%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE011+3 : 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 : n026.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 0.14s 0.71s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 128 ( 80 unt; 0 def)
% Number of atoms : 208 ( 118 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 143 ( 63 ~; 57 |; 13 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 102 ( 3 sgn 51 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5] :
( ( test(X4)
& test(X5) )
=> one = addition(addition(multiplication(addition(X5,c(X5)),X4),multiplication(addition(X4,c(X4)),X5)),multiplication(c(X4),c(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
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(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(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(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_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(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(test_4,axiom,
! [X4] :
( ~ test(X4)
=> c(X4) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_4) ).
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(c_0_14,negated_conjecture,
~ ! [X4,X5] :
( ( test(X4)
& test(X5) )
=> one = addition(addition(multiplication(addition(X5,c(X5)),X4),multiplication(addition(X4,c(X4)),X5)),multiplication(c(X4),c(X5))) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_15,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_16,negated_conjecture,
( one != addition(addition(multiplication(addition(esk3_0,c(esk3_0)),esk2_0),multiplication(addition(esk2_0,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_14])])])]) ).
fof(c_0_17,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])])])]) ).
fof(c_0_18,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_19,plain,
( ~ test(X1)
| complement(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_21,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])])])]) ).
cnf(c_0_22,plain,
( addition(X1,X2) != one
| multiplication(X2,X1) != zero
| multiplication(X1,X2) != zero
| complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( ~ complement(X2,X1)
| addition(X1,X2) = one ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,negated_conjecture,
complement(esk1_1(esk3_0),esk3_0),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
( ~ complement(X2,X1)
| multiplication(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
( ~ complement(X1,X2)
| multiplication(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_28,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_29,plain,
( ~ test(X1)
| c(X1) != X2
| complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,plain,
( multiplication(X2,X1) != zero
| multiplication(X1,X2) != zero
| addition(X1,X2) != one
| complement(X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_31,negated_conjecture,
addition(esk3_0,esk1_1(esk3_0)) = one,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,negated_conjecture,
multiplication(esk3_0,esk1_1(esk3_0)) = zero,
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_33,negated_conjecture,
multiplication(esk1_1(esk3_0),esk3_0) = zero,
inference(spm,[status(thm)],[c_0_27,c_0_25]) ).
cnf(c_0_34,negated_conjecture,
complement(esk1_1(esk2_0),esk2_0),
inference(spm,[status(thm)],[c_0_19,c_0_28]) ).
fof(c_0_35,plain,
! [X37,X38] :
( c(addition(X37,X38)) = multiplication(c(X37),c(X38))
| ~ test(X38)
| ~ test(X37) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_deMorgan1])])]) ).
cnf(c_0_36,plain,
( ~ test(X1)
| complement(X1,c(X1)) ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_37,plain,
( ~ test(X1)
| ~ complement(X1,X2)
| c(X1) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_38,plain,
( ~ complement(X1,X2)
| test(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_39,negated_conjecture,
complement(esk3_0,esk1_1(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33])]) ).
cnf(c_0_40,negated_conjecture,
addition(esk2_0,esk1_1(esk2_0)) = one,
inference(spm,[status(thm)],[c_0_24,c_0_34]) ).
cnf(c_0_41,negated_conjecture,
multiplication(esk2_0,esk1_1(esk2_0)) = zero,
inference(spm,[status(thm)],[c_0_26,c_0_34]) ).
cnf(c_0_42,negated_conjecture,
multiplication(esk1_1(esk2_0),esk2_0) = zero,
inference(spm,[status(thm)],[c_0_27,c_0_34]) ).
fof(c_0_43,plain,
! [X21,X22,X23] : multiplication(addition(X21,X22),X23) = addition(multiplication(X21,X23),multiplication(X22,X23)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_44,plain,
! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_45,plain,
( ~ test(X2)
| ~ test(X1)
| c(addition(X1,X2)) = multiplication(c(X1),c(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_46,negated_conjecture,
complement(esk3_0,c(esk3_0)),
inference(spm,[status(thm)],[c_0_36,c_0_20]) ).
