%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE023+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 12:58:38 PM UTC 2026
% Result : Theorem 117.95s 17.95s
% Output : CNFRefutation 117.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 18
% Syntax : Number of formulae : 140 ( 102 unt; 0 def)
% Number of atoms : 213 ( 137 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 123 ( 50 ~; 47 |; 15 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 163 ( 4 sgn 70 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(test_3,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(goals,conjecture,
! [X4,X5,X6] :
( ( test(X6)
& test(X5) )
=> ( addition(multiplication(X5,X4),multiplication(X4,X6)) = multiplication(X4,X6)
=> addition(multiplication(X4,c(X6)),multiplication(c(X5),X4)) = multiplication(c(X5),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(test_2,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( addition(X4,X5) = one
& multiplication(X5,X4) = zero
& multiplication(X4,X5) = zero ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(test_deMorgan2,axiom,
! [X4,X5] :
( ( test(X5)
& test(X4) )
=> c(multiplication(X4,X5)) = addition(c(X4),c(X5)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+2.ax',test_deMorgan2) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(test_deMorgan1,axiom,
! [X4,X5] :
( ( test(X5)
& test(X4) )
=> c(addition(X4,X5)) = multiplication(c(X4),c(X5)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+2.ax',test_deMorgan1) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(c_0_18,plain,
! [X12] : addition(X12,zero) = X12,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_19,plain,
! [X7,X8] : addition(X7,X8) = addition(X8,X7),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_20,plain,
! [X35,X36] :
( ( ~ test(X35)
| c(X35) = X36
| ~ complement(X35,X36) )
& ( ~ test(X35)
| complement(X35,X36)
| c(X35) != X36 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])])]) ).
fof(c_0_21,negated_conjecture,
~ ! [X4,X5,X6] :
( ( test(X6)
& test(X5) )
=> ( addition(multiplication(X5,X4),multiplication(X4,X6)) = multiplication(X4,X6)
=> addition(multiplication(X4,c(X6)),multiplication(c(X5),X4)) = multiplication(c(X5),X4) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_22,plain,
! [X33,X34] :
( ( complement(X34,X33)
| addition(X33,X34) != one
| multiplication(X34,X33) != zero
| multiplication(X33,X34) != zero )
& ( ~ complement(X34,X33)
| addition(X33,X34) = one )
& ( ~ complement(X34,X33)
| multiplication(X34,X33) = zero )
& ( ~ complement(X34,X33)
| multiplication(X33,X34) = zero ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])])]) ).
cnf(c_0_23,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_25,plain,
! [X25] : multiplication(X25,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
fof(c_0_26,plain,
! [X26] : multiplication(zero,X26) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_27,plain,
( ~ test(X1)
| c(X1) != X2
| complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_28,negated_conjecture,
( addition(multiplication(esk2_0,c(esk4_0)),multiplication(c(esk3_0),esk2_0)) != multiplication(c(esk3_0),esk2_0)
& addition(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)) = multiplication(esk2_0,esk4_0)
& test(esk4_0)
& test(esk3_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
cnf(c_0_29,plain,
( addition(X1,X2) != one
| multiplication(X2,X1) != zero
| multiplication(X1,X2) != zero
| complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
( ~ test(X1)
| complement(X1,c(X1)) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_34,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_35,plain,
! [X40,X41] :
( c(multiplication(X40,X41)) = addition(c(X40),c(X41))
| ~ test(X41)
| ~ test(X40) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_deMorgan2])])]) ).
fof(c_0_36,plain,
! [X29,X31,X32] :
( ( test(X31)
| ~ complement(X32,X31) )
& ( complement(esk1_1(X29),X29)
| ~ test(X29) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[test_1])])])])])]) ).
