(c_0_84,negated_conjecture,
( multiply(sk_c1,inverse(sk_c12)) = sk_c12
| multiply(sk_c6,inverse(sk_c12)) = sk_c12 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_57]),c_0_57]) ).
cnf(c_0_85,plain,
multiply(X1,multiply(inverse(X2),X2)) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_22]) ).
cnf(c_0_86,negated_conjecture,
( multiply(X9,X8) != X10
| inverse(X10) != X8
| inverse(X9) != X10
| multiply(X8,sk_c11) != sk_c12
| inverse(X7) != X8
| multiply(X7,X8) != sk_c12
| multiply(X6,sk_c11) != sk_c12
| inverse(X6) != sk_c12
| inverse(sk_c12) != sk_c11
| inverse(X5) != sk_c12
| multiply(X5,sk_c12) != X4
| multiply(sk_c12,X4) != sk_c11
| multiply(X3,sk_c12) != sk_c11
| inverse(X2) != X3
| multiply(X2,X3) != sk_c11
| multiply(X1,sk_c11) != sk_c12
| inverse(X1) != sk_c12 ),
c_0_79 ).
cnf(c_0_87,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c12
| inverse(sk_c1) = sk_c12 ),
prove_this_4 ).
cnf(c_0_88,negated_conjecture,
( inverse(sk_c1) = sk_c12
| multiply(sk_c7,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_39,c_0_80]) ).
cnf(c_0_89,negated_conjecture,
( identity = sk_c12
| multiply(sk_c2,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_39,c_0_81]) ).
cnf(c_0_90,negated_conjecture,
( inverse(sk_c6) = sk_c12
| multiply(sk_c2,sk_c3) = sk_c12 ),
inference(rw,[status(thm)],[c_0_82,c_0_73]) ).
cnf(c_0_91,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = multiply(sk_c12,sk_c12),
inference(rw,[status(thm)],[c_0_53,c_0_83]) ).
cnf(c_0_92,negated_conjecture,
( multiply(sk_c6,sk_c12) = sk_c12
| multiply(sk_c1,sk_c12) = sk_c12 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_73]),c_0_73]) ).
cnf(c_0_93,plain,
multiply(X1,multiply(sk_c12,sk_c12)) = X1,
inference(rw,[status(thm)],[c_0_85,c_0_77]) ).
cnf(c_0_94,negated_conjecture,
( inverse(X6) != sk_c12
| inverse(X1) != sk_c12
| inverse(X5) != sk_c12
| sk_c11 != inverse(sk_c12)
| multiply(X6,sk_c11) != sk_c12
| multiply(X5,sk_c11) != sk_c12
| multiply(X4,inverse(X4)) != sk_c11
| multiply(X3,inverse(X3)) != sk_c12
| multiply(X2,inverse(X3)) != inverse(X2)
| multiply(inverse(X4),sk_c12) != sk_c11
| multiply(inverse(X3),sk_c11) != sk_c12
| inverse(multiply(X2,inverse(X3))) != inverse(X3)
| multiply(sk_c12,multiply(X1,sk_c12)) != sk_c11 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_86])])])]) ).
cnf(c_0_95,negated_conjecture,
( identity = sk_c12
| inverse(sk_c1) = sk_c12 ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_96,negated_conjecture,
( identity = sk_c12
| inverse(sk_c6) = sk_c12 ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_97,negated_conjecture,
( sk_c6 = multiply(sk_c12,sk_c12)
| multiply(sk_c1,sk_c12) = sk_c12 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_73]),c_0_93]) ).
cnf(c_0_98,plain,
inverse(multiply(inverse(X1),X1)) = multiply(inverse(X1),X1),
inference(spm,[status(thm)],[c_0_69,c_0_22]) ).