cnf(c_0_47,negated_conjecture,
( ~ test(esk1_1(esk3_0))
| c(esk1_1(esk3_0)) = esk3_0 ),
inference(spm,[status(thm)],[c_0_37,c_0_25]) ).
cnf(c_0_48,negated_conjecture,
test(esk1_1(esk3_0)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_49,negated_conjecture,
esk1_1(esk3_0) = c(esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_39]),c_0_20])]) ).
cnf(c_0_50,negated_conjecture,
complement(esk2_0,esk1_1(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_40]),c_0_41]),c_0_42])]) ).
cnf(c_0_51,negated_conjecture,
complement(esk2_0,c(esk2_0)),
inference(spm,[status(thm)],[c_0_36,c_0_28]) ).
fof(c_0_52,plain,
! [X11] : addition(X11,zero) = X11,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_53,negated_conjecture,
one != addition(addition(multiplication(addition(esk3_0,c(esk3_0)),esk2_0),multiplication(addition(esk2_0,c(esk2_0)),esk3_0)),multiplication(c(esk2_0),c(esk3_0))),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_54,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_55,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_56,negated_conjecture,
( ~ test(X1)
| multiplication(c(X1),c(esk3_0)) = c(addition(X1,esk3_0)) ),
inference(spm,[status(thm)],[c_0_45,c_0_20]) ).
cnf(c_0_57,negated_conjecture,
test(c(esk3_0)),
inference(spm,[status(thm)],[c_0_38,c_0_46]) ).
cnf(c_0_58,negated_conjecture,
c(c(esk3_0)) = esk3_0,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]),c_0_49]) ).
cnf(c_0_59,negated_conjecture,
( ~ test(esk1_1(esk2_0))
| c(esk1_1(esk2_0)) = esk2_0 ),
inference(spm,[status(thm)],[c_0_37,c_0_34]) ).
cnf(c_0_60,negated_conjecture,
esk1_1(esk2_0) = c(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_50]),c_0_28])]) ).
cnf(c_0_61,negated_conjecture,
test(c(esk2_0)),
inference(spm,[status(thm)],[c_0_38,c_0_51]) ).
fof(c_0_62,plain,
! [X25] : multiplication(zero,X25) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_63,plain,
! [X24] : multiplication(X24,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_64,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_65,plain,
! [X4] :
( ~ test(X4)
=> c(X4) = zero ),
inference(fof_simplification,[status(thm)],[test_4]) ).
cnf(c_0_66,negated_conjecture,
addition(multiplication(c(esk2_0),c(esk3_0)),addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0))))) != one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_23]),c_0_23]),c_0_54]),c_0_54]),c_0_55]) ).
cnf(c_0_67,negated_conjecture,
multiplication(c(esk2_0),c(esk3_0)) = c(addition(esk2_0,esk3_0)),
inference(spm,[status(thm)],[c_0_56,c_0_28]) ).
cnf(c_0_68,negated_conjecture,
( ~ test(X1)
| multiplication(c(X1),esk3_0) = c(addition(X1,c(esk3_0))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_57]),c_0_58]) ).
cnf(c_0_69,negated_conjecture,
c(c(esk2_0)) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60]),c_0_60]),c_0_61])]) ).
cnf(c_0_70,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_71,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_72,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_64,c_0_23]) ).
fof(c_0_73,plain,
! [X36] :
( c(X36) = zero
| test(X36) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])]) ).
fof(c_0_74,plain,
! [X17] : multiplication(one,X17) = X17,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_75,negated_conjecture,
( ~ test(X1)
| multiplication(c(X1),c(esk2_0)) = c(addition(X1,esk2_0)) ),
inference(spm,[status(thm)],[c_0_45,c_0_28]) ).