cnf(c_0_37,plain,
( X1 != one
| complement(X1,zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_38,negated_conjecture,
test(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_39,plain,
( ~ complement(X2,X1)
| addition(X1,X2) = one ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_40,negated_conjecture,
complement(esk3_0,c(esk3_0)),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_41,plain,
( ~ complement(X1,X2)
| multiplication(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_42,plain,
( ~ complement(X2,X1)
| multiplication(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_43,plain,
( ~ test(X2)
| ~ test(X1)
| c(multiplication(X1,X2)) = addition(c(X1),c(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,plain,
( X1 != one
| complement(zero,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_23]),c_0_32]),c_0_31])]) ).
cnf(c_0_45,plain,
( ~ complement(X1,X2)
| test(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_46,plain,
complement(one,zero),
inference(er,[status(thm)],[c_0_37]) ).
cnf(c_0_47,negated_conjecture,
( c(esk4_0) != X1
| complement(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_38]) ).
fof(c_0_48,plain,
! [X38,X39] :
( c(addition(X38,X39)) = multiplication(c(X38),c(X39))
| ~ test(X39)
| ~ test(X38) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_deMorgan1])])]) ).
cnf(c_0_49,negated_conjecture,
addition(esk3_0,c(esk3_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_24]) ).
cnf(c_0_50,negated_conjecture,
multiplication(esk3_0,c(esk3_0)) = zero,
inference(spm,[status(thm)],[c_0_41,c_0_40]) ).
cnf(c_0_51,negated_conjecture,
multiplication(c(esk3_0),esk3_0) = zero,
inference(spm,[status(thm)],[c_0_42,c_0_40]) ).
cnf(c_0_52,negated_conjecture,
( ~ test(X1)
| addition(c(esk4_0),c(X1)) = c(multiplication(esk4_0,X1)) ),
inference(spm,[status(thm)],[c_0_43,c_0_38]) ).
cnf(c_0_53,plain,
( ~ test(X1)
| ~ complement(X1,X2)
| c(X1) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_54,plain,
complement(zero,one),
inference(er,[status(thm)],[c_0_44]) ).
cnf(c_0_55,plain,
test(zero),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_56,negated_conjecture,
complement(esk4_0,c(esk4_0)),
inference(er,[status(thm)],[c_0_47]) ).
cnf(c_0_57,plain,
( ~ test(X2)
| ~ test(X1)
| c(addition(X1,X2)) = multiplication(c(X1),c(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_58,negated_conjecture,
complement(c(esk3_0),esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_49]),c_0_50])]),c_0_51])]) ).
cnf(c_0_59,negated_conjecture,
test(c(esk3_0)),
inference(spm,[status(thm)],[c_0_45,c_0_40]) ).
fof(c_0_60,plain,
! [X9,X10,X11] : addition(X11,addition(X10,X9)) = addition(addition(X11,X10),X9),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_61,negated_conjecture,
addition(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)) = multiplication(esk2_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_62,negated_conjecture,
( ~ test(X1)
| addition(c(esk3_0),c(X1)) = c(multiplication(esk3_0,X1)) ),
inference(spm,[status(thm)],[c_0_43,c_0_34]) ).
cnf(c_0_63,negated_conjecture,
addition(c(esk3_0),c(esk4_0)) = c(multiplication(esk4_0,esk3_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_34]),c_0_24]) ).
cnf(c_0_64,plain,
c(zero) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55])]) ).
cnf(c_0_65,negated_conjecture,
addition(esk4_0,c(esk4_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_56]),c_0_24]) ).
cnf(c_0_66,negated_conjecture,
multiplication(esk4_0,c(esk4_0)) = zero,
inference(spm,[status(thm)],[c_0_41,c_0_56]) ).
cnf(c_0_67,negated_conjecture,
multiplication(c(esk4_0),esk4_0) = zero,
inference(spm,[status(thm)],[c_0_42,c_0_56]) ).
fof(c_0_68,plain,
! [X22,X23,X24] : multiplication(addition(X22,X23),X24) = addition(multiplication(X22,X24),multiplication(X23,X24)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_69,negated_conjecture,
( ~ test(X1)
| multiplication(c(esk4_0),c(X1)) = c(addition(esk4_0,X1)) ),
inference(spm,[status(thm)],[c_0_57,c_0_38]) ).
