%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE010+4 : 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 : n007.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 12:58:35 PM UTC 2026
% Result : Theorem 0.16s 5.52s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 107 ( 61 unt; 0 def)
% Number of atoms : 183 ( 97 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 138 ( 62 ~; 53 |; 15 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 140 ( 1 sgn 54 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(goals,conjecture,
! [X4,X5] :
( ( test(X4)
& test(X5) )
=> ( leq(addition(addition(addition(addition(multiplication(X5,X4),multiplication(c(X5),X4)),multiplication(X4,X5)),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))),one)
& leq(one,addition(addition(addition(addition(multiplication(X5,X4),multiplication(c(X5),X4)),multiplication(X4,X5)),multiplication(c(X4),X5)),multiplication(c(X4),c(X5)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
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(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
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(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
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(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(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(c_0_14,plain,
! [X34,X35] :
( ( ~ test(X34)
| c(X34) = X35
| ~ complement(X34,X35) )
& ( ~ test(X34)
| complement(X34,X35)
| c(X34) != X35 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])])]) ).
fof(c_0_15,plain,
! [X32,X33] :
( ( complement(X33,X32)
| addition(X32,X33) != one
| multiplication(X33,X32) != zero
| multiplication(X32,X33) != zero )
& ( ~ complement(X33,X32)
| addition(X32,X33) = one )
& ( ~ complement(X33,X32)
| multiplication(X33,X32) = zero )
& ( ~ complement(X33,X32)
| multiplication(X32,X33) = 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_16,plain,
( ~ test(X1)
| c(X1) != X2
| complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_17,negated_conjecture,
~ ! [X4,X5] :
( ( test(X4)
& test(X5) )
=> ( leq(addition(addition(addition(addition(multiplication(X5,X4),multiplication(c(X5),X4)),multiplication(X4,X5)),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))),one)
& leq(one,addition(addition(addition(addition(multiplication(X5,X4),multiplication(c(X5),X4)),multiplication(X4,X5)),multiplication(c(X4),X5)),multiplication(c(X4),c(X5)))) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_18,plain,
( ~ complement(X2,X1)
| multiplication(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( ~ test(X1)
| complement(X1,c(X1)) ),
inference(er,[status(thm)],[c_0_16]) ).
fof(c_0_20,negated_conjecture,
( ( ~ leq(addition(addition(addition(addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0)),multiplication(esk2_0,esk3_0)),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0)),multiplication(esk2_0,esk3_0)),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0)))) )
& test(esk2_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_17])])])]) ).
cnf(c_0_21,plain,
( ~ test(X1)
| multiplication(c(X1),X1) = zero ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,negated_conjecture,
zero = multiplication(c(esk3_0),esk3_0),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_24,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_25,plain,
( ~ complement(X1,X2)
| multiplication(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_26,plain,
( ~ test(X1)
| multiplication(c(X1),X1) = multiplication(c(esk3_0),esk3_0) ),
inference(rw,[status(thm)],[c_0_21,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_28,plain,
! [X11] : addition(X11,zero) = X11,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_29,plain,
( ~ complement(X2,X1)
| addition(X1,X2) = one ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_30,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( ~ complement(X1,X2)
| multiplication(X1,X2) = multiplication(c(esk3_0),esk3_0) ),
inference(rw,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_32,negated_conjecture,
multiplication(c(esk3_0),esk3_0) = multiplication(c(esk2_0),esk2_0),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
( ~ test(X1)
| addition(X1,c(X1)) = one ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_19]),c_0_30]) ).
cnf(c_0_35,plain,
( ~ complement(X1,X2)
| multiplication(X1,X2) = multiplication(c(esk2_0),esk2_0) ),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_33,c_0_30]) ).
cnf(c_0_37,negated_conjecture,
one = addition(esk3_0,c(esk3_0)),
inference(spm,[status(thm)],[c_0_34,c_0_22]) ).
cnf(c_0_38,plain,
( ~ test(X1)
| multiplication(X1,c(X1)) = multiplication(c(esk2_0),esk2_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_19]) ).
cnf(c_0_39,plain,
addition(multiplication(c(esk3_0),esk3_0),X1) = X1,
inference(rw,[status(thm)],[c_0_36,c_0_23]) ).
cnf(c_0_40,plain,
( ~ test(X1)
| addition(X1,c(X1)) = addition(esk3_0,c(esk3_0)) ),
inference(rw,[status(thm)],[c_0_34,c_0_37]) ).
