%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP218-1 : 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 12:42:55 PM UTC 2026
% Result : Unsatisfiable 2.29s 0.90s
% Output : CNFRefutation 2.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 27
% Syntax : Number of clauses : 139 ( 27 unt; 99 nHn; 119 RR)
% Number of literals : 341 ( 340 equ; 104 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 : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 78 ( 1 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_41,negated_conjecture,
( inverse(X8) != sk_c10
| multiply(X8,sk_c10) != X7
| multiply(sk_c10,X7) != sk_c9
| multiply(X6,sk_c9) != sk_c10
| inverse(X6) != sk_c10
| inverse(X5) != sk_c10
| multiply(X5,sk_c10) != X4
| multiply(sk_c10,X4) != sk_c9
| multiply(X3,sk_c10) != sk_c9
| inverse(X2) != X3
| multiply(X2,X3) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_2,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
cnf(prove_this_33,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_38,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
cnf(prove_this_28,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c10,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_6,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_18,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_8,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_1,negated_conjecture,
( inverse(sk_c6) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_14,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_40,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
cnf(prove_this_39,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_30,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c10,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_35,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_29,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c10,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
cnf(prove_this_34,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c4,sk_c10) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_31,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_32,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
cnf(prove_this_37,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
cnf(c_0_27,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_28,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_29,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_30,negated_conjecture,
( inverse(X8) != sk_c10
| multiply(X8,sk_c10) != X7
| multiply(sk_c10,X7) != sk_c9
| multiply(X6,sk_c9) != sk_c10
| inverse(X6) != sk_c10
| inverse(X5) != sk_c10
| multiply(X5,sk_c10) != X4
| multiply(sk_c10,X4) != sk_c9
| multiply(X3,sk_c10) != sk_c9
| inverse(X2) != X3
| multiply(X2,X3) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10 ),
inference(fof_simplification,[status(thm)],[prove_this_41]) ).
cnf(c_0_31,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
prove_this_7 ).
cnf(c_0_33,negated_conjecture,
( inverse(X8) != sk_c10
| multiply(X8,sk_c10) != X7
| multiply(sk_c10,X7) != sk_c9
| multiply(X6,sk_c9) != sk_c10
| inverse(X6) != sk_c10
| inverse(X5) != sk_c10
| multiply(X5,sk_c10) != X4
| multiply(sk_c10,X4) != sk_c9
| multiply(X3,sk_c10) != sk_c9
| inverse(X2) != X3
| multiply(X2,X3) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10 ),
c_0_30 ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(inverse(sk_c1),sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
prove_this_2 ).
cnf(c_0_36,negated_conjecture,
( inverse(X5) != sk_c10
| inverse(X2) != sk_c10
| inverse(X4) != sk_c10
| inverse(X1) != sk_c10
| multiply(X5,sk_c9) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(X3,inverse(X3)) != sk_c9
| multiply(inverse(X3),sk_c10) != sk_c9
| multiply(sk_c10,multiply(X2,sk_c10)) != sk_c9
| multiply(sk_c10,multiply(X1,sk_c10)) != sk_c9 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_33])])]) ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c5 ),
prove_this_33 ).
cnf(c_0_38,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c10 ),
prove_this_38 ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c10,sk_c5) = sk_c9 ),
prove_this_28 ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c10,sk_c10) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,negated_conjecture,
( inverse(X4) != sk_c10
| inverse(X1) != sk_c10
| inverse(X3) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| multiply(X2,inverse(X2)) != sk_c9
| multiply(inverse(X2),sk_c10) != sk_c9
| multiply(sk_c10,multiply(X1,sk_c10)) != sk_c9
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39]) ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c10,sk_c10) = sk_c9
| multiply(inverse(sk_c6),sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_31,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
prove_this_6 ).
