%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP232-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:39:02 PM UTC 2026
% Result : Unsatisfiable 2.11s 0.72s
% Output : CNFRefutation 2.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 24
% Syntax : Number of clauses : 146 ( 21 unt; 106 nHn; 132 RR)
% Number of literals : 369 ( 368 equ; 119 neg)
% Maximal clause size : 11 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 76 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_1,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_15,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_5,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_31,negated_conjecture,
( inverse(X6) != sk_c8
| multiply(X6,sk_c8) != X5
| multiply(sk_c8,X5) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(X4) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(X2) != X3
| multiply(X2,X3) != sk_c8
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_10,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_6,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_14,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_18,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_24,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_17,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_22,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_8,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_12,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_2,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
cnf(c_0_24,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_25,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_26,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_27,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_28,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_27,c_0_27]) ).
cnf(c_0_29,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_25]),c_0_28]) ).
cnf(c_0_30,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_29]) ).
cnf(c_0_31,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
prove_this_11 ).
cnf(c_0_32,negated_conjecture,
( inverse(sk_c8) = sk_c1
| inverse(sk_c4) = sk_c8 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c7 ),
prove_this_1 ).
cnf(c_0_34,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
prove_this_15 ).
cnf(c_0_35,negated_conjecture,
( inverse(sk_c8) = sk_c4
| inverse(sk_c8) = sk_c1 ),
inference(spm,[status(thm)],[c_0_30,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c8) = sk_c7 ),
prove_this_5 ).
cnf(c_0_37,negated_conjecture,
( inverse(sk_c8) = sk_c4
| inverse(sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_30,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( inverse(sk_c8) = sk_c1
| inverse(sk_c5) = sk_c8 ),
inference(spm,[status(thm)],[c_0_30,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
( sk_c1 != sk_c4
| inverse(sk_c8) = sk_c4 ),
inference(ef,[status(thm)],[c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( inverse(sk_c8) = sk_c5
| inverse(sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_30,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
( sk_c4 != sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(ef,[status(thm)],[c_0_37]) ).
cnf(c_0_42,negated_conjecture,
( inverse(X6) != sk_c8
| multiply(X6,sk_c8) != X5
| multiply(sk_c8,X5) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(X4) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(X2) != X3
| multiply(X2,X3) != sk_c8
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7 ),
inference(fof_simplification,[status(thm)],[prove_this_31]) ).
cnf(c_0_43,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
prove_this_10 ).
cnf(c_0_44,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
prove_this_6 ).
cnf(c_0_45,negated_conjecture,
( inverse(sk_c8) = sk_c5
| inverse(sk_c8) = sk_c1 ),
inference(spm,[status(thm)],[c_0_30,c_0_38]) ).
cnf(c_0_46,negated_conjecture,
( sk_c1 = sk_c7
| inverse(sk_c8) = sk_c4 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_35]),c_0_39]) ).
cnf(c_0_47,negated_conjecture,
( sk_c5 = sk_c4
| inverse(sk_c8) = sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_37]),c_0_41]) ).
cnf(c_0_48,negated_conjecture,
( inverse(X6) != sk_c8
| multiply(X6,sk_c8) != X5
| multiply(sk_c8,X5) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(X4) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(X2) != X3
| multiply(X2,X3) != sk_c8
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7 ),
c_0_42 ).
cnf(c_0_49,negated_conjecture,
( inverse(sk_c8) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_30,c_0_43]) ).
cnf(c_0_50,negated_conjecture,
( inverse(sk_c8) = sk_c4
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_30,c_0_44]) ).
cnf(c_0_51,negated_conjecture,
( sk_c1 = sk_c4
| sk_c5 = sk_c4
| sk_c1 = sk_c7 ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,negated_conjecture,
( sk_c1 = sk_c7
| sk_c4 = sk_c7
| sk_c5 = sk_c4 ),
inference(spm,[status(thm)],[c_0_35,c_0_47]) ).