fof(c_0_41,plain,
! [X17] : multiplication(one,X17) = X17,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_42,plain,
! [X39,X40] :
( c(multiplication(X39,X40)) = addition(c(X39),c(X40))
| ~ test(X40)
| ~ test(X39) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_deMorgan2])])]) ).
fof(c_0_43,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_44,plain,
addition(X1,multiplication(c(esk3_0),esk3_0)) = X1,
inference(rw,[status(thm)],[c_0_33,c_0_23]) ).
cnf(c_0_45,negated_conjecture,
multiplication(c(esk2_0),esk2_0) = multiplication(esk2_0,c(esk2_0)),
inference(spm,[status(thm)],[c_0_38,c_0_27]) ).
fof(c_0_46,plain,
! [X28,X30,X31] :
( ( test(X30)
| ~ complement(X31,X30) )
& ( complement(esk1_1(X28),X28)
| ~ test(X28) ) ),
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])])])])])]) ).
fof(c_0_47,plain,
! [X21,X22,X23] : multiplication(addition(X21,X22),X23) = addition(multiplication(X21,X23),multiplication(X22,X23)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_48,plain,
addition(multiplication(c(esk2_0),esk2_0),X1) = X1,
inference(rw,[status(thm)],[c_0_39,c_0_32]) ).
cnf(c_0_49,negated_conjecture,
addition(esk3_0,c(esk3_0)) = addition(esk2_0,c(esk2_0)),
inference(spm,[status(thm)],[c_0_40,c_0_27]) ).
cnf(c_0_50,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_51,plain,
( ~ test(X2)
| ~ test(X1)
| c(multiplication(X1,X2)) = addition(c(X1),c(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_52,plain,
! [X12] : addition(X12,X12) = X12,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_53,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_54,plain,
! [X18,X19,X20] : multiplication(X18,addition(X19,X20)) = addition(multiplication(X18,X19),multiplication(X18,X20)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_55,plain,
addition(X1,multiplication(c(esk2_0),esk2_0)) = X1,
inference(rw,[status(thm)],[c_0_44,c_0_32]) ).
cnf(c_0_56,plain,
( ~ complement(X1,X2)
| multiplication(X1,X2) = multiplication(esk2_0,c(esk2_0)) ),
inference(rw,[status(thm)],[c_0_35,c_0_45]) ).
cnf(c_0_57,plain,
( ~ test(X1)
| complement(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_58,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_59,plain,
addition(multiplication(esk2_0,c(esk2_0)),X1) = X1,
inference(rw,[status(thm)],[c_0_48,c_0_45]) ).
cnf(c_0_60,plain,
( ~ complement(X2,X1)
| addition(X1,X2) = addition(esk2_0,c(esk2_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_37]),c_0_49]) ).
cnf(c_0_61,plain,
multiplication(addition(esk3_0,c(esk3_0)),X1) = X1,
inference(rw,[status(thm)],[c_0_50,c_0_37]) ).
cnf(c_0_62,plain,
( ~ complement(X1,X2)
| test(X2) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_63,negated_conjecture,
( ~ test(X1)
| c(multiplication(X1,esk2_0)) = addition(c(X1),c(esk2_0)) ),
inference(spm,[status(thm)],[c_0_51,c_0_27]) ).
cnf(c_0_64,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_65,plain,
multiplication(X1,addition(esk3_0,c(esk3_0))) = X1,
inference(rw,[status(thm)],[c_0_53,c_0_37]) ).
cnf(c_0_66,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_67,plain,
addition(X1,multiplication(esk2_0,c(esk2_0))) = X1,
inference(rw,[status(thm)],[c_0_55,c_0_45]) ).
cnf(c_0_68,plain,
( ~ test(X1)
| multiplication(esk1_1(X1),X1) = multiplication(esk2_0,c(esk2_0)) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_69,plain,
multiplication(addition(esk2_0,X1),c(esk2_0)) = multiplication(X1,c(esk2_0)),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_70,plain,
( ~ test(X1)
| addition(X1,esk1_1(X1)) = addition(esk2_0,c(esk2_0)) ),
inference(spm,[status(thm)],[c_0_60,c_0_57]) ).
cnf(c_0_71,plain,
multiplication(addition(esk2_0,c(esk2_0)),X1) = X1,
inference(rw,[status(thm)],[c_0_61,c_0_49]) ).
