TSTP Solution File: KLE007+2 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : KLE007+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n027.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 : 600s
% DateTime : Sun Jul 17 01:55:13 EDT 2022
% Result : Theorem 0.22s 1.41s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 145 ( 91 unt; 0 def)
% Number of atoms : 233 ( 144 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 161 ( 73 ~; 66 |; 14 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 157 ( 14 sgn 61 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(goals,conjecture,
! [X4,X5] :
( ( test(X5)
& test(X4) )
=> ( leq(one,addition(multiplication(addition(X4,c(X4)),X5),multiplication(addition(X4,c(X4)),c(X5))))
& leq(addition(multiplication(addition(X4,c(X4)),X5),multiplication(addition(X4,c(X4)),c(X5))),one) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
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(test_4,axiom,
! [X4] :
( ~ test(X4)
=> c(X4) = zero ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_4) ).
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(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(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(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).
fof(c_0_16,plain,
! [X6,X7,X6,X7] :
( ( multiplication(X6,X7) = zero
| ~ complement(X7,X6) )
& ( multiplication(X7,X6) = zero
| ~ complement(X7,X6) )
& ( addition(X6,X7) = one
| ~ complement(X7,X6) )
& ( multiplication(X6,X7) != zero
| multiplication(X7,X6) != zero
| addition(X6,X7) != one
| complement(X7,X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])])])]) ).
fof(c_0_17,plain,
! [X6,X6,X8] :
( ( ~ test(X6)
| complement(esk3_1(X6),X6) )
& ( ~ complement(X8,X6)
| test(X6) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_1])])])])])]) ).
fof(c_0_18,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_19,plain,
( multiplication(X2,X1) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
( complement(esk3_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_21,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_22,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_23,negated_conjecture,
~ ! [X4,X5] :
( ( test(X5)
& test(X4) )
=> ( leq(one,addition(multiplication(addition(X4,c(X4)),X5),multiplication(addition(X4,c(X4)),c(X5))))
& leq(addition(multiplication(addition(X4,c(X4)),X5),multiplication(addition(X4,c(X4)),c(X5))),one) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_24,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( multiplication(X1,esk3_1(X1)) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
( test(X1)
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
( complement(X1,X2)
| addition(X2,X1) != one
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_28,plain,
! [X2] : multiplication(X2,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
fof(c_0_29,plain,
! [X2] : multiplication(zero,X2) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_30,plain,
! [X6,X7,X7] :
( ( c(X6) != X7
| complement(X6,X7)
| ~ test(X6) )
& ( ~ complement(X6,X7)
| c(X6) = X7
| ~ test(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])])])]) ).
cnf(c_0_31,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_32,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_33,plain,
( addition(X2,X1) = one
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_34,negated_conjecture,
( test(esk2_0)
& test(esk1_0)
& ( ~ leq(one,addition(multiplication(addition(esk1_0,c(esk1_0)),esk2_0),multiplication(addition(esk1_0,c(esk1_0)),c(esk2_0))))
| ~ leq(addition(multiplication(addition(esk1_0,c(esk1_0)),esk2_0),multiplication(addition(esk1_0,c(esk1_0)),c(esk2_0))),one) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
cnf(c_0_35,plain,
( esk3_1(one) = zero
| ~ test(one) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_36,plain,
( test(X1)
| addition(X1,X2) != one
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_37,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,plain,
( c(X1) = X2
| ~ test(X1)
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_41,plain,
( addition(X1,esk3_1(X1)) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_20]) ).
fof(c_0_42,plain,
! [X5] :
( test(X5)
| c(X5) = zero ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[test_4])])]) ).
cnf(c_0_43,plain,
( complement(X1,X2)
| ~ test(X1)
| c(X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_44,negated_conjecture,
test(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_45,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_46,plain,
( complement(zero,one)
| ~ test(one) ),
inference(spm,[status(thm)],[c_0_20,c_0_35]) ).
cnf(c_0_47,plain,
( test(X1)
| X1 != one ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_31]),c_0_38])]) ).
cnf(c_0_48,plain,
( c(esk3_1(X1)) = X1
| ~ test(esk3_1(X1))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_20]) ).
cnf(c_0_49,plain,
( esk3_1(zero) = one
| ~ test(zero) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_50,plain,
( c(X1) = zero
| test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_51,plain,
( test(zero)
| X1 != one ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_38]),c_0_40]),c_0_37])]) ).