cnf(c_0_76,negated_conjecture,
addition(c(addition(esk2_0,esk3_0)),addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0))))) != one,
inference(rw,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_77,negated_conjecture,
multiplication(esk2_0,esk3_0) = c(addition(c(esk2_0),c(esk3_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_61]),c_0_69]) ).
cnf(c_0_78,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_23]),c_0_55]) ).
cnf(c_0_79,negated_conjecture,
multiplication(c(esk2_0),esk3_0) = c(addition(esk2_0,c(esk3_0))),
inference(spm,[status(thm)],[c_0_68,c_0_28]) ).
fof(c_0_80,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])])]) ).
cnf(c_0_81,plain,
( X1 != one
| complement(zero,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_64]),c_0_70]),c_0_71])]) ).
cnf(c_0_82,plain,
( X1 != one
| complement(X1,zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_72]),c_0_71]),c_0_70])]) ).
cnf(c_0_83,plain,
( c(X1) = zero
| test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_84,negated_conjecture,
addition(esk3_0,c(esk3_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_46]),c_0_23]) ).
cnf(c_0_85,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_86,negated_conjecture,
multiplication(c(c(esk3_0)),c(esk2_0)) = c(addition(esk2_0,c(esk3_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_57]),c_0_23]) ).
cnf(c_0_87,negated_conjecture,
addition(c(addition(esk2_0,esk3_0)),addition(c(addition(esk2_0,c(esk3_0))),addition(c(addition(c(esk2_0),c(esk3_0))),addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0))))) != one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]),c_0_79]),c_0_78]),c_0_78]) ).
cnf(c_0_88,plain,
( ~ test(X2)
| ~ test(X1)
| c(multiplication(X1,X2)) = addition(c(X1),c(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_89,plain,
complement(zero,one),
inference(er,[status(thm)],[c_0_81]) ).
cnf(c_0_90,plain,
complement(one,zero),
inference(er,[status(thm)],[c_0_82]) ).
cnf(c_0_91,negated_conjecture,
( addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0)))) != one
| test(addition(esk2_0,esk3_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_83]),c_0_72]) ).
cnf(c_0_92,negated_conjecture,
addition(multiplication(esk3_0,X1),multiplication(c(esk3_0),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_84]),c_0_85]) ).
cnf(c_0_93,negated_conjecture,
multiplication(c(esk3_0),c(esk2_0)) = c(addition(esk2_0,esk3_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_20]),c_0_23]) ).
cnf(c_0_94,negated_conjecture,
multiplication(esk3_0,c(esk2_0)) = c(addition(esk2_0,c(esk3_0))),
inference(rw,[status(thm)],[c_0_86,c_0_58]) ).
cnf(c_0_95,negated_conjecture,
( addition(c(addition(esk2_0,esk3_0)),addition(c(addition(esk2_0,c(esk3_0))),addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0)))) != one
| test(addition(c(esk2_0),c(esk3_0))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_83]),c_0_72]) ).
cnf(c_0_96,negated_conjecture,
( ~ test(X1)
| c(multiplication(X1,esk2_0)) = addition(c(X1),c(esk2_0)) ),
inference(spm,[status(thm)],[c_0_88,c_0_28]) ).
cnf(c_0_97,plain,
( ~ test(zero)
| c(zero) = one ),
inference(spm,[status(thm)],[c_0_37,c_0_89]) ).
cnf(c_0_98,plain,
test(zero),
inference(spm,[status(thm)],[c_0_38,c_0_90]) ).
cnf(c_0_99,negated_conjecture,
( addition(multiplication(esk2_0,esk3_0),addition(multiplication(esk3_0,esk2_0),addition(multiplication(c(esk2_0),esk3_0),multiplication(c(esk3_0),esk2_0)))) != one
| test(addition(esk2_0,esk3_0)) ),
inference(rw,[status(thm)],[c_0_91,c_0_78]) ).
