%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE010+3 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n018.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 2.00s 1.95s
% Output : CNFRefutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 18
% Syntax : Number of formulae : 168 ( 88 unt; 0 def)
% Number of atoms : 293 ( 175 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 241 ( 116 ~; 102 |; 13 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 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 : 178 ( 6 sgn 67 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5] :
( ( test(X5)
& test(X4) )
=> 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/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(test_3,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(test_2,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( multiplication(X4,X5) = zero
& multiplication(X5,X4) = zero
& addition(X4,X5) = one ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(test_deMorgan1,axiom,
! [X4,X5] :
( ( test(X4)
& test(X5) )
=> c(addition(X4,X5)) = multiplication(c(X4),c(X5)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(test_4,axiom,
! [X4] :
( ~ test(X4)
=> c(X4) = zero ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_4) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(test_deMorgan2,axiom,
! [X4,X5] :
( ( test(X4)
& test(X5) )
=> c(multiplication(X4,X5)) = addition(c(X4),c(X5)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+2.ax',test_deMorgan2) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(c_0_18,negated_conjecture,
~ ! [X4,X5] :
( ( test(X5)
& test(X4) )
=> 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]) ).
fof(c_0_19,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_20,negated_conjecture,
( test(esk3_0)
& test(esk2_0)
& 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(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
fof(c_0_21,plain,
! [X41,X42] : addition(X41,X42) = addition(X42,X41),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_22,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])])]) ).
cnf(c_0_23,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
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]) ).
cnf(c_0_25,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_26,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_27,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_29,negated_conjecture,
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,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_25]),c_0_25]) ).
cnf(c_0_30,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
( addition(c(X1),X1) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_32,plain,
! [X52] : multiplication(one,X52) = X52,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_33,negated_conjecture,
addition(multiplication(c(esk2_0),c(esk3_0)),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,esk3_0),multiplication(addition(esk3_0,c(esk3_0)),esk2_0)))) != one,
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
( addition(X1,c(X1)) = one
| ~ test(X1) ),
inference(rw,[status(thm)],[c_0_31,c_0_25]) ).
cnf(c_0_35,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_37,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])]) ).
fof(c_0_38,plain,
! [X43,X44,X45] : addition(X45,addition(X44,X43)) = addition(addition(X45,X44),X43),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_39,negated_conjecture,
addition(multiplication(c(esk2_0),c(esk3_0)),addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,multiplication(esk2_0,esk3_0)))) != one,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_36])]),c_0_25]) ).
cnf(c_0_40,plain,
( c(addition(X1,X2)) = multiplication(c(X1),c(X2))
| ~ test(X1)
| ~ test(X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_41,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_42,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_43,negated_conjecture,
addition(c(addition(esk2_0,esk3_0)),addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,multiplication(esk2_0,esk3_0)))) != one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_36]),c_0_41])]) ).
cnf(c_0_44,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X3,X1)),
inference(spm,[status(thm)],[c_0_42,c_0_25]) ).
cnf(c_0_45,negated_conjecture,
addition(esk2_0,addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),c(addition(esk2_0,esk3_0))))) != one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_25]),c_0_42]) ).
cnf(c_0_46,plain,
addition(multiplication(X1,X2),addition(multiplication(X3,X2),X4)) = addition(multiplication(addition(X1,X3),X2),X4),
inference(spm,[status(thm)],[c_0_42,c_0_30]) ).
fof(c_0_47,plain,
! [X47] : addition(X47,X47) = X47,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_48,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_49,negated_conjecture,
addition(esk2_0,addition(c(addition(esk2_0,esk3_0)),multiplication(addition(esk2_0,c(esk2_0)),esk3_0))) != one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_25]) ).
fof(c_0_50,plain,
! [X4] :
( ~ test(X4)
=> c(X4) = zero ),
inference(fof_simplification,[status(thm)],[test_4]) ).
cnf(c_0_51,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_52,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
fof(c_0_53,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_54,negated_conjecture,
addition(esk2_0,addition(esk3_0,c(addition(esk2_0,esk3_0)))) != one,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_34]),c_0_35]),c_0_41])]),c_0_25]) ).
