%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP244-1 : 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 : n003.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 12:42:59 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 25
% Syntax : Number of clauses : 114 ( 32 unt; 73 nHn; 96 RR)
% Number of literals : 313 ( 312 equ; 134 neg)
% Maximal clause size : 15 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 91 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_55,negated_conjecture,
( multiply(X8,sk_c9) != sk_c10
| inverse(X7) != X8
| multiply(X7,X8) != sk_c10
| multiply(X6,sk_c10) != sk_c11
| inverse(X6) != sk_c11
| inverse(X5) != sk_c10
| multiply(X5,sk_c10) != sk_c9
| inverse(X4) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c11
| inverse(X3) != 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_55) ).
cnf(prove_this_17,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_16,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_18,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_5,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c4) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
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_7,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_8,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_22,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_30,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_31,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_50,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c3,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_50) ).
cnf(prove_this_51,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c3,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
cnf(prove_this_42,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
cnf(prove_this_41,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
cnf(c_0_25,negated_conjecture,
( multiply(X8,sk_c9) != sk_c10
| inverse(X7) != X8
| multiply(X7,X8) != sk_c10
| multiply(X6,sk_c10) != sk_c11
| inverse(X6) != sk_c11
| inverse(X5) != sk_c10
| multiply(X5,sk_c10) != sk_c9
| inverse(X4) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c11
| inverse(X3) != 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_55]) ).
cnf(c_0_26,negated_conjecture,
( multiply(X8,sk_c9) != sk_c10
| inverse(X7) != X8
| multiply(X7,X8) != sk_c10
| multiply(X6,sk_c10) != sk_c11
| inverse(X6) != sk_c11
| inverse(X5) != sk_c10
| multiply(X5,sk_c10) != sk_c9
| inverse(X4) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c11
| inverse(X3) != sk_c11
| inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10 ),
c_0_25 ).
cnf(c_0_27,negated_conjecture,
( inverse(X7) != sk_c11
| inverse(X6) != sk_c10
| inverse(X5) != sk_c11
| inverse(X4) != sk_c11
| inverse(X3) != sk_c10
| inverse(X2) != sk_c11
| multiply(X7,sk_c11) != sk_c10
| multiply(X6,sk_c10) != sk_c9
| multiply(X5,sk_c10) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(X2,sk_c10) != sk_c11
| multiply(X1,inverse(X1)) != sk_c10
| multiply(inverse(X1),sk_c9) != sk_c10 ),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_28,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c1) = sk_c11 ),
prove_this_17 ).
cnf(c_0_29,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c1) = sk_c11 ),
prove_this_16 ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c11 ),
prove_this_18 ).
cnf(c_0_31,negated_conjecture,
( inverse(X6) != sk_c11
| inverse(X5) != sk_c10
| inverse(X4) != sk_c11
| inverse(X3) != sk_c11
| inverse(X2) != sk_c10
| inverse(X1) != sk_c11
| multiply(X6,sk_c11) != sk_c10
| multiply(X5,sk_c10) != sk_c9
| multiply(X4,sk_c10) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| multiply(X1,sk_c10) != sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30]) ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
prove_this_6 ).
cnf(c_0_33,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
prove_this_5 ).
cnf(c_0_34,negated_conjecture,
( inverse(X5) != sk_c11
| inverse(X4) != sk_c10
| inverse(X3) != sk_c11
| inverse(X2) != sk_c11
| inverse(X1) != sk_c10
| multiply(X5,sk_c11) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(X3,sk_c10) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| multiply(X1,sk_c10) != sk_c9
| inverse(sk_c1) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c10 ),
prove_this_3 ).
cnf(c_0_36,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
prove_this_4 ).
cnf(c_0_37,negated_conjecture,
( inverse(X4) != sk_c11
| inverse(X3) != sk_c10
| inverse(X2) != sk_c11
| inverse(X1) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(X2,sk_c10) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| inverse(sk_c1) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_38,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
prove_this_1 ).
cnf(c_0_39,negated_conjecture,
( inverse(sk_c4) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
prove_this_2 ).
cnf(c_0_40,negated_conjecture,
( inverse(X3) != sk_c11
| inverse(X2) != sk_c10
| inverse(X1) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| multiply(X1,sk_c10) != sk_c11
| inverse(sk_c1) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_41,negated_conjecture,
( inverse(X2) != sk_c11
| inverse(X1) != sk_c10
| multiply(X2,sk_c11) != sk_c10
| multiply(X1,sk_c10) != sk_c9
| inverse(sk_c1) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_32]),c_0_33]) ).