cnf(c_0_44,negated_conjecture,
( inverse(X3) != sk_c10
| inverse(X2) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| multiply(X1,inverse(X1)) != sk_c9
| multiply(inverse(X1),sk_c10) != sk_c9
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_37]),c_0_38]),c_0_39]) ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c3 ),
prove_this_18 ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9 ),
prove_this_13 ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c9 ),
prove_this_23 ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c10,sk_c10) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
( inverse(X2) != sk_c10
| inverse(X1) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| multiply(X1,sk_c9) != sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_47]) ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
prove_this_8 ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
prove_this_3 ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c10,sk_c10) = sk_c9
| multiply(inverse(sk_c1),sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_31,c_0_48]) ).
cnf(c_0_53,negated_conjecture,
( inverse(sk_c6) = sk_c10
| inverse(sk_c1) = sk_c10 ),
prove_this_1 ).
cnf(c_0_54,negated_conjecture,
( inverse(X1) != sk_c10
| multiply(X1,sk_c9) != sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
cnf(c_0_55,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_56,negated_conjecture,
multiply(sk_c10,sk_c8) = sk_c9,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_51]),c_0_50]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c9 ),
prove_this_14 ).
cnf(c_0_58,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c4) = sk_c10 ),
prove_this_40 ).
cnf(c_0_59,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c4) = sk_c10 ),
prove_this_39 ).
cnf(c_0_60,negated_conjecture,
multiply(sk_c10,sk_c10) = sk_c9,
inference(spm,[status(thm)],[c_0_42,c_0_55]) ).
cnf(c_0_61,negated_conjecture,
multiply(inverse(sk_c10),sk_c9) = sk_c8,
inference(spm,[status(thm)],[c_0_31,c_0_56]) ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(inverse(sk_c2),sk_c9) = sk_c3 ),
inference(spm,[status(thm)],[c_0_31,c_0_57]) ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c2) = sk_c3 ),
prove_this_19 ).
cnf(c_0_64,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c10,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_58]) ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c10,sk_c4) = identity
| multiply(sk_c7,sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_28,c_0_59]) ).
cnf(c_0_66,negated_conjecture,
sk_c8 = sk_c10,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_60]),c_0_61]) ).
cnf(c_0_67,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c10,sk_c5) = sk_c9 ),
prove_this_30 ).
cnf(c_0_68,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c3
| multiply(sk_c7,sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_69,negated_conjecture,
( multiply(sk_c10,sk_c4) = identity
| multiply(sk_c10,multiply(sk_c7,X1)) = X1 ),
inference(spm,[status(thm)],[c_0_31,c_0_64]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c10
| multiply(sk_c10,sk_c4) = identity ),
inference(rw,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_71,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_31,c_0_31]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c10,sk_c7) = identity
| multiply(sk_c10,sk_c5) = sk_c9 ),
inference(spm,[status(thm)],[c_0_28,c_0_67]) ).
cnf(c_0_73,negated_conjecture,
( identity = sk_c9
| multiply(sk_c7,sk_c10) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_68]),c_0_28]) ).
cnf(c_0_74,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c10,sk_c4) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_60]) ).
cnf(c_0_75,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_28]),c_0_71]) ).
cnf(c_0_76,negated_conjecture,
( sk_c5 = sk_c8
| multiply(sk_c10,sk_c7) = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_72]),c_0_61]) ).
cnf(c_0_77,negated_conjecture,
( identity = sk_c9
| multiply(inverse(sk_c7),sk_c8) = sk_c10 ),
inference(spm,[status(thm)],[c_0_31,c_0_73]) ).
cnf(c_0_78,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c5 ),
prove_this_35 ).
cnf(c_0_79,negated_conjecture,
( sk_c9 = sk_c10
| inverse(sk_c10) = sk_c4 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_74]),c_0_75]) ).
cnf(c_0_80,negated_conjecture,
( sk_c5 = sk_c8
| multiply(sk_c10,multiply(sk_c7,X1)) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_76]),c_0_29]) ).
cnf(c_0_81,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c10,sk_c5) = sk_c9 ),
prove_this_29 ).
cnf(c_0_82,negated_conjecture,
( sk_c9 = sk_c10
| identity = sk_c9
| multiply(sk_c4,sk_c10) = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_56]) ).