cnf(c_0_70,negated_conjecture,
c(c(esk3_0)) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_58]),c_0_59])]) ).
fof(c_0_71,plain,
! [X14,X15,X16] : multiplication(X14,multiplication(X15,X16)) = multiplication(multiplication(X14,X15),X16),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_72,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_73,negated_conjecture,
addition(multiplication(esk2_0,esk4_0),multiplication(esk3_0,esk2_0)) = multiplication(esk2_0,esk4_0),
inference(rw,[status(thm)],[c_0_61,c_0_24]) ).
cnf(c_0_74,negated_conjecture,
c(multiplication(esk4_0,esk3_0)) = c(multiplication(esk3_0,esk4_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_38]),c_0_63]) ).
cnf(c_0_75,plain,
( ~ test(X1)
| addition(one,c(X1)) = one ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_55]),c_0_31]),c_0_64]),c_0_24]),c_0_64]) ).
fof(c_0_76,plain,
! [X19,X20,X21] : multiplication(X19,addition(X20,X21)) = addition(multiplication(X19,X20),multiplication(X19,X21)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_77,plain,
! [X17] : multiplication(X17,one) = X17,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_78,negated_conjecture,
complement(c(esk4_0),esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_65]),c_0_66])]),c_0_67])]) ).
cnf(c_0_79,negated_conjecture,
test(c(esk4_0)),
inference(spm,[status(thm)],[c_0_45,c_0_56]) ).
fof(c_0_80,plain,
! [X13] : addition(X13,X13) = X13,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_81,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_82,negated_conjecture,
( ~ test(X1)
| multiplication(c(X1),c(esk4_0)) = c(addition(X1,esk4_0)) ),
inference(spm,[status(thm)],[c_0_57,c_0_38]) ).
cnf(c_0_83,negated_conjecture,
c(addition(esk4_0,c(esk3_0))) = multiplication(c(esk4_0),esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_59]),c_0_70]) ).
cnf(c_0_84,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_85,negated_conjecture,
addition(multiplication(esk2_0,esk4_0),addition(multiplication(esk3_0,esk2_0),X1)) = addition(multiplication(esk2_0,esk4_0),X1),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_86,negated_conjecture,
addition(esk3_0,addition(c(esk3_0),X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_72,c_0_49]) ).
cnf(c_0_87,negated_conjecture,
addition(c(esk3_0),c(esk4_0)) = c(multiplication(esk3_0,esk4_0)),
inference(rw,[status(thm)],[c_0_63,c_0_74]) ).
cnf(c_0_88,negated_conjecture,
addition(one,c(esk4_0)) = one,
inference(spm,[status(thm)],[c_0_75,c_0_38]) ).
fof(c_0_89,plain,
! [X18] : multiplication(one,X18) = X18,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_90,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_91,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_92,negated_conjecture,
c(c(esk4_0)) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_78]),c_0_79])]) ).
cnf(c_0_93,negated_conjecture,
( ~ test(X1)
| multiplication(c(esk3_0),c(X1)) = c(addition(esk3_0,X1)) ),
inference(spm,[status(thm)],[c_0_57,c_0_34]) ).
cnf(c_0_94,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_95,negated_conjecture,
multiplication(addition(c(esk3_0),X1),esk3_0) = multiplication(X1,esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_51]),c_0_30]) ).
cnf(c_0_96,negated_conjecture,
multiplication(c(esk4_0),esk3_0) = multiplication(esk3_0,c(esk4_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_59]),c_0_70]),c_0_24]),c_0_83]) ).
cnf(c_0_97,plain,
addition(multiplication(X1,multiplication(X2,X3)),multiplication(X4,X3)) = multiplication(addition(multiplication(X1,X2),X4),X3),
inference(spm,[status(thm)],[c_0_81,c_0_84]) ).
