TSTP Solution File: KLE010+4 by E---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : KLE010+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n026.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 18:03:49 EDT 2023
% Result : Theorem 4.42s 1.09s
% Output : CNFRefutation 4.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 17
% Syntax : Number of formulae : 125 ( 76 unt; 0 def)
% Number of atoms : 206 ( 112 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 150 ( 69 ~; 56 |; 15 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 151 ( 4 sgn; 61 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(test_3,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Pmv7FneYhC/E---3.1_14125.p',test_3) ).
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/tmp/tmp.Pmv7FneYhC/E---3.1_14125.p',test_2) ).
fof(goals,conjecture,
! [X4,X5] :
( ( test(X5)
& test(X4) )
=> ( leq(one,addition(addition(addition(addition(multiplication(X5,X4),multiplication(c(X5),X4)),multiplication(X4,X5)),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))))
& leq(addition(addition(addition(addition(multiplication(X5,X4),multiplication(c(X5),X4)),multiplication(X4,X5)),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))),one) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Pmv7FneYhC/E---3.1_14125.p',goals) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/tmp/tmp.Pmv7FneYhC/E---3.1_14125.p',additive_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/tmp/tmp.Pmv7FneYhC/E---3.1_14125.p',additive_commutativity) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox2/tmp/tmp.Pmv7FneYhC/E---3.1_14125.p',right_annihilation) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/tmp/tmp.Pmv7FneYhC/E---3.1_14125.p',left_annihilation) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox2/tmp/tmp.Pmv7FneYhC/E---3.1_14125.p',test_1) ).
fof(test_4,axiom,
! [X4] :
( ~ test(X4)
=> c(X4) = zero ),
file('/export/starexec/sandbox2/tmp/tmp.Pmv7FneYhC/E---3.1_14125.p',test_4) ).
fof(test_deMorgan2,axiom,
! [X4,X5] :
( ( test(X4)
& test(X5) )
=> c(multiplication(X4,X5)) = addition(c(X4),c(X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.Pmv7FneYhC/E---3.1_14125.p',test_deMorgan2) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/tmp/tmp.Pmv7FneYhC/E---3.1_14125.p',multiplicative_left_identity) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/tmp/tmp.Pmv7FneYhC/E---3.1_14125.p',left_distributivity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/tmp/tmp.Pmv7FneYhC/E---3.1_14125.p',multiplicative_right_identity) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/tmp/tmp.Pmv7FneYhC/E---3.1_14125.p',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/tmp/tmp.Pmv7FneYhC/E---3.1_14125.p',additive_idempotence) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/tmp/tmp.Pmv7FneYhC/E---3.1_14125.p',right_distributivity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/tmp/tmp.Pmv7FneYhC/E---3.1_14125.p',order) ).
fof(c_0_17,plain,
! [X41,X42] :
( ( c(X41) != X42
| complement(X41,X42)
| ~ test(X41) )
& ( ~ complement(X41,X42)
| c(X41) = X42
| ~ test(X41) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])]) ).
fof(c_0_18,plain,
! [X12,X13] :
( ( multiplication(X12,X13) = zero
| ~ complement(X13,X12) )
& ( multiplication(X13,X12) = zero
| ~ complement(X13,X12) )
& ( addition(X12,X13) = one
| ~ complement(X13,X12) )
& ( multiplication(X12,X13) != zero
| multiplication(X13,X12) != zero
| addition(X12,X13) != one
| complement(X13,X12) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).
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,
~ ! [X4,X5] :
( ( test(X5)
& test(X4) )
=> ( leq(one,addition(addition(addition(addition(multiplication(X5,X4),multiplication(c(X5),X4)),multiplication(X4,X5)),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))))
& leq(addition(addition(addition(addition(multiplication(X5,X4),multiplication(c(X5),X4)),multiplication(X4,X5)),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))),one) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_21,plain,
! [X34] : addition(X34,zero) = X34,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_22,plain,
! [X14,X15] : addition(X14,X15) = addition(X15,X14),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_23,plain,
( multiplication(X1,X2) = zero
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_19]) ).