cnf(c_0_83,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c4,sk_c10) = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_79]) ).
cnf(c_0_84,negated_conjecture,
( sk_c9 = sk_c10
| sk_c5 = sk_c8
| multiply(sk_c10,sk_c5) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_56]) ).
cnf(c_0_85,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_28,c_0_75]) ).
cnf(c_0_86,negated_conjecture,
( identity = sk_c5
| identity = sk_c9
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_87,negated_conjecture,
( sk_c5 = sk_c8
| sk_c9 = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_84]),c_0_61])]) ).
cnf(c_0_88,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c4,sk_c10) = sk_c5 ),
prove_this_34 ).
cnf(c_0_89,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_75]),c_0_75]) ).
cnf(c_0_90,negated_conjecture,
( sk_c9 = sk_c10
| identity = sk_c9
| inverse(sk_c5) = sk_c5 ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_91,negated_conjecture,
( sk_c9 = sk_c10
| sk_c5 = sk_c10 ),
inference(rw,[status(thm)],[c_0_87,c_0_66]) ).
cnf(c_0_92,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(inverse(sk_c4),sk_c5) = sk_c10 ),
inference(spm,[status(thm)],[c_0_31,c_0_88]) ).
cnf(c_0_93,negated_conjecture,
( inverse(sk_c10) = sk_c4
| inverse(sk_c7) = sk_c10 ),
inference(spm,[status(thm)],[c_0_89,c_0_58]) ).
cnf(c_0_94,negated_conjecture,
multiply(sk_c10,multiply(sk_c8,X1)) = multiply(sk_c9,X1),
inference(spm,[status(thm)],[c_0_27,c_0_56]) ).
cnf(c_0_95,negated_conjecture,
( identity = sk_c9
| sk_c9 = sk_c10
| inverse(sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_96,negated_conjecture,
( multiply(sk_c10,sk_c5) = sk_c10
| multiply(sk_c7,sk_c10) = sk_c8 ),
inference(spm,[status(thm)],[c_0_92,c_0_59]) ).
cnf(c_0_97,negated_conjecture,
( inverse(sk_c10) = sk_c7
| inverse(sk_c10) = sk_c4 ),
inference(spm,[status(thm)],[c_0_89,c_0_93]) ).
cnf(c_0_98,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c5 ),
prove_this_31 ).
cnf(c_0_99,negated_conjecture,
multiply(sk_c10,multiply(sk_c10,X1)) = multiply(sk_c9,X1),
inference(spm,[status(thm)],[c_0_94,c_0_66]) ).
cnf(c_0_100,negated_conjecture,
( identity = sk_c9
| sk_c9 = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_95]),c_0_60])]) ).
cnf(c_0_101,negated_conjecture,
( multiply(sk_c10,sk_c5) = sk_c10
| multiply(inverse(sk_c7),sk_c8) = sk_c10 ),
inference(spm,[status(thm)],[c_0_31,c_0_96]) ).
cnf(c_0_102,negated_conjecture,
( sk_c4 != sk_c7
| inverse(sk_c10) = sk_c7 ),
inference(ef,[status(thm)],[c_0_97]) ).
cnf(c_0_103,negated_conjecture,
( inverse(sk_c10) = sk_c7
| multiply(sk_c4,sk_c10) = sk_c5 ),
inference(spm,[status(thm)],[c_0_89,c_0_78]) ).
cnf(c_0_104,negated_conjecture,
( inverse(sk_c10) = sk_c6
| multiply(sk_c4,sk_c10) = sk_c5 ),
inference(spm,[status(thm)],[c_0_89,c_0_98]) ).
cnf(c_0_105,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c9,sk_c4) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_74]),c_0_75]) ).
cnf(c_0_106,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c9,X1) = X1 ),
inference(spm,[status(thm)],[c_0_29,c_0_100]) ).
cnf(c_0_107,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c5 ),
prove_this_32 ).
cnf(c_0_108,negated_conjecture,
( multiply(sk_c10,sk_c5) = sk_c10
| multiply(inverse(sk_c7),sk_c10) = sk_c10 ),
inference(rw,[status(thm)],[c_0_101,c_0_66]) ).
