TSTP Solution File: KLE016+2 by Enigma---0.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : KLE016+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n025.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 01:49:35 EDT 2022
% Result : Theorem 13.73s 3.15s
% Output : CNFRefutation 13.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 16
% Syntax : Number of formulae : 144 ( 93 unt; 0 def)
% Number of atoms : 223 ( 136 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 143 ( 64 ~; 60 |; 12 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 5 ( 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 : 154 ( 8 sgn 60 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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_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(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
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(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(goals,conjecture,
! [X4,X5] :
( ( test(X5)
& test(X4) )
=> c(multiplication(X4,X5)) = addition(c(X4),c(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
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(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_1) ).
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(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(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
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,
! [X34,X35] :
( ( c(X34) != X35
| complement(X34,X35)
| ~ test(X34) )
& ( ~ complement(X34,X35)
| c(X34) = X35
| ~ test(X34) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])]) ).
fof(c_0_17,plain,
! [X32,X33] :
( ( multiplication(X32,X33) = zero
| ~ complement(X33,X32) )
& ( multiplication(X33,X32) = zero
| ~ complement(X33,X32) )
& ( addition(X32,X33) = one
| ~ complement(X33,X32) )
& ( multiplication(X32,X33) != zero
| multiplication(X33,X32) != zero
| addition(X32,X33) != one
| complement(X33,X32) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).
cnf(c_0_18,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_19,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_20,plain,
! [X21,X22,X23] : multiplication(addition(X21,X22),X23) = addition(multiplication(X21,X23),multiplication(X22,X23)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_21,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_24,plain,
! [X17] : multiplication(one,X17) = X17,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_25,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
( addition(X1,c(X1)) = one
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_27,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,plain,
( multiplication(X1,X2) = zero
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_29,plain,
! [X11] : addition(X11,zero) = X11,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_30,negated_conjecture,
~ ! [X4,X5] :
( ( test(X5)
& test(X4) )
=> c(multiplication(X4,X5)) = addition(c(X4),c(X5)) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_31,plain,
! [X13,X14,X15] : multiplication(X13,multiplication(X14,X15)) = multiplication(multiplication(X13,X14),X15),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_32,plain,
! [X25] : multiplication(zero,X25) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_33,plain,
( addition(multiplication(X1,X2),multiplication(c(X1),X2)) = X2
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_34,plain,
( multiplication(c(X1),X1) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_22]) ).
cnf(c_0_35,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_36,negated_conjecture,
( test(esk3_0)
& test(esk2_0)
& c(multiplication(esk2_0,esk3_0)) != addition(c(esk2_0),c(esk3_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])]) ).
cnf(c_0_37,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,plain,
( multiplication(X1,X1) = X1
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_40,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_42,plain,
( multiplication(c(X1),multiplication(X1,X2)) = zero
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_34]),c_0_38]) ).
cnf(c_0_43,negated_conjecture,
multiplication(esk3_0,esk3_0) = esk3_0,
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
fof(c_0_44,plain,
! [X28,X30,X31] :
( ( ~ test(X28)
| complement(esk1_1(X28),X28) )
& ( ~ complement(X31,X30)
| test(X30) ) ),
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_45,negated_conjecture,
multiplication(esk2_0,esk2_0) = esk2_0,
inference(spm,[status(thm)],[c_0_39,c_0_41]) ).
fof(c_0_46,plain,
! [X18,X19,X20] : multiplication(X18,addition(X19,X20)) = addition(multiplication(X18,X19),multiplication(X18,X20)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_47,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_48,negated_conjecture,
multiplication(c(esk3_0),esk3_0) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_40])]) ).
cnf(c_0_49,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_35,c_0_23]) ).
cnf(c_0_50,plain,
( test(X2)
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_51,negated_conjecture,
multiplication(c(esk2_0),esk2_0) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_45]),c_0_41])]) ).
cnf(c_0_52,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_53,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_54,negated_conjecture,
( multiplication(c(c(esk3_0)),esk3_0) = esk3_0
| ~ test(c(esk3_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_48]),c_0_49]) ).
cnf(c_0_55,plain,
( test(c(X1))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_22]) ).
cnf(c_0_56,negated_conjecture,
( multiplication(c(c(esk2_0)),esk2_0) = esk2_0
| ~ test(c(esk2_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_51]),c_0_49]) ).