cnf(c_0_72,plain,
( ~ test(X1)
| test(c(X1)) ),
inference(spm,[status(thm)],[c_0_62,c_0_19]) ).
cnf(c_0_73,negated_conjecture,
c(multiplication(esk2_0,esk2_0)) = c(esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_27]),c_0_64]) ).
cnf(c_0_74,plain,
multiplication(X1,addition(esk2_0,c(esk2_0))) = X1,
inference(rw,[status(thm)],[c_0_65,c_0_49]) ).
cnf(c_0_75,plain,
multiplication(esk2_0,addition(X1,c(esk2_0))) = multiplication(esk2_0,X1),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_76,negated_conjecture,
( ~ leq(addition(addition(addition(addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0)),multiplication(esk2_0,esk3_0)),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0)),multiplication(esk2_0,esk3_0)),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_77,plain,
! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_78,plain,
( ~ test(X1)
| multiplication(addition(esk1_1(X1),X2),X1) = multiplication(X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_68]),c_0_59]) ).
cnf(c_0_79,plain,
( ~ test(X1)
| multiplication(esk1_1(X1),addition(X1,X2)) = multiplication(esk1_1(X1),X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_68]),c_0_59]) ).
cnf(c_0_80,plain,
multiplication(esk1_1(esk2_0),c(esk2_0)) = c(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]),c_0_27])]) ).
cnf(c_0_81,negated_conjecture,
( ~ test(multiplication(esk2_0,esk2_0))
| test(c(esk2_0)) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_82,plain,
multiplication(esk2_0,esk2_0) = esk2_0,
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_83,negated_conjecture,
( ~ leq(addition(multiplication(c(esk2_0),c(esk3_0)),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,esk3_0),addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0))))),one)
| ~ leq(one,addition(multiplication(c(esk2_0),c(esk3_0)),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,esk3_0),addition(multiplication(esk3_0,esk2_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(rw,[status(thm)],[c_0_76,c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_30]) ).
cnf(c_0_84,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_85,plain,
( ~ test(X1)
| ~ test(esk1_1(X1))
| multiplication(esk1_1(esk1_1(X1)),X1) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_70]),c_0_71]) ).
cnf(c_0_86,plain,
esk1_1(esk2_0) = c(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_79]),c_0_80]),c_0_27])]) ).
cnf(c_0_87,negated_conjecture,
test(c(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82]),c_0_27])]) ).
cnf(c_0_88,negated_conjecture,
( ~ leq(addition(esk2_0,addition(multiplication(addition(esk2_0,c(esk2_0)),esk3_0),multiplication(c(esk2_0),c(esk3_0)))),addition(esk3_0,c(esk3_0)))
| ~ leq(addition(esk3_0,c(esk3_0)),addition(esk2_0,addition(multiplication(addition(esk2_0,c(esk2_0)),esk3_0),multiplication(c(esk2_0),c(esk3_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(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_83,c_0_37]),c_0_37]),c_0_58]),c_0_61]),c_0_30]),c_0_30]),c_0_84]),c_0_58]),c_0_30]),c_0_84]),c_0_58]),c_0_61]),c_0_30]),c_0_30]),c_0_84]),c_0_58]),c_0_30]),c_0_84]) ).
cnf(c_0_89,plain,
( ~ test(X1)
| multiplication(esk1_1(X1),addition(X2,X1)) = multiplication(esk1_1(X1),X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_68]),c_0_67]) ).
cnf(c_0_90,plain,
multiplication(esk1_1(c(esk2_0)),esk2_0) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]),c_0_27])]) ).
cnf(c_0_91,negated_conjecture,
( ~ leq(addition(esk2_0,addition(multiplication(addition(esk2_0,c(esk2_0)),esk3_0),multiplication(c(esk2_0),c(esk3_0)))),addition(esk2_0,c(esk2_0)))
| ~ leq(addition(esk2_0,c(esk2_0)),addition(esk2_0,addition(multiplication(addition(esk2_0,c(esk2_0)),esk3_0),multiplication(c(esk2_0),c(esk3_0))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_49]),c_0_49]) ).
cnf(c_0_92,plain,
addition(multiplication(addition(X1,X2),X3),X4) = addition(multiplication(X1,X3),addition(multiplication(X2,X3),X4)),
inference(spm,[status(thm)],[c_0_84,c_0_58]) ).
