%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP267-1 : 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 : n008.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 12:39:08 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.47s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 14
% Syntax : Number of clauses : 93 ( 25 unt; 46 nHn; 78 RR)
% Number of literals : 273 ( 272 equ; 143 neg)
% Maximal clause size : 10 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_5,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_22,negated_conjecture,
( inverse(sk_c6) != sk_c7
| inverse(X5) != sk_c8
| multiply(X5,sk_c8) != sk_c7
| inverse(X4) != sk_c7
| multiply(X4,sk_c7) != X3
| multiply(sk_c7,X3) != sk_c6
| inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_15,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_18,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_6,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_21,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
cnf(c_0_14,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_15,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_16,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_17,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_18,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
prove_this_1 ).
cnf(c_0_19,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(inverse(sk_c1),sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
prove_this_4 ).
cnf(c_0_21,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| multiply(inverse(sk_c5),sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
cnf(c_0_23,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
prove_this_2 ).
cnf(c_0_24,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| multiply(inverse(sk_c1),sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
cnf(c_0_26,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
prove_this_5 ).
cnf(c_0_27,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_28,negated_conjecture,
( inverse(sk_c6) != sk_c7
| inverse(X5) != sk_c8
| multiply(X5,sk_c8) != sk_c7
| inverse(X4) != sk_c7
| multiply(X4,sk_c7) != X3
| multiply(sk_c7,X3) != sk_c6
| inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7 ),
inference(fof_simplification,[status(thm)],[prove_this_22]) ).
cnf(c_0_29,negated_conjecture,
multiply(sk_c8,sk_c7) = sk_c8,
inference(spm,[status(thm)],[c_0_22,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( inverse(sk_c6) != sk_c7
| inverse(X5) != sk_c8
| multiply(X5,sk_c8) != sk_c7
| inverse(X4) != sk_c7
| multiply(X4,sk_c7) != X3
| multiply(sk_c7,X3) != sk_c6
| inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7 ),
c_0_28 ).
cnf(c_0_31,negated_conjecture,
identity = sk_c7,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_29]),c_0_15]) ).
cnf(c_0_32,negated_conjecture,
( inverse(X4) != sk_c8
| inverse(X3) != sk_c6
| inverse(X1) != sk_c7
| inverse(X2) != sk_c8
| inverse(sk_c6) != sk_c7
| multiply(X4,sk_c8) != sk_c7
| multiply(X3,sk_c6) != sk_c7
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c7,multiply(X1,sk_c7)) != sk_c6 ),
inference(er,[status(thm)],[c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c7,sk_c4) = sk_c6 ),
prove_this_15 ).
cnf(c_0_34,plain,
multiply(sk_c7,X1) = X1,
inference(rw,[status(thm)],[c_0_16,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( inverse(X4) != sk_c8
| inverse(X3) != sk_c6
| inverse(X1) != sk_c7
| inverse(X2) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| multiply(X3,sk_c6) != sk_c7
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c7,multiply(X1,sk_c7)) != sk_c6
| multiply(sk_c7,sk_c4) = sk_c6 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
( sk_c4 = sk_c6
| inverse(sk_c6) = sk_c7 ),
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c7,sk_c6) = identity
| multiply(sk_c7,sk_c4) = sk_c6 ),
inference(spm,[status(thm)],[c_0_15,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( inverse(X4) != sk_c8
| inverse(X3) != sk_c6
| inverse(X1) != sk_c7
| inverse(X2) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| multiply(X3,sk_c6) != sk_c7
| multiply(X2,sk_c8) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| sk_c4 = sk_c6 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_34]),c_0_34]) ).
cnf(c_0_39,negated_conjecture,
( sk_c4 = sk_c6
| multiply(sk_c6,X1) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_36]),c_0_34]) ).
cnf(c_0_40,negated_conjecture,
( sk_c4 = sk_c6
| sk_c6 = sk_c7 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_31]),c_0_34]),c_0_34]) ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c7,sk_c4) = sk_c6 ),
prove_this_13 ).
cnf(c_0_42,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c7,sk_c4) = sk_c6 ),
prove_this_14 ).
cnf(c_0_43,negated_conjecture,
( inverse(X3) != sk_c8
| inverse(X2) != sk_c6
| inverse(X1) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| multiply(X1,sk_c8) != sk_c7
| sk_c4 = sk_c6 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_36]) ).
cnf(c_0_44,negated_conjecture,
( sk_c4 = sk_c6
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(rw,[status(thm)],[c_0_41,c_0_34]) ).
cnf(c_0_45,negated_conjecture,
( sk_c4 = sk_c6
| inverse(sk_c5) = sk_c8 ),
inference(rw,[status(thm)],[c_0_42,c_0_34]) ).