fof(c_0_25,negated_conjecture,
( test(esk2_0)
& test(esk1_0)
& ( ~ leq(one,addition(addition(addition(addition(multiplication(esk2_0,esk1_0),multiplication(c(esk2_0),esk1_0)),multiplication(esk1_0,esk2_0)),multiplication(c(esk1_0),esk2_0)),multiplication(c(esk1_0),c(esk2_0))))
| ~ leq(addition(addition(addition(addition(multiplication(esk2_0,esk1_0),multiplication(c(esk2_0),esk1_0)),multiplication(esk1_0,esk2_0)),multiplication(c(esk1_0),esk2_0)),multiplication(c(esk1_0),c(esk2_0))),one) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
cnf(c_0_26,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_28,plain,
! [X35] : multiplication(X35,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
fof(c_0_29,plain,
! [X36] : multiplication(zero,X36) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_30,plain,
( multiplication(c(X1),X1) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_32,plain,
! [X37,X39,X40] :
( ( ~ test(X37)
| complement(esk3_1(X37),X37) )
& ( ~ complement(X40,X39)
| test(X39) ) ),
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_33,plain,
( complement(X2,X1)
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero
| addition(X1,X2) != one ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_34,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,negated_conjecture,
zero = multiplication(c(esk2_0),esk2_0),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,plain,
( test(X2)
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,plain,
complement(one,zero),
inference(er,[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])])]) ).
fof(c_0_40,plain,
! [X4] :
( ~ test(X4)
=> c(X4) = zero ),
inference(fof_simplification,[status(thm)],[test_4]) ).
cnf(c_0_41,plain,
( multiplication(c(X1),X1) = multiplication(c(esk2_0),esk2_0)
| ~ test(X1) ),
inference(rw,[status(thm)],[c_0_30,c_0_37]) ).
cnf(c_0_42,negated_conjecture,
test(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_43,plain,
( c(X1) = X2
| ~ complement(X1,X2)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_44,plain,
complement(zero,one),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_26]),c_0_36]),c_0_35])])]) ).
cnf(c_0_45,plain,
test(zero),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
fof(c_0_46,plain,
! [X32,X33] :
( ~ test(X32)
| ~ test(X33)
| c(multiplication(X32,X33)) = addition(c(X32),c(X33)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_deMorgan2])]) ).
fof(c_0_47,plain,
! [X29] :
( test(X29)
| c(X29) = zero ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])]) ).
cnf(c_0_48,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_49,negated_conjecture,
multiplication(c(esk2_0),esk2_0) = multiplication(c(esk1_0),esk1_0),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_50,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_51,plain,
one = c(zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
cnf(c_0_52,plain,
( c(multiplication(X1,X2)) = addition(c(X1),c(X2))
| ~ test(X1)
| ~ test(X2) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_53,plain,
( test(X1)
| c(X1) = zero ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_54,plain,
( test(c(X1))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_24]) ).
cnf(c_0_55,plain,
( multiplication(X1,X2) = multiplication(c(esk1_0),esk1_0)
| ~ complement(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_37]),c_0_49]) ).
fof(c_0_56,plain,
! [X11] : multiplication(one,X11) = X11,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_57,plain,
( addition(X1,X2) = c(zero)
| ~ complement(X2,X1) ),
inference(rw,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_58,negated_conjecture,
( c(multiplication(X1,esk1_0)) = addition(c(X1),c(esk1_0))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_42]) ).
cnf(c_0_59,plain,
test(c(X1)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_53]),c_0_54]) ).
cnf(c_0_60,plain,
( multiplication(X1,c(X1)) = multiplication(c(esk1_0),esk1_0)
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_24]) ).
cnf(c_0_61,negated_conjecture,
( ~ leq(one,addition(addition(addition(addition(multiplication(esk2_0,esk1_0),multiplication(c(esk2_0),esk1_0)),multiplication(esk1_0,esk2_0)),multiplication(c(esk1_0),esk2_0)),multiplication(c(esk1_0),c(esk2_0))))
| ~ leq(addition(addition(addition(addition(multiplication(esk2_0,esk1_0),multiplication(c(esk2_0),esk1_0)),multiplication(esk1_0,esk2_0)),multiplication(c(esk1_0),esk2_0)),multiplication(c(esk1_0),c(esk2_0))),one) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_62,plain,
! [X23,X24,X25] : multiplication(addition(X23,X24),X25) = addition(multiplication(X23,X25),multiplication(X24,X25)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_63,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_64,plain,
( addition(X1,X2) = c(multiplication(c(esk2_0),esk2_0))
| ~ complement(X2,X1) ),
inference(rw,[status(thm)],[c_0_57,c_0_37]) ).
