%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP309-1 : 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 : n018.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 12:43:10 PM UTC 2026
% Result : Unsatisfiable 0.39s 0.55s
% Output : CNFRefutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 19
% Syntax : Number of clauses : 110 ( 31 unt; 75 nHn; 86 RR)
% Number of literals : 219 ( 218 equ; 38 neg)
% Maximal clause size : 10 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_19,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_15,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_18,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_14,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_21,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_20,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_17,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_16,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_6,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_13,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_9,negated_conjecture,
multiply(sk_c5,sk_c6) = sk_c7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_12,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_22,negated_conjecture,
( inverse(X4) != sk_c6
| multiply(X4,sk_c6) != sk_c5
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != X1
| multiply(sk_c7,X1) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c6) != sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
cnf(c_0_19,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_20,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_21,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_22,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_23,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_24,plain,
multiply(inverse(inverse(inverse(X1))),X1) = identity,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_24]),c_0_23]) ).
cnf(c_0_26,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_20,c_0_25]) ).
cnf(c_0_27,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
prove_this_19 ).
cnf(c_0_28,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c2 ),
prove_this_15 ).
cnf(c_0_29,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c7,sk_c3) = identity
| multiply(sk_c1,sk_c7) = sk_c2 ),
inference(spm,[status(thm)],[c_0_20,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c7,sk_c3) = identity
| multiply(sk_c1,sk_c7) = identity ),
inference(spm,[status(thm)],[c_0_20,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
prove_this_18 ).
cnf(c_0_33,negated_conjecture,
( identity = sk_c2
| multiply(sk_c7,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_23,c_0_25]) ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c2 ),
prove_this_14 ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c3,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_26,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( identity = sk_c2
| inverse(sk_c7) = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_33]),c_0_34]) ).
cnf(c_0_38,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
prove_this_21 ).
cnf(c_0_39,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
prove_this_11 ).
cnf(c_0_40,negated_conjecture,
( identity = sk_c2
| multiply(sk_c3,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
( identity = sk_c2
| multiply(sk_c3,sk_c7) = identity ),
inference(spm,[status(thm)],[c_0_20,c_0_37]) ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c1) = sk_c7 ),
prove_this_20 ).
cnf(c_0_43,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c2 ),
prove_this_17 ).
cnf(c_0_44,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_38]) ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
prove_this_10 ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c3,sk_c7) = identity
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(spm,[status(thm)],[c_0_26,c_0_39]) ).
cnf(c_0_47,negated_conjecture,
( identity = sk_c6
| identity = sk_c2 ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c2 ),
prove_this_16 ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c4,sk_c6) = sk_c5 ),
inference(spm,[status(thm)],[c_0_26,c_0_42]) ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c4,sk_c6) = identity
| multiply(sk_c1,sk_c7) = sk_c2 ),
inference(spm,[status(thm)],[c_0_26,c_0_43]) ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c4,sk_c6) = identity
| multiply(sk_c1,sk_c7) = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_44]) ).
cnf(c_0_52,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c5 ),
prove_this_6 ).
cnf(c_0_53,negated_conjecture,
( inverse(sk_c7) = sk_c1
| inverse(sk_c3) = sk_c7 ),
inference(spm,[status(thm)],[c_0_25,c_0_27]) ).
cnf(c_0_54,negated_conjecture,
( identity = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_55,negated_conjecture,
( identity = sk_c6
| multiply(X1,sk_c2) = X1 ),
inference(spm,[status(thm)],[c_0_34,c_0_47]) ).
cnf(c_0_56,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
prove_this_13 ).
cnf(c_0_57,negated_conjecture,
( identity = sk_c2
| multiply(sk_c4,sk_c6) = sk_c5 ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_58,negated_conjecture,
( identity = sk_c2
| multiply(sk_c4,sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_59,negated_conjecture,
( inverse(sk_c7) = sk_c5
| multiply(sk_c7,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_20,c_0_52]) ).
cnf(c_0_60,negated_conjecture,
( inverse(sk_c7) = sk_c1
| multiply(sk_c7,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_20,c_0_53]) ).
cnf(c_0_61,negated_conjecture,
multiply(sk_c5,sk_c6) = sk_c7,
prove_this_9 ).