cnf(c_0_109,negated_conjecture,
( sk_c4 != sk_c7
| inverse(sk_c7) = sk_c10 ),
inference(spm,[status(thm)],[c_0_89,c_0_102]) ).
cnf(c_0_110,negated_conjecture,
( sk_c7 = sk_c6
| multiply(sk_c4,sk_c10) = sk_c5 ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_111,negated_conjecture,
( sk_c4 = sk_c10
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_112,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(inverse(sk_c4),sk_c5) = sk_c10 ),
inference(spm,[status(thm)],[c_0_31,c_0_107]) ).
cnf(c_0_113,negated_conjecture,
( sk_c4 != sk_c7
| sk_c9 = sk_c10
| multiply(sk_c10,sk_c5) = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_60]) ).
cnf(c_0_114,negated_conjecture,
( sk_c5 = sk_c9
| sk_c7 = sk_c6
| sk_c9 = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_60]) ).
cnf(c_0_115,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c6,sk_c9) = sk_c10
| multiply(inverse(sk_c4),sk_c10) = sk_c10 ),
inference(spm,[status(thm)],[c_0_112,c_0_91]) ).
cnf(c_0_116,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
prove_this_37 ).
cnf(c_0_117,negated_conjecture,
( sk_c7 != sk_c10
| sk_c9 = sk_c10
| multiply(sk_c10,sk_c5) = sk_c10 ),
inference(spm,[status(thm)],[c_0_113,c_0_111]) ).
cnf(c_0_118,negated_conjecture,
( sk_c9 = sk_c10
| sk_c7 = sk_c6 ),
inference(spm,[status(thm)],[c_0_91,c_0_114]) ).
cnf(c_0_119,negated_conjecture,
( sk_c9 = sk_c10
| multiply(X1,sk_c9) = X1 ),
inference(spm,[status(thm)],[c_0_75,c_0_100]) ).
cnf(c_0_120,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c6,sk_c9) = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_60])]) ).
cnf(c_0_121,negated_conjecture,
( multiply(sk_c10,sk_c5) = sk_c9
| multiply(inverse(sk_c7),sk_c8) = sk_c10 ),
inference(spm,[status(thm)],[c_0_31,c_0_81]) ).
cnf(c_0_122,negated_conjecture,
( sk_c6 != sk_c10
| sk_c9 = sk_c10
| multiply(sk_c10,sk_c5) = sk_c10 ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_123,negated_conjecture,
( sk_c6 = sk_c10
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_124,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c10,sk_c5) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_67]),c_0_56]) ).
cnf(c_0_125,negated_conjecture,
( sk_c9 = sk_c10
| multiply(sk_c10,sk_c5) = sk_c10 ),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_126,negated_conjecture,
multiply(inverse(sk_c10),sk_c9) = sk_c10,
inference(rw,[status(thm)],[c_0_61,c_0_66]) ).
cnf(c_0_127,negated_conjecture,
sk_c9 = sk_c10,
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_128,negated_conjecture,
( inverse(X4) != sk_c10
| inverse(X1) != sk_c10
| inverse(X3) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| inverse(inverse(sk_c10)) != sk_c10
| multiply(X2,inverse(X2)) != sk_c9
| multiply(sk_c10,identity) != sk_c9
| multiply(inverse(X2),sk_c10) != sk_c9
| multiply(sk_c10,multiply(X1,sk_c10)) != sk_c9 ),
inference(spm,[status(thm)],[c_0_36,c_0_28]) ).
cnf(c_0_129,negated_conjecture,
identity = sk_c10,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_127]),c_0_28]) ).
cnf(c_0_130,negated_conjecture,
( sk_c9 != sk_c10
| inverse(X4) != sk_c10
| inverse(X1) != sk_c10
| inverse(X3) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| inverse(inverse(sk_c10)) != sk_c10
| multiply(X2,inverse(X2)) != sk_c9
| multiply(inverse(X2),sk_c10) != sk_c9
| multiply(sk_c10,multiply(X1,sk_c10)) != sk_c9 ),
inference(rw,[status(thm)],[c_0_128,c_0_75]) ).
