%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP298-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:39:13 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.45s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 24
% Syntax : Number of clauses : 99 ( 21 unt; 71 nHn; 82 RR)
% Number of literals : 266 ( 265 equ; 95 neg)
% Maximal clause size : 12 ( 2 avg)
% Maximal term depth : 5 ( 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 : 65 ( 3 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_6,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_33,negated_conjecture,
( multiply(X5,sk_c6) != sk_c7
| inverse(X4) != X5
| multiply(X4,X5) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_7,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_11,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_30,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_31,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_20,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_18,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_17,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_23,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_22,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_24,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_14,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_15,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_29,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
cnf(prove_this_28,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
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,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
prove_this_6 ).
cnf(c_0_29,negated_conjecture,
( multiply(X5,sk_c6) != sk_c7
| inverse(X4) != X5
| multiply(X4,X5) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(fof_simplification,[status(thm)],[prove_this_33]) ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(inverse(sk_c4),sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c8,sk_c7) = sk_c6 ),
prove_this_7 ).
cnf(c_0_32,negated_conjecture,
( multiply(X5,sk_c6) != sk_c7
| inverse(X4) != X5
| multiply(X4,X5) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
c_0_29 ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c5
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
prove_this_11 ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
prove_this_30 ).
cnf(c_0_36,negated_conjecture,
( inverse(X4) != sk_c8
| inverse(X3) != sk_c8
| inverse(X2) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| multiply(X3,sk_c8) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| multiply(X1,inverse(X1)) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(inverse(X1),sk_c6) != sk_c7 ),
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( identity = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_33]),c_0_25]) ).
cnf(c_0_38,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_34]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
prove_this_19 ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(inverse(sk_c4),sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_27,c_0_35]) ).
cnf(c_0_41,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c6,sk_c8) = sk_c7 ),
prove_this_31 ).
cnf(c_0_42,negated_conjecture,
( inverse(X4) != sk_c8
| inverse(X3) != sk_c8
| inverse(X2) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| multiply(X3,sk_c8) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| multiply(X1,inverse(X1)) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(inverse(X1),sk_c6) != sk_c7
| identity = sk_c7 ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c5
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
( inverse(X4) != sk_c8
| inverse(X3) != sk_c8
| inverse(X2) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| multiply(X3,sk_c8) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| multiply(X1,inverse(X1)) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(inverse(X1),sk_c6) != sk_c7
| identity = sk_c7
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_46,negated_conjecture,
( identity = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_44]),c_0_25]) ).
cnf(c_0_47,negated_conjecture,
( inverse(X4) != sk_c8
| inverse(X3) != sk_c8
| inverse(X2) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| multiply(X3,sk_c8) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| multiply(X1,inverse(X1)) != sk_c7
| multiply(inverse(X1),sk_c6) != sk_c7
| identity = sk_c7
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_48,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
prove_this_20 ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
prove_this_21 ).
cnf(c_0_50,negated_conjecture,
( inverse(X3) != sk_c8
| inverse(X2) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(X2,sk_c8) != sk_c7
| multiply(X1,inverse(X1)) != sk_c7
| multiply(inverse(X1),sk_c6) != sk_c7
| identity = sk_c7
| inverse(sk_c1) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_51,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c1) = sk_c8 ),
prove_this_18 ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
prove_this_17 ).
cnf(c_0_53,negated_conjecture,
( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(X1,inverse(X1)) != sk_c7
| multiply(inverse(X1),sk_c6) != sk_c7
| identity = sk_c7
| inverse(sk_c1) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_54,negated_conjecture,
( multiply(X1,inverse(X1)) != sk_c7
| multiply(inverse(X1),sk_c6) != sk_c7
| identity = sk_c7
| inverse(sk_c1) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_51]),c_0_52]) ).
cnf(c_0_55,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c8 ),
prove_this_23 ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
prove_this_22 ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
prove_this_24 ).
cnf(c_0_58,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_25]) ).
cnf(c_0_59,negated_conjecture,
( identity = sk_c7
| inverse(sk_c1) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]),c_0_57]) ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
prove_this_14 ).
cnf(c_0_61,negated_conjecture,
( identity = sk_c7
| multiply(sk_c8,sk_c7) = sk_c8
| multiply(inverse(sk_c8),identity) = sk_c1 ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(inverse(sk_c4),sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_27,c_0_60]) ).
cnf(c_0_63,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c7 ),
prove_this_15 ).