cnf(c_0_62,negated_conjecture,
( sk_c6 = sk_c7
| identity = sk_c6 ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c7,sk_c2) = sk_c6 ),
prove_this_12 ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c4,sk_c6) = identity
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(spm,[status(thm)],[c_0_26,c_0_56]) ).
cnf(c_0_65,negated_conjecture,
( identity = sk_c5
| identity = sk_c2 ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_66,negated_conjecture,
( sk_c1 = sk_c5
| multiply(sk_c7,sk_c3) = identity ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_67,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_20,c_0_27]) ).
cnf(c_0_68,negated_conjecture,
multiply(sk_c5,multiply(sk_c6,X1)) = multiply(sk_c7,X1),
inference(spm,[status(thm)],[c_0_19,c_0_61]) ).
cnf(c_0_69,negated_conjecture,
( sk_c6 = sk_c7
| multiply(sk_c6,X1) = X1 ),
inference(spm,[status(thm)],[c_0_21,c_0_62]) ).
cnf(c_0_70,negated_conjecture,
( identity = sk_c5
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_71,negated_conjecture,
( identity = sk_c5
| multiply(X1,sk_c2) = X1 ),
inference(spm,[status(thm)],[c_0_34,c_0_65]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c7) = sk_c5 ),
prove_this_5 ).
cnf(c_0_73,negated_conjecture,
( inverse(sk_c7) = sk_c1
| multiply(sk_c3,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_25,c_0_32]) ).
cnf(c_0_74,negated_conjecture,
( sk_c1 = sk_c5
| inverse(sk_c7) = sk_c3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_66]),c_0_34]) ).
cnf(c_0_75,negated_conjecture,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c3,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_20,c_0_32]) ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c3,sk_c7) = identity
| multiply(sk_c7,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_67]) ).
cnf(c_0_77,negated_conjecture,
multiply(sk_c7,inverse(sk_c6)) = sk_c5,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_26]),c_0_34]) ).
cnf(c_0_78,negated_conjecture,
( sk_c6 = sk_c7
| inverse(sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_69]) ).
cnf(c_0_79,negated_conjecture,
( sk_c6 = sk_c7
| identity = sk_c5 ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_80,negated_conjecture,
( sk_c1 = sk_c5
| multiply(sk_c3,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_81,negated_conjecture,
( sk_c1 = sk_c5
| multiply(sk_c3,sk_c7) = identity ),
inference(spm,[status(thm)],[c_0_20,c_0_74]) ).
cnf(c_0_82,negated_conjecture,
( identity = sk_c6
| multiply(sk_c7,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_83,negated_conjecture,
( sk_c5 = sk_c7
| sk_c6 = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_34]) ).
cnf(c_0_84,negated_conjecture,
( sk_c5 = sk_c6
| sk_c6 = sk_c7 ),
inference(spm,[status(thm)],[c_0_62,c_0_79]) ).
cnf(c_0_85,negated_conjecture,
( identity = sk_c6
| sk_c1 = sk_c5 ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_86,negated_conjecture,
multiply(inverse(sk_c5),sk_c7) = sk_c6,
inference(spm,[status(thm)],[c_0_22,c_0_61]) ).
cnf(c_0_87,negated_conjecture,
( identity = sk_c6
| inverse(sk_c7) = sk_c1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_82]),c_0_34]) ).
cnf(c_0_88,negated_conjecture,
sk_c6 = sk_c7,
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_89,negated_conjecture,
( sk_c1 = sk_c5
| multiply(sk_c6,X1) = X1 ),
inference(spm,[status(thm)],[c_0_21,c_0_85]) ).
cnf(c_0_90,negated_conjecture,
multiply(inverse(sk_c5),multiply(sk_c7,X1)) = multiply(sk_c6,X1),
inference(spm,[status(thm)],[c_0_19,c_0_86]) ).
cnf(c_0_91,negated_conjecture,
( identity = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(spm,[status(thm)],[c_0_25,c_0_87]) ).
cnf(c_0_92,negated_conjecture,
identity = sk_c5,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_88]),c_0_26]) ).
cnf(c_0_93,negated_conjecture,
( sk_c1 = sk_c5
| inverse(sk_c6) = identity ),
inference(spm,[status(thm)],[c_0_26,c_0_89]) ).
