%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP307-1 : 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 12:43:10 PM UTC 2026
% Result : Unsatisfiable 18.14s 3.08s
% Output : CNFRefutation 18.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 27
% Syntax : Number of clauses : 154 ( 23 unt; 113 nHn; 135 RR)
% Number of literals : 372 ( 371 equ; 106 neg)
% Maximal clause size : 16 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 67 ( 1 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_52,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_52) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c11) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_51,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
cnf(prove_this_45,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
cnf(prove_this_35,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c11,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_11,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c11) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_36,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c11,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_46,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_54,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_54) ).
cnf(prove_this_56,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_56) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c9,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_16,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c11) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_55,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_55) ).
cnf(prove_this_26,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c9,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_15,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c11) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_6,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c11,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c11,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_53,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_53) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c11) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c11) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_61,negated_conjecture,
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| inverse(X2) != sk_c11
| multiply(X2,sk_c11) != X1
| multiply(sk_c11,X1) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c11
| inverse(sk_c11) != sk_c9
| multiply(sk_c11,sk_c10) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_61) ).
cnf(c_0_27,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_28,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_29,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_30,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_31,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_30]) ).
cnf(c_0_32,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_28,c_0_31]) ).
cnf(c_0_33,plain,
multiply(inverse(X1),identity) = inverse(X1),
inference(spm,[status(thm)],[c_0_30,c_0_32]) ).
cnf(c_0_34,plain,
inverse(inverse(X1)) = multiply(X1,identity),
inference(spm,[status(thm)],[c_0_31,c_0_33]) ).
cnf(c_0_35,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_28]),c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c11 ),
prove_this_52 ).
cnf(c_0_37,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c11) = sk_c9 ),
prove_this_12 ).
cnf(c_0_38,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
prove_this_51 ).
cnf(c_0_41,negated_conjecture,
( inverse(sk_c11) = sk_c9
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_37]) ).
cnf(c_0_42,negated_conjecture,
( inverse(sk_c11) = sk_c1
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c2 ),
prove_this_45 ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c11,sk_c2) = sk_c10 ),
prove_this_35 ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c11) = sk_c9 ),
prove_this_11 ).
cnf(c_0_46,negated_conjecture,
( inverse(sk_c11) = sk_c1
| multiply(sk_c3,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_38,c_0_40]) ).
cnf(c_0_47,negated_conjecture,
( sk_c1 = sk_c9
| multiply(sk_c11,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c2
| multiply(inverse(sk_c5),sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_30,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c11,sk_c2) = sk_c10
| multiply(inverse(sk_c5),sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_30,c_0_44]) ).
cnf(c_0_50,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c11,sk_c2) = sk_c10 ),
prove_this_36 ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c9 ),
prove_this_5 ).
cnf(c_0_52,negated_conjecture,
( sk_c1 = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_53,negated_conjecture,
( sk_c1 = sk_c9
| inverse(sk_c11) = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_47]),c_0_33]) ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c2
| multiply(inverse(inverse(sk_c5)),sk_c8) = sk_c11 ),
inference(spm,[status(thm)],[c_0_30,c_0_48]) ).
cnf(c_0_55,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c2 ),
prove_this_46 ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c8
| multiply(sk_c11,sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| multiply(sk_c5,multiply(sk_c8,X1)) = multiply(sk_c11,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_51]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c9 ),
prove_this_7 ).
cnf(c_0_59,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c11 ),
prove_this_54 ).
cnf(c_0_60,negated_conjecture,
( sk_c1 = sk_c9
| multiply(inverse(sk_c3),sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_30,c_0_52]) ).
cnf(c_0_61,negated_conjecture,
( sk_c1 = sk_c9
| inverse(sk_c3) = sk_c11 ),
inference(spm,[status(thm)],[c_0_38,c_0_53]) ).
cnf(c_0_62,negated_conjecture,
( identity = sk_c11
| multiply(sk_c1,sk_c11) = sk_c2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_28]) ).