cnf(c_0_98,negated_conjecture,
addition(multiplication(esk2_0,esk4_0),multiplication(addition(esk3_0,X1),esk2_0)) = addition(multiplication(esk2_0,esk4_0),multiplication(X1,esk2_0)),
inference(spm,[status(thm)],[c_0_85,c_0_81]) ).
cnf(c_0_99,negated_conjecture,
addition(esk3_0,c(multiplication(esk3_0,esk4_0))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88]) ).
cnf(c_0_100,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_101,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_24]) ).
cnf(c_0_102,negated_conjecture,
addition(one,esk4_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_79]),c_0_92]) ).
cnf(c_0_103,plain,
addition(multiplication(X1,X2),multiplication(X3,multiplication(X4,X2))) = multiplication(addition(X1,multiplication(X3,X4)),X2),
inference(spm,[status(thm)],[c_0_81,c_0_84]) ).
cnf(c_0_104,negated_conjecture,
multiplication(c(esk3_0),c(esk3_0)) = c(esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_34]),c_0_94]) ).
cnf(c_0_105,negated_conjecture,
multiplication(esk4_0,addition(X1,c(esk4_0))) = multiplication(esk4_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_66]),c_0_23]) ).
cnf(c_0_106,negated_conjecture,
multiplication(c(multiplication(esk3_0,esk4_0)),esk3_0) = multiplication(esk3_0,c(esk4_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_87]),c_0_96]) ).
cnf(c_0_107,negated_conjecture,
multiplication(addition(multiplication(X1,esk4_0),X2),c(esk4_0)) = multiplication(X2,c(esk4_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_66]),c_0_31]),c_0_30]) ).
cnf(c_0_108,negated_conjecture,
addition(multiplication(esk2_0,esk4_0),multiplication(c(multiplication(esk3_0,esk4_0)),esk2_0)) = esk2_0,
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(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100]),c_0_24]),c_0_101]),c_0_24]),c_0_102]),c_0_91]) ).
cnf(c_0_109,negated_conjecture,
addition(multiplication(esk2_0,esk4_0),multiplication(addition(esk3_0,multiplication(X1,X2)),esk2_0)) = addition(multiplication(esk2_0,esk4_0),multiplication(X1,multiplication(X2,esk2_0))),
inference(spm,[status(thm)],[c_0_85,c_0_103]) ).
cnf(c_0_110,negated_conjecture,
multiplication(c(esk3_0),multiplication(c(esk3_0),X1)) = multiplication(c(esk3_0),X1),
inference(spm,[status(thm)],[c_0_84,c_0_104]) ).
cnf(c_0_111,negated_conjecture,
multiplication(esk4_0,c(multiplication(esk3_0,esk4_0))) = multiplication(esk4_0,c(esk3_0)),
inference(spm,[status(thm)],[c_0_105,c_0_87]) ).
cnf(c_0_112,negated_conjecture,
addition(multiplication(esk3_0,c(esk4_0)),multiplication(c(multiplication(esk3_0,esk4_0)),X1)) = multiplication(c(multiplication(esk3_0,esk4_0)),addition(esk3_0,X1)),
inference(spm,[status(thm)],[c_0_90,c_0_106]) ).
cnf(c_0_113,negated_conjecture,
multiplication(c(multiplication(esk3_0,esk4_0)),multiplication(esk2_0,c(esk4_0))) = multiplication(esk2_0,c(esk4_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_84]) ).
cnf(c_0_114,negated_conjecture,
addition(multiplication(esk2_0,esk4_0),multiplication(c(esk3_0),esk2_0)) = esk2_0,
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(spm,[status(thm)],[c_0_109,c_0_104]),c_0_49]),c_0_100]),c_0_24]),c_0_101]),c_0_24]),c_0_102]),c_0_91]),c_0_110]) ).
cnf(c_0_115,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_72,c_0_94]) ).
cnf(c_0_116,negated_conjecture,
multiplication(esk4_0,multiplication(c(multiplication(esk3_0,esk4_0)),X1)) = multiplication(esk4_0,multiplication(c(esk3_0),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_111]),c_0_84]) ).
