%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE009+4 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:35:27 PM UTC 2026
% Result : Theorem 4.75s 3.43s
% Output : CNFRefutation 4.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of formulae : 162 ( 95 unt; 0 def)
% Number of atoms : 266 ( 132 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 172 ( 68 ~; 77 |; 16 &)
% ( 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 173 ( 4 sgn 67 !; 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(goals,conjecture,
! [X4,X5] :
( ( test(X5)
& test(X4) )
=> ( leq(one,addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))))
& leq(addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))),one) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(test_2,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( multiplication(X4,X5) = zero
& multiplication(X5,X4) = zero
& addition(X4,X5) = one ) ),
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_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
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_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(test_deMorgan2,axiom,
! [X4,X5] :
( ( test(X4)
& test(X5) )
=> c(multiplication(X4,X5)) = addition(c(X4),c(X5)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+2.ax',test_deMorgan2) ).
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(test_4,axiom,
! [X4] :
( ~ test(X4)
=> c(X4) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_4) ).
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(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(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(test_deMorgan1,axiom,
! [X4,X5] :
( ( test(X4)
& test(X5) )
=> c(addition(X4,X5)) = multiplication(c(X4),c(X5)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+2.ax',test_deMorgan1) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(c_0_17,plain,
! [X69,X70] :
( ( c(X69) != X70
| complement(X69,X70)
| ~ test(X69) )
& ( ~ complement(X69,X70)
| c(X69) = X70
| ~ test(X69) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])]) ).
fof(c_0_18,negated_conjecture,
~ ! [X4,X5] :
( ( test(X5)
& test(X4) )
=> ( leq(one,addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))))
& leq(addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))),one) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_19,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_20,negated_conjecture,
( test(esk3_0)
& test(esk2_0)
& ( ~ leq(one,addition(addition(addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))))
| ~ leq(addition(addition(addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))),one) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
fof(c_0_21,plain,
! [X67,X68] :
( ( multiplication(X67,X68) = zero
| ~ complement(X68,X67) )
& ( multiplication(X68,X67) = zero
| ~ complement(X68,X67) )
& ( addition(X67,X68) = one
| ~ complement(X68,X67) )
& ( multiplication(X67,X68) != zero
| multiplication(X68,X67) != zero
| addition(X67,X68) != one
| complement(X68,X67) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).
fof(c_0_22,plain,
! [X41,X42] : addition(X41,X42) = addition(X42,X41),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_23,plain,
! [X63,X65,X66] :
( ( ~ test(X63)
| complement(esk1_1(X63),X63) )
& ( ~ complement(X66,X65)
| test(X65) ) ),
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_24,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_26,plain,
! [X43,X44,X45] : addition(X45,addition(X44,X43)) = addition(addition(X45,X44),X43),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_27,plain,
! [X47] : addition(X47,X47) = X47,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_28,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_31,plain,
! [X74,X75] :
( ~ test(X74)
| ~ test(X75)
| c(multiplication(X74,X75)) = addition(c(X74),c(X75)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_deMorgan2])]) ).
fof(c_0_32,plain,
! [X53,X54,X55] : multiplication(X53,addition(X54,X55)) = addition(multiplication(X53,X54),multiplication(X53,X55)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_33,negated_conjecture,
complement(esk3_0,c(esk3_0)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_34,plain,
! [X51] : multiplication(X51,one) = X51,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_35,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,plain,
( addition(X1,X2) = one
| ~ complement(X1,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_38,negated_conjecture,
complement(esk1_1(esk3_0),esk3_0),
inference(spm,[status(thm)],[c_0_30,c_0_25]) ).
fof(c_0_39,plain,
! [X4] :
( ~ test(X4)
=> c(X4) = zero ),
inference(fof_simplification,[status(thm)],[test_4]) ).
cnf(c_0_40,plain,
( c(multiplication(X1,X2)) = addition(c(X1),c(X2))
| ~ test(X1)
| ~ test(X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,plain,
( test(X2)
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_42,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_43,negated_conjecture,
addition(esk3_0,c(esk3_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_33]),c_0_29]) ).