cnf(c_0_42,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_43,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_44,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_45,negated_conjecture,
( inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| inverse(sk_c1) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_35]),c_0_36]) ).
cnf(c_0_46,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_47,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_38]),c_0_39]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
prove_this_7 ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c11,multiply(sk_c1,X1)) = X1 ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(inverse(sk_c7),sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_46,c_0_48]) ).
cnf(c_0_51,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c10 ),
prove_this_8 ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(inverse(sk_c11),X1) = multiply(sk_c1,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c1,sk_c11) = identity
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_43,c_0_52]) ).
cnf(c_0_55,negated_conjecture,
( identity = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_53]),c_0_43]) ).
cnf(c_0_56,negated_conjecture,
multiply(sk_c1,sk_c11) = sk_c10,
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_54]),c_0_55]) ).
cnf(c_0_57,negated_conjecture,
multiply(inverse(sk_c1),sk_c10) = sk_c11,
inference(spm,[status(thm)],[c_0_46,c_0_56]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
prove_this_10 ).
cnf(c_0_59,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c11
| multiply(sk_c4,sk_c11) = sk_c10 ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c11,sk_c10) = sk_c11
| multiply(inverse(sk_c4),sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_46,c_0_59]) ).
cnf(c_0_61,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c1) = sk_c11 ),
prove_this_11 ).
cnf(c_0_62,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_63,negated_conjecture,
multiply(sk_c11,sk_c10) = sk_c11,
inference(spm,[status(thm)],[c_0_57,c_0_62]) ).
cnf(c_0_64,negated_conjecture,
identity = sk_c10,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_63]),c_0_43]) ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
prove_this_21 ).
cnf(c_0_66,negated_conjecture,
multiply(inverse(inverse(sk_c1)),sk_c11) = sk_c10,
inference(spm,[status(thm)],[c_0_46,c_0_57]) ).
cnf(c_0_67,plain,
multiply(inverse(X1),X1) = sk_c10,
inference(rw,[status(thm)],[c_0_43,c_0_64]) ).
cnf(c_0_68,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(inverse(sk_c5),sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_46,c_0_65]) ).
cnf(c_0_69,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
prove_this_22 ).
cnf(c_0_70,negated_conjecture,
multiply(inverse(inverse(inverse(sk_c1))),sk_c10) = sk_c11,
inference(spm,[status(thm)],[c_0_46,c_0_66]) ).
cnf(c_0_71,plain,
multiply(inverse(inverse(X1)),sk_c10) = X1,
inference(spm,[status(thm)],[c_0_46,c_0_67]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_73,plain,
multiply(sk_c10,X1) = X1,
inference(rw,[status(thm)],[c_0_44,c_0_64]) ).
cnf(c_0_74,negated_conjecture,
inverse(sk_c1) = sk_c11,
inference(rw,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_75,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| multiply(inverse(sk_c2),sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_46,c_0_72]) ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
prove_this_30 ).
cnf(c_0_77,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c2) = sk_c10 ),
prove_this_31 ).
cnf(c_0_78,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_71]),c_0_73]) ).
cnf(c_0_79,negated_conjecture,
multiply(inverse(sk_c11),sk_c10) = sk_c1,
inference(spm,[status(thm)],[c_0_71,c_0_74]) ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c10
| multiply(sk_c5,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_81,negated_conjecture,
( sk_c5 = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_77]),c_0_73]) ).
cnf(c_0_82,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c3,sk_c10) = sk_c11 ),
prove_this_50 ).
cnf(c_0_83,plain,
multiply(X1,sk_c10) = X1,
inference(rw,[status(thm)],[c_0_71,c_0_78]) ).
cnf(c_0_84,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c3,sk_c10) = sk_c11 ),
prove_this_51 ).
cnf(c_0_85,negated_conjecture,
multiply(inverse(sk_c11),X1) = multiply(sk_c1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_79]),c_0_73]) ).
cnf(c_0_86,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c5,sk_c10) = sk_c9 ),
inference(rw,[status(thm)],[c_0_80,c_0_73]) ).
cnf(c_0_87,negated_conjecture,
( sk_c2 = sk_c10
| sk_c5 = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_81]),c_0_73]) ).
cnf(c_0_88,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
prove_this_42 ).
cnf(c_0_89,negated_conjecture,
( sk_c3 = sk_c11
| inverse(sk_c6) = sk_c11 ),
inference(rw,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_90,negated_conjecture,
( sk_c6 = sk_c11
| sk_c3 = sk_c11 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_83]),c_0_83]) ).
cnf(c_0_91,negated_conjecture,
inverse(sk_c11) = sk_c1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_83]),c_0_83]) ).