cnf(c_0_117,negated_conjecture,
multiplication(c(multiplication(esk3_0,esk4_0)),addition(esk3_0,multiplication(esk2_0,c(esk4_0)))) = multiplication(addition(esk2_0,esk3_0),c(esk4_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_81]),c_0_24]) ).
cnf(c_0_118,negated_conjecture,
multiplication(c(esk3_0),addition(esk3_0,X1)) = multiplication(c(esk3_0),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_51]),c_0_30]) ).
cnf(c_0_119,negated_conjecture,
multiplication(c(esk3_0),multiplication(esk2_0,c(esk4_0))) = multiplication(esk2_0,c(esk4_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_114]),c_0_84]) ).
cnf(c_0_120,negated_conjecture,
addition(c(esk3_0),c(multiplication(esk4_0,esk3_0))) = c(multiplication(esk4_0,esk3_0)),
inference(spm,[status(thm)],[c_0_115,c_0_63]) ).
fof(c_0_121,plain,
! [X27,X28] :
( ( leq(X27,X28)
| addition(X27,X28) != X28 )
& ( addition(X27,X28) = X28
| ~ leq(X27,X28) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])]) ).
cnf(c_0_122,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_100]),c_0_24]) ).
cnf(c_0_123,negated_conjecture,
multiplication(esk4_0,multiplication(addition(esk2_0,esk3_0),c(esk4_0))) = multiplication(esk4_0,multiplication(esk2_0,c(esk4_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_118]),c_0_119]) ).
cnf(c_0_124,negated_conjecture,
addition(c(esk3_0),c(multiplication(esk3_0,esk4_0))) = c(multiplication(esk3_0,esk4_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_74]),c_0_74]) ).
cnf(c_0_125,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_126,negated_conjecture,
multiplication(addition(esk2_0,addition(esk3_0,multiplication(esk4_0,esk2_0))),c(esk4_0)) = multiplication(addition(esk2_0,esk3_0),c(esk4_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_103]),c_0_72]),c_0_24]),c_0_102]),c_0_100]) ).
cnf(c_0_127,negated_conjecture,
addition(one,c(multiplication(esk3_0,esk4_0))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_124]),c_0_99]) ).
cnf(c_0_128,plain,
( multiplication(X1,addition(X2,X3)) != multiplication(X1,X3)
| leq(multiplication(X1,X2),multiplication(X1,X3)) ),
inference(spm,[status(thm)],[c_0_125,c_0_90]) ).
cnf(c_0_129,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_24,c_0_72]) ).
cnf(c_0_130,negated_conjecture,
multiplication(c(esk3_0),addition(X1,addition(esk3_0,X2))) = multiplication(c(esk3_0),addition(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_118]),c_0_90]) ).
cnf(c_0_131,negated_conjecture,
addition(esk2_0,addition(esk3_0,addition(multiplication(esk4_0,esk2_0),multiplication(addition(esk2_0,esk3_0),c(esk4_0))))) = addition(esk2_0,addition(esk3_0,multiplication(esk4_0,esk2_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_126]),c_0_72]),c_0_72]),c_0_24]),c_0_88]),c_0_91]) ).
cnf(c_0_132,negated_conjecture,
addition(esk3_0,multiplication(addition(esk2_0,esk3_0),c(esk4_0))) = addition(esk3_0,multiplication(esk2_0,c(esk4_0))),
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(spm,[status(thm)],[c_0_122,c_0_117]),c_0_72]),c_0_81]),c_0_115]),c_0_24]),c_0_127]),c_0_100]) ).
cnf(c_0_133,plain,
( multiplication(X1,addition(X3,addition(X4,X2))) != multiplication(X1,addition(X3,X4))
| leq(multiplication(X1,X2),multiplication(X1,addition(X3,X4))) ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_134,negated_conjecture,
multiplication(c(esk3_0),addition(esk2_0,addition(multiplication(esk4_0,esk2_0),multiplication(addition(esk2_0,esk3_0),c(esk4_0))))) = multiplication(c(esk3_0),esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_130]),c_0_122]),c_0_24]),c_0_102]),c_0_100]) ).