cnf(c_0_44,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_45,plain,
! [X48,X49,X50] : multiplication(X48,multiplication(X49,X50)) = multiplication(multiplication(X48,X49),X50),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_46,plain,
! [X52] : multiplication(one,X52) = X52,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_47,plain,
( multiplication(X1,X2) = zero
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_48,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_49,plain,
! [X61,X62] :
( ( ~ leq(X61,X62)
| addition(X61,X62) = X62 )
& ( addition(X61,X62) != X62
| leq(X61,X62) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(c_0_50,plain,
! [X56,X57,X58] : multiplication(addition(X56,X57),X58) = addition(multiplication(X56,X58),multiplication(X57,X58)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_51,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_52,negated_conjecture,
addition(esk3_0,esk1_1(esk3_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_29]) ).
fof(c_0_53,plain,
! [X71] :
( test(X71)
| c(X71) = zero ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])]) ).
cnf(c_0_54,negated_conjecture,
( c(multiplication(X1,esk3_0)) = addition(c(X1),c(esk3_0))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_25]) ).
cnf(c_0_55,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_56,plain,
! [X72,X73] :
( ~ test(X72)
| ~ test(X73)
| c(addition(X72,X73)) = multiplication(c(X72),c(X73)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_deMorgan1])]) ).
cnf(c_0_57,plain,
( c(X1) = X2
| ~ complement(X1,X2)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_58,negated_conjecture,
test(c(esk3_0)),
inference(spm,[status(thm)],[c_0_41,c_0_33]) ).
cnf(c_0_59,plain,
( complement(X2,X1)
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero
| addition(X1,X2) != one ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_60,negated_conjecture,
addition(multiplication(X1,esk3_0),multiplication(X1,c(esk3_0))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_61,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_62,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_63,negated_conjecture,
multiplication(c(esk3_0),esk3_0) = zero,
inference(spm,[status(thm)],[c_0_47,c_0_33]) ).
cnf(c_0_64,negated_conjecture,
multiplication(esk3_0,c(esk3_0)) = zero,
inference(spm,[status(thm)],[c_0_48,c_0_33]) ).
cnf(c_0_65,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_66,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_67,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_68,negated_conjecture,
addition(one,esk3_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_29]) ).
cnf(c_0_69,plain,
( test(X1)
| c(X1) = zero ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_70,negated_conjecture,
c(multiplication(esk2_0,esk3_0)) = addition(c(esk2_0),c(esk3_0)),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
fof(c_0_71,plain,
! [X46] : addition(X46,zero) = X46,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_72,plain,
( c(addition(X1,X2)) = multiplication(c(X1),c(X2))
| ~ test(X1)
| ~ test(X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_73,negated_conjecture,
( c(c(esk3_0)) = X1
| ~ complement(c(esk3_0),X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_74,negated_conjecture,
complement(c(esk3_0),esk3_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(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]),c_0_61])]),c_0_62]),c_0_62]),c_0_62]),c_0_63]),c_0_62]),c_0_62]),c_0_64]),c_0_62])]) ).
cnf(c_0_75,plain,
( addition(X1,addition(X2,X3)) = X3
| ~ leq(addition(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_65,c_0_35]) ).
cnf(c_0_76,plain,
( leq(X1,X2)
| addition(X2,X1) != X2 ),
inference(spm,[status(thm)],[c_0_66,c_0_29]) ).
cnf(c_0_77,negated_conjecture,
addition(X1,multiplication(esk3_0,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_62]),c_0_62]) ).
cnf(c_0_78,plain,
( leq(addition(X1,X2),X3)
| addition(X1,addition(X2,X3)) != X3 ),
inference(spm,[status(thm)],[c_0_66,c_0_35]) ).
cnf(c_0_79,negated_conjecture,
( addition(c(esk2_0),c(esk3_0)) = zero
| test(multiplication(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_80,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_81,negated_conjecture,
( c(addition(X1,esk2_0)) = multiplication(c(X1),c(esk2_0))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_72,c_0_55]) ).
cnf(c_0_82,negated_conjecture,
c(c(esk3_0)) = esk3_0,
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_83,negated_conjecture,
complement(esk1_1(esk2_0),esk2_0),
inference(spm,[status(thm)],[c_0_30,c_0_55]) ).
cnf(c_0_84,plain,
( addition(X1,X2) = X2
| ~ leq(addition(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_75,c_0_36]) ).
cnf(c_0_85,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_29,c_0_35]) ).
cnf(c_0_86,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_66,c_0_51]) ).
cnf(c_0_87,negated_conjecture,
leq(multiplication(esk3_0,X1),X1),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_88,negated_conjecture,
( test(multiplication(esk2_0,esk3_0))
| leq(addition(c(esk2_0),c(esk3_0)),c(esk3_0)) ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80])]),c_0_29]) ).
