%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP242-1 : 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 : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:39:04 PM UTC 2026
% Result : Unsatisfiable 19.38s 2.99s
% Output : CNFRefutation 19.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 25
% Syntax : Number of clauses : 128 ( 20 unt; 101 nHn; 111 RR)
% Number of literals : 298 ( 297 equ; 69 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 : 58 ( 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_10,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_8,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_22,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_17,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_27,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| multiply(sk_c3,sk_c6) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_20,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_33,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_16,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_37,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c6,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_18,negated_conjecture,
( inverse(sk_c8) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_24,negated_conjecture,
( inverse(sk_c8) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_28,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c3,sk_c6) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_34,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_61,negated_conjecture,
( inverse(X8) != sk_c11
| multiply(X8,sk_c11) != sk_c9
| inverse(X7) != sk_c10
| multiply(X7,sk_c10) != sk_c11
| inverse(sk_c10) != sk_c9
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(X5,X4) != X6
| inverse(X6) != X4
| inverse(X5) != X6
| multiply(X4,sk_c10) != sk_c11
| inverse(X3) != X4
| multiply(X3,X4) != sk_c11
| inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_61) ).
cnf(c_0_25,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_26,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_27,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_28,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_29,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_28,c_0_28]) ).
cnf(c_0_30,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_26]),c_0_29]) ).
cnf(c_0_31,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_30]) ).
cnf(c_0_32,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c11 ),
prove_this_10 ).
cnf(c_0_33,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
prove_this_4 ).
cnf(c_0_34,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c1) = sk_c11 ),
prove_this_8 ).
cnf(c_0_35,negated_conjecture,
( inverse(sk_c11) = sk_c1
| inverse(sk_c7) = sk_c10 ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c10 ),
prove_this_2 ).
cnf(c_0_37,negated_conjecture,
( inverse(sk_c10) = sk_c7
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_31,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( inverse(sk_c11) = sk_c1
| inverse(sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_31,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
( inverse(sk_c10) = sk_c7
| inverse(sk_c11) = sk_c1 ),
inference(spm,[status(thm)],[c_0_31,c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( sk_c7 = sk_c9
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
( sk_c7 = sk_c9
| inverse(sk_c11) = sk_c1 ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c2) = sk_c10 ),
prove_this_22 ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
prove_this_17 ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| multiply(sk_c3,sk_c6) = sk_c11 ),
prove_this_27 ).
cnf(c_0_45,negated_conjecture,
( sk_c7 = sk_c9
| multiply(inverse(sk_c1),sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_28,c_0_40]) ).
cnf(c_0_46,negated_conjecture,
( sk_c7 = sk_c9
| inverse(sk_c1) = sk_c11 ),
inference(spm,[status(thm)],[c_0_31,c_0_41]) ).
cnf(c_0_47,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
prove_this_20 ).
cnf(c_0_48,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c10,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_42]) ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c9
| multiply(inverse(sk_c2),sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_28,c_0_43]) ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c9
| inverse(sk_c2) = sk_c10 ),
prove_this_23 ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| multiply(inverse(sk_c3),sk_c11) = sk_c6 ),
inference(spm,[status(thm)],[c_0_28,c_0_44]) ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c6 ),
prove_this_33 ).
cnf(c_0_53,negated_conjecture,
( sk_c7 = sk_c9
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_54,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c10,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_47]) ).
cnf(c_0_55,negated_conjecture,
( inverse(sk_c10) = sk_c7
| multiply(sk_c10,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_31,c_0_48]) ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
prove_this_13 ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| multiply(sk_c8,sk_c11) = sk_c9 ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c6
| multiply(sk_c7,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_59,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
prove_this_16 ).
cnf(c_0_60,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_26,c_0_30]) ).
cnf(c_0_61,negated_conjecture,
( identity = sk_c10
| sk_c7 = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_53]),c_0_26]) ).
cnf(c_0_62,negated_conjecture,
( sk_c7 = sk_c9
| multiply(sk_c10,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c6,sk_c10) = sk_c11 ),
prove_this_37 ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(inverse(sk_c2),sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_28,c_0_56]) ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c2) = sk_c10 ),
prove_this_19 ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| multiply(inverse(sk_c8),sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_28,c_0_57]) ).
cnf(c_0_67,negated_conjecture,
( inverse(sk_c8) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
prove_this_18 ).
cnf(c_0_68,negated_conjecture,
( inverse(sk_c8) = sk_c11
| inverse(sk_c2) = sk_c10 ),
prove_this_24 ).
cnf(c_0_69,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c6
| multiply(inverse(sk_c7),sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_28,c_0_58]) ).
cnf(c_0_70,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c3,sk_c6) = sk_c11 ),
prove_this_28 ).