fof(c_0_52,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_53,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_54,negated_conjecture,
( complement(esk1_0,X1)
| c(esk1_0) != X1 ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_55,negated_conjecture,
( complement(esk2_0,X1)
| c(esk2_0) != X1 ),
inference(spm,[status(thm)],[c_0_43,c_0_45]) ).
cnf(c_0_56,plain,
complement(zero,one),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_57,plain,
( c(one) = zero
| ~ test(zero) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_58,plain,
test(zero),
inference(er,[status(thm)],[c_0_51]) ).
cnf(c_0_59,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_60,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_61,negated_conjecture,
( addition(X1,esk1_0) = one
| c(esk1_0) != X1 ),
inference(spm,[status(thm)],[c_0_33,c_0_54]) ).
cnf(c_0_62,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_63,negated_conjecture,
( addition(X1,esk2_0) = one
| c(esk2_0) != X1 ),
inference(spm,[status(thm)],[c_0_33,c_0_55]) ).
cnf(c_0_64,plain,
test(one),
inference(spm,[status(thm)],[c_0_26,c_0_56]) ).
cnf(c_0_65,plain,
c(one) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).
fof(c_0_66,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_67,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_68,negated_conjecture,
addition(esk1_0,c(esk1_0)) = one,
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_61]),c_0_32]) ).
fof(c_0_69,plain,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_70,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_71,negated_conjecture,
( multiplication(X1,esk2_0) = zero
| c(esk2_0) != X1 ),
inference(spm,[status(thm)],[c_0_19,c_0_55]) ).
cnf(c_0_72,negated_conjecture,
( multiplication(esk2_0,X1) = zero
| c(esk2_0) != X1 ),
inference(spm,[status(thm)],[c_0_62,c_0_55]) ).
cnf(c_0_73,negated_conjecture,
addition(esk2_0,c(esk2_0)) = one,
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_63]),c_0_32]) ).
cnf(c_0_74,plain,
( c(X1) = zero
| complement(X1,X2)
| c(X1) != X2 ),
inference(spm,[status(thm)],[c_0_43,c_0_50]) ).
cnf(c_0_75,plain,
( complement(one,X1)
| zero != X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_64]),c_0_65]) ).
cnf(c_0_76,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_77,negated_conjecture,
addition(one,esk1_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_32]) ).
cnf(c_0_78,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_79,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_80,negated_conjecture,
multiplication(c(esk2_0),esk2_0) = zero,
inference(er,[status(thm)],[c_0_71]) ).
cnf(c_0_81,negated_conjecture,
multiplication(esk2_0,c(esk2_0)) = zero,
inference(er,[status(thm)],[c_0_72]) ).
cnf(c_0_82,negated_conjecture,
( ~ leq(addition(multiplication(addition(esk1_0,c(esk1_0)),esk2_0),multiplication(addition(esk1_0,c(esk1_0)),c(esk2_0))),one)
| ~ leq(one,addition(multiplication(addition(esk1_0,c(esk1_0)),esk2_0),multiplication(addition(esk1_0,c(esk1_0)),c(esk2_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_83,negated_conjecture,
addition(esk2_0,one) = one,
inference(spm,[status(thm)],[c_0_67,c_0_73]) ).
cnf(c_0_84,negated_conjecture,
( multiplication(X1,esk1_0) = zero
| c(esk1_0) != X1 ),
inference(spm,[status(thm)],[c_0_19,c_0_54]) ).
cnf(c_0_85,negated_conjecture,
( multiplication(esk1_0,X1) = zero
| c(esk1_0) != X1 ),
inference(spm,[status(thm)],[c_0_62,c_0_54]) ).
cnf(c_0_86,plain,
( c(X1) = zero
| test(X2)
| c(X1) != X2 ),
inference(spm,[status(thm)],[c_0_26,c_0_74]) ).
cnf(c_0_87,plain,
( test(X1)
| zero != X1 ),
inference(spm,[status(thm)],[c_0_26,c_0_75]) ).
cnf(c_0_88,negated_conjecture,
addition(X1,multiplication(esk1_0,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_24]),c_0_24]) ).
cnf(c_0_89,negated_conjecture,
addition(multiplication(X1,esk2_0),multiplication(X1,c(esk2_0))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_73]),c_0_79]) ).
cnf(c_0_90,plain,
( multiplication(esk3_1(X1),X1) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_20]) ).
cnf(c_0_91,negated_conjecture,
test(c(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_80]),c_0_32]),c_0_73]),c_0_81])]) ).