cnf(c_0_89,negated_conjecture,
c(addition(esk2_0,c(esk3_0))) = multiplication(esk3_0,c(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_58]),c_0_29]),c_0_82]) ).
cnf(c_0_90,plain,
( complement(X1,X2)
| addition(X1,X2) != one
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero ),
inference(spm,[status(thm)],[c_0_59,c_0_29]) ).
cnf(c_0_91,negated_conjecture,
addition(esk2_0,esk1_1(esk2_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_83]),c_0_29]) ).
cnf(c_0_92,negated_conjecture,
multiplication(esk2_0,esk1_1(esk2_0)) = zero,
inference(spm,[status(thm)],[c_0_47,c_0_83]) ).
cnf(c_0_93,negated_conjecture,
multiplication(esk1_1(esk2_0),esk2_0) = zero,
inference(spm,[status(thm)],[c_0_48,c_0_83]) ).
cnf(c_0_94,negated_conjecture,
complement(esk2_0,c(esk2_0)),
inference(spm,[status(thm)],[c_0_24,c_0_55]) ).
cnf(c_0_95,negated_conjecture,
complement(esk1_1(c(esk3_0)),c(esk3_0)),
inference(spm,[status(thm)],[c_0_30,c_0_58]) ).
cnf(c_0_96,plain,
( addition(X1,addition(X2,X3)) = addition(X3,X1)
| ~ leq(addition(X1,addition(X2,X3)),addition(X3,X1)) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_97,plain,
leq(X1,addition(X2,X1)),
inference(spm,[status(thm)],[c_0_86,c_0_29]) ).
cnf(c_0_98,negated_conjecture,
leq(addition(multiplication(esk3_0,X1),multiplication(esk3_0,X2)),addition(X1,X2)),
inference(spm,[status(thm)],[c_0_87,c_0_42]) ).
cnf(c_0_99,negated_conjecture,
( addition(c(esk2_0),c(esk3_0)) = c(esk3_0)
| test(multiplication(esk2_0,esk3_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_88]),c_0_35]),c_0_36]) ).
cnf(c_0_100,negated_conjecture,
multiplication(esk3_0,c(esk2_0)) = multiplication(c(esk2_0),esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_89]),c_0_82]),c_0_58]),c_0_55])]) ).
cnf(c_0_101,negated_conjecture,
( c(esk2_0) = X1
| ~ complement(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_55]) ).
cnf(c_0_102,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_90,c_0_91]),c_0_92]),c_0_93])]) ).
cnf(c_0_103,negated_conjecture,
( ~ leq(one,addition(addition(addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))))
| ~ leq(addition(addition(addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))),one) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_104,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_85,c_0_36]) ).
cnf(c_0_105,negated_conjecture,
addition(esk2_0,c(esk2_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_94]),c_0_29]) ).
cnf(c_0_106,negated_conjecture,
addition(c(esk3_0),esk1_1(c(esk3_0))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_95]),c_0_29]) ).
cnf(c_0_107,negated_conjecture,
( addition(c(esk3_0),X1) = X1
| test(multiplication(esk2_0,esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_79]),c_0_80]),c_0_80]),c_0_97])]) ).
cnf(c_0_108,negated_conjecture,
( test(multiplication(esk2_0,esk3_0))
| leq(multiplication(c(esk2_0),esk3_0),c(esk3_0)) ),
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_64]),c_0_80]) ).
cnf(c_0_109,negated_conjecture,
test(c(esk2_0)),
inference(spm,[status(thm)],[c_0_41,c_0_94]) ).
cnf(c_0_110,negated_conjecture,
esk1_1(esk2_0) = c(esk2_0),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_111,negated_conjecture,
( ~ leq(one,addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,esk3_0),addition(multiplication(esk2_0,c(esk3_0)),multiplication(c(esk2_0),c(esk3_0))))))
| ~ leq(addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,esk3_0),addition(multiplication(esk2_0,c(esk3_0)),multiplication(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)],[c_0_103,c_0_29]),c_0_29]),c_0_35]),c_0_35]),c_0_35]),c_0_35]) ).
cnf(c_0_112,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_29]),c_0_35]) ).
cnf(c_0_113,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_80,c_0_29]) ).
cnf(c_0_114,plain,
( leq(addition(X1,X2),X1)
| addition(X2,X1) != X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_36]),c_0_35]),c_0_104]) ).
cnf(c_0_115,negated_conjecture,
addition(esk2_0,addition(c(esk2_0),X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_35,c_0_105]) ).
