%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP239-1 : 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 : n016.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 12:42:58 PM UTC 2026
% Result : Unsatisfiable 35.87s 5.68s
% Output : CNFRefutation 35.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 20
% Syntax : Number of clauses : 111 ( 28 unt; 78 nHn; 92 RR)
% Number of literals : 236 ( 235 equ; 52 neg)
% Maximal clause size : 13 ( 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 : 54 ( 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_16,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_15,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_9,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_8,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_39,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_38,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
cnf(prove_this_17,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_26,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_31,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_27,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_18,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_32,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_43,negated_conjecture,
( multiply(X7,sk_c9) != sk_c8
| inverse(X6) != X7
| multiply(X6,X7) != sk_c8
| inverse(X5) != sk_c8
| multiply(X5,sk_c8) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c9
| inverse(X3) != sk_c9
| multiply(X3,sk_c9) != X2
| multiply(sk_c9,X2) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c9
| inverse(sk_c9) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
cnf(c_0_20,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_21,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_22,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_23,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_24,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
prove_this_16 ).
cnf(c_0_25,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(inverse(sk_c4),sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
prove_this_15 ).
cnf(c_0_27,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_28,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c8
| multiply(inverse(sk_c1),sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_23,c_0_27]) ).
cnf(c_0_29,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
prove_this_9 ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c9,sk_c9) = sk_c8
| multiply(inverse(sk_c4),sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_23,c_0_30]) ).
cnf(c_0_32,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
prove_this_8 ).
cnf(c_0_33,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c9,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_34,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_23,c_0_23]) ).
cnf(c_0_35,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_23,c_0_20]) ).
cnf(c_0_36,negated_conjecture,
multiply(sk_c9,sk_c9) = sk_c8,
inference(spm,[status(thm)],[c_0_28,c_0_33]) ).
cnf(c_0_37,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_21]),c_0_34]) ).
cnf(c_0_38,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c9 ),
prove_this_11 ).
cnf(c_0_39,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
prove_this_39 ).
cnf(c_0_40,negated_conjecture,
multiply(inverse(multiply(X1,sk_c9)),multiply(X1,sk_c8)) = sk_c9,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c9) = sk_c8 ),
prove_this_4 ).
cnf(c_0_42,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_37]),c_0_37]) ).
cnf(c_0_43,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c8,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_21,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c8,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_21,c_0_39]) ).
cnf(c_0_45,negated_conjecture,
inverse(multiply(inverse(sk_c8),sk_c9)) = sk_c9,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_21]),c_0_37]) ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
prove_this_10 ).
cnf(c_0_47,negated_conjecture,
( inverse(sk_c9) = sk_c8
| multiply(sk_c8,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_21,c_0_41]) ).
cnf(c_0_48,negated_conjecture,
( inverse(sk_c9) = sk_c1
| multiply(sk_c8,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
prove_this_38 ).
cnf(c_0_50,negated_conjecture,
( inverse(sk_c9) = sk_c2
| multiply(sk_c8,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_42,c_0_44]) ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
prove_this_17 ).
cnf(c_0_52,negated_conjecture,
multiply(inverse(sk_c9),sk_c8) = sk_c9,
inference(spm,[status(thm)],[c_0_23,c_0_36]) ).
cnf(c_0_53,negated_conjecture,
multiply(inverse(sk_c8),sk_c9) = inverse(sk_c9),
inference(spm,[status(thm)],[c_0_42,c_0_45]) ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c9) = sk_c8 ),
prove_this_3 ).
cnf(c_0_55,negated_conjecture,
( inverse(sk_c9) = sk_c1
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_46]) ).
cnf(c_0_56,negated_conjecture,
( sk_c1 = sk_c8
| multiply(sk_c8,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
prove_this_26 ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
prove_this_31 ).
cnf(c_0_59,negated_conjecture,
( inverse(sk_c9) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_49]) ).
cnf(c_0_60,negated_conjecture,
( sk_c2 = sk_c8
| multiply(sk_c8,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_47,c_0_50]) ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(inverse(sk_c5),sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_23,c_0_51]) ).
cnf(c_0_62,negated_conjecture,
multiply(inverse(sk_c9),multiply(sk_c8,X1)) = multiply(sk_c9,X1),
inference(spm,[status(thm)],[c_0_20,c_0_52]) ).