cnf(c_0_92,negated_conjecture,
( ~ leq(one,addition(multiplication(esk1_0,esk2_0),addition(multiplication(c(esk1_0),esk2_0),addition(multiplication(esk1_0,c(esk2_0)),multiplication(c(esk1_0),c(esk2_0))))))
| ~ leq(addition(multiplication(esk1_0,esk2_0),addition(multiplication(c(esk1_0),esk2_0),addition(multiplication(esk1_0,c(esk2_0)),multiplication(c(esk1_0),c(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)],[c_0_82,c_0_76]),c_0_76]),c_0_59]),c_0_76]),c_0_76]),c_0_59]) ).
cnf(c_0_93,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_32]),c_0_59]) ).
cnf(c_0_94,negated_conjecture,
addition(X1,multiplication(esk2_0,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_83]),c_0_24]),c_0_24]),c_0_32]) ).
cnf(c_0_95,negated_conjecture,
multiplication(c(esk1_0),esk1_0) = zero,
inference(er,[status(thm)],[c_0_84]) ).
cnf(c_0_96,negated_conjecture,
multiplication(esk1_0,c(esk1_0)) = zero,
inference(er,[status(thm)],[c_0_85]) ).
cnf(c_0_97,plain,
( addition(multiplication(X1,X2),multiplication(X1,esk3_1(X2))) = X1
| ~ test(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_41]),c_0_79]) ).
cnf(c_0_98,plain,
test(c(X1)),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_86]),c_0_87]) ).
cnf(c_0_99,negated_conjecture,
addition(multiplication(X1,X2),multiplication(X1,multiplication(esk1_0,X2))) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_78,c_0_88]) ).
cnf(c_0_100,plain,
( addition(multiplication(X1,X2),multiplication(esk3_1(X1),X2)) = X2
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_41]),c_0_24]) ).
cnf(c_0_101,negated_conjecture,
multiplication(esk3_1(c(esk2_0)),esk2_0) = esk3_1(c(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_31]),c_0_91])]) ).
cnf(c_0_102,negated_conjecture,
( ~ leq(one,addition(multiplication(esk1_0,esk2_0),addition(multiplication(esk1_0,c(esk2_0)),addition(multiplication(c(esk1_0),esk2_0),multiplication(c(esk1_0),c(esk2_0))))))
| ~ leq(addition(multiplication(esk1_0,esk2_0),addition(multiplication(esk1_0,c(esk2_0)),addition(multiplication(c(esk1_0),esk2_0),multiplication(c(esk1_0),c(esk2_0))))),one) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93]),c_0_93]) ).
fof(c_0_103,plain,
! [X3,X4,X3,X4] :
( ( ~ leq(X3,X4)
| addition(X3,X4) = X4 )
& ( addition(X3,X4) != X4
| leq(X3,X4) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])])]) ).
cnf(c_0_104,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_67,c_0_32]) ).
cnf(c_0_105,negated_conjecture,
addition(esk2_0,addition(c(esk2_0),X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_59,c_0_73]) ).
cnf(c_0_106,negated_conjecture,
addition(one,addition(esk1_0,X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_59,c_0_77]) ).
cnf(c_0_107,negated_conjecture,
addition(X1,multiplication(X1,esk2_0)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_83]),c_0_79]),c_0_79]),c_0_32]) ).
cnf(c_0_108,plain,
( addition(X1,one) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_67,c_0_41]) ).
cnf(c_0_109,negated_conjecture,
addition(multiplication(X1,X2),multiplication(X1,multiplication(esk2_0,X2))) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_78,c_0_94]) ).
cnf(c_0_110,negated_conjecture,
addition(multiplication(esk1_0,X1),multiplication(c(esk1_0),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_68]),c_0_24]) ).
cnf(c_0_111,negated_conjecture,
test(c(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_95]),c_0_32]),c_0_68]),c_0_96])]) ).
cnf(c_0_112,negated_conjecture,
multiplication(esk1_0,esk3_1(c(esk1_0))) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_96]),c_0_40]),c_0_98])]) ).
cnf(c_0_113,negated_conjecture,
multiplication(c(esk2_0),multiplication(esk1_0,esk2_0)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_80]),c_0_40]) ).
cnf(c_0_114,negated_conjecture,
esk3_1(c(esk2_0)) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_80]),c_0_40]),c_0_98])]) ).
cnf(c_0_115,negated_conjecture,
( ~ leq(one,addition(multiplication(esk1_0,esk2_0),addition(multiplication(esk1_0,c(esk2_0)),c(esk1_0))))
| ~ leq(addition(multiplication(esk1_0,esk2_0),addition(multiplication(esk1_0,c(esk2_0)),c(esk1_0))),one) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_89]),c_0_89]) ).