cnf(c_0_46,negated_conjecture,
( inverse(X2) != sk_c8
| inverse(X1) != sk_c6
| multiply(X2,sk_c8) != sk_c7
| multiply(X1,sk_c6) != sk_c7
| sk_c4 = sk_c6 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_47,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c4 ),
prove_this_18 ).
cnf(c_0_48,negated_conjecture,
( inverse(X1) != sk_c8
| inverse(sk_c6) != sk_c6
| multiply(X1,sk_c8) != sk_c7
| sk_c4 = sk_c6 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_39]),c_0_40]) ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c7,sk_c6) = identity
| multiply(sk_c3,sk_c7) = sk_c4 ),
inference(spm,[status(thm)],[c_0_15,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| sk_c4 = sk_c6 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_36]),c_0_40]) ).
cnf(c_0_51,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
prove_this_6 ).
cnf(c_0_52,negated_conjecture,
( sk_c6 = sk_c7
| multiply(sk_c3,sk_c7) = sk_c4 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_31]),c_0_34]) ).
cnf(c_0_53,negated_conjecture,
sk_c4 = sk_c6,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_45]),c_0_44]) ).
cnf(c_0_54,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c8,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_15,c_0_51]) ).
cnf(c_0_55,negated_conjecture,
( sk_c6 = sk_c7
| multiply(sk_c3,sk_c7) = sk_c6 ),
inference(rw,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_56,negated_conjecture,
( inverse(X4) != sk_c8
| inverse(X3) != sk_c6
| inverse(X1) != sk_c7
| inverse(X2) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| multiply(X3,sk_c6) != sk_c7
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c7,multiply(X1,sk_c7)) != sk_c6
| multiply(sk_c8,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_32,c_0_54]) ).
cnf(c_0_57,negated_conjecture,
( sk_c6 = sk_c7
| multiply(sk_c3,X1) = multiply(sk_c6,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_55]),c_0_34]) ).
cnf(c_0_58,negated_conjecture,
( sk_c6 = sk_c7
| multiply(inverse(sk_c3),sk_c4) = sk_c7 ),
inference(spm,[status(thm)],[c_0_17,c_0_52]) ).
cnf(c_0_59,negated_conjecture,
( inverse(X3) != sk_c8
| inverse(X2) != sk_c6
| inverse(X1) != sk_c8
| inverse(identity) != sk_c7
| multiply(X3,sk_c8) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| multiply(sk_c8,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_56,c_0_16]) ).
cnf(c_0_60,negated_conjecture,
( sk_c6 = sk_c7
| multiply(sk_c6,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_55,c_0_57]) ).
cnf(c_0_61,negated_conjecture,
( sk_c6 = sk_c7
| multiply(inverse(sk_c3),sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_58,c_0_40]) ).
cnf(c_0_62,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c3) = sk_c7 ),
prove_this_21 ).
cnf(c_0_63,plain,
multiply(inverse(sk_c7),X1) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_34]) ).
cnf(c_0_64,negated_conjecture,
( inverse(X3) != sk_c8
| inverse(X2) != sk_c6
| inverse(X1) != sk_c8
| inverse(sk_c7) != sk_c7
| multiply(X3,sk_c8) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| multiply(sk_c8,sk_c1) = sk_c7 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_31]),c_0_31]) ).
cnf(c_0_65,negated_conjecture,
( sk_c6 = sk_c7
| multiply(inverse(sk_c6),sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_17,c_0_60]) ).
cnf(c_0_66,negated_conjecture,
( sk_c6 = sk_c7
| inverse(sk_c6) = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_34])]) ).
cnf(c_0_67,plain,
multiply(inverse(X1),X1) = sk_c7,
inference(rw,[status(thm)],[c_0_15,c_0_31]) ).
cnf(c_0_68,plain,
multiply(inverse(inverse(sk_c7)),X1) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_63]) ).
cnf(c_0_69,negated_conjecture,
( sk_c6 != sk_c7
| inverse(X3) != sk_c8
| inverse(X2) != sk_c6
| inverse(X1) != sk_c8
| inverse(sk_c7) != sk_c7
| multiply(X3,sk_c8) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c8,sk_c1) = sk_c7 ),
inference(rw,[status(thm)],[c_0_64,c_0_34]) ).
cnf(c_0_70,negated_conjecture,
sk_c6 = sk_c7,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_34])]) ).
cnf(c_0_71,plain,
inverse(sk_c7) = sk_c7,
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c8,sk_c1) = identity
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_15,c_0_20]) ).