cnf(c_0_63,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c11 ),
prove_this_56 ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c9,sk_c10) = sk_c11 ),
prove_this_25 ).
cnf(c_0_65,negated_conjecture,
( identity = sk_c11
| multiply(sk_c11,sk_c2) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_56]),c_0_28]) ).
cnf(c_0_66,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c11) = sk_c9 ),
prove_this_16 ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| multiply(sk_c5,sk_c11) = multiply(sk_c11,sk_c10) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_68,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c10) = multiply(sk_c4,identity) ),
inference(spm,[status(thm)],[c_0_34,c_0_59]) ).
cnf(c_0_69,negated_conjecture,
( sk_c1 = sk_c9
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_70,negated_conjecture,
( identity = sk_c11
| multiply(inverse(sk_c1),sk_c2) = sk_c11 ),
inference(spm,[status(thm)],[c_0_30,c_0_62]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c11 ),
prove_this_55 ).
cnf(c_0_72,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c5,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_32,c_0_63]) ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(inverse(sk_c5),sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_30,c_0_64]) ).
cnf(c_0_74,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c9,sk_c10) = sk_c11 ),
prove_this_26 ).
cnf(c_0_75,negated_conjecture,
( identity = sk_c11
| multiply(inverse(sk_c11),sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_30,c_0_65]) ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c11) = sk_c9 ),
prove_this_15 ).
cnf(c_0_77,negated_conjecture,
( inverse(sk_c11) = sk_c9
| multiply(sk_c5,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_32,c_0_66]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| multiply(inverse(sk_c5),multiply(sk_c11,sk_c10)) = sk_c11 ),
inference(spm,[status(thm)],[c_0_30,c_0_67]) ).
cnf(c_0_79,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c11,sk_c10) = sk_c9 ),
prove_this_6 ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c11,sk_c10) = sk_c9 ),
prove_this_1 ).
cnf(c_0_81,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c11 ),
prove_this_53 ).
cnf(c_0_82,negated_conjecture,
( inverse(sk_c10) = sk_c4
| inverse(sk_c1) = sk_c11 ),
inference(rw,[status(thm)],[c_0_68,c_0_35]) ).
cnf(c_0_83,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_29,c_0_32]) ).
cnf(c_0_84,negated_conjecture,
( identity = sk_c10
| sk_c1 = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_69]),c_0_28]) ).
cnf(c_0_85,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c11) = sk_c9 ),
prove_this_14 ).
cnf(c_0_86,negated_conjecture,
( identity = sk_c11
| multiply(sk_c11,sk_c2) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_87,negated_conjecture,
( identity = sk_c11
| multiply(sk_c11,sk_c2) = sk_c11
| multiply(sk_c5,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_70,c_0_72]) ).
cnf(c_0_88,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c8
| multiply(sk_c9,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_89,negated_conjecture,
( identity = sk_c11
| multiply(sk_c9,sk_c10) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c11 ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_90,negated_conjecture,
( identity = sk_c11
| multiply(sk_c9,sk_c10) = sk_c2
| multiply(sk_c5,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_75,c_0_77]) ).
cnf(c_0_91,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| multiply(sk_c8,multiply(sk_c11,sk_c10)) = sk_c11 ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_92,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| multiply(inverse(sk_c3),sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_30,c_0_80]) ).
cnf(c_0_93,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c9 ),
prove_this_2 ).
cnf(c_0_94,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c11) = sk_c9 ),
prove_this_13 ).
cnf(c_0_95,negated_conjecture,
( inverse(sk_c11) = sk_c1
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_38,c_0_81]) ).
cnf(c_0_96,negated_conjecture,
( inverse(sk_c11) = sk_c1
| inverse(sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_38,c_0_82]) ).
cnf(c_0_97,negated_conjecture,
( sk_c1 = sk_c9
| inverse(sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_98,negated_conjecture,
( inverse(sk_c10) = sk_c4
| inverse(sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_38,c_0_85]) ).