cnf(c_0_131,plain,
multiply(inverse(X1),X1) = sk_c10,
inference(rw,[status(thm)],[c_0_28,c_0_129]) ).
cnf(c_0_132,negated_conjecture,
( sk_c9 != sk_c10
| inverse(X4) != sk_c10
| inverse(X1) != sk_c10
| inverse(X3) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| multiply(X2,inverse(X2)) != sk_c9
| multiply(inverse(X2),sk_c10) != sk_c9
| multiply(sk_c10,multiply(X1,sk_c10)) != sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_89])]) ).
cnf(c_0_133,plain,
multiply(X1,sk_c10) = X1,
inference(rw,[status(thm)],[c_0_75,c_0_129]) ).
cnf(c_0_134,plain,
multiply(sk_c10,X1) = X1,
inference(rw,[status(thm)],[c_0_29,c_0_129]) ).
cnf(c_0_135,plain,
multiply(X1,inverse(X1)) = sk_c10,
inference(spm,[status(thm)],[c_0_131,c_0_89]) ).
cnf(c_0_136,plain,
inverse(sk_c10) = sk_c10,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_129]),c_0_129]) ).
cnf(c_0_137,negated_conjecture,
inverse(X1) != sk_c10,
inference(cn,[status(thm)],[inference(rw,[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(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)],[c_0_132,c_0_127]),c_0_127]),c_0_127]),c_0_127]),c_0_127]),c_0_127])]),c_0_133]),c_0_134]),c_0_133]),c_0_135]),c_0_133]),c_0_133])])])])]),c_0_136])]) ).
cnf(c_0_138,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_53,c_0_137]),c_0_137]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP218-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n016.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 20 20:11:21 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.52 Running first-order theorem proving
% 0.25/0.52 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
% 2.29/0.90 % Version: 3.5.1
% 2.29/0.90 % Preprocessing class: FSMSSMSMSSSNFFN.
% 2.29/0.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.29/0.90 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 2.29/0.90 % Starting new_bool_3 with 300s (1) cores
% 2.29/0.90 % Starting new_bool_1 with 300s (1) cores
% 2.29/0.90 % Starting sh5l with 300s (1) cores
% 2.29/0.90 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 687929 completed with status 0
% 2.29/0.90 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 2.29/0.90 % Preprocessing class: FSMSSMSMSSSNFFN.
% 2.29/0.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.29/0.90 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 2.29/0.90 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.29/0.90 % No SInE strategy applied
% 2.29/0.90 % Search class: FGHPS-FFMM21-SFFFFFNN
% 2.29/0.90 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.29/0.90 % Starting SubtermCWHack with 136s (1) cores
% 2.29/0.90 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 2.29/0.90 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.29/0.90 % Starting new_bool_3 with 136s (1) cores
% 2.29/0.90 % Starting new_bool_1 with 136s (1) cores
% 2.29/0.90 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 687935 completed with status 0
% 2.29/0.90 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 2.29/0.90 % Preprocessing class: FSMSSMSMSSSNFFN.
% 2.29/0.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.29/0.90 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 2.29/0.90 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.29/0.90 % No SInE strategy applied
% 2.29/0.90 % Search class: FGHPS-FFMM21-SFFFFFNN
% 2.29/0.90 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.29/0.90 % Starting SubtermCWHack with 136s (1) cores
% 2.29/0.90 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 2.29/0.90 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.29/0.90 % Preprocessing time : 0.002 s
% 2.29/0.90 % Presaturation interreduction done
% 2.29/0.90
% 2.29/0.90 % Proof found!