cnf(c_0_65,negated_conjecture,
c(multiplication(c(X1),esk1_0)) = addition(c(c(X1)),c(esk1_0)),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_66,negated_conjecture,
multiplication(c(esk1_0),esk1_0) = multiplication(esk1_0,c(esk1_0)),
inference(spm,[status(thm)],[c_0_60,c_0_42]) ).
fof(c_0_67,plain,
! [X10] : multiplication(X10,one) = X10,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_68,negated_conjecture,
( ~ leq(one,addition(multiplication(c(esk1_0),c(esk2_0)),addition(multiplication(c(esk1_0),esk2_0),addition(multiplication(esk1_0,esk2_0),addition(multiplication(esk2_0,esk1_0),multiplication(c(esk2_0),esk1_0))))))
| ~ leq(addition(multiplication(c(esk1_0),c(esk2_0)),addition(multiplication(c(esk1_0),esk2_0),addition(multiplication(esk1_0,esk2_0),addition(multiplication(esk2_0,esk1_0),multiplication(c(esk2_0),esk1_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_61,c_0_27]),c_0_27]),c_0_27]),c_0_27]),c_0_27]),c_0_27]) ).
cnf(c_0_69,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_70,plain,
multiplication(c(zero),X1) = X1,
inference(rw,[status(thm)],[c_0_63,c_0_51]) ).
cnf(c_0_71,plain,
( addition(X1,X2) = c(multiplication(c(esk1_0),esk1_0))
| ~ complement(X2,X1) ),
inference(rw,[status(thm)],[c_0_64,c_0_49]) ).
cnf(c_0_72,negated_conjecture,
c(multiplication(esk1_0,c(esk1_0))) = addition(c(esk1_0),c(c(esk1_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_27]) ).
cnf(c_0_73,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_74,negated_conjecture,
( ~ leq(one,addition(multiplication(c(esk1_0),c(esk2_0)),addition(multiplication(c(esk1_0),esk2_0),addition(multiplication(esk1_0,esk2_0),multiplication(addition(esk2_0,c(esk2_0)),esk1_0)))))
| ~ leq(addition(multiplication(c(esk1_0),c(esk2_0)),addition(multiplication(c(esk1_0),esk2_0),addition(multiplication(esk1_0,esk2_0),multiplication(addition(esk2_0,c(esk2_0)),esk1_0)))),one) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_75,plain,
addition(multiplication(c(esk2_0),esk2_0),X1) = X1,
inference(rw,[status(thm)],[c_0_34,c_0_37]) ).
cnf(c_0_76,negated_conjecture,
multiplication(c(multiplication(c(esk2_0),esk2_0)),X1) = X1,
inference(spm,[status(thm)],[c_0_70,c_0_37]) ).
cnf(c_0_77,plain,
( addition(X1,X2) = addition(c(esk1_0),c(c(esk1_0)))
| ~ complement(X2,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_66]),c_0_72]) ).
cnf(c_0_78,plain,
multiplication(X1,c(zero)) = X1,
inference(rw,[status(thm)],[c_0_73,c_0_51]) ).
cnf(c_0_79,negated_conjecture,
( ~ leq(c(zero),addition(multiplication(c(esk1_0),c(esk2_0)),addition(multiplication(c(esk1_0),esk2_0),addition(multiplication(esk1_0,esk2_0),multiplication(addition(esk2_0,c(esk2_0)),esk1_0)))))
| ~ leq(addition(multiplication(c(esk1_0),c(esk2_0)),addition(multiplication(c(esk1_0),esk2_0),addition(multiplication(esk1_0,esk2_0),multiplication(addition(esk2_0,c(esk2_0)),esk1_0)))),c(zero)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_51]),c_0_51]) ).