cnf(c_0_71,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c3) = sk_c6 ),
prove_this_34 ).
cnf(c_0_72,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
prove_this_14 ).
cnf(c_0_73,negated_conjecture,
( inverse(sk_c10) = sk_c7
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_31,c_0_59]) ).
cnf(c_0_74,negated_conjecture,
( sk_c7 = sk_c9
| inverse(sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_75,negated_conjecture,
( sk_c7 = sk_c9
| inverse(sk_c10) = sk_c2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_62]),c_0_30]) ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c6,multiply(sk_c10,X1)) = multiply(sk_c11,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_63]) ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_78,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_28,c_0_25]) ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_80,negated_conjecture,
( inverse(sk_c8) = sk_c11
| multiply(sk_c10,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_68]) ).
cnf(c_0_81,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c10
| multiply(sk_c6,sk_c11) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c11 ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_82,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c6,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_71]) ).
cnf(c_0_83,negated_conjecture,
( sk_c7 = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_84,negated_conjecture,
( sk_c2 = sk_c10
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_85,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c6,sk_c10) = multiply(sk_c11,sk_c9) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_86,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c11
| multiply(inverse(multiply(X1,sk_c2)),multiply(X1,sk_c9)) = sk_c10 ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_87,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c10
| multiply(sk_c10,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_66,c_0_80]) ).
cnf(c_0_88,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c6
| multiply(sk_c10,sk_c11) = sk_c10
| multiply(inverse(multiply(X1,sk_c3)),multiply(X1,sk_c11)) = sk_c6 ),
inference(spm,[status(thm)],[c_0_78,c_0_81]) ).
cnf(c_0_89,negated_conjecture,
( multiply(sk_c10,sk_c11) = sk_c10
| multiply(sk_c6,sk_c11) = sk_c6
| multiply(sk_c6,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_69,c_0_82]) ).
cnf(c_0_90,negated_conjecture,
( sk_c7 = sk_c9
| multiply(sk_c10,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_74]) ).
cnf(c_0_91,negated_conjecture,
( sk_c7 = sk_c9
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_92,negated_conjecture,
( sk_c7 = sk_c9
| multiply(sk_c10,X1) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_53]),c_0_28]) ).
cnf(c_0_93,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_63,c_0_85]) ).
cnf(c_0_94,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_60]),c_0_27])]) ).
cnf(c_0_95,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c6
| multiply(sk_c10,sk_c11) = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_60]),c_0_27])]) ).
cnf(c_0_96,negated_conjecture,
( identity = sk_c9
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_97,negated_conjecture,
( identity = sk_c2
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_62,c_0_92]) ).
cnf(c_0_98,negated_conjecture,
( sk_c10 = sk_c11
| multiply(sk_c11,sk_c9) = sk_c11 ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_99,negated_conjecture,
( identity = sk_c11
| multiply(sk_c10,sk_c11) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_95]),c_0_26]) ).
cnf(c_0_100,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
prove_this_1 ).
cnf(c_0_101,negated_conjecture,
( sk_c7 = sk_c9
| inverse(sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_31,c_0_75]) ).
cnf(c_0_102,negated_conjecture,
( sk_c7 = sk_c9
| sk_c2 = sk_c9 ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_103,negated_conjecture,
( identity = sk_c9
| sk_c10 = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_98]),c_0_26]) ).
cnf(c_0_104,negated_conjecture,
identity = sk_c11,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_99]),c_0_26])]) ).
cnf(c_0_105,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(inverse(sk_c1),sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_28,c_0_100]) ).
cnf(c_0_106,negated_conjecture,
( sk_c7 = sk_c9
| inverse(sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_107,negated_conjecture,
( sk_c10 = sk_c11
| sk_c9 = sk_c11 ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_108,plain,
inverse(sk_c11) = sk_c11,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_104]),c_0_104]) ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(inverse(inverse(sk_c1)),sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_28,c_0_105]) ).
cnf(c_0_110,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c1) = sk_c11 ),
prove_this_7 ).
cnf(c_0_111,negated_conjecture,
( sk_c10 = sk_c11
| sk_c7 = sk_c11 ),
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,
( identity = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_26]) ).
cnf(c_0_113,negated_conjecture,
( sk_c10 != sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(ef,[status(thm)],[c_0_77]) ).
cnf(c_0_114,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c10,multiply(sk_c2,X1)) = X1 ),
inference(spm,[status(thm)],[c_0_28,c_0_42]) ).
cnf(c_0_115,negated_conjecture,
( sk_c10 = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_111]),c_0_108])]) ).
cnf(c_0_116,negated_conjecture,
multiply(sk_c10,sk_c9) = sk_c11,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_104]),c_0_113]) ).