cnf(c_0_99,negated_conjecture,
( inverse(X6) != sk_c12
| inverse(X1) != sk_c12
| inverse(X5) != sk_c12
| multiply(X3,inverse(X3)) != sk_c12
| multiply(X6,inverse(sk_c12)) != sk_c12
| multiply(X5,inverse(sk_c12)) != sk_c12
| multiply(X2,inverse(X3)) != inverse(X2)
| multiply(X4,inverse(X4)) != inverse(sk_c12)
| multiply(inverse(X4),sk_c12) != inverse(sk_c12)
| multiply(inverse(X3),inverse(sk_c12)) != sk_c12
| inverse(multiply(X2,inverse(X3))) != inverse(X3)
| multiply(sk_c12,multiply(X1,sk_c12)) != inverse(sk_c12) ),
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)],[c_0_94,c_0_57]),c_0_57]),c_0_57]),c_0_57]),c_0_57]),c_0_57]),c_0_57])]) ).
cnf(c_0_100,negated_conjecture,
( identity = sk_c12
| multiply(sk_c12,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_22,c_0_95]) ).
cnf(c_0_101,negated_conjecture,
( inverse(sk_c6) = sk_c12
| multiply(sk_c12,sk_c12) = sk_c12 ),
inference(rw,[status(thm)],[c_0_96,c_0_83]) ).
cnf(c_0_102,negated_conjecture,
( sk_c1 = multiply(sk_c12,sk_c12)
| sk_c6 = multiply(sk_c12,sk_c12) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_97]),c_0_55]) ).
cnf(c_0_103,plain,
inverse(multiply(sk_c12,sk_c12)) = multiply(sk_c12,sk_c12),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_77]),c_0_77]) ).
cnf(c_0_104,negated_conjecture,
( inverse(X5) != sk_c12
| inverse(X4) != sk_c12
| inverse(sk_c12) != sk_c12
| multiply(X2,inverse(X2)) != sk_c12
| multiply(X5,inverse(sk_c12)) != sk_c12
| multiply(X4,inverse(sk_c12)) != sk_c12
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(X3,inverse(X3)) != inverse(sk_c12)
| multiply(inverse(X3),sk_c12) != inverse(sk_c12)
| multiply(inverse(X2),inverse(sk_c12)) != sk_c12
| inverse(multiply(X1,inverse(X2))) != inverse(X2) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_72]),c_0_33])]),c_0_85]) ).
cnf(c_0_105,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(spm,[status(thm)],[c_0_39,c_0_39]) ).
cnf(c_0_106,negated_conjecture,
( multiply(sk_c12,sk_c12) = sk_c12
| multiply(sk_c12,sk_c1) = multiply(sk_c12,sk_c12) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_83]),c_0_83]) ).
cnf(c_0_107,negated_conjecture,
( multiply(sk_c12,sk_c12) = sk_c12
| sk_c1 = multiply(sk_c12,sk_c12) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103])]) ).
cnf(c_0_108,negated_conjecture,
multiply(sk_c12,multiply(sk_c12,X1)) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_73]) ).
cnf(c_0_109,negated_conjecture,
( inverse(X5) != sk_c12
| inverse(X4) != sk_c12
| multiply(X5,sk_c12) != sk_c12
| multiply(X4,sk_c12) != sk_c12
| multiply(X2,inverse(X2)) != sk_c12
| multiply(X3,inverse(X3)) != sk_c12
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(inverse(X3),sk_c12) != sk_c12
| multiply(inverse(X2),sk_c12) != sk_c12
| inverse(multiply(X1,inverse(X2))) != inverse(X2) ),
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_104,c_0_73]),c_0_73]),c_0_73]),c_0_73]),c_0_73]),c_0_73])]) ).
cnf(c_0_110,negated_conjecture,
multiply(X1,inverse(X1)) = multiply(sk_c12,sk_c12),
inference(spm,[status(thm)],[c_0_105,c_0_73]) ).
cnf(c_0_111,negated_conjecture,
multiply(sk_c12,sk_c12) = sk_c12,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108])]) ).