cnf(c_0_55,plain,
( addition(X1,addition(X2,c(addition(X1,X2)))) = one
| ~ test(addition(X1,X2)) ),
inference(spm,[status(thm)],[c_0_42,c_0_34]) ).
fof(c_0_56,plain,
! [X71] :
( test(X71)
| c(X71) = zero ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])]) ).
fof(c_0_57,plain,
! [X46] : addition(X46,zero) = X46,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_58,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_42,c_0_51]) ).
cnf(c_0_59,plain,
( addition(X1,esk1_1(X1)) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_52]) ).
cnf(c_0_60,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_61,negated_conjecture,
~ test(addition(esk2_0,esk3_0)),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_62,plain,
( test(X1)
| c(X1) = zero ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_63,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_64,plain,
( addition(X1,one) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_65,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_66,plain,
( addition(c(addition(X1,X2)),multiplication(c(X1),X3)) = multiplication(c(X1),addition(c(X2),X3))
| ~ test(X2)
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_40]) ).
cnf(c_0_67,negated_conjecture,
c(addition(esk2_0,esk3_0)) = zero,
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_68,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_63,c_0_25]) ).
fof(c_0_69,plain,
! [X51] : multiplication(X51,one) = X51,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_70,negated_conjecture,
addition(one,esk2_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_41]),c_0_25]) ).
cnf(c_0_71,plain,
( multiplication(X1,c(X1)) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_28]) ).
fof(c_0_72,plain,
! [X60] : multiplication(zero,X60) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_73,plain,
( test(X2)
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_74,plain,
( complement(X2,X1)
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero
| addition(X1,X2) != one ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_75,plain,
! [X59] : multiplication(X59,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_76,negated_conjecture,
multiplication(c(esk2_0),addition(c(esk3_0),X1)) = multiplication(c(esk2_0),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),c_0_36]),c_0_41])]) ).
cnf(c_0_77,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_78,negated_conjecture,
addition(one,addition(esk2_0,X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_42,c_0_70]) ).
cnf(c_0_79,plain,
c(one) = zero,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_71]),c_0_62]) ).
cnf(c_0_80,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_81,plain,
( test(X1)
| addition(X1,X2) != one
| multiplication(X2,X1) != zero
| multiplication(X1,X2) != zero ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_82,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_83,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_35]),c_0_25]) ).
cnf(c_0_84,negated_conjecture,
( multiplication(c(esk2_0),c(c(esk3_0))) = c(esk2_0)
| ~ test(c(esk3_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_34]),c_0_77]) ).
cnf(c_0_85,negated_conjecture,
addition(one,c(esk2_0)) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_34]),c_0_51]),c_0_41])]) ).
cnf(c_0_86,plain,
( c(addition(one,X1)) = zero
| ~ test(one)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_79]),c_0_80]) ).
cnf(c_0_87,plain,
test(one),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_63]),c_0_80]),c_0_82])])]) ).
cnf(c_0_88,plain,
( addition(X1,addition(c(X1),X2)) = addition(one,X2)
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_34]) ).
cnf(c_0_89,negated_conjecture,
( addition(c(esk2_0),c(c(esk3_0))) = c(c(esk3_0))
| ~ test(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_83,c_0_84]),c_0_25]),c_0_85]),c_0_35]),c_0_25]) ).
cnf(c_0_90,plain,
( c(addition(one,X1)) = zero
| ~ test(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_87])]) ).
fof(c_0_91,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])]) ).
cnf(c_0_92,plain,
( c(zero) = one
| ~ test(zero) ),
inference(spm,[status(thm)],[c_0_63,c_0_31]) ).
cnf(c_0_93,plain,
test(zero),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_68]),c_0_82]),c_0_80])])]) ).
cnf(c_0_94,negated_conjecture,
( addition(esk2_0,c(c(esk3_0))) = addition(one,c(c(esk3_0)))
| ~ test(c(esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_41])]) ).
cnf(c_0_95,plain,
c(addition(one,X1)) = zero,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_58]),c_0_62]) ).