cnf(c_0_63,negated_conjecture,
multiply(sk_c8,inverse(sk_c9)) = sk_c9,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_53]),c_0_42]) ).
cnf(c_0_64,negated_conjecture,
( sk_c1 = sk_c8
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_65,negated_conjecture,
( sk_c1 = sk_c8
| inverse(sk_c8) = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_56]),c_0_37]) ).
cnf(c_0_66,negated_conjecture,
multiply(sk_c9,multiply(sk_c9,X1)) = multiply(sk_c8,X1),
inference(spm,[status(thm)],[c_0_20,c_0_36]) ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(inverse(sk_c6),sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_23,c_0_57]) ).
cnf(c_0_68,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
prove_this_27 ).
cnf(c_0_69,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(inverse(sk_c5),sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_23,c_0_58]) ).
cnf(c_0_70,negated_conjecture,
( sk_c2 = sk_c8
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_54,c_0_59]) ).
cnf(c_0_71,negated_conjecture,
( sk_c2 = sk_c8
| inverse(sk_c8) = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_60]),c_0_37]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(inverse(sk_c5),multiply(sk_c9,X1)) = multiply(sk_c8,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_61]) ).
cnf(c_0_73,negated_conjecture,
multiply(sk_c9,inverse(sk_c9)) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_21]) ).
cnf(c_0_74,negated_conjecture,
( sk_c1 = sk_c8
| multiply(inverse(sk_c5),sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_23,c_0_64]) ).
cnf(c_0_75,negated_conjecture,
( sk_c1 = sk_c8
| inverse(sk_c5) = sk_c8 ),
inference(spm,[status(thm)],[c_0_42,c_0_65]) ).
cnf(c_0_76,negated_conjecture,
multiply(sk_c8,sk_c9) = multiply(sk_c9,sk_c8),
inference(spm,[status(thm)],[c_0_66,c_0_36]) ).
cnf(c_0_77,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(inverse(sk_c5),multiply(sk_c9,X1)) = multiply(sk_c8,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_69]) ).
cnf(c_0_79,negated_conjecture,
( sk_c2 = sk_c8
| multiply(inverse(sk_c5),sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_23,c_0_70]) ).
cnf(c_0_80,negated_conjecture,
( sk_c2 = sk_c8
| inverse(sk_c5) = sk_c8 ),
inference(spm,[status(thm)],[c_0_42,c_0_71]) ).
cnf(c_0_81,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
prove_this_18 ).
cnf(c_0_82,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_37]),c_0_63]) ).
cnf(c_0_83,negated_conjecture,
( sk_c1 = sk_c8
| multiply(sk_c9,sk_c8) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).
cnf(c_0_84,negated_conjecture,
( identity = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_77]),c_0_21]) ).
cnf(c_0_85,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
prove_this_32 ).
cnf(c_0_86,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_73]),c_0_37]),c_0_63]) ).
cnf(c_0_87,negated_conjecture,
( sk_c2 = sk_c8
| multiply(sk_c9,sk_c8) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_76]) ).
cnf(c_0_88,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_89,negated_conjecture,
( sk_c8 = sk_c9
| sk_c1 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_83]),c_0_52]) ).
cnf(c_0_90,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c9),sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_23,c_0_84]) ).
cnf(c_0_91,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_92,negated_conjecture,
( sk_c8 = sk_c9
| sk_c2 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_87]),c_0_52]) ).
cnf(c_0_93,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c8,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_94,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c3),multiply(sk_c9,X1)) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_90]),c_0_62]) ).
cnf(c_0_95,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c9,sk_c8) = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_76]) ).
cnf(c_0_96,negated_conjecture,
( sk_c8 = sk_c9
| inverse(sk_c9) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_93]),c_0_53]) ).
cnf(c_0_97,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_21,c_0_37]) ).
cnf(c_0_98,negated_conjecture,
( identity = sk_c8
| sk_c8 = sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_21])]) ).
cnf(c_0_99,negated_conjecture,
( sk_c8 = sk_c9
| inverse(sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_96]) ).