cnf(c_0_53,negated_conjecture,
( inverse(X4) != sk_c8
| inverse(X3) != sk_c8
| inverse(X1) != sk_c8
| inverse(sk_c8) != sk_c7
| multiply(X4,sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(X2,inverse(X2)) != sk_c8
| multiply(inverse(X2),sk_c7) != sk_c8
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_48])]) ).
cnf(c_0_54,negated_conjecture,
( sk_c5 = sk_c4
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_55,negated_conjecture,
( sk_c1 = sk_c7
| sk_c5 = sk_c4 ),
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_51]),c_0_52]) ).
cnf(c_0_56,negated_conjecture,
( inverse(X4) != sk_c8
| inverse(X3) != sk_c8
| inverse(X1) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(X2,inverse(X2)) != sk_c8
| multiply(inverse(X2),sk_c7) != sk_c8
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| sk_c5 = sk_c4 ),
inference(spm,[status(thm)],[c_0_53,c_0_47]) ).
cnf(c_0_57,negated_conjecture,
( sk_c5 = sk_c4
| inverse(sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_30,c_0_47]) ).
cnf(c_0_58,negated_conjecture,
( sk_c5 = sk_c4
| multiply(sk_c7,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_59,negated_conjecture,
( inverse(X3) != sk_c8
| inverse(X2) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| multiply(X1,inverse(X1)) != sk_c8
| multiply(inverse(X1),sk_c7) != sk_c8
| multiply(sk_c8,multiply(sk_c7,sk_c8)) != sk_c7
| sk_c5 = sk_c4 ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_60,negated_conjecture,
( sk_c5 = sk_c4
| multiply(sk_c7,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_25,c_0_47]) ).
cnf(c_0_61,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_25,c_0_29]) ).
cnf(c_0_62,negated_conjecture,
( identity = sk_c8
| sk_c5 = sk_c4 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_58]),c_0_25]) ).
cnf(c_0_63,negated_conjecture,
( inverse(X3) != sk_c8
| inverse(X2) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| multiply(X1,inverse(X1)) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c7
| multiply(inverse(X1),sk_c7) != sk_c8
| sk_c5 = sk_c4 ),
inference(spm,[status(thm)],[c_0_59,c_0_58]) ).
cnf(c_0_64,negated_conjecture,
( sk_c5 = sk_c4
| multiply(sk_c8,sk_c7) = identity ),
inference(spm,[status(thm)],[c_0_25,c_0_57]) ).
cnf(c_0_65,negated_conjecture,
( identity = sk_c7
| sk_c5 = sk_c4 ),
inference(spm,[status(thm)],[c_0_58,c_0_60]) ).
cnf(c_0_66,negated_conjecture,
( sk_c5 = sk_c4
| inverse(sk_c8) = sk_c8 ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
prove_this_13 ).
cnf(c_0_68,negated_conjecture,
( inverse(X3) != sk_c8
| inverse(X2) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| multiply(X1,inverse(X1)) != sk_c8
| multiply(inverse(X1),sk_c7) != sk_c8
| sk_c5 = sk_c4 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]) ).
cnf(c_0_69,negated_conjecture,
( sk_c7 = sk_c8
| sk_c5 = sk_c4 ),
inference(spm,[status(thm)],[c_0_47,c_0_66]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c8) = sk_c7 ),
prove_this_3 ).
cnf(c_0_71,negated_conjecture,
( inverse(sk_c8) = sk_c1
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_30,c_0_67]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
prove_this_14 ).
cnf(c_0_73,negated_conjecture,
( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(X1,inverse(X1)) != sk_c8
| multiply(inverse(X1),sk_c7) != sk_c8
| sk_c5 = sk_c4 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_61]),c_0_26]),c_0_62]),c_0_69]) ).
cnf(c_0_74,negated_conjecture,
( sk_c1 = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_75,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c7 ),
prove_this_4 ).
cnf(c_0_76,negated_conjecture,
( inverse(sk_c8) = sk_c1
| multiply(sk_c5,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_30,c_0_72]) ).