fof(c_0_57,plain,
! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_58,plain,
! [X12] : addition(X12,X12) = X12,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_59,plain,
( addition(multiplication(X1,X2),multiplication(X1,c(X2))) = X1
| ~ test(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_26]),c_0_53]) ).
cnf(c_0_60,negated_conjecture,
multiplication(c(c(esk3_0)),esk3_0) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_40])]) ).
cnf(c_0_61,negated_conjecture,
multiplication(c(c(esk2_0)),esk2_0) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_55]),c_0_41])]) ).
cnf(c_0_62,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_63,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_64,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_65,negated_conjecture,
addition(esk3_0,multiplication(c(c(esk3_0)),c(esk3_0))) = c(c(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_40])]) ).
cnf(c_0_66,negated_conjecture,
addition(esk2_0,multiplication(c(c(esk2_0)),c(esk2_0))) = c(c(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_61]),c_0_41])]) ).
cnf(c_0_67,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_68,plain,
( addition(X1,esk1_1(X1)) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_64]) ).
cnf(c_0_69,negated_conjecture,
( c(c(esk3_0)) = esk3_0
| ~ test(c(esk3_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_34]),c_0_35]) ).
cnf(c_0_70,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_71,negated_conjecture,
( c(c(esk2_0)) = esk2_0
| ~ test(c(esk2_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_34]),c_0_35]) ).
cnf(c_0_72,plain,
( addition(X1,one) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_73,negated_conjecture,
c(c(esk3_0)) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_55]),c_0_40])]) ).
cnf(c_0_74,plain,
( multiplication(X1,c(X1)) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_22]) ).
cnf(c_0_75,negated_conjecture,
c(c(esk2_0)) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_55]),c_0_41])]) ).
cnf(c_0_76,negated_conjecture,
addition(one,esk2_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_41]),c_0_23]) ).
cnf(c_0_77,plain,
( complement(X2,X1)
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero
| addition(X1,X2) != one ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_78,negated_conjecture,
( addition(esk3_0,c(esk3_0)) = one
| ~ test(c(esk3_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_73]),c_0_23]) ).
cnf(c_0_79,plain,
( multiplication(X1,multiplication(c(X1),X2)) = zero
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_74]),c_0_38]) ).
cnf(c_0_80,negated_conjecture,
multiplication(c(esk3_0),c(esk3_0)) = c(esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_48]),c_0_49]),c_0_40])]) ).
cnf(c_0_81,negated_conjecture,
addition(one,esk3_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_40]),c_0_23]) ).
cnf(c_0_82,negated_conjecture,
( addition(esk2_0,c(esk2_0)) = one
| ~ test(c(esk2_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_75]),c_0_23]) ).
cnf(c_0_83,negated_conjecture,
multiplication(c(esk2_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_59,c_0_51]),c_0_49]),c_0_41])]) ).
cnf(c_0_84,negated_conjecture,
addition(X1,multiplication(esk2_0,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_76]),c_0_27]),c_0_27]) ).
cnf(c_0_85,plain,
( complement(X1,X2)
| addition(X1,X2) != one
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero ),
inference(spm,[status(thm)],[c_0_77,c_0_23]) ).
cnf(c_0_86,negated_conjecture,
addition(esk3_0,c(esk3_0)) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_55]),c_0_40])]) ).
cnf(c_0_87,negated_conjecture,
multiplication(esk3_0,c(esk3_0)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_40])]) ).
cnf(c_0_88,negated_conjecture,
addition(X1,multiplication(esk3_0,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_81]),c_0_27]),c_0_27]) ).
cnf(c_0_89,negated_conjecture,
addition(esk2_0,c(esk2_0)) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_55]),c_0_41])]) ).
cnf(c_0_90,negated_conjecture,
multiplication(esk2_0,c(esk2_0)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_83]),c_0_41])]) ).
cnf(c_0_91,negated_conjecture,
addition(multiplication(X1,X2),multiplication(X1,multiplication(esk2_0,X2))) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_52,c_0_84]) ).
cnf(c_0_92,negated_conjecture,
complement(esk3_0,c(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]),c_0_48])]) ).
cnf(c_0_93,negated_conjecture,
addition(multiplication(X1,X2),multiplication(X1,multiplication(esk3_0,X2))) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_52,c_0_88]) ).