cnf(c_0_135,negated_conjecture,
multiplication(c(esk3_0),multiplication(addition(esk2_0,esk3_0),c(esk4_0))) = multiplication(esk2_0,c(esk4_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_132]),c_0_118]),c_0_119]) ).
cnf(c_0_136,plain,
( ~ leq(X1,X2)
| addition(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_137,negated_conjecture,
leq(multiplication(esk2_0,c(esk4_0)),multiplication(c(esk3_0),esk2_0)),
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(spm,[status(thm)],[c_0_133,c_0_134]),c_0_135]),c_0_122]),c_0_24]),c_0_102]),c_0_100]),c_0_122]),c_0_24]),c_0_102]),c_0_100])]) ).
cnf(c_0_138,negated_conjecture,
addition(multiplication(esk2_0,c(esk4_0)),multiplication(c(esk3_0),esk2_0)) != multiplication(c(esk3_0),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_139,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_138]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE023+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.45 % Computer : n017.cluster.edu
% 0.21/0.45 % Model : x86_64 x86_64
% 0.21/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.45 % Memory : 8046.5625MB
% 0.21/0.45 % OS : Linux 6.8.0-71-generic
% 0.21/0.45 % CPULimit : 300
% 0.21/0.45 % WCLimit : 300
% 0.21/0.45 % DateTime : Sun Sep 20 22:33:42 UTC 2026
% 0.21/0.46 % CPUTime :
% 0.21/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 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
% 117.95/17.95 % Version: 3.5.1
% 117.95/17.95 % Preprocessing class: FSMSSMSSSSSNFFN.
% 117.95/17.95 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 117.95/17.95 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 117.95/17.95 % Starting new_bool_3 with 300s (1) cores
% 117.95/17.95 % Starting new_bool_1 with 300s (1) cores
% 117.95/17.95 % Starting sh5l with 300s (1) cores
% 117.95/17.95 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 781061 completed with status 0
% 117.95/17.95 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 117.95/17.95 % Preprocessing class: FSMSSMSSSSSNFFN.
% 117.95/17.95 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 117.95/17.95 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 117.95/17.95 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 117.95/17.95 % No SInE strategy applied
% 117.95/17.95 % Search class: FGUSM-FFMS21-MFFFFFNN
% 117.95/17.95 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 117.95/17.95 % Starting SubtermCWHack with 136s (1) cores
% 117.95/17.95 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 117.95/17.95 % Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 117.95/17.95 % Starting new_bool_3 with 136s (1) cores
% 117.95/17.95 % Starting new_bool_1 with 136s (1) cores
% 117.95/17.95 % G-E--_208_C18_F1_AE_CS_SP_PI_S0a with pid 781067 completed with status 0
% 117.95/17.95 % Result found by G-E--_208_C18_F1_AE_CS_SP_PI_S0a
% 117.95/17.95 % Preprocessing class: FSMSSMSSSSSNFFN.
% 117.95/17.95 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 117.95/17.95 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 117.95/17.95 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 117.95/17.95 % No SInE strategy applied
% 117.95/17.95 % Search class: FGUSM-FFMS21-MFFFFFNN
% 117.95/17.95 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 117.95/17.95 % Starting SubtermCWHack with 136s (1) cores
% 117.95/17.95 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 117.95/17.95 % Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 117.95/17.95 % Preprocessing time : 0.002 s
% 117.95/17.95
% 117.95/17.95 % Proof found!