cnf(c_0_100,negated_conjecture,
addition(c(addition(esk2_0,esk3_0)),c(addition(esk2_0,c(esk3_0)))) = c(esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94]),c_0_23]) ).
cnf(c_0_101,negated_conjecture,
( addition(esk2_0,addition(c(addition(esk2_0,esk3_0)),c(addition(esk2_0,c(esk3_0))))) != one
| test(addition(c(esk2_0),c(esk3_0))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_92]),c_0_23]),c_0_78]) ).
cnf(c_0_102,negated_conjecture,
addition(esk2_0,c(esk2_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_51]),c_0_23]) ).
cnf(c_0_103,negated_conjecture,
c(multiplication(c(esk3_0),esk2_0)) = addition(c(esk2_0),c(c(esk3_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_57]),c_0_23]) ).
cnf(c_0_104,plain,
c(zero) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_98])]) ).
cnf(c_0_105,negated_conjecture,
( addition(c(addition(esk2_0,c(esk3_0))),addition(c(addition(c(esk2_0),c(esk3_0))),addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0)))) != one
| test(addition(esk2_0,esk3_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_77]),c_0_79]),c_0_78]),c_0_78]) ).
cnf(c_0_106,negated_conjecture,
( test(addition(esk2_0,esk3_0))
| c(addition(esk2_0,c(esk3_0))) = c(esk2_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_83]),c_0_72]) ).
cnf(c_0_107,negated_conjecture,
test(addition(c(esk2_0),c(esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_100]),c_0_102])]) ).
cnf(c_0_108,negated_conjecture,
multiplication(c(esk2_0),esk2_0) = zero,
inference(spm,[status(thm)],[c_0_26,c_0_51]) ).
cnf(c_0_109,negated_conjecture,
c(multiplication(c(esk3_0),esk2_0)) = addition(esk3_0,c(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_58]),c_0_23]) ).
cnf(c_0_110,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_88,c_0_98]),c_0_71]),c_0_104]),c_0_23]),c_0_104]) ).
cnf(c_0_111,negated_conjecture,
( addition(esk2_0,addition(c(esk2_0),c(addition(c(esk2_0),c(esk3_0))))) != one
| test(addition(esk2_0,esk3_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_92]),c_0_23]),c_0_78]) ).
cnf(c_0_112,negated_conjecture,
addition(c(esk2_0),c(addition(c(esk2_0),c(esk3_0)))) = addition(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(spm,[status(thm)],[c_0_96,c_0_107]),c_0_54]),c_0_108]),c_0_72]),c_0_109]),c_0_23]) ).
cnf(c_0_113,negated_conjecture,
addition(esk2_0,addition(c(esk2_0),X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_55,c_0_102]) ).
cnf(c_0_114,negated_conjecture,
addition(one,c(addition(c(esk2_0),c(esk3_0)))) = one,
inference(spm,[status(thm)],[c_0_110,c_0_107]) ).
cnf(c_0_115,negated_conjecture,
multiplication(c(c(esk2_0)),c(esk3_0)) = c(addition(esk3_0,c(esk2_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_61]),c_0_23]) ).
cnf(c_0_116,negated_conjecture,
( addition(esk2_0,addition(esk3_0,c(esk2_0))) != one
| test(addition(esk2_0,esk3_0)) ),
inference(rw,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_117,negated_conjecture,
addition(esk2_0,addition(esk3_0,c(esk2_0))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_112]),c_0_114]) ).
cnf(c_0_118,negated_conjecture,
( ~ test(X1)
| c(multiplication(X1,c(esk3_0))) = addition(esk3_0,c(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_57]),c_0_58]),c_0_23]) ).
cnf(c_0_119,negated_conjecture,
multiplication(esk2_0,c(esk3_0)) = c(addition(esk3_0,c(esk2_0))),
inference(rw,[status(thm)],[c_0_115,c_0_69]) ).