cnf(c_0_116,negated_conjecture,
addition(one,c(esk3_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_106]),c_0_29]) ).
cnf(c_0_117,negated_conjecture,
( addition(X1,c(esk3_0)) = X1
| test(multiplication(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_29,c_0_107]) ).
cnf(c_0_118,negated_conjecture,
( addition(multiplication(c(esk2_0),esk3_0),c(esk3_0)) = c(esk3_0)
| test(multiplication(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_65,c_0_108]) ).
cnf(c_0_119,negated_conjecture,
( c(c(esk2_0)) = X1
| ~ complement(c(esk2_0),X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_109]) ).
cnf(c_0_120,negated_conjecture,
complement(c(esk2_0),esk2_0),
inference(rw,[status(thm)],[c_0_83,c_0_110]) ).
cnf(c_0_121,negated_conjecture,
( ~ leq(one,addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,c(esk3_0)),multiplication(c(esk2_0),c(esk3_0))))))
| ~ leq(addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,c(esk3_0)),multiplication(c(esk2_0),c(esk3_0))))),one) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_112]),c_0_112]) ).
cnf(c_0_122,negated_conjecture,
addition(multiplication(esk2_0,X1),multiplication(c(esk2_0),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_105]),c_0_62]) ).
cnf(c_0_123,plain,
leq(zero,X1),
inference(spm,[status(thm)],[c_0_66,c_0_113]) ).
cnf(c_0_124,plain,
leq(addition(X1,X2),addition(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_51]),c_0_35]),c_0_104]) ).
cnf(c_0_125,negated_conjecture,
( addition(esk2_0,c(esk3_0)) = one
| test(multiplication(esk2_0,esk3_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_99]),c_0_116]) ).
cnf(c_0_126,negated_conjecture,
( c(esk3_0) = multiplication(c(esk2_0),esk3_0)
| test(multiplication(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_127,negated_conjecture,
c(multiplication(c(esk2_0),esk3_0)) = addition(c(c(esk2_0)),c(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_100]),c_0_29]),c_0_109]),c_0_25])]) ).
cnf(c_0_128,negated_conjecture,
c(c(esk2_0)) = esk2_0,
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_129,negated_conjecture,
( ~ leq(one,addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),c(esk3_0))))
| ~ leq(addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),c(esk3_0))),one) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_122]),c_0_122]) ).
cnf(c_0_130,negated_conjecture,
( c(esk3_0) = zero
| test(multiplication(esk2_0,esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_79]),c_0_123])]) ).
cnf(c_0_131,negated_conjecture,
leq(esk3_0,one),
inference(spm,[status(thm)],[c_0_76,c_0_68]) ).
cnf(c_0_132,negated_conjecture,
( test(multiplication(esk2_0,esk3_0))
| leq(one,addition(esk2_0,c(esk3_0))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_29]) ).
cnf(c_0_133,negated_conjecture,
( addition(esk2_0,c(esk3_0)) = esk3_0
| test(multiplication(esk2_0,esk3_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_126]),c_0_127]),c_0_128]) ).
cnf(c_0_134,negated_conjecture,
( test(multiplication(esk2_0,esk3_0))
| ~ leq(one,esk3_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(spm,[status(thm)],[c_0_129,c_0_130]),c_0_80]),c_0_122]),c_0_80]),c_0_122]),c_0_131])]) ).
cnf(c_0_135,negated_conjecture,
c(multiplication(c(esk2_0),esk3_0)) = addition(esk2_0,c(esk3_0)),
inference(rw,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_136,negated_conjecture,
test(multiplication(esk2_0,esk3_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_134]) ).
cnf(c_0_137,negated_conjecture,
( c(addition(X1,c(esk3_0))) = multiplication(c(X1),esk3_0)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_58]),c_0_82]) ).
cnf(c_0_138,negated_conjecture,
( addition(esk2_0,c(esk3_0)) = zero
| test(multiplication(c(esk2_0),esk3_0)) ),
inference(spm,[status(thm)],[c_0_69,c_0_135]) ).
cnf(c_0_139,negated_conjecture,
complement(multiplication(esk2_0,esk3_0),addition(c(esk2_0),c(esk3_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_136]),c_0_70]) ).
cnf(c_0_140,negated_conjecture,
c(addition(multiplication(esk2_0,esk3_0),c(esk3_0))) = multiplication(c(esk2_0),esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_136]),c_0_70]),c_0_67]),c_0_63]),c_0_80]) ).