cnf(c_0_96,plain,
( c(multiplication(X1,X2)) = addition(c(X1),c(X2))
| ~ test(X1)
| ~ test(X2) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_97,plain,
c(zero) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93])]) ).
cnf(c_0_98,negated_conjecture,
( addition(esk2_0,c(c(esk3_0))) = one
| ~ test(addition(one,c(c(esk3_0))))
| ~ test(c(esk3_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_94]),c_0_95]),c_0_63]) ).
cnf(c_0_99,plain,
( addition(one,c(X1)) = one
| ~ test(X1) ),
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_97]),c_0_80]),c_0_97]),c_0_93])]) ).
cnf(c_0_100,plain,
( test(c(X1))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_28]) ).
cnf(c_0_101,negated_conjecture,
( c(addition(esk2_0,c(esk3_0))) = c(esk2_0)
| ~ test(c(esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_84]),c_0_41])]) ).
cnf(c_0_102,plain,
( multiplication(X1,addition(X2,c(X1))) = multiplication(X1,X2)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_71]),c_0_63]) ).
cnf(c_0_103,negated_conjecture,
( addition(esk2_0,c(c(esk3_0))) = one
| ~ test(c(esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_87])]) ).
cnf(c_0_104,negated_conjecture,
addition(one,esk3_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_36]),c_0_25]) ).
cnf(c_0_105,negated_conjecture,
( test(c(esk2_0))
| ~ test(addition(esk2_0,c(esk3_0)))
| ~ test(c(esk3_0)) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_106,plain,
( multiplication(X1,X2) = zero
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_107,negated_conjecture,
( multiplication(c(esk3_0),esk2_0) = c(esk3_0)
| ~ test(c(esk3_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_77]) ).
cnf(c_0_108,negated_conjecture,
addition(one,addition(esk3_0,X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_42,c_0_104]) ).
cnf(c_0_109,negated_conjecture,
( c(addition(esk2_0,c(esk3_0))) = zero
| test(c(esk2_0))
| ~ test(c(esk3_0)) ),
inference(spm,[status(thm)],[c_0_105,c_0_62]) ).
cnf(c_0_110,plain,
( test(X1)
| addition(X2,X1) != one
| multiplication(X2,X1) != zero
| multiplication(X1,X2) != zero ),
inference(spm,[status(thm)],[c_0_81,c_0_25]) ).
fof(c_0_111,plain,
! [X48,X49,X50] : multiplication(X48,multiplication(X49,X50)) = multiplication(multiplication(X48,X49),X50),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_112,plain,
( multiplication(c(X1),X1) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_28]) ).
cnf(c_0_113,negated_conjecture,
multiplication(c(esk3_0),esk2_0) = c(esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_100]),c_0_36])]) ).
cnf(c_0_114,negated_conjecture,
addition(one,c(esk3_0)) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_34]),c_0_51]),c_0_36])]) ).
cnf(c_0_115,negated_conjecture,
( c(addition(esk2_0,c(esk3_0))) = zero
| test(c(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_100]),c_0_36])]) ).
cnf(c_0_116,negated_conjecture,
( test(c(esk2_0))
| c(esk2_0) != zero ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_85]),c_0_35]),c_0_77])]) ).
cnf(c_0_117,plain,
( c(multiplication(X1,X1)) = c(X1)
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_96]) ).
cnf(c_0_118,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_119,plain,
( multiplication(c(X1),addition(X1,X2)) = multiplication(c(X1),X2)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_112]),c_0_68]) ).
cnf(c_0_120,negated_conjecture,
addition(esk2_0,c(esk3_0)) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_113]),c_0_25]),c_0_114]),c_0_35]) ).
cnf(c_0_121,negated_conjecture,
multiplication(c(esk2_0),c(esk3_0)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_63]),c_0_82]) ).
cnf(c_0_122,negated_conjecture,
( test(c(esk2_0))
| ~ test(c(esk3_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_115]),c_0_116]) ).
cnf(c_0_123,plain,
( addition(c(X1),c(X2)) = c(multiplication(X1,multiplication(X1,X2)))
| ~ test(multiplication(X1,X1))
| ~ test(X2)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_117]),c_0_118]) ).