cnf(c_0_120,negated_conjecture,
addition(multiplication(esk2_0,X1),multiplication(c(esk2_0),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_102]),c_0_85]) ).
cnf(c_0_121,negated_conjecture,
test(addition(esk2_0,esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_117])]) ).
cnf(c_0_122,negated_conjecture,
multiplication(esk3_0,c(esk3_0)) = zero,
inference(spm,[status(thm)],[c_0_27,c_0_46]) ).
cnf(c_0_123,negated_conjecture,
c(c(addition(esk3_0,c(esk2_0)))) = addition(esk3_0,c(esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_28]),c_0_119]) ).
cnf(c_0_124,negated_conjecture,
addition(esk2_0,addition(c(addition(esk2_0,esk3_0)),addition(c(addition(esk2_0,c(esk3_0))),c(addition(c(esk2_0),c(esk3_0)))))) != one,
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_76,c_0_92]),c_0_77]),c_0_79]),c_0_23]),c_0_23]),c_0_55]),c_0_78]) ).
cnf(c_0_125,negated_conjecture,
addition(c(addition(esk2_0,c(esk3_0))),c(addition(c(esk2_0),c(esk3_0)))) = esk3_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_79]),c_0_77]),c_0_23]) ).
cnf(c_0_126,negated_conjecture,
addition(esk3_0,c(addition(esk2_0,esk3_0))) = addition(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(spm,[status(thm)],[c_0_118,c_0_121]),c_0_54]),c_0_119]),c_0_122]),c_0_64]),c_0_123]) ).
cnf(c_0_127,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_23]),c_0_126]),c_0_117])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE011+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.57 % Computer : n026.cluster.edu
% 0.11/0.57 % Model : x86_64 x86_64
% 0.11/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57 % Memory : 8046.5625MB
% 0.11/0.57 % OS : Linux 6.8.0-71-generic
% 0.11/0.57 % CPULimit : 300
% 0.11/0.57 % WCLimit : 300
% 0.11/0.57 % DateTime : Sun Sep 20 22:40:51 UTC 2026
% 0.11/0.57 % CPUTime :
% 0.11/0.57 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.62 Running first-order theorem proving
% 0.11/0.62 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
% 0.14/0.71 % Version: 3.5.1
% 0.14/0.71 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.71 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.71 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.71 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.71 % Starting sh5l with 300s (1) cores
% 0.14/0.71 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 746697 completed with status 0
% 0.14/0.71 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.71 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.71 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.71 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.71 % No SInE strategy applied
% 0.14/0.71 % Search class: FGUSM-FFMF21-MFFFFFNN
% 0.14/0.71 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.71 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.71 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.71 % Starting G-E--_200_B02_F1_AE_CS_SP_PI_S0S with 136s (1) cores
% 0.14/0.71 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.71 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.71 % G-E--_200_B02_F1_AE_CS_SP_PI_S0S with pid 746704 completed with status 0
% 0.14/0.71 % Result found by G-E--_200_B02_F1_AE_CS_SP_PI_S0S
% 0.14/0.71 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.71 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.71 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.71 % No SInE strategy applied
% 0.14/0.71 % Search class: FGUSM-FFMF21-MFFFFFNN
% 0.14/0.71 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.71 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.71 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.71 % Starting G-E--_200_B02_F1_AE_CS_SP_PI_S0S with 136s (1) cores
% 0.14/0.71 % Preprocessing time : 0.002 s
% 0.14/0.71
% 0.14/0.71 % Proof found!