cnf(c_0_77,negated_conjecture,
( multiply(X1,inverse(X1)) != sk_c8
| multiply(inverse(X1),sk_c7) != sk_c8
| sk_c5 = sk_c4 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_30])]),c_0_25]),c_0_65]) ).
cnf(c_0_78,negated_conjecture,
( sk_c1 = sk_c7
| multiply(inverse(sk_c8),sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_27,c_0_74]) ).
cnf(c_0_79,negated_conjecture,
( sk_c1 = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_80,negated_conjecture,
sk_c5 = sk_c4,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_61]),c_0_26]),c_0_29]),c_0_62]),c_0_69]) ).
cnf(c_0_81,negated_conjecture,
( sk_c1 = sk_c7
| multiply(sk_c4,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_78,c_0_46]) ).
cnf(c_0_82,negated_conjecture,
( sk_c1 = sk_c7
| multiply(sk_c4,sk_c8) = sk_c6 ),
inference(rw,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c8 ),
prove_this_19 ).
cnf(c_0_84,negated_conjecture,
( multiply(sk_c8,sk_c4) = identity
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_25,c_0_44]) ).
cnf(c_0_85,negated_conjecture,
( sk_c1 = sk_c7
| multiply(inverse(sk_c4),sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_27,c_0_81]) ).
cnf(c_0_86,negated_conjecture,
( sk_c1 = sk_c7
| multiply(inverse(sk_c4),sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_27,c_0_82]) ).
cnf(c_0_87,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c8 ),
prove_this_18 ).
cnf(c_0_88,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(inverse(sk_c2),sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_27,c_0_83]) ).
cnf(c_0_89,negated_conjecture,
( multiply(sk_c8,sk_c4) = identity
| multiply(inverse(sk_c1),sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_27,c_0_84]) ).
cnf(c_0_90,negated_conjecture,
( sk_c7 = sk_c8
| sk_c1 = sk_c7 ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_91,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(inverse(sk_c2),sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_27,c_0_87]) ).
cnf(c_0_92,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
prove_this_23 ).
cnf(c_0_93,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(inverse(inverse(sk_c2)),sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_27,c_0_88]) ).
cnf(c_0_94,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c3 ),
prove_this_24 ).
cnf(c_0_95,negated_conjecture,
( identity = sk_c8
| sk_c7 = sk_c8
| multiply(sk_c8,sk_c4) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_25]) ).
cnf(c_0_96,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
prove_this_17 ).
cnf(c_0_97,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c3
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_98,negated_conjecture,
( identity = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_25]) ).
cnf(c_0_99,negated_conjecture,
( sk_c7 = sk_c8
| identity = sk_c8
| inverse(sk_c8) = sk_c4 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_95]),c_0_29]) ).
cnf(c_0_100,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(inverse(sk_c2),sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_27,c_0_96]) ).
cnf(c_0_101,negated_conjecture,
( identity = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_97]),c_0_25]) ).
cnf(c_0_102,negated_conjecture,
( identity = sk_c8
| multiply(sk_c4,sk_c8) = sk_c6 ),
inference(rw,[status(thm)],[c_0_98,c_0_80]) ).
cnf(c_0_103,negated_conjecture,
( identity = sk_c8
| sk_c7 = sk_c8
| multiply(sk_c4,sk_c8) = identity ),
inference(spm,[status(thm)],[c_0_25,c_0_99]) ).
cnf(c_0_104,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
prove_this_7 ).
cnf(c_0_105,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(inverse(inverse(sk_c2)),sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_27,c_0_100]) ).
cnf(c_0_106,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
prove_this_22 ).
cnf(c_0_107,negated_conjecture,
( identity = sk_c8
| multiply(inverse(sk_c8),sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_27,c_0_101]) ).
cnf(c_0_108,negated_conjecture,
( identity = sk_c6
| identity = sk_c8
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(inverse(sk_c1),sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_27,c_0_104]) ).
cnf(c_0_110,negated_conjecture,
( identity = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_25]) ).
cnf(c_0_111,negated_conjecture,
( identity = sk_c8
| sk_c7 = sk_c8
| multiply(sk_c4,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_107,c_0_99]) ).