cnf(c_0_99,negated_conjecture,
( identity = sk_c11
| multiply(sk_c11,sk_c2) = sk_c11 ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_100,negated_conjecture,
( identity = sk_c11
| multiply(sk_c9,sk_c10) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_88]),c_0_28]) ).
cnf(c_0_101,negated_conjecture,
( identity = sk_c11
| multiply(sk_c9,sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_102,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| multiply(inverse(sk_c8),sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_30,c_0_58]) ).
cnf(c_0_103,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| multiply(inverse(sk_c8),sk_c11) = multiply(sk_c11,sk_c10) ),
inference(spm,[status(thm)],[c_0_30,c_0_91]) ).
cnf(c_0_104,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_105,negated_conjecture,
( sk_c1 = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_106,negated_conjecture,
( sk_c4 = sk_c10
| sk_c1 = sk_c9
| inverse(sk_c11) = sk_c1 ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_107,negated_conjecture,
( sk_c4 = sk_c10
| sk_c1 = sk_c9
| inverse(sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_98,c_0_97]) ).
cnf(c_0_108,negated_conjecture,
( identity = sk_c2
| identity = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_99]),c_0_28]) ).
cnf(c_0_109,negated_conjecture,
( sk_c2 = sk_c11
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_110,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c10
| multiply(sk_c11,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_111,negated_conjecture,
( sk_c9 != sk_c11
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(ef,[status(thm)],[c_0_104]) ).
cnf(c_0_112,negated_conjecture,
( sk_c1 = sk_c9
| multiply(inverse(sk_c4),sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_30,c_0_105]) ).
cnf(c_0_113,negated_conjecture,
( sk_c1 = sk_c9
| sk_c4 = sk_c10 ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_114,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c9
| multiply(inverse(sk_c5),sk_c11) = sk_c8 ),
inference(spm,[status(thm)],[c_0_30,c_0_51]) ).
cnf(c_0_115,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c4,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_32,c_0_59]) ).
cnf(c_0_116,negated_conjecture,
identity = sk_c11,
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_108]),c_0_109]) ).
cnf(c_0_117,negated_conjecture,
( sk_c9 != sk_c10
| multiply(sk_c11,sk_c10) = sk_c10 ),
inference(ef,[status(thm)],[c_0_110]) ).
cnf(c_0_118,negated_conjecture,
( sk_c9 != sk_c11
| identity = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_111]),c_0_28]) ).
cnf(c_0_119,negated_conjecture,
( sk_c1 = sk_c9
| multiply(inverse(sk_c10),sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_120,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c8
| multiply(sk_c11,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_114,c_0_79]) ).
cnf(c_0_121,negated_conjecture,
( multiply(sk_c11,sk_c1) = identity
| multiply(sk_c4,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_115]) ).
cnf(c_0_122,plain,
inverse(sk_c11) = sk_c11,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_116]),c_0_116]) ).
cnf(c_0_123,negated_conjecture,
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| inverse(X2) != sk_c11
| multiply(X2,sk_c11) != X1
| multiply(sk_c11,X1) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c11
| inverse(sk_c11) != sk_c9
| multiply(sk_c11,sk_c10) != sk_c9 ),
inference(fof_simplification,[status(thm)],[prove_this_61]) ).
cnf(c_0_124,negated_conjecture,
( sk_c9 != sk_c10
| multiply(inverse(sk_c11),sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_30,c_0_117]) ).
cnf(c_0_125,negated_conjecture,
( sk_c9 != sk_c11
| multiply(X1,sk_c10) = X1 ),
inference(spm,[status(thm)],[c_0_35,c_0_118]) ).
cnf(c_0_126,negated_conjecture,
( sk_c1 = sk_c9
| multiply(sk_c10,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_119,c_0_97]) ).
cnf(c_0_127,negated_conjecture,
( identity = sk_c11
| multiply(sk_c11,sk_c10) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_120]),c_0_28]) ).
cnf(c_0_128,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c11
| multiply(sk_c11,sk_c1) = sk_c11 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_116]),c_0_116]) ).
cnf(c_0_129,negated_conjecture,
( sk_c9 = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_94,c_0_122]) ).