fof(c_0_80,plain,
! [X16,X17,X18] : addition(X18,addition(X17,X16)) = addition(addition(X18,X17),X16),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_81,plain,
addition(X1,multiplication(c(esk2_0),esk2_0)) = X1,
inference(rw,[status(thm)],[c_0_26,c_0_37]) ).
cnf(c_0_82,plain,
addition(multiplication(c(esk1_0),esk1_0),X1) = X1,
inference(rw,[status(thm)],[c_0_75,c_0_49]) ).
cnf(c_0_83,negated_conjecture,
multiplication(c(multiplication(c(esk1_0),esk1_0)),X1) = X1,
inference(spm,[status(thm)],[c_0_76,c_0_49]) ).
fof(c_0_84,plain,
! [X19] : addition(X19,X19) = X19,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_85,plain,
( addition(X1,c(X1)) = addition(c(esk1_0),c(c(esk1_0)))
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_24]),c_0_27]) ).
cnf(c_0_86,negated_conjecture,
multiplication(X1,c(multiplication(c(esk2_0),esk2_0))) = X1,
inference(spm,[status(thm)],[c_0_78,c_0_37]) ).
cnf(c_0_87,negated_conjecture,
( ~ leq(c(multiplication(c(esk2_0),esk2_0)),addition(multiplication(c(esk1_0),c(esk2_0)),addition(multiplication(c(esk1_0),esk2_0),addition(multiplication(esk1_0,esk2_0),multiplication(addition(esk2_0,c(esk2_0)),esk1_0)))))
| ~ leq(addition(multiplication(c(esk1_0),c(esk2_0)),addition(multiplication(c(esk1_0),esk2_0),addition(multiplication(esk1_0,esk2_0),multiplication(addition(esk2_0,c(esk2_0)),esk1_0)))),c(multiplication(c(esk2_0),esk2_0))) ),
inference(spm,[status(thm)],[c_0_79,c_0_37]) ).
cnf(c_0_88,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_89,plain,
addition(X1,multiplication(c(esk1_0),esk1_0)) = X1,
inference(rw,[status(thm)],[c_0_81,c_0_49]) ).
cnf(c_0_90,plain,
multiplication(addition(c(esk1_0),X1),esk1_0) = multiplication(X1,esk1_0),
inference(spm,[status(thm)],[c_0_69,c_0_82]) ).
cnf(c_0_91,negated_conjecture,
multiplication(addition(c(esk1_0),c(c(esk1_0))),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_65]),c_0_27]) ).
fof(c_0_92,plain,
! [X20,X21,X22] : multiplication(X20,addition(X21,X22)) = addition(multiplication(X20,X21),multiplication(X20,X22)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_93,plain,
( c(multiplication(X1,c(X2))) = addition(c(X1),c(c(X2)))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_59]) ).
cnf(c_0_94,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_95,negated_conjecture,
addition(esk2_0,c(esk2_0)) = addition(c(esk1_0),c(c(esk1_0))),
inference(spm,[status(thm)],[c_0_85,c_0_31]) ).
cnf(c_0_96,negated_conjecture,
addition(c(esk1_0),c(c(esk1_0))) = addition(esk1_0,c(esk1_0)),
inference(spm,[status(thm)],[c_0_85,c_0_42]) ).
cnf(c_0_97,negated_conjecture,
multiplication(X1,c(multiplication(c(esk1_0),esk1_0))) = X1,
inference(spm,[status(thm)],[c_0_86,c_0_49]) ).
cnf(c_0_98,negated_conjecture,
( ~ leq(c(multiplication(c(esk1_0),esk1_0)),addition(multiplication(c(esk1_0),c(esk2_0)),addition(multiplication(c(esk1_0),esk2_0),addition(multiplication(esk1_0,esk2_0),multiplication(addition(esk2_0,c(esk2_0)),esk1_0)))))
| ~ leq(addition(multiplication(c(esk1_0),c(esk2_0)),addition(multiplication(c(esk1_0),esk2_0),addition(multiplication(esk1_0,esk2_0),multiplication(addition(esk2_0,c(esk2_0)),esk1_0)))),c(multiplication(c(esk1_0),esk1_0))) ),
inference(spm,[status(thm)],[c_0_87,c_0_49]) ).