cnf(c_0_64,negated_conjecture,
( identity = sk_c7
| multiply(sk_c8,sk_c7) = sk_c8
| multiply(inverse(inverse(sk_c8)),sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_27,c_0_61]) ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_66,negated_conjecture,
( identity = sk_c7
| inverse(sk_c8) = sk_c1
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_64]),c_0_58]) ).
cnf(c_0_67,negated_conjecture,
( identity = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_65]),c_0_25]) ).
cnf(c_0_68,negated_conjecture,
( identity = sk_c7
| multiply(sk_c1,sk_c8) = identity
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_25,c_0_66]) ).
cnf(c_0_69,negated_conjecture,
( identity = sk_c7
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_70,negated_conjecture,
identity = sk_c7,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_69]),c_0_25])]) ).
cnf(c_0_71,plain,
multiply(inverse(inverse(X1)),sk_c7) = X1,
inference(rw,[status(thm)],[c_0_58,c_0_70]) ).
cnf(c_0_72,plain,
multiply(inverse(inverse(inverse(X1))),X1) = sk_c7,
inference(spm,[status(thm)],[c_0_27,c_0_71]) ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
prove_this_3 ).
cnf(c_0_74,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_72]),c_0_71]) ).
cnf(c_0_75,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,multiply(sk_c6,X1)) = multiply(sk_c7,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_73]) ).
cnf(c_0_76,plain,
multiply(sk_c7,X1) = X1,
inference(rw,[status(thm)],[c_0_26,c_0_70]) ).
cnf(c_0_77,plain,
multiply(X1,sk_c7) = X1,
inference(rw,[status(thm)],[c_0_71,c_0_74]) ).
cnf(c_0_78,plain,
multiply(inverse(X1),X1) = sk_c7,
inference(rw,[status(thm)],[c_0_25,c_0_70]) ).
cnf(c_0_79,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
prove_this_4 ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
prove_this_5 ).
cnf(c_0_81,negated_conjecture,
( sk_c6 = sk_c8
| multiply(sk_c8,multiply(sk_c6,X1)) = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_76]),c_0_77]) ).
cnf(c_0_82,plain,
multiply(X1,inverse(X1)) = sk_c7,
inference(spm,[status(thm)],[c_0_78,c_0_74]) ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
prove_this_29 ).
cnf(c_0_84,negated_conjecture,
( sk_c6 = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(rw,[status(thm)],[c_0_79,c_0_77]) ).
cnf(c_0_85,negated_conjecture,
( sk_c6 = sk_c8
| sk_c3 = sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_77]),c_0_77]) ).
cnf(c_0_86,negated_conjecture,
( sk_c6 = sk_c8
| inverse(sk_c6) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_77]) ).
cnf(c_0_87,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(inverse(sk_c3),sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_27,c_0_83]) ).
cnf(c_0_88,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
prove_this_28 ).
cnf(c_0_89,negated_conjecture,
( sk_c6 = sk_c8
| inverse(sk_c8) = sk_c8 ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_90,negated_conjecture,
( sk_c6 = sk_c8
| inverse(sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_74,c_0_86]) ).
cnf(c_0_91,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_92,negated_conjecture,
sk_c6 = sk_c8,
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_93,negated_conjecture,
multiply(sk_c8,sk_c8) = sk_c7,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92])]) ).
cnf(c_0_94,negated_conjecture,
inverse(sk_c8) = sk_c8,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_93]),c_0_77]) ).
cnf(c_0_95,negated_conjecture,
( inverse(X3) != sk_c8
| inverse(X2) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(X2,sk_c8) != sk_c7
| multiply(inverse(X1),sk_c8) != sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_77]),c_0_77])]),c_0_92]),c_0_92]),c_0_92]),c_0_93]),c_0_92]),c_0_93]),c_0_82]),c_0_94])]) ).
cnf(c_0_96,negated_conjecture,
( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(inverse(X1),sk_c8) != sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_94]),c_0_93])]) ).
cnf(c_0_97,negated_conjecture,
multiply(inverse(X1),sk_c8) != sk_c7,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_94]),c_0_93])]) ).
cnf(c_0_98,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_94]),c_0_93])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP298-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 20 20:09:10 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.45 % Version: 3.5.1
% 0.12/0.45 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.12/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.45 % Starting sh5l with 300s (1) cores
% 0.12/0.45 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 3499199 completed with status 0
% 0.12/0.45 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.12/0.45 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.12/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.45 % No SInE strategy applied
% 0.12/0.45 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.12/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.12/0.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.12/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.12/0.45 % Starting new_bool_1 with 136s (1) cores
% 0.12/0.45 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 3499204 completed with status 0
% 0.12/0.45 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.12/0.45 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.12/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.45 % No SInE strategy applied
% 0.12/0.45 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.12/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.12/0.45 % Preprocessing time : 0.001 s
% 0.12/0.45 % Presaturation interreduction done
% 0.12/0.45
% 0.12/0.45 % Proof found!