% 2.29/0.90 % SZS status Unsatisfiable
% 2.29/0.90 % SZS output start CNFRefutation
% See solution above
% 2.29/0.90 % Parsed axioms : 44
% 2.29/0.90 % Removed by relevancy pruning/SinE : 0
% 2.29/0.90 % Initial clauses : 44
% 2.29/0.90 % Removed in clause preprocessing : 0
% 2.29/0.90 % Initial clauses in saturation : 44
% 2.29/0.90 % Processed clauses : 2747
% 2.29/0.90 % ...of these trivial : 53
% 2.29/0.90 % ...subsumed : 1913
% 2.29/0.90 % ...remaining for further processing : 781
% 2.29/0.90 % Other redundant clauses eliminated : 6
% 2.29/0.90 % Clauses deleted for lack of memory : 0
% 2.29/0.90 % Backward-subsumed : 77
% 2.29/0.90 % Backward-rewritten : 521
% 2.29/0.90 % Generated clauses : 11222
% 2.29/0.90 % ...of the previous two non-redundant : 10794
% 2.29/0.90 % ...aggressively subsumed : 0
% 2.29/0.90 % Contextual simplify-reflections : 16
% 2.29/0.90 % Paramodulations : 11186
% 2.29/0.90 % Factorizations : 6
% 2.29/0.90 % NegExts : 0
% 2.29/0.90 % Equation resolutions : 6
% 2.29/0.90 % Disequality decompositions : 0
% 2.29/0.90 % Total rewrite steps : 4243
% 2.29/0.90 % ...of those cached : 3955
% 2.29/0.90 % Propositional unsat checks : 0
% 2.29/0.90 % Propositional check models : 0
% 2.29/0.90 % Propositional check unsatisfiable : 0
% 2.29/0.90 % Propositional clauses : 0
% 2.29/0.90 % Propositional clauses after purity: 0
% 2.29/0.90 % Propositional unsat core size : 0
% 2.29/0.90 % Propositional preprocessing time : 0.000
% 2.29/0.90 % Propositional encoding time : 0.000
% 2.29/0.90 % Propositional solver time : 0.000
% 2.29/0.90 % Success case prop preproc time : 0.000
% 2.29/0.90 % Success case prop encoding time : 0.000
% 2.29/0.90 % Success case prop solver time : 0.000
% 2.29/0.90 % Current number of processed clauses : 109
% 2.29/0.90 % Positive orientable unit clauses : 12
% 2.29/0.90 % Positive unorientable unit clauses: 0
% 2.29/0.90 % Negative unit clauses : 1
% 2.29/0.90 % Non-unit-clauses : 96
% 2.29/0.90 % Current number of unprocessed clauses: 7704
% 2.29/0.90 % ...number of literals in the above : 36952
% 2.29/0.90 % Current number of archived formulas : 0
% 2.29/0.90 % Current number of archived clauses : 670
% 2.29/0.90 % Clause-clause subsumption calls (NU) : 20851
% 2.29/0.90 % Rec. Clause-clause subsumption calls : 17387
% 2.29/0.90 % Non-unit clause-clause subsumptions : 2001
% 2.29/0.90 % Unit Clause-clause subsumption calls : 653
% 2.29/0.90 % Rewrite failures with RHS unbound : 0
% 2.29/0.90 % BW rewrite match attempts : 59
% 2.29/0.90 % BW rewrite match successes : 45
% 2.29/0.90 % Condensation attempts : 0
% 2.29/0.90 % Condensation successes : 0
% 2.29/0.90 % Termbank termtop insertions : 146417
% 2.29/0.90 % Search garbage collected termcells : 38
% 2.29/0.90
% 2.29/0.90 % -------------------------------------------------
% 2.29/0.90 % User time : 0.324 s
% 2.29/0.90 % System time : 0.022 s
% 2.29/0.90 % Total time : 0.345 s
% 2.29/0.90 % Maximum resident set size: 3656 pages
% 2.29/0.90
% 2.29/0.90 % -------------------------------------------------
% 2.29/0.90 % User time : 1.591 s
% 2.29/0.90 % System time : 0.081 s
% 2.29/0.90 % Total time : 1.672 s
% 2.29/0.90 % Maximum resident set size: 4608 pages
% 2.29/0.90 % E exiting
%------------------------------------------------------------------------------