cnf(c_0_99,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_27]),c_0_88]) ).
cnf(c_0_100,plain,
multiplication(addition(X1,c(esk1_0)),esk1_0) = multiplication(X1,esk1_0),
inference(spm,[status(thm)],[c_0_69,c_0_89]) ).
cnf(c_0_101,negated_conjecture,
multiplication(c(c(esk1_0)),esk1_0) = esk1_0,
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_102,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_103,negated_conjecture,
c(multiplication(esk1_0,c(X1))) = addition(c(esk1_0),c(c(X1))),
inference(spm,[status(thm)],[c_0_93,c_0_42]) ).
cnf(c_0_104,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_88,c_0_94]) ).
cnf(c_0_105,negated_conjecture,
addition(esk2_0,c(esk2_0)) = addition(esk1_0,c(esk1_0)),
inference(rw,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_106,negated_conjecture,
multiplication(X1,addition(c(esk1_0),c(c(esk1_0)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_65]),c_0_27]) ).
cnf(c_0_107,negated_conjecture,
( ~ leq(c(multiplication(c(esk1_0),esk1_0)),addition(multiplication(esk1_0,esk2_0),addition(multiplication(c(esk1_0),esk2_0),addition(multiplication(c(esk1_0),c(esk2_0)),multiplication(addition(esk2_0,c(esk2_0)),esk1_0)))))
| ~ leq(addition(multiplication(esk1_0,esk2_0),addition(multiplication(c(esk1_0),esk2_0),addition(multiplication(c(esk1_0),c(esk2_0)),multiplication(addition(esk2_0,c(esk2_0)),esk1_0)))),c(multiplication(c(esk1_0),esk1_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_98,c_0_99]),c_0_99]),c_0_99]),c_0_99]),c_0_99]),c_0_99]) ).
cnf(c_0_108,negated_conjecture,
multiplication(esk1_0,esk1_0) = esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_96]),c_0_100]),c_0_101]) ).
cnf(c_0_109,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(esk1_0,addition(c(esk1_0),X2))),
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_102,c_0_78]),c_0_37]),c_0_49]),c_0_66]),c_0_103]),c_0_96]),c_0_88]) ).
cnf(c_0_110,negated_conjecture,
addition(esk1_0,addition(c(esk1_0),esk2_0)) = addition(esk1_0,c(esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_27]),c_0_88]) ).
cnf(c_0_111,negated_conjecture,
multiplication(X1,addition(esk1_0,c(esk1_0))) = X1,
inference(rw,[status(thm)],[c_0_106,c_0_96]) ).
cnf(c_0_112,negated_conjecture,
( ~ leq(addition(c(esk1_0),c(c(esk1_0))),addition(multiplication(esk1_0,esk2_0),addition(multiplication(c(esk1_0),esk2_0),addition(multiplication(c(esk1_0),c(esk2_0)),multiplication(addition(esk2_0,c(esk2_0)),esk1_0)))))
| ~ leq(addition(multiplication(esk1_0,esk2_0),addition(multiplication(c(esk1_0),esk2_0),addition(multiplication(c(esk1_0),c(esk2_0)),multiplication(addition(esk2_0,c(esk2_0)),esk1_0)))),addition(c(esk1_0),c(c(esk1_0)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_65]),c_0_27]),c_0_65]),c_0_27]) ).
fof(c_0_113,plain,
! [X8,X9] :
( ( ~ leq(X8,X9)
| addition(X8,X9) = X9 )
& ( addition(X8,X9) != X9
| leq(X8,X9) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
cnf(c_0_114,negated_conjecture,
addition(esk1_0,multiplication(esk1_0,X1)) = multiplication(esk1_0,addition(esk1_0,X1)),
inference(spm,[status(thm)],[c_0_102,c_0_108]) ).
cnf(c_0_115,negated_conjecture,
addition(X1,multiplication(X1,esk2_0)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_111]) ).