cnf(c_0_141,negated_conjecture,
( c(esk3_0) = zero
| test(multiplication(c(esk2_0),esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_138]),c_0_123])]) ).
cnf(c_0_142,negated_conjecture,
test(addition(c(esk2_0),c(esk3_0))),
inference(spm,[status(thm)],[c_0_41,c_0_139]) ).
cnf(c_0_143,negated_conjecture,
( addition(c(esk2_0),c(esk3_0)) = multiplication(c(esk2_0),esk3_0)
| test(multiplication(c(esk2_0),esk3_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_80]),c_0_70]) ).
cnf(c_0_144,plain,
( multiplication(c(X1),c(X1)) = c(X1)
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_72,c_0_36]) ).
cnf(c_0_145,negated_conjecture,
test(multiplication(c(esk2_0),esk3_0)),
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_146,negated_conjecture,
addition(one,esk2_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_91]),c_0_29]) ).
cnf(c_0_147,negated_conjecture,
multiplication(c(c(esk2_0)),c(c(esk2_0))) = c(c(esk2_0)),
inference(spm,[status(thm)],[c_0_144,c_0_109]) ).
cnf(c_0_148,negated_conjecture,
complement(multiplication(c(esk2_0),esk3_0),addition(esk2_0,c(esk3_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_145]),c_0_127]),c_0_128]) ).
cnf(c_0_149,negated_conjecture,
addition(X1,multiplication(esk2_0,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_146]),c_0_62]),c_0_62]) ).
cnf(c_0_150,negated_conjecture,
addition(esk3_0,addition(c(esk3_0),X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_35,c_0_43]) ).
cnf(c_0_151,negated_conjecture,
multiplication(esk2_0,esk2_0) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_147,c_0_128]),c_0_128]),c_0_128]) ).
cnf(c_0_152,negated_conjecture,
test(addition(esk2_0,c(esk3_0))),
inference(spm,[status(thm)],[c_0_41,c_0_148]) ).
cnf(c_0_153,negated_conjecture,
c(addition(esk2_0,c(esk3_0))) = multiplication(c(esk2_0),esk3_0),
inference(rw,[status(thm)],[c_0_89,c_0_100]) ).
cnf(c_0_154,negated_conjecture,
addition(X1,addition(X2,addition(multiplication(esk2_0,X1),multiplication(esk2_0,X2)))) = addition(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_149]),c_0_42]) ).
cnf(c_0_155,negated_conjecture,
addition(multiplication(X1,esk3_0),addition(multiplication(X1,c(esk3_0)),multiplication(X1,X2))) = addition(X1,multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_150]),c_0_42]),c_0_44]),c_0_42]) ).
cnf(c_0_156,negated_conjecture,
multiplication(esk2_0,multiplication(esk2_0,X1)) = multiplication(esk2_0,X1),
inference(spm,[status(thm)],[c_0_61,c_0_151]) ).
cnf(c_0_157,negated_conjecture,
addition(X1,multiplication(X1,esk3_0)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_68]),c_0_44]),c_0_44]) ).
cnf(c_0_158,negated_conjecture,
addition(multiplication(c(esk2_0),esk3_0),c(esk3_0)) = addition(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(spm,[status(thm)],[c_0_54,c_0_152]),c_0_67]),c_0_63]),c_0_80]),c_0_70]),c_0_153]) ).
cnf(c_0_159,negated_conjecture,
addition(multiplication(esk2_0,esk3_0),c(esk3_0)) = addition(esk2_0,c(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_156]),c_0_157]),c_0_29]),c_0_29]) ).
cnf(c_0_160,plain,
leq(X1,X1),
inference(spm,[status(thm)],[c_0_66,c_0_36]) ).
cnf(c_0_161,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_129,c_0_158]),c_0_112]),c_0_159]),c_0_112]),c_0_115]),c_0_116]),c_0_160]),c_0_158]),c_0_112]),c_0_159]),c_0_112]),c_0_115]),c_0_116]),c_0_160])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE009+4 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n015.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 20:25:31 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 4.75/3.43 % Version : CSE_E---1.7
% 4.75/3.43 % Problem : theBenchmark.p
% 4.75/3.43 % SZS status Theorem for theBenchmark.p
% 4.75/3.43 % SZS output start CNFRefutation
% See solution above
% 4.75/3.45 % Total time : 2.374s
%------------------------------------------------------------------------------