cnf(c_0_112,negated_conjecture,
( inverse(X5) != sk_c12
| inverse(X4) != sk_c12
| multiply(X5,sk_c12) != sk_c12
| multiply(X4,sk_c12) != sk_c12
| multiply(sk_c12,sk_c12) != sk_c12
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(inverse(X3),sk_c12) != sk_c12
| multiply(inverse(X2),sk_c12) != sk_c12
| inverse(multiply(X1,inverse(X2))) != inverse(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110]),c_0_110])]) ).
cnf(c_0_113,plain,
multiply(X1,sk_c12) = X1,
inference(rw,[status(thm)],[c_0_93,c_0_111]) ).
cnf(c_0_114,negated_conjecture,
( inverse(X3) != sk_c12
| inverse(X2) != sk_c12
| multiply(X1,inverse(X2)) != inverse(X1)
| inverse(multiply(X1,inverse(X2))) != inverse(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[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)],[c_0_112,c_0_111])]),c_0_113]),c_0_113]),c_0_113]),c_0_113])])]),c_0_73])]) ).
cnf(c_0_115,negated_conjecture,
multiply(inverse(X1),X1) = sk_c12,
inference(rw,[status(thm)],[c_0_77,c_0_111]) ).
cnf(c_0_116,negated_conjecture,
( inverse(X2) != sk_c12
| inverse(X1) != sk_c12 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_73]),c_0_33])]) ).
cnf(c_0_117,negated_conjecture,
inverse(X1) != sk_c12,
inference(spm,[status(thm)],[c_0_116,c_0_73]) ).
cnf(c_0_118,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_73,c_0_117]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP220-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n005.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 20:06:33 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 9.90/1.78 % Version: 3.5.1
% 9.90/1.78 % Preprocessing class: FSLSSMSMSSSNFFN.
% 9.90/1.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.90/1.78 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 9.90/1.78 % Starting new_bool_3 with 300s (1) cores
% 9.90/1.78 % Starting new_bool_1 with 300s (1) cores
% 9.90/1.78 % Starting sh5l with 300s (1) cores
% 9.90/1.78 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1648606 completed with status 0
% 9.90/1.78 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 9.90/1.78 % Preprocessing class: FSLSSMSMSSSNFFN.
% 9.90/1.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.90/1.78 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 9.90/1.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 9.90/1.78 % No SInE strategy applied
% 9.90/1.78 % Search class: FGHPS-FFMM21-SFFFFFNN
% 9.90/1.78 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 9.90/1.78 % Starting SubtermCWHack with 136s (1) cores
% 9.90/1.78 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 9.90/1.78 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 9.90/1.78 % Starting new_bool_3 with 136s (1) cores
% 9.90/1.78 % Starting new_bool_1 with 136s (1) cores
% 9.90/1.78 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1648611 completed with status 0
% 9.90/1.78 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 9.90/1.78 % Preprocessing class: FSLSSMSMSSSNFFN.
% 9.90/1.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.90/1.78 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 9.90/1.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 9.90/1.78 % No SInE strategy applied
% 9.90/1.78 % Search class: FGHPS-FFMM21-SFFFFFNN
% 9.90/1.78 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 9.90/1.78 % Starting SubtermCWHack with 136s (1) cores
% 9.90/1.78 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 9.90/1.78 % Preprocessing time : 0.003 s
% 9.90/1.78 % Presaturation interreduction done
% 9.90/1.78
% 9.90/1.78 % Proof found!