cnf(c_0_94,negated_conjecture,
multiply(sk_c6,inverse(sk_c7)) = inverse(sk_c5),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_26]),c_0_34]) ).
cnf(c_0_95,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_96,negated_conjecture,
( inverse(X4) != sk_c6
| multiply(X4,sk_c6) != sk_c5
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != X1
| multiply(sk_c7,X1) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(fof_simplification,[status(thm)],[prove_this_22]) ).
cnf(c_0_97,negated_conjecture,
( sk_c5 = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_88]),c_0_92]) ).
cnf(c_0_98,negated_conjecture,
( sk_c5 = sk_c7
| sk_c1 = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_93]),c_0_34]) ).
cnf(c_0_99,negated_conjecture,
inverse(sk_c5) = sk_c5,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_88]),c_0_26]),c_0_92]) ).
cnf(c_0_100,negated_conjecture,
multiply(sk_c7,multiply(inverse(sk_c6),X1)) = multiply(sk_c5,X1),
inference(spm,[status(thm)],[c_0_68,c_0_95]) ).
cnf(c_0_101,negated_conjecture,
( inverse(X4) != sk_c6
| multiply(X4,sk_c6) != sk_c5
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != X1
| multiply(sk_c7,X1) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c6) != sk_c5 ),
c_0_96 ).
cnf(c_0_102,plain,
multiply(X1,sk_c5) = X1,
inference(rw,[status(thm)],[c_0_34,c_0_92]) ).
cnf(c_0_103,negated_conjecture,
sk_c5 = sk_c7,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99])]) ).
cnf(c_0_104,negated_conjecture,
multiply(sk_c5,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_88]),c_0_95]) ).
cnf(c_0_105,negated_conjecture,
( inverse(X1) != sk_c7
| inverse(X3) != sk_c7
| inverse(X2) != sk_c6
| inverse(sk_c7) != sk_c5
| multiply(X3,sk_c7) != sk_c6
| multiply(X2,sk_c6) != sk_c5
| multiply(sk_c7,sk_c6) != sk_c5
| multiply(sk_c7,multiply(X1,sk_c7)) != sk_c6 ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_61])])]) ).
cnf(c_0_106,plain,
multiply(X1,sk_c7) = X1,
inference(rw,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_107,negated_conjecture,
multiply(sk_c7,X1) = X1,
inference(rw,[status(thm)],[c_0_104,c_0_103]) ).
cnf(c_0_108,negated_conjecture,
inverse(sk_c7) = sk_c7,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_103]),c_0_103]) ).
cnf(c_0_109,negated_conjecture,
$false,
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_88]),c_0_88]),c_0_88]),c_0_88]),c_0_88]),c_0_106]),c_0_107]),c_0_106]),c_0_103]),c_0_106]),c_0_103]),c_0_106]),c_0_108]),c_0_103])])])])]),c_0_108])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP309-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n018.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 20:10:58 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.39/0.55 % Version: 3.5.1
% 0.39/0.55 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.39/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.39/0.55 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.39/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.39/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.39/0.55 % Starting sh5l with 300s (1) cores
% 0.39/0.55 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 81493 completed with status 0
% 0.39/0.55 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.39/0.55 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.39/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.39/0.55 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.39/0.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.39/0.55 % No SInE strategy applied
% 0.39/0.55 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.39/0.55 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.39/0.55 % Starting SubtermCWHack with 136s (1) cores
% 0.39/0.55 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.39/0.55 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.39/0.55 % Starting new_bool_3 with 136s (1) cores
% 0.39/0.55 % Starting new_bool_1 with 136s (1) cores
% 0.39/0.55 % SubtermCWHack with pid 81497 completed with status 0
% 0.39/0.55 % Result found by SubtermCWHack
% 0.39/0.55 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.39/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.39/0.55 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.39/0.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.39/0.55 % No SInE strategy applied
% 0.39/0.55 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.39/0.55 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.39/0.55 % Starting SubtermCWHack with 136s (1) cores
% 0.39/0.55 % Preprocessing time : 0.001 s
% 0.39/0.55
% 0.39/0.55 % Proof found!