cnf(c_0_92,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_83]),c_0_83]) ).
cnf(c_0_93,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c3) = sk_c11 ),
prove_this_41 ).
cnf(c_0_94,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(rw,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_95,negated_conjecture,
( sk_c9 = sk_c10
| sk_c2 = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_73])]) ).
cnf(c_0_96,plain,
multiply(inverse(sk_c10),X1) = X1,
inference(spm,[status(thm)],[c_0_46,c_0_73]) ).
cnf(c_0_97,negated_conjecture,
( sk_c6 = sk_c11
| inverse(sk_c3) = sk_c11 ),
inference(rw,[status(thm)],[c_0_88,c_0_83]) ).
cnf(c_0_98,negated_conjecture,
( sk_c1 = sk_c11
| sk_c3 = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]) ).
cnf(c_0_99,negated_conjecture,
( sk_c6 = sk_c1
| inverse(sk_c3) = sk_c11 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_91]) ).
cnf(c_0_100,negated_conjecture,
( identity != sk_c10
| inverse(X6) != sk_c11
| inverse(X5) != sk_c10
| inverse(X4) != sk_c11
| inverse(X3) != sk_c11
| inverse(X2) != sk_c10
| inverse(X1) != sk_c11
| multiply(X6,sk_c11) != sk_c10
| multiply(X5,sk_c10) != sk_c9
| multiply(X4,sk_c10) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| multiply(X1,sk_c10) != sk_c11
| multiply(sk_c9,inverse(sk_c9)) != sk_c10 ),
inference(spm,[status(thm)],[c_0_27,c_0_43]) ).
cnf(c_0_101,negated_conjecture,
sk_c9 = sk_c10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_73])]) ).
cnf(c_0_102,plain,
multiply(inverse(inverse(sk_c10)),X1) = X1,
inference(spm,[status(thm)],[c_0_46,c_0_96]) ).
cnf(c_0_103,negated_conjecture,
( sk_c1 = sk_c11
| sk_c6 = sk_c11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_91])]) ).
cnf(c_0_104,negated_conjecture,
( sk_c1 = sk_c11
| sk_c6 = sk_c1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_98]),c_0_91])]) ).
cnf(c_0_105,negated_conjecture,
( inverse(X6) != sk_c11
| inverse(X5) != sk_c10
| inverse(X4) != sk_c11
| inverse(X3) != sk_c11
| inverse(X2) != sk_c10
| inverse(X1) != sk_c11
| inverse(sk_c10) != sk_c10
| multiply(X6,sk_c11) != sk_c10
| multiply(X5,sk_c10) != sk_c10
| multiply(X4,sk_c10) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| multiply(X2,sk_c10) != sk_c10
| multiply(X1,sk_c10) != sk_c11 ),
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_100,c_0_64])]),c_0_101]),c_0_101]),c_0_73]),c_0_101]),c_0_101]) ).
cnf(c_0_106,plain,
inverse(sk_c10) = sk_c10,
inference(spm,[status(thm)],[c_0_67,c_0_102]) ).
cnf(c_0_107,negated_conjecture,
sk_c1 = sk_c11,
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_108,negated_conjecture,
multiply(sk_c11,sk_c1) = sk_c10,
inference(spm,[status(thm)],[c_0_67,c_0_74]) ).
cnf(c_0_109,negated_conjecture,
( inverse(X2) != sk_c11
| inverse(X1) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| multiply(X1,sk_c11) != sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[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(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_106])]),c_0_83]),c_0_83]),c_0_83]),c_0_83])])])])]),c_0_91]),c_0_107]),c_0_106])]) ).
cnf(c_0_110,negated_conjecture,
multiply(sk_c11,sk_c11) = sk_c10,
inference(rw,[status(thm)],[c_0_108,c_0_107]) ).
cnf(c_0_111,negated_conjecture,
( inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_91]),c_0_107])]) ).
cnf(c_0_112,negated_conjecture,
inverse(sk_c11) = sk_c11,
inference(rw,[status(thm)],[c_0_91,c_0_107]) ).
cnf(c_0_113,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_110])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP244-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:09:00 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.44 % Version: 3.5.1
% 0.10/0.44 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.44 % Starting sh5l with 300s (1) cores
% 0.10/0.44 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 2468942 completed with status 0
% 0.10/0.44 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.10/0.44 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.10/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.44 % No SInE strategy applied
% 0.10/0.44 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.10/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.10/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 136s (1) cores
% 0.10/0.44 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 2468949 completed with status 0
% 0.10/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.10/0.44 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.10/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.44 % No SInE strategy applied
% 0.10/0.44 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.10/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.10/0.44 % Preprocessing time : 0.001 s
% 0.10/0.44 % Presaturation interreduction done
% 0.10/0.44
% 0.10/0.44 % Proof found!