cnf(c_0_124,negated_conjecture,
multiplication(c(esk2_0),esk2_0) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_121]),c_0_41])]) ).
cnf(c_0_125,negated_conjecture,
test(c(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_100]),c_0_36])]) ).
cnf(c_0_126,plain,
( c(X1) = X2
| ~ complement(X1,X2)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_127,negated_conjecture,
( addition(c(esk2_0),c(c(esk2_0))) = one
| ~ test(multiplication(c(esk2_0),c(esk2_0))) ),
inference(rw,[status(thm)],[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_123,c_0_124]),c_0_82]),c_0_97]),c_0_41]),c_0_125])]),c_0_25]) ).
cnf(c_0_128,plain,
( c(X1) = X2
| addition(X2,X1) != one
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_74]),c_0_110]) ).
cnf(c_0_129,plain,
( multiplication(X1,addition(c(X1),X2)) = multiplication(X1,X2)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_71]),c_0_68]) ).
cnf(c_0_130,negated_conjecture,
addition(c(esk2_0),c(c(esk2_0))) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_40]),c_0_51]),c_0_125]),c_0_41])]) ).
cnf(c_0_131,plain,
( multiplication(addition(c(X1),X2),X1) = multiplication(X2,X1)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_112]),c_0_68]) ).
cnf(c_0_132,plain,
( multiplication(X1,multiplication(c(X1),X2)) = zero
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_71]),c_0_80]) ).
cnf(c_0_133,negated_conjecture,
( c(c(esk2_0)) = one
| c(esk2_0) != zero ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_85]),c_0_77]),c_0_35])]) ).
cnf(c_0_134,plain,
( c(multiplication(X1,multiplication(X2,multiplication(X1,X2)))) = c(multiplication(X1,X2))
| ~ test(multiplication(X1,X2)) ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_135,negated_conjecture,
multiplication(esk2_0,c(c(esk2_0))) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_77]),c_0_41])]) ).
cnf(c_0_136,negated_conjecture,
multiplication(c(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_131,c_0_130]),c_0_35]),c_0_41])]) ).
cnf(c_0_137,negated_conjecture,
( addition(esk2_0,addition(c(esk2_0),c(esk3_0))) = one
| ~ test(addition(esk2_0,c(esk3_0)))
| ~ test(c(esk3_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_101]),c_0_42]),c_0_25]) ).
cnf(c_0_138,plain,
( multiplication(addition(X1,X2),c(X1)) = multiplication(X2,c(X1))
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_71]),c_0_68]) ).
cnf(c_0_139,negated_conjecture,
addition(esk2_0,addition(multiplication(esk2_0,esk3_0),multiplication(c(esk2_0),addition(esk3_0,c(esk3_0))))) != one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_44]),c_0_60]),c_0_25]),c_0_42]) ).
cnf(c_0_140,negated_conjecture,
( multiplication(c(esk2_0),X1) = zero
| c(esk2_0) != zero ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_35]),c_0_125])]) ).
cnf(c_0_141,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_77]),c_0_25]) ).
cnf(c_0_142,negated_conjecture,
c(multiplication(esk2_0,esk2_0)) = c(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_136]),c_0_41])]) ).
cnf(c_0_143,negated_conjecture,
( addition(esk2_0,addition(c(esk2_0),c(esk3_0))) = one
| ~ test(c(esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_120]),c_0_41])]) ).
cnf(c_0_144,negated_conjecture,
( addition(c(esk2_0),X1) = X1
| c(esk2_0) != zero ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_133]),c_0_77]),c_0_77]),c_0_125])]) ).
cnf(c_0_145,negated_conjecture,
( c(esk2_0) != zero
| esk2_0 != one ),
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_139,c_0_140]),c_0_63]),c_0_141]),c_0_25]),c_0_104]),c_0_77]) ).
cnf(c_0_146,plain,
( multiplication(addition(X1,X2),c(X2)) = multiplication(X1,c(X2))
| ~ test(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_71]),c_0_63]) ).
cnf(c_0_147,negated_conjecture,
( addition(multiplication(esk2_0,esk2_0),c(esk2_0)) = one
| ~ test(multiplication(esk2_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_142]) ).