% 0.14/0.71 % SZS status Theorem
% 0.14/0.71 % SZS output start CNFRefutation
% See solution above
% 0.14/0.71 % Parsed axioms : 19
% 0.14/0.71 % Removed by relevancy pruning/SinE : 0
% 0.14/0.71 % Initial clauses : 27
% 0.14/0.71 % Removed in clause preprocessing : 0
% 0.14/0.71 % Initial clauses in saturation : 27
% 0.14/0.71 % Processed clauses : 601
% 0.14/0.71 % ...of these trivial : 56
% 0.14/0.71 % ...subsumed : 171
% 0.14/0.71 % ...remaining for further processing : 373
% 0.14/0.71 % Other redundant clauses eliminated : 0
% 0.14/0.71 % Clauses deleted for lack of memory : 0
% 0.14/0.71 % Backward-subsumed : 14
% 0.14/0.71 % Backward-rewritten : 96
% 0.14/0.71 % Generated clauses : 3231
% 0.14/0.71 % ...of the previous two non-redundant : 2274
% 0.14/0.71 % ...aggressively subsumed : 0
% 0.14/0.71 % Contextual simplify-reflections : 0
% 0.14/0.71 % Paramodulations : 3224
% 0.14/0.71 % Factorizations : 0
% 0.14/0.71 % NegExts : 0
% 0.14/0.71 % Equation resolutions : 7
% 0.14/0.71 % Disequality decompositions : 0
% 0.14/0.71 % Total rewrite steps : 4426
% 0.14/0.71 % ...of those cached : 3671
% 0.14/0.71 % Propositional unsat checks : 0
% 0.14/0.71 % Propositional check models : 0
% 0.14/0.71 % Propositional check unsatisfiable : 0
% 0.14/0.71 % Propositional clauses : 0
% 0.14/0.71 % Propositional clauses after purity: 0
% 0.14/0.71 % Propositional unsat core size : 0
% 0.14/0.71 % Propositional preprocessing time : 0.000
% 0.14/0.71 % Propositional encoding time : 0.000
% 0.14/0.71 % Propositional solver time : 0.000
% 0.14/0.71 % Success case prop preproc time : 0.000
% 0.14/0.71 % Success case prop encoding time : 0.000
% 0.14/0.71 % Success case prop solver time : 0.000
% 0.14/0.71 % Current number of processed clauses : 263
% 0.14/0.71 % Positive orientable unit clauses : 148
% 0.14/0.71 % Positive unorientable unit clauses: 3
% 0.14/0.71 % Negative unit clauses : 4
% 0.14/0.71 % Non-unit-clauses : 108
% 0.14/0.71 % Current number of unprocessed clauses: 1647
% 0.14/0.71 % ...number of literals in the above : 3174
% 0.14/0.71 % Current number of archived formulas : 0
% 0.14/0.71 % Current number of archived clauses : 110
% 0.14/0.71 % Clause-clause subsumption calls (NU) : 3481
% 0.14/0.71 % Rec. Clause-clause subsumption calls : 3285
% 0.14/0.71 % Non-unit clause-clause subsumptions : 164
% 0.14/0.71 % Unit Clause-clause subsumption calls : 1433
% 0.14/0.71 % Rewrite failures with RHS unbound : 0
% 0.14/0.71 % BW rewrite match attempts : 181
% 0.14/0.71 % BW rewrite match successes : 66
% 0.14/0.71 % Condensation attempts : 0
% 0.14/0.71 % Condensation successes : 0
% 0.14/0.71 % Termbank termtop insertions : 43054
% 0.14/0.71 % Search garbage collected termcells : 205
% 0.14/0.71
% 0.14/0.71 % -------------------------------------------------
% 0.14/0.71 % User time : 0.061 s
% 0.14/0.71 % System time : 0.008 s
% 0.14/0.71 % Total time : 0.069 s
% 0.14/0.71 % Maximum resident set size: 3652 pages
% 0.14/0.71
% 0.14/0.71 % -------------------------------------------------
% 0.14/0.71 % User time : 0.307 s
% 0.14/0.71 % System time : 0.029 s
% 0.14/0.71 % Total time : 0.336 s
% 0.14/0.71 % Maximum resident set size: 4864 pages
% 0.14/0.71 % E exiting
%------------------------------------------------------------------------------