cnf(c_0_117,negated_conjecture,
( sk_c10 = sk_c11
| inverse(sk_c7) = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_116])]) ).
cnf(c_0_118,negated_conjecture,
( inverse(X8) != sk_c11
| multiply(X8,sk_c11) != sk_c9
| inverse(X7) != sk_c10
| multiply(X7,sk_c10) != sk_c11
| inverse(sk_c10) != sk_c9
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(X5,X4) != X6
| inverse(X6) != X4
| inverse(X5) != X6
| multiply(X4,sk_c10) != sk_c11
| inverse(X3) != X4
| multiply(X3,X4) != sk_c11
| inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10 ),
inference(fof_simplification,[status(thm)],[prove_this_61]) ).
cnf(c_0_119,negated_conjecture,
sk_c10 = sk_c11,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_111]),c_0_108])]) ).
cnf(c_0_120,negated_conjecture,
( inverse(X8) != sk_c11
| multiply(X8,sk_c11) != sk_c9
| inverse(X7) != sk_c10
| multiply(X7,sk_c10) != sk_c11
| inverse(sk_c10) != sk_c9
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(X5,X4) != X6
| inverse(X6) != X4
| inverse(X5) != X6
| multiply(X4,sk_c10) != sk_c11
| inverse(X3) != X4
| multiply(X3,X4) != sk_c11
| inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10 ),
c_0_118 ).
cnf(c_0_121,negated_conjecture,
multiply(sk_c11,sk_c9) = sk_c11,
inference(rw,[status(thm)],[c_0_116,c_0_119]) ).
cnf(c_0_122,negated_conjecture,
( inverse(X6) != sk_c11
| inverse(X5) != sk_c10
| inverse(X4) != sk_c10
| inverse(X3) != sk_c11
| inverse(sk_c10) != sk_c9
| multiply(X6,sk_c11) != sk_c10
| multiply(X5,sk_c10) != sk_c9
| multiply(X4,sk_c10) != sk_c11
| multiply(X3,sk_c11) != sk_c9
| multiply(X2,inverse(X2)) != sk_c11
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(X1,inverse(X2)) != inverse(X1)
| multiply(inverse(X2),sk_c10) != sk_c11
| inverse(multiply(X1,inverse(X2))) != inverse(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_120])]) ).
cnf(c_0_123,plain,
multiply(X1,sk_c11) = X1,
inference(rw,[status(thm)],[c_0_30,c_0_104]) ).
cnf(c_0_124,negated_conjecture,
sk_c9 = sk_c11,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_121]),c_0_26]),c_0_104]) ).
cnf(c_0_125,negated_conjecture,
( inverse(X2) != sk_c11
| multiply(X2,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(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(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_116])]),c_0_119]),c_0_123]),c_0_123]),c_0_124]),c_0_119]),c_0_123]),c_0_119]),c_0_123]),c_0_124]),c_0_123]),c_0_119]),c_0_119]),c_0_108]),c_0_124]),c_0_119]),c_0_119])])])])])]),c_0_108])]) ).
cnf(c_0_126,negated_conjecture,
( inverse(X1) != X1
| 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_125,c_0_108]),c_0_123]),c_0_123]),c_0_123])]) ).
cnf(c_0_127,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_126,c_0_108]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP242-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 % Computer : n006.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sun Sep 20 20:06:42 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 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
% 19.38/2.99 % Version: 3.5.1
% 19.38/2.99 % Preprocessing class: FSMSSMSMSSSNFFN.
% 19.38/2.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.38/2.99 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 19.38/2.99 % Starting new_bool_3 with 300s (1) cores
% 19.38/2.99 % Starting new_bool_1 with 300s (1) cores
% 19.38/2.99 % Starting sh5l with 300s (1) cores
% 19.38/2.99 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1149015 completed with status 0
% 19.38/2.99 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 19.38/2.99 % Preprocessing class: FSMSSMSMSSSNFFN.
% 19.38/2.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.38/2.99 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 19.38/2.99 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 19.38/2.99 % No SInE strategy applied
% 19.38/2.99 % Search class: FGHPS-FFMM21-SFFFFFNN
% 19.38/2.99 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 19.38/2.99 % Starting SubtermCWHack with 136s (1) cores
% 19.38/2.99 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 19.38/2.99 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 19.38/2.99 % Starting new_bool_3 with 136s (1) cores
% 19.38/2.99 % Starting new_bool_1 with 136s (1) cores
% 19.38/2.99 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1149021 completed with status 0
% 19.38/2.99 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 19.38/2.99 % Preprocessing class: FSMSSMSMSSSNFFN.