% 9.90/1.78 % SZS status Unsatisfiable
% 9.90/1.78 % SZS output start CNFRefutation
% See solution above
% 9.90/1.78 % Parsed axioms : 76
% 9.90/1.78 % Removed by relevancy pruning/SinE : 0
% 9.90/1.78 % Initial clauses : 76
% 9.90/1.78 % Removed in clause preprocessing : 0
% 9.90/1.78 % Initial clauses in saturation : 76
% 9.90/1.78 % Processed clauses : 15288
% 9.90/1.78 % ...of these trivial : 95
% 9.90/1.78 % ...subsumed : 13061
% 9.90/1.78 % ...remaining for further processing : 2132
% 9.90/1.78 % Other redundant clauses eliminated : 23
% 9.90/1.78 % Clauses deleted for lack of memory : 0
% 9.90/1.78 % Backward-subsumed : 243
% 9.90/1.78 % Backward-rewritten : 1564
% 9.90/1.78 % Generated clauses : 107384
% 9.90/1.78 % ...of the previous two non-redundant : 101046
% 9.90/1.78 % ...aggressively subsumed : 0
% 9.90/1.78 % Contextual simplify-reflections : 19
% 9.90/1.78 % Paramodulations : 107315
% 9.90/1.78 % Factorizations : 4
% 9.90/1.78 % NegExts : 0
% 9.90/1.78 % Equation resolutions : 23
% 9.90/1.78 % Disequality decompositions : 0
% 9.90/1.78 % Total rewrite steps : 37539
% 9.90/1.78 % ...of those cached : 36812
% 9.90/1.78 % Propositional unsat checks : 0
% 9.90/1.78 % Propositional check models : 0
% 9.90/1.78 % Propositional check unsatisfiable : 0
% 9.90/1.78 % Propositional clauses : 0
% 9.90/1.78 % Propositional clauses after purity: 0
% 9.90/1.78 % Propositional unsat core size : 0
% 9.90/1.78 % Propositional preprocessing time : 0.000
% 9.90/1.78 % Propositional encoding time : 0.000
% 9.90/1.78 % Propositional solver time : 0.000
% 9.90/1.78 % Success case prop preproc time : 0.000
% 9.90/1.78 % Success case prop encoding time : 0.000
% 9.90/1.78 % Success case prop solver time : 0.000
% 9.90/1.78 % Current number of processed clauses : 201
% 9.90/1.78 % Positive orientable unit clauses : 19
% 9.90/1.78 % Positive unorientable unit clauses: 0
% 9.90/1.78 % Negative unit clauses : 1
% 9.90/1.78 % Non-unit-clauses : 181
% 9.90/1.78 % Current number of unprocessed clauses: 82155
% 9.90/1.78 % ...number of literals in the above : 276090
% 9.90/1.78 % Current number of archived formulas : 0
% 9.90/1.78 % Current number of archived clauses : 1929
% 9.90/1.78 % Clause-clause subsumption calls (NU) : 216185
% 9.90/1.78 % Rec. Clause-clause subsumption calls : 127130
% 9.90/1.78 % Non-unit clause-clause subsumptions : 13100
% 9.90/1.78 % Unit Clause-clause subsumption calls : 2757
% 9.90/1.78 % Rewrite failures with RHS unbound : 94
% 9.90/1.78 % BW rewrite match attempts : 171
% 9.90/1.78 % BW rewrite match successes : 79
% 9.90/1.78 % Condensation attempts : 0
% 9.90/1.78 % Condensation successes : 0
% 9.90/1.78 % Termbank termtop insertions : 1008502
% 9.90/1.78 % Search garbage collected termcells : 49
% 9.90/1.78
% 9.90/1.78 % -------------------------------------------------
% 9.90/1.78 % User time : 1.236 s
% 9.90/1.78 % System time : 0.058 s
% 9.90/1.78 % Total time : 1.295 s
% 9.90/1.78 % Maximum resident set size: 3604 pages
% 9.90/1.78
% 9.90/1.78 % -------------------------------------------------
% 9.90/1.78 % User time : 6.089 s
% 9.90/1.78 % System time : 0.262 s
% 9.90/1.78 % Total time : 6.351 s
% 9.90/1.78 % Maximum resident set size: 4864 pages
% 9.90/1.78 % E exiting
%------------------------------------------------------------------------------