cnf(c_0_112,negated_conjecture,
( sk_c6 != sk_c8
| sk_c7 = sk_c8
| identity = sk_c8 ),
inference(ef,[status(thm)],[c_0_108]) ).
cnf(c_0_113,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
prove_this_8 ).
cnf(c_0_114,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(inverse(inverse(sk_c1)),sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_27,c_0_109]) ).
cnf(c_0_115,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
prove_this_12 ).
cnf(c_0_116,negated_conjecture,
( identity = sk_c8
| sk_c7 = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112]) ).
cnf(c_0_117,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(inverse(sk_c1),sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_27,c_0_113]) ).
cnf(c_0_118,negated_conjecture,
( identity = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_25]) ).
cnf(c_0_119,negated_conjecture,
( sk_c7 = sk_c8
| inverse(sk_c8) = sk_c8 ),
inference(spm,[status(thm)],[c_0_61,c_0_116]) ).
cnf(c_0_120,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(inverse(inverse(sk_c1)),sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_27,c_0_117]) ).
cnf(c_0_121,negated_conjecture,
( identity = sk_c7
| multiply(inverse(sk_c4),sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_27,c_0_118]) ).
cnf(c_0_122,negated_conjecture,
( sk_c7 = sk_c8
| sk_c4 = sk_c8 ),
inference(spm,[status(thm)],[c_0_37,c_0_119]) ).
cnf(c_0_123,negated_conjecture,
( identity = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_67]),c_0_25]) ).
cnf(c_0_124,negated_conjecture,
( identity = sk_c7
| sk_c7 = sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_25])]) ).
cnf(c_0_125,negated_conjecture,
( identity = sk_c7
| multiply(inverse(sk_c8),sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_27,c_0_123]) ).
cnf(c_0_126,negated_conjecture,
sk_c7 = sk_c8,
inference(spm,[status(thm)],[c_0_116,c_0_124]) ).
cnf(c_0_127,negated_conjecture,
( identity = sk_c6
| identity = sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_126]),c_0_25]),c_0_126]) ).
cnf(c_0_128,negated_conjecture,
( identity = sk_c8
| multiply(sk_c4,sk_c8) = sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_126]),c_0_126]) ).
cnf(c_0_129,negated_conjecture,
( sk_c6 != sk_c8
| identity = sk_c8 ),
inference(ef,[status(thm)],[c_0_127]) ).
cnf(c_0_130,negated_conjecture,
( sk_c5 != sk_c7
| inverse(X4) != sk_c8
| inverse(X3) != sk_c8
| inverse(X1) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(X2,inverse(X2)) != sk_c8
| multiply(inverse(X2),sk_c7) != sk_c8
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_40]),c_0_53]) ).
cnf(c_0_131,negated_conjecture,
identity = sk_c8,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_128]),c_0_129]) ).
cnf(c_0_132,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c7 ),
prove_this_2 ).
cnf(c_0_133,negated_conjecture,
( sk_c4 != sk_c7
| inverse(X4) != sk_c8
| inverse(X3) != sk_c8
| inverse(X1) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(X2,inverse(X2)) != sk_c8
| multiply(inverse(X2),sk_c7) != sk_c8
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7 ),
inference(rw,[status(thm)],[c_0_130,c_0_80]) ).
cnf(c_0_134,plain,
multiply(X1,sk_c8) = X1,
inference(rw,[status(thm)],[c_0_29,c_0_131]) ).
cnf(c_0_135,plain,
multiply(sk_c8,X1) = X1,
inference(rw,[status(thm)],[c_0_26,c_0_131]) ).
cnf(c_0_136,plain,
inverse(sk_c8) = sk_c8,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_131]),c_0_131]) ).
cnf(c_0_137,plain,
multiply(inverse(X1),X1) = sk_c8,
inference(rw,[status(thm)],[c_0_25,c_0_131]) ).