cnf(c_0_148,negated_conjecture,
( c(esk2_0) != zero
| ~ test(c(esk3_0)) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_120]),c_0_145]) ).
cnf(c_0_149,negated_conjecture,
( c(c(esk2_0)) = multiplication(esk2_0,esk2_0)
| ~ test(multiplication(esk2_0,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_146,c_0_147]),c_0_35]),c_0_118]),c_0_135]),c_0_125])]) ).
cnf(c_0_150,negated_conjecture,
c(esk2_0) != zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_100]),c_0_36])]) ).
cnf(c_0_151,negated_conjecture,
addition(esk2_0,addition(c(esk2_0),c(esk3_0))) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_120]),c_0_25]),c_0_41])]) ).
cnf(c_0_152,plain,
( multiplication(X1,X1) = X1
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_34]),c_0_77]) ).
cnf(c_0_153,negated_conjecture,
addition(esk2_0,c(c(esk2_0))) = c(c(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_135]),c_0_25]),c_0_70]),c_0_35]),c_0_25]) ).
cnf(c_0_154,negated_conjecture,
c(c(esk2_0)) = multiplication(esk2_0,esk2_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_62]),c_0_142]),c_0_150]) ).
cnf(c_0_155,negated_conjecture,
addition(esk2_0,c(multiplication(esk2_0,esk3_0))) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_96]),c_0_36]),c_0_41])]) ).
cnf(c_0_156,negated_conjecture,
addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(c(esk2_0),c(esk3_0)),multiplication(addition(esk3_0,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_44]),c_0_42]),c_0_25]),c_0_44]),c_0_42]),c_0_25]),c_0_44]),c_0_25]) ).
cnf(c_0_157,plain,
addition(multiplication(X1,X2),addition(multiplication(X1,X3),X4)) = addition(multiplication(X1,addition(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_42,c_0_60]) ).
cnf(c_0_158,plain,
( addition(multiplication(X1,X1),c(X1)) = one
| ~ test(multiplication(X1,X1))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_117]) ).
cnf(c_0_159,negated_conjecture,
multiplication(esk3_0,esk3_0) = esk3_0,
inference(spm,[status(thm)],[c_0_152,c_0_36]) ).
cnf(c_0_160,negated_conjecture,
multiplication(esk2_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)],[c_0_153,c_0_154]),c_0_141]),c_0_25]),c_0_70]),c_0_77]),c_0_154]) ).
cnf(c_0_161,negated_conjecture,
multiplication(c(multiplication(esk2_0,esk3_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_138,c_0_155]),c_0_35]),c_0_41])]) ).
cnf(c_0_162,plain,
( addition(X1,one) = one
| c(X1) = zero ),
inference(spm,[status(thm)],[c_0_64,c_0_62]) ).
cnf(c_0_163,negated_conjecture,
addition(multiplication(esk2_0,esk3_0),addition(multiplication(addition(esk3_0,c(esk3_0)),esk2_0),multiplication(c(esk2_0),addition(esk3_0,c(esk3_0))))) != one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_156,c_0_157]),c_0_25]) ).
cnf(c_0_164,negated_conjecture,
addition(esk3_0,c(esk3_0)) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_36])]) ).
cnf(c_0_165,negated_conjecture,
addition(esk2_0,c(esk2_0)) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_147,c_0_160]),c_0_160]),c_0_41])]) ).
cnf(c_0_166,negated_conjecture,
addition(one,multiplication(esk2_0,esk3_0)) = one,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_80]),c_0_25]),c_0_150]) ).
cnf(c_0_167,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)],[c_0_163,c_0_164]),c_0_35]),c_0_164]),c_0_77]),c_0_165]),c_0_25]),c_0_166])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE010+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n018.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 20:25:17 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 2.00/1.95 % Version : CSE_E---1.7
% 2.00/1.95 % Problem : theBenchmark.p
% 2.00/1.95 % SZS status Theorem for theBenchmark.p
% 2.00/1.95 % SZS output start CNFRefutation
% See solution above
% 2.00/1.96 % Total time : 1.375s
%------------------------------------------------------------------------------