fof(c_0_93,plain,
! [X26,X27] :
( ( leq(X26,X27)
| addition(X26,X27) != X27 )
& ( addition(X26,X27) = X27
| ~ leq(X26,X27) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])]) ).
cnf(c_0_94,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_84,c_0_64]) ).
cnf(c_0_95,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(esk2_0,addition(c(esk2_0),X2)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_71]),c_0_84]) ).
cnf(c_0_96,plain,
esk1_1(c(esk2_0)) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_89]),c_0_90]),c_0_87])]) ).
cnf(c_0_97,negated_conjecture,
( ~ leq(addition(esk2_0,addition(multiplication(esk2_0,esk3_0),c(esk2_0))),addition(esk2_0,c(esk2_0)))
| ~ leq(addition(esk2_0,c(esk2_0)),addition(esk2_0,addition(multiplication(esk2_0,esk3_0),c(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_91,c_0_92]),c_0_66]),c_0_49]),c_0_74]),c_0_66]),c_0_49]),c_0_74]) ).
cnf(c_0_98,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_99,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_94,c_0_30]) ).
cnf(c_0_100,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_30]),c_0_84]) ).
cnf(c_0_101,plain,
addition(X1,multiplication(esk2_0,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_70]),c_0_96]),c_0_94]),c_0_71]),c_0_87])]) ).
cnf(c_0_102,negated_conjecture,
( ~ leq(addition(esk2_0,c(esk2_0)),addition(esk2_0,addition(multiplication(esk2_0,esk3_0),c(esk2_0))))
| addition(esk2_0,addition(multiplication(esk2_0,esk3_0),c(esk2_0))) != addition(esk2_0,c(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_97,c_0_98]),c_0_84]),c_0_84]),c_0_99]),c_0_100]),c_0_94]) ).
cnf(c_0_103,negated_conjecture,
addition(esk3_0,addition(c(esk3_0),X1)) = addition(esk2_0,addition(c(esk2_0),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_49]),c_0_84]) ).
cnf(c_0_104,plain,
addition(X1,addition(X2,multiplication(esk2_0,X1))) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_105,negated_conjecture,
addition(esk2_0,addition(multiplication(esk2_0,esk3_0),c(esk2_0))) != addition(esk2_0,c(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_98]),c_0_84]),c_0_100]),c_0_99]),c_0_94])]) ).
cnf(c_0_106,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_30]),c_0_49]),c_0_30]),c_0_105]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE010+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/5.38 % Computer : n007.cluster.edu
% 0.13/5.38 % Model : x86_64 x86_64
% 0.13/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.38 % Memory : 8046.5625MB
% 0.13/5.38 % OS : Linux 6.8.0-71-generic
% 0.13/5.38 % CPULimit : 300
% 0.13/5.38 % WCLimit : 300
% 0.13/5.38 % DateTime : Sun Sep 20 22:35:55 UTC 2026
% 0.13/5.39 % CPUTime :
% 0.13/5.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/5.42 Running first-order theorem proving
% 0.16/5.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.52 % Version: 3.5.1
% 0.16/5.52 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/5.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/5.52 % Starting new_bool_3 with 300s (1) cores
% 0.16/5.52 % Starting new_bool_1 with 300s (1) cores
% 0.16/5.52 % Starting sh5l with 300s (1) cores
% 0.16/5.52 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3733598 completed with status 0
% 0.16/5.52 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.16/5.52 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/5.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/5.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/5.52 % No SInE strategy applied
% 0.16/5.52 % Search class: FGHSM-FFMF21-DFFFFFNN
% 0.16/5.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/5.52 % Starting SubtermCWHack with 136s (1) cores
% 0.16/5.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.16/5.52 % Starting G-E--_208_B07AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.16/5.52 % Starting new_bool_3 with 136s (1) cores
% 0.16/5.52 % Starting new_bool_1 with 136s (1) cores
% 0.16/5.52 % G-E--_208_B07AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 3733604 completed with status 0
% 0.16/5.52 % Result found by G-E--_208_B07AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.16/5.52 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/5.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/5.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/5.52 % No SInE strategy applied
% 0.16/5.52 % Search class: FGHSM-FFMF21-DFFFFFNN
% 0.16/5.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/5.52 % Starting SubtermCWHack with 136s (1) cores
% 0.16/5.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.16/5.52 % Starting G-E--_208_B07AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.16/5.52 % Preprocessing time : 0.001 s
% 0.16/5.52 % Presaturation interreduction done
% 0.16/5.52
% 0.16/5.52 % Proof found!