% 19.38/2.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.38/2.99 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 19.38/2.99 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 19.38/2.99 % No SInE strategy applied
% 19.38/2.99 % Search class: FGHPS-FFMM21-SFFFFFNN
% 19.38/2.99 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 19.38/2.99 % Starting SubtermCWHack with 136s (1) cores
% 19.38/2.99 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 19.38/2.99 % Preprocessing time : 0.002 s
% 19.38/2.99 % Presaturation interreduction done
% 19.38/2.99
% 19.38/2.99 % Proof found!
% 19.38/2.99 % SZS status Unsatisfiable
% 19.38/2.99 % SZS output start CNFRefutation
% See solution above
% 19.38/2.99 % Parsed axioms : 64
% 19.38/2.99 % Removed by relevancy pruning/SinE : 0
% 19.38/2.99 % Initial clauses : 64
% 19.38/2.99 % Removed in clause preprocessing : 0
% 19.38/2.99 % Initial clauses in saturation : 64
% 19.38/2.99 % Processed clauses : 24967
% 19.38/2.99 % ...of these trivial : 590
% 19.38/2.99 % ...subsumed : 21037
% 19.38/2.99 % ...remaining for further processing : 3340
% 19.38/2.99 % Other redundant clauses eliminated : 161
% 19.38/2.99 % Clauses deleted for lack of memory : 0
% 19.38/2.99 % Backward-subsumed : 418
% 19.38/2.99 % Backward-rewritten : 2670
% 19.38/2.99 % Generated clauses : 194248
% 19.38/2.99 % ...of the previous two non-redundant : 192424
% 19.38/2.99 % ...aggressively subsumed : 0
% 19.38/2.99 % Contextual simplify-reflections : 65
% 19.38/2.99 % Paramodulations : 194091
% 19.38/2.99 % Factorizations : 6
% 19.38/2.99 % NegExts : 0
% 19.38/2.99 % Equation resolutions : 161
% 19.38/2.99 % Disequality decompositions : 0
% 19.38/2.99 % Total rewrite steps : 57725
% 19.38/2.99 % ...of those cached : 55527
% 19.38/2.99 % Propositional unsat checks : 0
% 19.38/2.99 % Propositional check models : 0
% 19.38/2.99 % Propositional check unsatisfiable : 0
% 19.38/2.99 % Propositional clauses : 0
% 19.38/2.99 % Propositional clauses after purity: 0
% 19.38/2.99 % Propositional unsat core size : 0
% 19.38/2.99 % Propositional preprocessing time : 0.000
% 19.38/2.99 % Propositional encoding time : 0.000
% 19.38/2.99 % Propositional solver time : 0.000
% 19.38/2.99 % Success case prop preproc time : 0.000
% 19.38/2.99 % Success case prop encoding time : 0.000
% 19.38/2.99 % Success case prop solver time : 0.000
% 19.38/2.99 % Current number of processed clauses : 134
% 19.38/2.99 % Positive orientable unit clauses : 20
% 19.38/2.99 % Positive unorientable unit clauses: 0
% 19.38/2.99 % Negative unit clauses : 0
% 19.38/2.99 % Non-unit-clauses : 114
% 19.38/2.99 % Current number of unprocessed clauses: 162976
% 19.38/2.99 % ...number of literals in the above : 575746
% 19.38/2.99 % Current number of archived formulas : 0
% 19.38/2.99 % Current number of archived clauses : 3152
% 19.38/2.99 % Clause-clause subsumption calls (NU) : 439119
% 19.38/2.99 % Rec. Clause-clause subsumption calls : 247331
% 19.38/2.99 % Non-unit clause-clause subsumptions : 21470
% 19.38/2.99 % Unit Clause-clause subsumption calls : 3334
% 19.38/2.99 % Rewrite failures with RHS unbound : 0
% 19.38/2.99 % BW rewrite match attempts : 188
% 19.38/2.99 % BW rewrite match successes : 79
% 19.38/2.99 % Condensation attempts : 0
% 19.38/2.99 % Condensation successes : 0
% 19.38/2.99 % Termbank termtop insertions : 2281174
% 19.38/2.99 % Search garbage collected termcells : 45
% 19.38/2.99
% 19.38/2.99 % -------------------------------------------------
% 19.38/2.99 % User time : 2.359 s
% 19.38/2.99 % System time : 0.100 s
% 19.38/2.99 % Total time : 2.459 s
% 19.38/2.99 % Maximum resident set size: 3664 pages
% 19.38/2.99
% 19.38/2.99 % -------------------------------------------------
% 19.38/2.99 % User time : 11.882 s
% 19.38/2.99 % System time : 0.517 s
% 19.38/2.99 % Total time : 12.399 s
% 19.38/2.99 % Maximum resident set size: 4864 pages
% 19.38/2.99 % E exiting
%------------------------------------------------------------------------------