cnf(c_0_100,negated_conjecture,
( sk_c8 = sk_c9
| inverse(sk_c8) = sk_c8 ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_101,negated_conjecture,
( multiply(X7,sk_c9) != sk_c8
| inverse(X6) != X7
| multiply(X6,X7) != sk_c8
| inverse(X5) != sk_c8
| multiply(X5,sk_c8) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c9
| inverse(X3) != sk_c9
| multiply(X3,sk_c9) != X2
| multiply(sk_c9,X2) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(fof_simplification,[status(thm)],[prove_this_43]) ).
cnf(c_0_102,negated_conjecture,
sk_c8 = sk_c9,
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_103,negated_conjecture,
( multiply(X7,sk_c9) != sk_c8
| inverse(X6) != X7
| multiply(X6,X7) != sk_c8
| inverse(X5) != sk_c8
| multiply(X5,sk_c8) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c9
| inverse(X3) != sk_c9
| multiply(X3,sk_c9) != X2
| multiply(sk_c9,X2) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c9
| inverse(sk_c9) != sk_c8 ),
c_0_101 ).
cnf(c_0_104,negated_conjecture,
identity = sk_c9,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_102]),c_0_73]) ).
cnf(c_0_105,negated_conjecture,
( inverse(X5) != sk_c9
| inverse(X1) != sk_c9
| inverse(X4) != sk_c9
| inverse(X3) != sk_c8
| inverse(sk_c9) != sk_c8
| multiply(X5,sk_c8) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| multiply(X2,inverse(X2)) != sk_c8
| multiply(inverse(X2),sk_c9) != sk_c8
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_103])]) ).
cnf(c_0_106,plain,
multiply(X1,sk_c9) = X1,
inference(rw,[status(thm)],[c_0_37,c_0_104]) ).
cnf(c_0_107,plain,
multiply(sk_c9,X1) = X1,
inference(rw,[status(thm)],[c_0_22,c_0_104]) ).
cnf(c_0_108,plain,
inverse(sk_c9) = sk_c9,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_104]),c_0_104]) ).
cnf(c_0_109,negated_conjecture,
( inverse(X1) != sk_c9
| multiply(X1,inverse(X1)) != sk_c9 ),
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)],[c_0_105,c_0_102]),c_0_102]),c_0_102]),c_0_102]),c_0_102]),c_0_102]),c_0_102]),c_0_102]),c_0_106]),c_0_107]),c_0_106]),c_0_106]),c_0_106]),c_0_106]),c_0_108])])])])])]),c_0_108])]) ).
cnf(c_0_110,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_108]),c_0_106])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP239-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:11:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 35.87/5.68 % Version: 3.5.1
% 35.87/5.68 % Preprocessing class: FSMSSMSMSSSNFFN.
% 35.87/5.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 35.87/5.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 35.87/5.68 % Starting new_bool_3 with 300s (1) cores
% 35.87/5.68 % Starting new_bool_1 with 300s (1) cores
% 35.87/5.68 % Starting sh5l with 300s (1) cores
% 35.87/5.68 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 689569 completed with status 0
% 35.87/5.68 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 35.87/5.68 % Preprocessing class: FSMSSMSMSSSNFFN.
% 35.87/5.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 35.87/5.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 35.87/5.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 35.87/5.68 % No SInE strategy applied
% 35.87/5.68 % Search class: FGHPS-FFMM21-SFFFFFNN
% 35.87/5.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 35.87/5.68 % Starting SubtermCWHack with 136s (1) cores
% 35.87/5.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 35.87/5.68 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 35.87/5.68 % Starting new_bool_3 with 136s (1) cores
% 35.87/5.68 % Starting new_bool_1 with 136s (1) cores
% 35.87/5.68 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 689574 completed with status 0
% 35.87/5.68 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 35.87/5.68 % Preprocessing class: FSMSSMSMSSSNFFN.
% 35.87/5.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 35.87/5.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 35.87/5.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 35.87/5.68 % No SInE strategy applied
% 35.87/5.68 % Search class: FGHPS-FFMM21-SFFFFFNN
% 35.87/5.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 35.87/5.68 % Starting SubtermCWHack with 136s (1) cores
% 35.87/5.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 35.87/5.68 % Preprocessing time : 0.002 s
% 35.87/5.68 % Presaturation interreduction done
% 35.87/5.68
% 35.87/5.68 % Proof found!