cnf(c_0_138,negated_conjecture,
( inverse(X4) != sk_c8
| inverse(X3) != sk_c8
| inverse(X1) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(X2,inverse(X2)) != sk_c8
| multiply(inverse(X2),sk_c7) != sk_c8
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_53,c_0_132]) ).
cnf(c_0_139,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_30,c_0_132]) ).
cnf(c_0_140,negated_conjecture,
( sk_c4 != sk_c8
| inverse(X1) != sk_c8
| multiply(X1,inverse(X1)) != sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(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_133,c_0_126]),c_0_126]),c_0_126]),c_0_126]),c_0_126]),c_0_134]),c_0_135]),c_0_134]),c_0_134]),c_0_134])])])]),c_0_136])]) ).
cnf(c_0_141,plain,
multiply(X1,inverse(X1)) = sk_c8,
inference(spm,[status(thm)],[c_0_137,c_0_30]) ).
cnf(c_0_142,negated_conjecture,
( inverse(X3) != sk_c8
| inverse(X2) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| multiply(X1,inverse(X1)) != sk_c8
| multiply(inverse(X1),sk_c7) != sk_c8
| multiply(sk_c8,multiply(sk_c7,sk_c8)) != sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_143,negated_conjecture,
( sk_c4 != sk_c8
| inverse(X1) != sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_140,c_0_141])]) ).
cnf(c_0_144,negated_conjecture,
inverse(X1) != sk_c8,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(csr,[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)],[c_0_142,c_0_126]),c_0_126]),c_0_126]),c_0_126]),c_0_126]),c_0_126]),c_0_134]),c_0_134]),c_0_134]),c_0_134]),c_0_141]),c_0_134]),c_0_134])]),c_0_143])])]),c_0_136])]) ).
cnf(c_0_145,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_31,c_0_144]),c_0_144]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP232-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n001.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 20:12:43 UTC 2026
% 0.05/0.38 % CPUTime :
% 0.05/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.43 Running first-order theorem proving
% 0.05/0.43 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 2.11/0.72 % Version: 3.5.1
% 2.11/0.72 % Preprocessing class: FSMSSMSMSSSNFFN.
% 2.11/0.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.11/0.72 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 2.11/0.72 % Starting new_bool_3 with 300s (1) cores
% 2.11/0.72 % Starting new_bool_1 with 300s (1) cores
% 2.11/0.72 % Starting sh5l with 300s (1) cores
% 2.11/0.72 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1293259 completed with status 0
% 2.11/0.72 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 2.11/0.72 % Preprocessing class: FSMSSMSMSSSNFFN.
% 2.11/0.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.11/0.72 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 2.11/0.72 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.11/0.72 % No SInE strategy applied
% 2.11/0.72 % Search class: FGHPS-FFMM21-SFFFFFNN
% 2.11/0.72 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.11/0.72 % Starting SubtermCWHack with 136s (1) cores
% 2.11/0.72 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 2.11/0.72 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.11/0.72 % Starting new_bool_3 with 136s (1) cores
% 2.11/0.72 % Starting new_bool_1 with 136s (1) cores
% 2.11/0.72 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1293265 completed with status 0
% 2.11/0.72 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 2.11/0.72 % Preprocessing class: FSMSSMSMSSSNFFN.
% 2.11/0.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.11/0.72 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 2.11/0.72 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.11/0.72 % No SInE strategy applied
% 2.11/0.72 % Search class: FGHPS-FFMM21-SFFFFFNN
% 2.11/0.72 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.11/0.72 % Starting SubtermCWHack with 136s (1) cores
% 2.11/0.72 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 2.11/0.72 % Preprocessing time : 0.002 s
% 2.11/0.72 % Presaturation interreduction done
% 2.11/0.72
% 2.11/0.72 % Proof found!