cnf(c_0_116,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_117,negated_conjecture,
addition(one,c(esk1_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_68]),c_0_32]) ).
cnf(c_0_118,negated_conjecture,
addition(one,multiplication(esk1_0,c(esk2_0))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_88]),c_0_73]) ).
cnf(c_0_119,negated_conjecture,
addition(one,multiplication(esk1_0,esk2_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_77]) ).
cnf(c_0_120,plain,
addition(one,c(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_98]),c_0_32]) ).
cnf(c_0_121,negated_conjecture,
addition(X1,multiplication(X1,esk1_0)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_77]),c_0_79]),c_0_79]) ).
cnf(c_0_122,negated_conjecture,
multiplication(c(esk1_0),multiplication(esk2_0,esk1_0)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_95]),c_0_40]) ).
cnf(c_0_123,negated_conjecture,
esk3_1(c(esk1_0)) = esk1_0,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_25]),c_0_31]),c_0_111])]),c_0_112]) ).
cnf(c_0_124,negated_conjecture,
addition(multiplication(X1,X2),multiplication(X1,multiplication(X2,esk2_0))) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_78,c_0_107]) ).
cnf(c_0_125,negated_conjecture,
multiplication(esk2_0,multiplication(esk1_0,esk2_0)) = multiplication(esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_113]),c_0_114]),c_0_40]),c_0_98])]) ).
cnf(c_0_126,negated_conjecture,
~ leq(one,addition(multiplication(esk1_0,esk2_0),addition(multiplication(esk1_0,c(esk2_0)),c(esk1_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(spm,[status(thm)],[c_0_115,c_0_116]),c_0_59]),c_0_59]),c_0_32]),c_0_117]),c_0_32]),c_0_118]),c_0_32]),c_0_119])]) ).
cnf(c_0_127,plain,
addition(X1,multiplication(X1,c(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_120]),c_0_79]),c_0_79]) ).
cnf(c_0_128,negated_conjecture,
addition(multiplication(X1,X2),multiplication(X1,multiplication(X2,esk1_0))) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_78,c_0_121]) ).
cnf(c_0_129,negated_conjecture,
multiplication(esk1_0,multiplication(esk2_0,esk1_0)) = multiplication(esk2_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_122]),c_0_123]),c_0_40]),c_0_98])]) ).
cnf(c_0_130,negated_conjecture,
addition(multiplication(esk2_0,esk1_0),multiplication(esk1_0,esk2_0)) = multiplication(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_131,negated_conjecture,
multiplication(esk3_1(esk2_0),c(esk2_0)) = esk3_1(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_40]),c_0_45])]) ).
cnf(c_0_132,negated_conjecture,
addition(one,addition(multiplication(esk1_0,esk2_0),addition(multiplication(esk1_0,c(esk2_0)),c(esk1_0)))) != addition(multiplication(esk1_0,esk2_0),addition(multiplication(esk1_0,c(esk2_0)),c(esk1_0))),
inference(spm,[status(thm)],[c_0_126,c_0_116]) ).
cnf(c_0_133,negated_conjecture,
addition(one,addition(multiplication(esk1_0,esk2_0),X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_59,c_0_119]) ).
cnf(c_0_134,negated_conjecture,
addition(one,addition(X1,c(esk1_0))) = addition(X1,one),
inference(spm,[status(thm)],[c_0_93,c_0_117]) ).
cnf(c_0_135,negated_conjecture,
addition(one,multiplication(esk1_0,c(X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_127]),c_0_77]) ).
cnf(c_0_136,negated_conjecture,
multiplication(esk1_0,esk2_0) = multiplication(esk2_0,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_32]),c_0_130]) ).
cnf(c_0_137,negated_conjecture,
esk3_1(esk2_0) = c(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_131]),c_0_81]),c_0_40]),c_0_45])]) ).
cnf(c_0_138,negated_conjecture,
multiplication(c(esk1_0),esk3_1(esk1_0)) = esk3_1(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_25]),c_0_40]),c_0_44])]) ).
cnf(c_0_139,negated_conjecture,
addition(multiplication(esk1_0,esk2_0),addition(multiplication(esk1_0,c(esk2_0)),c(esk1_0))) != one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_132,c_0_133]),c_0_134]),c_0_32]),c_0_135]) ).
cnf(c_0_140,plain,
( addition(X1,addition(X2,esk3_1(addition(X1,X2)))) = one
| ~ test(addition(X1,X2)) ),
inference(spm,[status(thm)],[c_0_59,c_0_41]) ).