% 0.12/0.45 % SZS status Unsatisfiable
% 0.12/0.45 % SZS output start CNFRefutation
% See solution above
% 0.12/0.45 % Parsed axioms : 36
% 0.12/0.45 % Removed by relevancy pruning/SinE : 0
% 0.12/0.45 % Initial clauses : 36
% 0.12/0.45 % Removed in clause preprocessing : 0
% 0.12/0.45 % Initial clauses in saturation : 36
% 0.12/0.45 % Processed clauses : 372
% 0.12/0.45 % ...of these trivial : 22
% 0.12/0.45 % ...subsumed : 99
% 0.12/0.45 % ...remaining for further processing : 251
% 0.12/0.45 % Other redundant clauses eliminated : 4
% 0.12/0.45 % Clauses deleted for lack of memory : 0
% 0.12/0.45 % Backward-subsumed : 17
% 0.12/0.45 % Backward-rewritten : 126
% 0.12/0.45 % Generated clauses : 1043
% 0.12/0.45 % ...of the previous two non-redundant : 1049
% 0.12/0.45 % ...aggressively subsumed : 0
% 0.12/0.45 % Contextual simplify-reflections : 5
% 0.12/0.45 % Paramodulations : 1037
% 0.12/0.45 % Factorizations : 1
% 0.12/0.45 % NegExts : 0
% 0.12/0.45 % Equation resolutions : 4
% 0.12/0.45 % Disequality decompositions : 0
% 0.12/0.45 % Total rewrite steps : 457
% 0.12/0.45 % ...of those cached : 400
% 0.12/0.45 % Propositional unsat checks : 0
% 0.12/0.45 % Propositional check models : 0
% 0.12/0.45 % Propositional check unsatisfiable : 0
% 0.12/0.45 % Propositional clauses : 0
% 0.12/0.45 % Propositional clauses after purity: 0
% 0.12/0.45 % Propositional unsat core size : 0
% 0.12/0.45 % Propositional preprocessing time : 0.000
% 0.12/0.45 % Propositional encoding time : 0.000
% 0.12/0.45 % Propositional solver time : 0.000
% 0.12/0.45 % Success case prop preproc time : 0.000
% 0.12/0.45 % Success case prop encoding time : 0.000
% 0.12/0.45 % Success case prop solver time : 0.000
% 0.12/0.45 % Current number of processed clauses : 70
% 0.12/0.45 % Positive orientable unit clauses : 12
% 0.12/0.45 % Positive unorientable unit clauses: 0
% 0.12/0.45 % Negative unit clauses : 1
% 0.12/0.45 % Non-unit-clauses : 57
% 0.12/0.45 % Current number of unprocessed clauses: 680
% 0.12/0.45 % ...number of literals in the above : 2172
% 0.12/0.45 % Current number of archived formulas : 0
% 0.12/0.45 % Current number of archived clauses : 180
% 0.12/0.45 % Clause-clause subsumption calls (NU) : 1018
% 0.12/0.45 % Rec. Clause-clause subsumption calls : 860
% 0.12/0.45 % Non-unit clause-clause subsumptions : 120
% 0.12/0.45 % Unit Clause-clause subsumption calls : 286
% 0.12/0.45 % Rewrite failures with RHS unbound : 0
% 0.12/0.45 % BW rewrite match attempts : 32
% 0.12/0.45 % BW rewrite match successes : 20
% 0.12/0.45 % Condensation attempts : 0
% 0.12/0.45 % Condensation successes : 0
% 0.12/0.45 % Termbank termtop insertions : 12295
% 0.12/0.45 % Search garbage collected termcells : 32
% 0.12/0.45
% 0.12/0.45 % -------------------------------------------------
% 0.12/0.45 % User time : 0.014 s
% 0.12/0.45 % System time : 0.002 s
% 0.12/0.45 % Total time : 0.015 s
% 0.12/0.45 % Maximum resident set size: 3652 pages
% 0.12/0.45
% 0.12/0.45 % -------------------------------------------------
% 0.12/0.45 % User time : 0.052 s
% 0.12/0.45 % System time : 0.013 s
% 0.12/0.45 % Total time : 0.065 s
% 0.12/0.45 % Maximum resident set size: 4608 pages
% 0.12/0.45 % E exiting
%------------------------------------------------------------------------------