% 35.87/5.68 % SZS status Unsatisfiable
% 35.87/5.68 % SZS output start CNFRefutation
% See solution above
% 35.87/5.68 % Parsed axioms : 46
% 35.87/5.68 % Removed by relevancy pruning/SinE : 0
% 35.87/5.68 % Initial clauses : 46
% 35.87/5.68 % Removed in clause preprocessing : 0
% 35.87/5.68 % Initial clauses in saturation : 46
% 35.87/5.68 % Processed clauses : 33816
% 35.87/5.68 % ...of these trivial : 821
% 35.87/5.68 % ...subsumed : 29473
% 35.87/5.68 % ...remaining for further processing : 3522
% 35.87/5.68 % Other redundant clauses eliminated : 67
% 35.87/5.68 % Clauses deleted for lack of memory : 0
% 35.87/5.68 % Backward-subsumed : 785
% 35.87/5.68 % Backward-rewritten : 2638
% 35.87/5.68 % Generated clauses : 490796
% 35.87/5.68 % ...of the previous two non-redundant : 485636
% 35.87/5.68 % ...aggressively subsumed : 0
% 35.87/5.68 % Contextual simplify-reflections : 32
% 35.87/5.68 % Paramodulations : 490738
% 35.87/5.68 % Factorizations : 17
% 35.87/5.68 % NegExts : 0
% 35.87/5.68 % Equation resolutions : 67
% 35.87/5.68 % Disequality decompositions : 0
% 35.87/5.68 % Total rewrite steps : 210308
% 35.87/5.68 % ...of those cached : 204785
% 35.87/5.68 % Propositional unsat checks : 0
% 35.87/5.68 % Propositional check models : 0
% 35.87/5.68 % Propositional check unsatisfiable : 0
% 35.87/5.68 % Propositional clauses : 0
% 35.87/5.68 % Propositional clauses after purity: 0
% 35.87/5.68 % Propositional unsat core size : 0
% 35.87/5.68 % Propositional preprocessing time : 0.000
% 35.87/5.68 % Propositional encoding time : 0.000
% 35.87/5.68 % Propositional solver time : 0.000
% 35.87/5.68 % Success case prop preproc time : 0.000
% 35.87/5.68 % Success case prop encoding time : 0.000
% 35.87/5.68 % Success case prop solver time : 0.000
% 35.87/5.68 % Current number of processed clauses : 38
% 35.87/5.68 % Positive orientable unit clauses : 19
% 35.87/5.68 % Positive unorientable unit clauses: 0
% 35.87/5.68 % Negative unit clauses : 0
% 35.87/5.68 % Non-unit-clauses : 19
% 35.87/5.68 % Current number of unprocessed clauses: 79885
% 35.87/5.68 % ...number of literals in the above : 267836
% 35.87/5.68 % Current number of archived formulas : 0
% 35.87/5.68 % Current number of archived clauses : 3469
% 35.87/5.68 % Clause-clause subsumption calls (NU) : 439557
% 35.87/5.68 % Rec. Clause-clause subsumption calls : 317348
% 35.87/5.68 % Non-unit clause-clause subsumptions : 30262
% 35.87/5.68 % Unit Clause-clause subsumption calls : 4110
% 35.87/5.68 % Rewrite failures with RHS unbound : 0
% 35.87/5.68 % BW rewrite match attempts : 188
% 35.87/5.68 % BW rewrite match successes : 92
% 35.87/5.68 % Condensation attempts : 0
% 35.87/5.68 % Condensation successes : 0
% 35.87/5.68 % Termbank termtop insertions : 5589035
% 35.87/5.68 % Search garbage collected termcells : 37
% 35.87/5.68
% 35.87/5.68 % -------------------------------------------------
% 35.87/5.68 % User time : 4.815 s
% 35.87/5.68 % System time : 0.288 s
% 35.87/5.68 % Total time : 5.102 s
% 35.87/5.68 % Maximum resident set size: 3656 pages
% 35.87/5.68
% 35.87/5.68 % -------------------------------------------------
% 35.87/5.68 % User time : 24.104 s
% 35.87/5.68 % System time : 1.396 s
% 35.87/5.68 % Total time : 25.500 s
% 35.87/5.68 % Maximum resident set size: 4608 pages
% 35.87/5.68 % E exiting
%------------------------------------------------------------------------------