% 2.11/0.72 % SZS status Unsatisfiable
% 2.11/0.72 % SZS output start CNFRefutation
% See solution above
% 2.11/0.72 % Parsed axioms : 34
% 2.11/0.72 % Removed by relevancy pruning/SinE : 0
% 2.11/0.72 % Initial clauses : 34
% 2.11/0.72 % Removed in clause preprocessing : 0
% 2.11/0.72 % Initial clauses in saturation : 34
% 2.11/0.72 % Processed clauses : 3000
% 2.11/0.72 % ...of these trivial : 27
% 2.11/0.72 % ...subsumed : 2114
% 2.11/0.72 % ...remaining for further processing : 859
% 2.11/0.72 % Other redundant clauses eliminated : 25
% 2.11/0.72 % Clauses deleted for lack of memory : 0
% 2.11/0.72 % Backward-subsumed : 91
% 2.11/0.72 % Backward-rewritten : 689
% 2.11/0.72 % Generated clauses : 12842
% 2.11/0.72 % ...of the previous two non-redundant : 13241
% 2.11/0.72 % ...aggressively subsumed : 0
% 2.11/0.72 % Contextual simplify-reflections : 20
% 2.11/0.72 % Paramodulations : 12806
% 2.11/0.72 % Factorizations : 9
% 2.11/0.72 % NegExts : 0
% 2.11/0.72 % Equation resolutions : 25
% 2.11/0.72 % Disequality decompositions : 0
% 2.11/0.72 % Total rewrite steps : 3181
% 2.11/0.72 % ...of those cached : 2999
% 2.11/0.72 % Propositional unsat checks : 0
% 2.11/0.72 % Propositional check models : 0
% 2.11/0.72 % Propositional check unsatisfiable : 0
% 2.11/0.72 % Propositional clauses : 0
% 2.11/0.72 % Propositional clauses after purity: 0
% 2.11/0.72 % Propositional unsat core size : 0
% 2.11/0.72 % Propositional preprocessing time : 0.000
% 2.11/0.72 % Propositional encoding time : 0.000
% 2.11/0.72 % Propositional solver time : 0.000
% 2.11/0.72 % Success case prop preproc time : 0.000
% 2.11/0.72 % Success case prop encoding time : 0.000
% 2.11/0.72 % Success case prop solver time : 0.000
% 2.11/0.72 % Current number of processed clauses : 33
% 2.11/0.72 % Positive orientable unit clauses : 13
% 2.11/0.72 % Positive unorientable unit clauses: 0
% 2.11/0.72 % Negative unit clauses : 1
% 2.11/0.72 % Non-unit-clauses : 19
% 2.11/0.72 % Current number of unprocessed clauses: 9903
% 2.11/0.72 % ...number of literals in the above : 42350
% 2.11/0.72 % Current number of archived formulas : 0
% 2.11/0.72 % Current number of archived clauses : 822
% 2.11/0.72 % Clause-clause subsumption calls (NU) : 15514
% 2.11/0.72 % Rec. Clause-clause subsumption calls : 7628
% 2.11/0.72 % Non-unit clause-clause subsumptions : 2214
% 2.11/0.72 % Unit Clause-clause subsumption calls : 177
% 2.11/0.72 % Rewrite failures with RHS unbound : 0
% 2.11/0.72 % BW rewrite match attempts : 35
% 2.11/0.72 % BW rewrite match successes : 32
% 2.11/0.72 % Condensation attempts : 0
% 2.11/0.72 % Condensation successes : 0
% 2.11/0.72 % Termbank termtop insertions : 162212
% 2.11/0.72 % Search garbage collected termcells : 31
% 2.11/0.72
% 2.11/0.72 % -------------------------------------------------
% 2.11/0.72 % User time : 0.212 s
% 2.11/0.72 % System time : 0.017 s
% 2.11/0.72 % Total time : 0.228 s
% 2.11/0.72 % Maximum resident set size: 3648 pages
% 2.11/0.72
% 2.11/0.72 % -------------------------------------------------
% 2.11/0.72 % User time : 1.198 s
% 2.11/0.72 % System time : 0.091 s
% 2.11/0.72 % Total time : 1.289 s
% 2.11/0.72 % Maximum resident set size: 4608 pages
% 2.11/0.72 % E exiting
%------------------------------------------------------------------------------