cnf(c_0_130,negated_conjecture,
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| inverse(X2) != sk_c11
| multiply(X2,sk_c11) != X1
| multiply(sk_c11,X1) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c11
| inverse(sk_c11) != sk_c9
| multiply(sk_c11,sk_c10) != sk_c9 ),
c_0_123 ).
cnf(c_0_131,negated_conjecture,
( sk_c9 != sk_c11
| multiply(sk_c10,X1) = X1 ),
inference(spm,[status(thm)],[c_0_29,c_0_118]) ).
cnf(c_0_132,negated_conjecture,
( sk_c9 != sk_c11
| sk_c9 != sk_c10
| inverse(sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_133,negated_conjecture,
( identity = sk_c9
| sk_c1 = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_126]),c_0_28]) ).
cnf(c_0_134,negated_conjecture,
( sk_c9 = sk_c11
| identity = sk_c11
| sk_c1 = sk_c9 ),
inference(spm,[status(thm)],[c_0_127,c_0_69]) ).
cnf(c_0_135,negated_conjecture,
( sk_c9 = sk_c11
| multiply(sk_c11,sk_c1) = sk_c11 ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_136,negated_conjecture,
( inverse(X1) != sk_c11
| inverse(X5) != sk_c11
| inverse(X4) != sk_c10
| inverse(sk_c11) != sk_c9
| multiply(X5,sk_c11) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X3,inverse(X3)) != sk_c11
| multiply(sk_c9,sk_c10) != sk_c11
| multiply(sk_c11,sk_c10) != sk_c9
| multiply(X2,inverse(X3)) != inverse(X2)
| multiply(inverse(X3),sk_c10) != sk_c11
| inverse(multiply(X2,inverse(X3))) != inverse(X3)
| multiply(sk_c11,multiply(X1,sk_c11)) != sk_c10 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_130])])]) ).
cnf(c_0_137,negated_conjecture,
( sk_c9 != sk_c11
| inverse(sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_131,c_0_32]) ).
cnf(c_0_138,negated_conjecture,
( sk_c9 != sk_c11
| sk_c9 != sk_c10
| inverse(sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_38,c_0_132]) ).
cnf(c_0_139,negated_conjecture,
( sk_c10 = sk_c11
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_65,c_0_99]) ).
cnf(c_0_140,negated_conjecture,
( sk_c1 = sk_c9
| sk_c9 = sk_c11 ),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_141,negated_conjecture,
( sk_c1 = sk_c11
| sk_c9 = sk_c11 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_135]),c_0_28]),c_0_116]) ).
cnf(c_0_142,negated_conjecture,
( identity != sk_c11
| inverse(X1) != sk_c11
| inverse(X5) != sk_c11
| inverse(X4) != sk_c10
| inverse(sk_c11) != sk_c9
| multiply(X5,sk_c11) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(sk_c9,sk_c10) != sk_c11
| multiply(sk_c11,sk_c10) != sk_c9
| multiply(X2,inverse(X3)) != inverse(X2)
| multiply(inverse(X3),sk_c10) != sk_c11
| inverse(multiply(X2,inverse(X3))) != inverse(X3)
| multiply(sk_c11,multiply(X1,sk_c11)) != sk_c10 ),
inference(rw,[status(thm)],[c_0_136,c_0_32]) ).
cnf(c_0_143,negated_conjecture,
( sk_c9 != sk_c10
| sk_c9 != sk_c11
| identity = sk_c11 ),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_144,negated_conjecture,
( sk_c9 != sk_c11
| sk_c10 = sk_c11 ),
inference(spm,[status(thm)],[c_0_118,c_0_139]) ).