% 117.95/17.95 % SZS status Theorem
% 117.95/17.95 % SZS output start CNFRefutation
% See solution above
% 117.95/17.96 % Parsed axioms : 19
% 117.95/17.96 % Removed by relevancy pruning/SinE : 0
% 117.95/17.96 % Initial clauses : 28
% 117.95/17.96 % Removed in clause preprocessing : 0
% 117.95/17.96 % Initial clauses in saturation : 28
% 117.95/17.96 % Processed clauses : 22771
% 117.95/17.96 % ...of these trivial : 1524
% 117.95/17.96 % ...subsumed : 17709
% 117.95/17.96 % ...remaining for further processing : 3538
% 117.95/17.96 % Other redundant clauses eliminated : 0
% 117.95/17.96 % Clauses deleted for lack of memory : 0
% 117.95/17.96 % Backward-subsumed : 189
% 117.95/17.96 % Backward-rewritten : 662
% 117.95/17.96 % Generated clauses : 463516
% 117.95/17.96 % ...of the previous two non-redundant : 398562
% 117.95/17.96 % ...aggressively subsumed : 0
% 117.95/17.96 % Contextual simplify-reflections : 8
% 117.95/17.96 % Paramodulations : 463476
% 117.95/17.96 % Factorizations : 2
% 117.95/17.96 % NegExts : 0
% 117.95/17.96 % Equation resolutions : 38
% 117.95/17.96 % Disequality decompositions : 0
% 117.95/17.96 % Total rewrite steps : 876272
% 117.95/17.96 % ...of those cached : 791195
% 117.95/17.96 % Propositional unsat checks : 0
% 117.95/17.96 % Propositional check models : 0
% 117.95/17.96 % Propositional check unsatisfiable : 0
% 117.95/17.96 % Propositional clauses : 0
% 117.95/17.96 % Propositional clauses after purity: 0
% 117.95/17.96 % Propositional unsat core size : 0
% 117.95/17.96 % Propositional preprocessing time : 0.000
% 117.95/17.96 % Propositional encoding time : 0.000
% 117.95/17.96 % Propositional solver time : 0.000
% 117.95/17.96 % Success case prop preproc time : 0.000
% 117.95/17.96 % Success case prop encoding time : 0.000
% 117.95/17.96 % Success case prop solver time : 0.000
% 117.95/17.96 % Current number of processed clauses : 2687
% 117.95/17.96 % Positive orientable unit clauses : 1256
% 117.95/17.96 % Positive unorientable unit clauses: 20
% 117.95/17.96 % Negative unit clauses : 1
% 117.95/17.96 % Non-unit-clauses : 1410
% 117.95/17.96 % Current number of unprocessed clauses: 373460
% 117.95/17.96 % ...number of literals in the above : 823472
% 117.95/17.96 % Current number of archived formulas : 0
% 117.95/17.96 % Current number of archived clauses : 851
% 117.95/17.96 % Clause-clause subsumption calls (NU) : 821301
% 117.95/17.96 % Rec. Clause-clause subsumption calls : 755289
% 117.95/17.96 % Non-unit clause-clause subsumptions : 17296
% 117.95/17.96 % Unit Clause-clause subsumption calls : 18582
% 117.95/17.96 % Rewrite failures with RHS unbound : 0
% 117.95/17.96 % BW rewrite match attempts : 4829
% 117.95/17.96 % BW rewrite match successes : 434
% 117.95/17.96 % Condensation attempts : 0
% 117.95/17.96 % Condensation successes : 0
% 117.95/17.96 % Termbank termtop insertions : 12108715
% 117.95/17.96 % Search garbage collected termcells : 220
% 117.95/17.96
% 117.95/17.96 % -------------------------------------------------
% 117.95/17.96 % User time : 16.183 s
% 117.95/17.96 % System time : 0.605 s
% 117.95/17.96 % Total time : 16.788 s
% 117.95/17.96 % Maximum resident set size: 3652 pages
% 117.95/17.96
% 117.95/17.96 % -------------------------------------------------
% 117.95/17.96 % User time : 81.239 s
% 117.95/17.96 % System time : 3.203 s
% 117.95/17.96 % Total time : 84.442 s
% 117.95/17.96 % Maximum resident set size: 4608 pages
% 117.95/17.96 % E exiting
%------------------------------------------------------------------------------