cnf(c_0_73,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c8,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_15,c_0_26]) ).
cnf(c_0_74,negated_conjecture,
( inverse(X3) != sk_c8
| inverse(X2) != sk_c7
| inverse(X1) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(X2,sk_c7) != sk_c7
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c8,sk_c1) = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70]),c_0_70]),c_0_70])]),c_0_71])]) ).
cnf(c_0_75,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c8,sk_c1) = sk_c7 ),
inference(rw,[status(thm)],[c_0_72,c_0_31]) ).
cnf(c_0_76,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c8,sk_c1) = sk_c7 ),
inference(rw,[status(thm)],[c_0_73,c_0_31]) ).
cnf(c_0_77,negated_conjecture,
( inverse(X2) != sk_c8
| inverse(X1) != sk_c7
| multiply(X2,sk_c8) != sk_c7
| multiply(X1,sk_c7) != sk_c7
| multiply(sk_c8,sk_c1) = sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).
cnf(c_0_78,negated_conjecture,
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c8,sk_c1) = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_34]),c_0_71])]) ).
cnf(c_0_79,negated_conjecture,
multiply(sk_c8,sk_c1) = sk_c7,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_76]),c_0_75]) ).
cnf(c_0_80,negated_conjecture,
multiply(inverse(sk_c8),sk_c7) = sk_c1,
inference(spm,[status(thm)],[c_0_17,c_0_79]) ).
cnf(c_0_81,negated_conjecture,
multiply(inverse(sk_c8),X1) = multiply(sk_c1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_80]),c_0_34]) ).
cnf(c_0_82,negated_conjecture,
multiply(sk_c1,sk_c8) = sk_c7,
inference(spm,[status(thm)],[c_0_67,c_0_81]) ).
cnf(c_0_83,negated_conjecture,
( inverse(X4) != sk_c8
| inverse(X3) != sk_c6
| inverse(X1) != sk_c7
| inverse(X2) != sk_c8
| inverse(sk_c6) != sk_c7
| multiply(X4,sk_c8) != sk_c7
| multiply(X3,sk_c6) != sk_c7
| multiply(X2,sk_c8) != sk_c7
| multiply(X1,sk_c7) != sk_c6 ),
inference(rw,[status(thm)],[c_0_32,c_0_34]) ).
cnf(c_0_84,negated_conjecture,
multiply(inverse(sk_c1),sk_c7) = sk_c8,
inference(spm,[status(thm)],[c_0_17,c_0_82]) ).
cnf(c_0_85,negated_conjecture,
( inverse(X4) != sk_c8
| inverse(X3) != sk_c7
| inverse(X1) != sk_c7
| inverse(X2) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c7
| multiply(X2,sk_c8) != sk_c7
| multiply(X1,sk_c7) != sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_70]),c_0_70]),c_0_70]),c_0_70]),c_0_71])]) ).
cnf(c_0_86,negated_conjecture,
multiply(inverse(inverse(sk_c1)),sk_c8) = sk_c7,
inference(spm,[status(thm)],[c_0_17,c_0_84]) ).
cnf(c_0_87,plain,
multiply(inverse(inverse(X1)),sk_c7) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_67]) ).
cnf(c_0_88,negated_conjecture,
( inverse(X3) != sk_c8
| inverse(X2) != sk_c7
| inverse(X1) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(X2,sk_c7) != sk_c7
| multiply(X1,sk_c8) != sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_34]),c_0_71])]) ).
cnf(c_0_89,negated_conjecture,
inverse(sk_c1) = sk_c8,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_86]),c_0_87]) ).
cnf(c_0_90,negated_conjecture,
( inverse(X2) != sk_c8
| inverse(X1) != sk_c7
| multiply(X2,sk_c8) != sk_c7
| multiply(X1,sk_c7) != sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_82]),c_0_89])]) ).
cnf(c_0_91,negated_conjecture,
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_34]),c_0_71])]) ).
cnf(c_0_92,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_89]),c_0_82])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP267-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 20 20:08:38 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 0.19/0.47 % Version: 3.5.1
% 0.19/0.47 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.19/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.19/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.19/0.47 % Starting sh5l with 300s (1) cores
% 0.19/0.47 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 3497565 completed with status 0
% 0.19/0.47 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.19/0.47 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.19/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.19/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/0.47 % No SInE strategy applied
% 0.19/0.47 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.19/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.19/0.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.19/0.47 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.19/0.47 % Starting new_bool_3 with 136s (1) cores
% 0.19/0.47 % Starting new_bool_1 with 136s (1) cores
% 0.19/0.47 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 3497572 completed with status 0
% 0.19/0.47 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.19/0.47 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.19/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.19/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/0.47 % No SInE strategy applied
% 0.19/0.47 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.19/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.19/0.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.19/0.47 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.19/0.47 % Preprocessing time : 0.001 s
% 0.19/0.47 % Presaturation interreduction done
% 0.19/0.47
% 0.19/0.47 % Proof found!