cnf(c_0_141,negated_conjecture,
addition(multiplication(esk2_0,esk1_0),multiplication(esk1_0,c(esk2_0))) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_136]),c_0_137]),c_0_45])]) ).
cnf(c_0_142,negated_conjecture,
esk3_1(esk1_0) = c(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_138]),c_0_95]),c_0_40]),c_0_44])]) ).
cnf(c_0_143,negated_conjecture,
addition(multiplication(esk2_0,esk1_0),addition(multiplication(esk1_0,c(esk2_0)),c(esk1_0))) != one,
inference(rw,[status(thm)],[c_0_139,c_0_136]) ).
cnf(c_0_144,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_142]),c_0_44])]),c_0_143]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KLE007+2 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 13:44:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.22/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.41 # Preprocessing time : 0.015 s
% 0.22/1.41
% 0.22/1.41 # Proof found!
% 0.22/1.41 # SZS status Theorem
% 0.22/1.41 # SZS output start CNFRefutation
% See solution above
% 0.22/1.41 # Proof object total steps : 145
% 0.22/1.41 # Proof object clause steps : 112
% 0.22/1.41 # Proof object formula steps : 33
% 0.22/1.41 # Proof object conjectures : 65
% 0.22/1.41 # Proof object clause conjectures : 62
% 0.22/1.41 # Proof object formula conjectures : 3
% 0.22/1.41 # Proof object initial clauses used : 23
% 0.22/1.41 # Proof object initial formulas used : 16
% 0.22/1.41 # Proof object generating inferences : 83
% 0.22/1.41 # Proof object simplifying inferences : 115
% 0.22/1.41 # Training examples: 0 positive, 0 negative
% 0.22/1.41 # Parsed axioms : 17
% 0.22/1.41 # Removed by relevancy pruning/SinE : 0
% 0.22/1.41 # Initial clauses : 25
% 0.22/1.41 # Removed in clause preprocessing : 0
% 0.22/1.41 # Initial clauses in saturation : 25
% 0.22/1.41 # Processed clauses : 2430
% 0.22/1.41 # ...of these trivial : 355
% 0.22/1.41 # ...subsumed : 1495
% 0.22/1.41 # ...remaining for further processing : 580
% 0.22/1.41 # Other redundant clauses eliminated : 85
% 0.22/1.41 # Clauses deleted for lack of memory : 0
% 0.22/1.41 # Backward-subsumed : 73
% 0.22/1.41 # Backward-rewritten : 141
% 0.22/1.41 # Generated clauses : 16333
% 0.22/1.41 # ...of the previous two non-trivial : 9456
% 0.22/1.41 # Contextual simplify-reflections : 415
% 0.22/1.41 # Paramodulations : 16196
% 0.22/1.41 # Factorizations : 0
% 0.22/1.41 # Equation resolutions : 137
% 0.22/1.41 # Current number of processed clauses : 366
% 0.22/1.41 # Positive orientable unit clauses : 157
% 0.22/1.41 # Positive unorientable unit clauses: 8
% 0.22/1.41 # Negative unit clauses : 10
% 0.22/1.41 # Non-unit-clauses : 191
% 0.22/1.41 # Current number of unprocessed clauses: 4990
% 0.22/1.41 # ...number of literals in the above : 9979
% 0.22/1.41 # Current number of archived formulas : 0
% 0.22/1.41 # Current number of archived clauses : 214
% 0.22/1.41 # Clause-clause subsumption calls (NU) : 22214
% 0.22/1.41 # Rec. Clause-clause subsumption calls : 18462
% 0.22/1.41 # Non-unit clause-clause subsumptions : 900
% 0.22/1.41 # Unit Clause-clause subsumption calls : 1380
% 0.22/1.41 # Rewrite failures with RHS unbound : 0
% 0.22/1.41 # BW rewrite match attempts : 667
% 0.22/1.41 # BW rewrite match successes : 209
% 0.22/1.41 # Condensation attempts : 0
% 0.22/1.41 # Condensation successes : 0
% 0.22/1.41 # Termbank termtop insertions : 190518
% 0.22/1.41
% 0.22/1.41 # -------------------------------------------------
% 0.22/1.41 # User time : 0.236 s
% 0.22/1.41 # System time : 0.005 s
% 0.22/1.41 # Total time : 0.241 s
% 0.22/1.41 # Maximum resident set size: 9416 pages
%------------------------------------------------------------------------------