% 0.39/0.55 % SZS status Unsatisfiable
% 0.39/0.55 % SZS output start CNFRefutation
% See solution above
% 0.39/0.56 % Parsed axioms : 25
% 0.39/0.56 % Removed by relevancy pruning/SinE : 0
% 0.39/0.56 % Initial clauses : 25
% 0.39/0.56 % Removed in clause preprocessing : 0
% 0.39/0.56 % Initial clauses in saturation : 25
% 0.39/0.56 % Processed clauses : 5434
% 0.39/0.56 % ...of these trivial : 188
% 0.39/0.56 % ...subsumed : 4335
% 0.39/0.56 % ...remaining for further processing : 911
% 0.39/0.56 % Other redundant clauses eliminated : 4
% 0.39/0.56 % Clauses deleted for lack of memory : 0
% 0.39/0.56 % Backward-subsumed : 35
% 0.39/0.56 % Backward-rewritten : 668
% 0.39/0.56 % Generated clauses : 25612
% 0.39/0.56 % ...of the previous two non-redundant : 24466
% 0.39/0.56 % ...aggressively subsumed : 0
% 0.39/0.56 % Contextual simplify-reflections : 3
% 0.39/0.56 % Paramodulations : 25601
% 0.39/0.56 % Factorizations : 9
% 0.39/0.56 % NegExts : 0
% 0.39/0.56 % Equation resolutions : 4
% 0.39/0.56 % Disequality decompositions : 0
% 0.39/0.56 % Total rewrite steps : 12846
% 0.39/0.56 % ...of those cached : 11873
% 0.39/0.56 % Propositional unsat checks : 0
% 0.39/0.56 % Propositional check models : 0
% 0.39/0.56 % Propositional check unsatisfiable : 0
% 0.39/0.56 % Propositional clauses : 0
% 0.39/0.56 % Propositional clauses after purity: 0
% 0.39/0.56 % Propositional unsat core size : 0
% 0.39/0.56 % Propositional preprocessing time : 0.000
% 0.39/0.56 % Propositional encoding time : 0.000
% 0.39/0.56 % Propositional solver time : 0.000
% 0.39/0.56 % Success case prop preproc time : 0.000
% 0.39/0.56 % Success case prop encoding time : 0.000
% 0.39/0.56 % Success case prop solver time : 0.000
% 0.39/0.56 % Current number of processed clauses : 206
% 0.39/0.56 % Positive orientable unit clauses : 23
% 0.39/0.56 % Positive unorientable unit clauses: 0
% 0.39/0.56 % Negative unit clauses : 0
% 0.39/0.56 % Non-unit-clauses : 183
% 0.39/0.56 % Current number of unprocessed clauses: 3348
% 0.39/0.56 % ...number of literals in the above : 8063
% 0.39/0.56 % Current number of archived formulas : 0
% 0.39/0.56 % Current number of archived clauses : 703
% 0.39/0.56 % Clause-clause subsumption calls (NU) : 20150
% 0.39/0.56 % Rec. Clause-clause subsumption calls : 18831
% 0.39/0.56 % Non-unit clause-clause subsumptions : 4357
% 0.39/0.56 % Unit Clause-clause subsumption calls : 370
% 0.39/0.56 % Rewrite failures with RHS unbound : 0
% 0.39/0.56 % BW rewrite match attempts : 88
% 0.39/0.56 % BW rewrite match successes : 44
% 0.39/0.56 % Condensation attempts : 0
% 0.39/0.56 % Condensation successes : 0
% 0.39/0.56 % Termbank termtop insertions : 187206
% 0.39/0.56 % Search garbage collected termcells : 26
% 0.39/0.56
% 0.39/0.56 % -------------------------------------------------
% 0.39/0.56 % User time : 0.115 s
% 0.39/0.56 % System time : 0.009 s
% 0.39/0.56 % Total time : 0.124 s
% 0.39/0.56 % Maximum resident set size: 3644 pages
% 0.39/0.56
% 0.39/0.56 % -------------------------------------------------
% 0.39/0.56 % User time : 0.534 s
% 0.39/0.56 % System time : 0.036 s
% 0.39/0.56 % Total time : 0.570 s
% 0.39/0.56 % Maximum resident set size: 4608 pages
% 0.39/0.56 % E exiting
%------------------------------------------------------------------------------