% 0.19/0.47 % SZS status Unsatisfiable
% 0.19/0.47 % SZS output start CNFRefutation
% See solution above
% 0.19/0.47 % Parsed axioms : 25
% 0.19/0.47 % Removed by relevancy pruning/SinE : 0
% 0.19/0.47 % Initial clauses : 25
% 0.19/0.47 % Removed in clause preprocessing : 0
% 0.19/0.47 % Initial clauses in saturation : 25
% 0.19/0.47 % Processed clauses : 550
% 0.19/0.47 % ...of these trivial : 20
% 0.19/0.47 % ...subsumed : 163
% 0.19/0.47 % ...remaining for further processing : 367
% 0.19/0.47 % Other redundant clauses eliminated : 11
% 0.19/0.47 % Clauses deleted for lack of memory : 0
% 0.19/0.47 % Backward-subsumed : 72
% 0.19/0.47 % Backward-rewritten : 226
% 0.19/0.47 % Generated clauses : 1846
% 0.19/0.47 % ...of the previous two non-redundant : 1654
% 0.19/0.47 % ...aggressively subsumed : 0
% 0.19/0.47 % Contextual simplify-reflections : 18
% 0.19/0.47 % Paramodulations : 1834
% 0.19/0.47 % Factorizations : 1
% 0.19/0.47 % NegExts : 0
% 0.19/0.47 % Equation resolutions : 11
% 0.19/0.47 % Disequality decompositions : 0
% 0.19/0.47 % Total rewrite steps : 1190
% 0.19/0.47 % ...of those cached : 1123
% 0.19/0.47 % Propositional unsat checks : 0
% 0.19/0.47 % Propositional check models : 0
% 0.19/0.47 % Propositional check unsatisfiable : 0
% 0.19/0.47 % Propositional clauses : 0
% 0.19/0.47 % Propositional clauses after purity: 0
% 0.19/0.47 % Propositional unsat core size : 0
% 0.19/0.47 % Propositional preprocessing time : 0.000
% 0.19/0.47 % Propositional encoding time : 0.000
% 0.19/0.47 % Propositional solver time : 0.000
% 0.19/0.47 % Success case prop preproc time : 0.000
% 0.19/0.47 % Success case prop encoding time : 0.000
% 0.19/0.47 % Success case prop solver time : 0.000
% 0.19/0.47 % Current number of processed clauses : 43
% 0.19/0.47 % Positive orientable unit clauses : 21
% 0.19/0.47 % Positive unorientable unit clauses: 0
% 0.19/0.47 % Negative unit clauses : 0
% 0.19/0.48 % Non-unit-clauses : 22
% 0.19/0.48 % Current number of unprocessed clauses: 890
% 0.19/0.48 % ...number of literals in the above : 6039
% 0.19/0.48 % Current number of archived formulas : 0
% 0.19/0.48 % Current number of archived clauses : 323
% 0.19/0.48 % Clause-clause subsumption calls (NU) : 1406
% 0.19/0.48 % Rec. Clause-clause subsumption calls : 1015
% 0.19/0.48 % Non-unit clause-clause subsumptions : 228
% 0.19/0.48 % Unit Clause-clause subsumption calls : 234
% 0.19/0.48 % Rewrite failures with RHS unbound : 0
% 0.19/0.48 % BW rewrite match attempts : 34
% 0.19/0.48 % BW rewrite match successes : 24
% 0.19/0.48 % Condensation attempts : 0
% 0.19/0.48 % Condensation successes : 0
% 0.19/0.48 % Termbank termtop insertions : 31899
% 0.19/0.48 % Search garbage collected termcells : 28
% 0.19/0.48
% 0.19/0.48 % -------------------------------------------------
% 0.19/0.48 % User time : 0.027 s
% 0.19/0.48 % System time : 0.005 s
% 0.19/0.48 % Total time : 0.032 s
% 0.19/0.48 % Maximum resident set size: 3388 pages
% 0.19/0.48
% 0.19/0.48 % -------------------------------------------------
% 0.19/0.48 % User time : 0.107 s
% 0.19/0.48 % System time : 0.020 s
% 0.19/0.48 % Total time : 0.127 s
% 0.19/0.48 % Maximum resident set size: 4608 pages
% 0.19/0.48 % E exiting
%------------------------------------------------------------------------------