cnf(c_0_116,negated_conjecture,
( ~ leq(addition(esk1_0,c(esk1_0)),addition(esk1_0,addition(c(esk1_0),multiplication(esk1_0,esk2_0))))
| ~ leq(addition(esk1_0,addition(c(esk1_0),multiplication(esk1_0,esk2_0))),addition(esk1_0,c(esk1_0))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_96]),c_0_96]),c_0_105]),c_0_100]),c_0_108]),c_0_27]),c_0_99]),c_0_102]),c_0_105]),c_0_111]),c_0_27]),c_0_88]),c_0_105]),c_0_100]),c_0_108]),c_0_27]),c_0_99]),c_0_102]),c_0_105]),c_0_111]),c_0_27]),c_0_88]) ).
cnf(c_0_117,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_118,plain,
addition(multiplication(X1,addition(X2,X3)),X4) = addition(multiplication(X1,X2),addition(multiplication(X1,X3),X4)),
inference(spm,[status(thm)],[c_0_88,c_0_102]) ).
cnf(c_0_119,negated_conjecture,
multiplication(esk1_0,addition(esk1_0,esk2_0)) = esk1_0,
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_120,negated_conjecture,
( addition(esk1_0,addition(c(esk1_0),multiplication(esk1_0,esk2_0))) != addition(esk1_0,c(esk1_0))
| ~ leq(addition(esk1_0,c(esk1_0)),addition(esk1_0,addition(c(esk1_0),multiplication(esk1_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)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_88]),c_0_88]),c_0_27]),c_0_88]),c_0_99]),c_0_104]),c_0_104]) ).
cnf(c_0_121,negated_conjecture,
addition(esk1_0,addition(multiplication(esk1_0,esk2_0),X1)) = addition(esk1_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_108]) ).
cnf(c_0_122,negated_conjecture,
addition(esk1_0,addition(c(esk1_0),multiplication(esk1_0,esk2_0))) != addition(esk1_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(spm,[status(thm)],[c_0_120,c_0_117]),c_0_88]),c_0_99]),c_0_104]),c_0_104])]) ).
cnf(c_0_123,negated_conjecture,
addition(esk1_0,addition(X1,multiplication(esk1_0,esk2_0))) = addition(esk1_0,X1),
inference(spm,[status(thm)],[c_0_121,c_0_27]) ).
cnf(c_0_124,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_123])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE010+4 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 2400
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Oct 3 05:05:44 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.Pmv7FneYhC/E---3.1_14125.p
% 4.42/1.09 # Version: 3.1pre001
% 4.42/1.09 # Preprocessing class: FSMSSMSSSSSNFFN.
% 4.42/1.09 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.42/1.09 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.42/1.09 # Starting new_bool_3 with 300s (1) cores
% 4.42/1.09 # Starting new_bool_1 with 300s (1) cores
% 4.42/1.09 # Starting sh5l with 300s (1) cores
% 4.42/1.09 # new_bool_3 with pid 14204 completed with status 0
% 4.42/1.09 # Result found by new_bool_3
% 4.42/1.09 # Preprocessing class: FSMSSMSSSSSNFFN.
% 4.42/1.09 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.42/1.09 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.42/1.09 # Starting new_bool_3 with 300s (1) cores
% 4.42/1.09 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 4.42/1.09 # Search class: FGHSM-FFMF21-DFFFFFNN
% 4.42/1.09 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 4.42/1.09 # Starting G-E--_208_B07--C_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 4.42/1.09 # G-E--_208_B07--C_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 14212 completed with status 0
% 4.42/1.09 # Result found by G-E--_208_B07--C_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 4.42/1.09 # Preprocessing class: FSMSSMSSSSSNFFN.
% 4.42/1.09 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.42/1.09 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.42/1.09 # Starting new_bool_3 with 300s (1) cores
% 4.42/1.09 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 4.42/1.09 # Search class: FGHSM-FFMF21-DFFFFFNN
% 4.42/1.09 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 4.42/1.09 # Starting G-E--_208_B07--C_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 4.42/1.09 # Preprocessing time : 0.001 s
% 4.42/1.09 # Presaturation interreduction done
% 4.42/1.09
% 4.42/1.09 # Proof found!