% 0.10/0.44 % SZS status Unsatisfiable
% 0.10/0.44 % SZS output start CNFRefutation
% See solution above
% 0.10/0.45 % Parsed axioms : 58
% 0.10/0.45 % Removed by relevancy pruning/SinE : 0
% 0.10/0.45 % Initial clauses : 58
% 0.10/0.45 % Removed in clause preprocessing : 0
% 0.10/0.45 % Initial clauses in saturation : 58
% 0.10/0.45 % Processed clauses : 789
% 0.10/0.45 % ...of these trivial : 39
% 0.10/0.45 % ...subsumed : 309
% 0.10/0.45 % ...remaining for further processing : 441
% 0.10/0.45 % Other redundant clauses eliminated : 9
% 0.10/0.45 % Clauses deleted for lack of memory : 0
% 0.10/0.45 % Backward-subsumed : 41
% 0.10/0.45 % Backward-rewritten : 245
% 0.10/0.45 % Generated clauses : 2214
% 0.10/0.45 % ...of the previous two non-redundant : 1956
% 0.10/0.45 % ...aggressively subsumed : 0
% 0.10/0.45 % Contextual simplify-reflections : 9
% 0.10/0.45 % Paramodulations : 2210
% 0.10/0.45 % Factorizations : 1
% 0.10/0.45 % NegExts : 0
% 0.10/0.45 % Equation resolutions : 9
% 0.10/0.45 % Disequality decompositions : 0
% 0.10/0.45 % Total rewrite steps : 1461
% 0.10/0.45 % ...of those cached : 1364
% 0.10/0.45 % Propositional unsat checks : 0
% 0.10/0.45 % Propositional check models : 0
% 0.10/0.45 % Propositional check unsatisfiable : 0
% 0.10/0.45 % Propositional clauses : 0
% 0.10/0.45 % Propositional clauses after purity: 0
% 0.10/0.45 % Propositional unsat core size : 0
% 0.10/0.45 % Propositional preprocessing time : 0.000
% 0.10/0.45 % Propositional encoding time : 0.000
% 0.10/0.45 % Propositional solver time : 0.000
% 0.10/0.45 % Success case prop preproc time : 0.000
% 0.10/0.45 % Success case prop encoding time : 0.000
% 0.10/0.45 % Success case prop solver time : 0.000
% 0.10/0.45 % Current number of processed clauses : 94
% 0.10/0.45 % Positive orientable unit clauses : 14
% 0.10/0.45 % Positive unorientable unit clauses: 0
% 0.10/0.45 % Negative unit clauses : 0
% 0.10/0.45 % Non-unit-clauses : 80
% 0.10/0.45 % Current number of unprocessed clauses: 1149
% 0.10/0.45 % ...number of literals in the above : 5616
% 0.10/0.45 % Current number of archived formulas : 0
% 0.10/0.45 % Current number of archived clauses : 344
% 0.10/0.45 % Clause-clause subsumption calls (NU) : 3828
% 0.10/0.45 % Rec. Clause-clause subsumption calls : 3133
% 0.10/0.45 % Non-unit clause-clause subsumptions : 337
% 0.10/0.45 % Unit Clause-clause subsumption calls : 379
% 0.10/0.45 % Rewrite failures with RHS unbound : 0
% 0.10/0.45 % BW rewrite match attempts : 49
% 0.10/0.45 % BW rewrite match successes : 34
% 0.10/0.45 % Condensation attempts : 0
% 0.10/0.45 % Condensation successes : 0
% 0.10/0.45 % Termbank termtop insertions : 29109
% 0.10/0.45 % Search garbage collected termcells : 44
% 0.10/0.45
% 0.10/0.45 % -------------------------------------------------
% 0.10/0.45 % User time : 0.027 s
% 0.10/0.45 % System time : 0.002 s
% 0.10/0.45 % Total time : 0.029 s
% 0.10/0.45 % Maximum resident set size: 3660 pages
% 0.10/0.45
% 0.10/0.45 % -------------------------------------------------
% 0.10/0.45 % User time : 0.104 s
% 0.10/0.45 % System time : 0.012 s
% 0.10/0.45 % Total time : 0.116 s
% 0.10/0.45 % Maximum resident set size: 4608 pages
% 0.10/0.45 % E exiting
%------------------------------------------------------------------------------