cnf(c_0_145,negated_conjecture,
sk_c9 = sk_c11,
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_146,negated_conjecture,
( sk_c9 != sk_c10
| sk_c9 != sk_c11
| inverse(X1) != sk_c11
| inverse(X5) != sk_c11
| inverse(X4) != sk_c10
| inverse(sk_c11) != sk_c9
| multiply(X5,sk_c11) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(sk_c9,sk_c10) != sk_c11
| multiply(sk_c11,sk_c10) != sk_c9
| multiply(X2,inverse(X3)) != inverse(X2)
| multiply(inverse(X3),sk_c10) != sk_c11
| inverse(multiply(X2,inverse(X3))) != inverse(X3)
| multiply(sk_c11,multiply(X1,sk_c11)) != sk_c10 ),
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_147,plain,
multiply(X1,sk_c11) = X1,
inference(rw,[status(thm)],[c_0_35,c_0_116]) ).
cnf(c_0_148,plain,
multiply(sk_c11,X1) = X1,
inference(rw,[status(thm)],[c_0_29,c_0_116]) ).
cnf(c_0_149,negated_conjecture,
sk_c10 = sk_c11,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_144,c_0_145])]) ).
cnf(c_0_150,negated_conjecture,
( inverse(X2) != sk_c11
| 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(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(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)],[c_0_146,c_0_122])]),c_0_147]),c_0_148]),c_0_149]),c_0_149]),c_0_147]),c_0_149]),c_0_147]),c_0_145]),c_0_145]),c_0_149]),c_0_147]),c_0_149]),c_0_147]),c_0_145]),c_0_147]),c_0_149]),c_0_145]),c_0_149]),c_0_145]),c_0_149])])])])]),c_0_122])]) ).
cnf(c_0_151,plain,
multiply(inverse(X1),X1) = sk_c11,
inference(rw,[status(thm)],[c_0_28,c_0_116]) ).
cnf(c_0_152,negated_conjecture,
inverse(X1) != sk_c11,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_122]),c_0_34]),c_0_35])]) ).
cnf(c_0_153,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_36,c_0_152]),c_0_152]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP307-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % 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 20:08:48 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 18.14/3.08 % Version: 3.5.1
% 18.14/3.08 % Preprocessing class: FSMSSMSMSSSNFFN.
% 18.14/3.08 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 18.14/3.08 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 18.14/3.08 % Starting new_bool_3 with 300s (1) cores
% 18.14/3.08 % Starting new_bool_1 with 300s (1) cores
% 18.14/3.08 % Starting sh5l with 300s (1) cores
% 18.14/3.08 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1655945 completed with status 0
% 18.14/3.08 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 18.14/3.08 % Preprocessing class: FSMSSMSMSSSNFFN.
% 18.14/3.08 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 18.14/3.08 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 18.14/3.08 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 18.14/3.08 % No SInE strategy applied
% 18.14/3.08 % Search class: FGHPS-FFMM21-SFFFFFNN
% 18.14/3.08 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 18.14/3.08 % Starting SubtermCWHack with 136s (1) cores
% 18.14/3.08 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 18.14/3.08 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 18.14/3.08 % Starting new_bool_3 with 136s (1) cores
% 18.14/3.08 % Starting new_bool_1 with 136s (1) cores
% 18.14/3.08 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 1655952 completed with status 0
% 18.14/3.08 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 18.14/3.08 % Preprocessing class: FSMSSMSMSSSNFFN.
% 18.14/3.08 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 18.14/3.08 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 18.14/3.08 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 18.14/3.08 % No SInE strategy applied
% 18.14/3.08 % Search class: FGHPS-FFMM21-SFFFFFNN
% 18.14/3.08 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 18.14/3.08 % Starting SubtermCWHack with 136s (1) cores
% 18.14/3.08 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 18.14/3.08 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 18.14/3.08 % Preprocessing time : 0.002 s
% 18.14/3.08 % Presaturation interreduction done
% 18.14/3.08
% 18.14/3.08 % Proof found!