% 0.16/5.52 % SZS status Theorem
% 0.16/5.52 % SZS output start CNFRefutation
% See solution above
% 0.16/5.52 % Parsed axioms : 19
% 0.16/5.52 % Removed by relevancy pruning/SinE : 0
% 0.16/5.52 % Initial clauses : 27
% 0.16/5.52 % Removed in clause preprocessing : 0
% 0.16/5.52 % Initial clauses in saturation : 27
% 0.16/5.52 % Processed clauses : 805
% 0.16/5.52 % ...of these trivial : 146
% 0.16/5.52 % ...subsumed : 133
% 0.16/5.52 % ...remaining for further processing : 525
% 0.16/5.52 % Other redundant clauses eliminated : 1
% 0.16/5.52 % Clauses deleted for lack of memory : 0
% 0.16/5.52 % Backward-subsumed : 3
% 0.16/5.52 % Backward-rewritten : 156
% 0.16/5.52 % Generated clauses : 7012
% 0.16/5.52 % ...of the previous two non-redundant : 5067
% 0.16/5.52 % ...aggressively subsumed : 0
% 0.16/5.52 % Contextual simplify-reflections : 0
% 0.16/5.52 % Paramodulations : 7009
% 0.16/5.52 % Factorizations : 2
% 0.16/5.52 % NegExts : 0
% 0.16/5.52 % Equation resolutions : 1
% 0.16/5.52 % Disequality decompositions : 0
% 0.16/5.52 % Total rewrite steps : 11730
% 0.16/5.52 % ...of those cached : 9944
% 0.16/5.52 % Propositional unsat checks : 0
% 0.16/5.52 % Propositional check models : 0
% 0.16/5.52 % Propositional check unsatisfiable : 0
% 0.16/5.52 % Propositional clauses : 0
% 0.16/5.52 % Propositional clauses after purity: 0
% 0.16/5.52 % Propositional unsat core size : 0
% 0.16/5.52 % Propositional preprocessing time : 0.000
% 0.16/5.52 % Propositional encoding time : 0.000
% 0.16/5.52 % Propositional solver time : 0.000
% 0.16/5.52 % Success case prop preproc time : 0.000
% 0.16/5.52 % Success case prop encoding time : 0.000
% 0.16/5.52 % Success case prop solver time : 0.000
% 0.16/5.52 % Current number of processed clauses : 338
% 0.16/5.52 % Positive orientable unit clauses : 168
% 0.16/5.52 % Positive unorientable unit clauses: 7
% 0.16/5.52 % Negative unit clauses : 3
% 0.16/5.52 % Non-unit-clauses : 160
% 0.16/5.52 % Current number of unprocessed clauses: 4185
% 0.16/5.52 % ...number of literals in the above : 6816
% 0.16/5.52 % Current number of archived formulas : 0
% 0.16/5.52 % Current number of archived clauses : 186
% 0.16/5.52 % Clause-clause subsumption calls (NU) : 5136
% 0.16/5.52 % Rec. Clause-clause subsumption calls : 5083
% 0.16/5.52 % Non-unit clause-clause subsumptions : 104
% 0.16/5.52 % Unit Clause-clause subsumption calls : 3776
% 0.16/5.52 % Rewrite failures with RHS unbound : 0
% 0.16/5.52 % BW rewrite match attempts : 636
% 0.16/5.52 % BW rewrite match successes : 171
% 0.16/5.52 % Condensation attempts : 0
% 0.16/5.52 % Condensation successes : 0
% 0.16/5.52 % Termbank termtop insertions : 120823
% 0.16/5.52 % Search garbage collected termcells : 217
% 0.16/5.52
% 0.16/5.52 % -------------------------------------------------
% 0.16/5.52 % User time : 0.069 s
% 0.16/5.52 % System time : 0.008 s
% 0.16/5.52 % Total time : 0.077 s
% 0.16/5.52 % Maximum resident set size: 3656 pages
% 0.16/5.52
% 0.16/5.52 % -------------------------------------------------
% 0.16/5.52 % User time : 0.353 s
% 0.16/5.52 % System time : 0.024 s
% 0.16/5.52 % Total time : 0.377 s
% 0.16/5.52 % Maximum resident set size: 4608 pages
% 0.16/5.52 % E exiting
%------------------------------------------------------------------------------