% 4.42/1.09 # SZS status Theorem
% 4.42/1.09 # SZS output start CNFRefutation
% See solution above
% 4.42/1.09 # Parsed axioms : 19
% 4.42/1.09 # Removed by relevancy pruning/SinE : 0
% 4.42/1.09 # Initial clauses : 27
% 4.42/1.09 # Removed in clause preprocessing : 0
% 4.42/1.09 # Initial clauses in saturation : 27
% 4.42/1.09 # Processed clauses : 3120
% 4.42/1.09 # ...of these trivial : 381
% 4.42/1.09 # ...subsumed : 1334
% 4.42/1.09 # ...remaining for further processing : 1405
% 4.42/1.09 # Other redundant clauses eliminated : 4
% 4.42/1.09 # Clauses deleted for lack of memory : 0
% 4.42/1.09 # Backward-subsumed : 57
% 4.42/1.09 # Backward-rewritten : 736
% 4.42/1.09 # Generated clauses : 28036
% 4.42/1.09 # ...of the previous two non-redundant : 19049
% 4.42/1.09 # ...aggressively subsumed : 0
% 4.42/1.09 # Contextual simplify-reflections : 6
% 4.42/1.09 # Paramodulations : 28031
% 4.42/1.09 # Factorizations : 1
% 4.42/1.09 # NegExts : 0
% 4.42/1.09 # Equation resolutions : 4
% 4.42/1.09 # Total rewrite steps : 88473
% 4.42/1.09 # Propositional unsat checks : 0
% 4.42/1.09 # Propositional check models : 0
% 4.42/1.09 # Propositional check unsatisfiable : 0
% 4.42/1.09 # Propositional clauses : 0
% 4.42/1.09 # Propositional clauses after purity: 0
% 4.42/1.09 # Propositional unsat core size : 0
% 4.42/1.09 # Propositional preprocessing time : 0.000
% 4.42/1.09 # Propositional encoding time : 0.000
% 4.42/1.09 # Propositional solver time : 0.000
% 4.42/1.09 # Success case prop preproc time : 0.000
% 4.42/1.09 # Success case prop encoding time : 0.000
% 4.42/1.09 # Success case prop solver time : 0.000
% 4.42/1.09 # Current number of processed clauses : 584
% 4.42/1.09 # Positive orientable unit clauses : 355
% 4.42/1.09 # Positive unorientable unit clauses: 9
% 4.42/1.09 # Negative unit clauses : 1
% 4.42/1.09 # Non-unit-clauses : 219
% 4.42/1.09 # Current number of unprocessed clauses: 15402
% 4.42/1.09 # ...number of literals in the above : 32619
% 4.42/1.09 # Current number of archived formulas : 0
% 4.42/1.09 # Current number of archived clauses : 820
% 4.42/1.09 # Clause-clause subsumption calls (NU) : 35155
% 4.42/1.09 # Rec. Clause-clause subsumption calls : 31845
% 4.42/1.09 # Non-unit clause-clause subsumptions : 1313
% 4.42/1.09 # Unit Clause-clause subsumption calls : 24499
% 4.42/1.09 # Rewrite failures with RHS unbound : 0
% 4.42/1.09 # BW rewrite match attempts : 3470
% 4.42/1.09 # BW rewrite match successes : 391
% 4.42/1.09 # Condensation attempts : 0
% 4.42/1.09 # Condensation successes : 0
% 4.42/1.09 # Termbank termtop insertions : 902209
% 4.42/1.09
% 4.42/1.09 # -------------------------------------------------
% 4.42/1.09 # User time : 0.556 s
% 4.42/1.09 # System time : 0.014 s
% 4.42/1.09 # Total time : 0.569 s
% 4.42/1.09 # Maximum resident set size: 1716 pages
% 4.42/1.09
% 4.42/1.09 # -------------------------------------------------
% 4.42/1.09 # User time : 0.557 s
% 4.42/1.09 # System time : 0.015 s
% 4.42/1.09 # Total time : 0.573 s
% 4.42/1.09 # Maximum resident set size: 1732 pages
% 4.42/1.09 % E---3.1 exiting
% 4.42/1.09 % E---3.1 exiting
%------------------------------------------------------------------------------