% 18.14/3.08 % SZS status Unsatisfiable
% 18.14/3.08 % SZS output start CNFRefutation
% See solution above
% 18.14/3.08 % Parsed axioms : 64
% 18.14/3.08 % Removed by relevancy pruning/SinE : 0
% 18.14/3.08 % Initial clauses : 64
% 18.14/3.08 % Removed in clause preprocessing : 0
% 18.14/3.08 % Initial clauses in saturation : 64
% 18.14/3.08 % Processed clauses : 29305
% 18.14/3.08 % ...of these trivial : 727
% 18.14/3.08 % ...subsumed : 24364
% 18.14/3.08 % ...remaining for further processing : 4214
% 18.14/3.08 % Other redundant clauses eliminated : 28
% 18.14/3.08 % Clauses deleted for lack of memory : 0
% 18.14/3.08 % Backward-subsumed : 538
% 18.14/3.08 % Backward-rewritten : 3362
% 18.14/3.08 % Generated clauses : 158968
% 18.14/3.08 % ...of the previous two non-redundant : 157395
% 18.14/3.08 % ...aggressively subsumed : 0
% 18.14/3.08 % Contextual simplify-reflections : 173
% 18.14/3.08 % Paramodulations : 158899
% 18.14/3.08 % Factorizations : 5
% 18.14/3.08 % NegExts : 0
% 18.14/3.08 % Equation resolutions : 28
% 18.14/3.08 % Disequality decompositions : 0
% 18.14/3.08 % Total rewrite steps : 42377
% 18.14/3.08 % ...of those cached : 41591
% 18.14/3.08 % Propositional unsat checks : 0
% 18.14/3.08 % Propositional check models : 0
% 18.14/3.08 % Propositional check unsatisfiable : 0
% 18.14/3.08 % Propositional clauses : 0
% 18.14/3.08 % Propositional clauses after purity: 0
% 18.14/3.08 % Propositional unsat core size : 0
% 18.14/3.08 % Propositional preprocessing time : 0.000
% 18.14/3.08 % Propositional encoding time : 0.000
% 18.14/3.08 % Propositional solver time : 0.000
% 18.14/3.08 % Success case prop preproc time : 0.000
% 18.14/3.08 % Success case prop encoding time : 0.000
% 18.14/3.08 % Success case prop solver time : 0.000
% 18.14/3.08 % Current number of processed clauses : 200
% 18.14/3.08 % Positive orientable unit clauses : 14
% 18.14/3.08 % Positive unorientable unit clauses: 0
% 18.14/3.08 % Negative unit clauses : 1
% 18.14/3.08 % Non-unit-clauses : 185
% 18.14/3.08 % Current number of unprocessed clauses: 124389
% 18.14/3.08 % ...number of literals in the above : 426700
% 18.14/3.08 % Current number of archived formulas : 0
% 18.14/3.08 % Current number of archived clauses : 4008
% 18.14/3.08 % Clause-clause subsumption calls (NU) : 609251
% 18.14/3.08 % Rec. Clause-clause subsumption calls : 284683
% 18.14/3.08 % Non-unit clause-clause subsumptions : 25046
% 18.14/3.08 % Unit Clause-clause subsumption calls : 3999
% 18.14/3.08 % Rewrite failures with RHS unbound : 0
% 18.14/3.08 % BW rewrite match attempts : 144
% 18.14/3.08 % BW rewrite match successes : 97
% 18.14/3.08 % Condensation attempts : 0
% 18.14/3.08 % Condensation successes : 0
% 18.14/3.08 % Termbank termtop insertions : 1639094
% 18.14/3.08 % Search garbage collected termcells : 44
% 18.14/3.08
% 18.14/3.08 % -------------------------------------------------
% 18.14/3.08 % User time : 2.302 s
% 18.14/3.08 % System time : 0.087 s
% 18.14/3.08 % Total time : 2.389 s
% 18.14/3.08 % Maximum resident set size: 3664 pages
% 18.14/3.08
% 18.14/3.08 % -------------------------------------------------
% 18.14/3.08 % User time : 12.401 s
% 18.14/3.08 % System time : 0.466 s
% 18.14/3.08 % Total time : 12.867 s
% 18.14/3.08 % Maximum resident set size: 4864 pages
% 18.14/3.08 % E exiting
%------------------------------------------------------------------------------