cnf(c_0_94,negated_conjecture,
complement(esk2_0,c(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_89]),c_0_90]),c_0_51])]) ).
cnf(c_0_95,negated_conjecture,
addition(X1,multiplication(X1,esk3_0)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_81]),c_0_53]),c_0_53]) ).
cnf(c_0_96,negated_conjecture,
multiplication(c(esk3_0),multiplication(esk2_0,esk3_0)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_48]),c_0_49]) ).
cnf(c_0_97,negated_conjecture,
test(c(esk3_0)),
inference(spm,[status(thm)],[c_0_50,c_0_92]) ).
cnf(c_0_98,negated_conjecture,
addition(X1,multiplication(X1,esk2_0)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_76]),c_0_53]),c_0_53]) ).
cnf(c_0_99,negated_conjecture,
multiplication(c(esk2_0),multiplication(esk3_0,esk2_0)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_51]),c_0_49]) ).
cnf(c_0_100,negated_conjecture,
test(c(esk2_0)),
inference(spm,[status(thm)],[c_0_50,c_0_94]) ).
cnf(c_0_101,negated_conjecture,
addition(multiplication(X1,X2),multiplication(X1,multiplication(X2,esk3_0))) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_52,c_0_95]) ).
cnf(c_0_102,negated_conjecture,
multiplication(esk3_0,multiplication(esk2_0,esk3_0)) = multiplication(esk2_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_96]),c_0_73]),c_0_49]),c_0_97])]) ).
cnf(c_0_103,plain,
( multiplication(esk1_1(X1),X1) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_64]) ).
cnf(c_0_104,negated_conjecture,
addition(multiplication(X1,X2),multiplication(X1,multiplication(X2,esk2_0))) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_52,c_0_98]) ).
cnf(c_0_105,negated_conjecture,
multiplication(esk2_0,multiplication(esk3_0,esk2_0)) = multiplication(esk3_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_33,c_0_99]),c_0_75]),c_0_49]),c_0_100])]) ).
cnf(c_0_106,negated_conjecture,
addition(multiplication(esk2_0,esk3_0),multiplication(esk3_0,esk2_0)) = multiplication(esk3_0,esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_23]) ).
cnf(c_0_107,plain,
( addition(multiplication(X1,X2),multiplication(esk1_1(X1),X2)) = X2
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_68]),c_0_27]) ).
cnf(c_0_108,plain,
( multiplication(esk1_1(X1),multiplication(X1,X2)) = zero
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_103]),c_0_38]) ).
cnf(c_0_109,negated_conjecture,
multiplication(esk3_0,esk2_0) = multiplication(esk2_0,esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106]) ).
cnf(c_0_110,negated_conjecture,
multiplication(esk1_1(esk3_0),c(esk3_0)) = c(esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_87]),c_0_49]),c_0_40])]) ).
cnf(c_0_111,negated_conjecture,
multiplication(esk1_1(esk3_0),esk3_0) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_43]),c_0_40])]) ).
cnf(c_0_112,plain,
( addition(X1,addition(X2,esk1_1(addition(X1,X2)))) = one
| ~ test(addition(X1,X2)) ),
inference(spm,[status(thm)],[c_0_62,c_0_68]) ).
cnf(c_0_113,negated_conjecture,
addition(multiplication(esk2_0,esk3_0),multiplication(esk3_0,c(esk2_0))) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_109]),c_0_41])]) ).
cnf(c_0_114,negated_conjecture,
esk1_1(esk3_0) = c(esk3_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_59,c_0_110]),c_0_73]),c_0_111]),c_0_35]),c_0_97])]) ).
fof(c_0_115,plain,
! [X24] : multiplication(X24,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
fof(c_0_116,plain,
! [X26,X27] :
( ( ~ leq(X26,X27)
| addition(X26,X27) = X27 )
& ( addition(X26,X27) != X27
| leq(X26,X27) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
cnf(c_0_117,negated_conjecture,
addition(multiplication(esk2_0,esk3_0),addition(multiplication(esk3_0,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_112,c_0_113]),c_0_114]),c_0_40])]) ).
cnf(c_0_118,negated_conjecture,
multiplication(c(esk2_0),multiplication(esk2_0,X1)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_75]),c_0_100])]) ).
cnf(c_0_119,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_120,negated_conjecture,
multiplication(esk3_0,multiplication(esk3_0,X1)) = multiplication(esk3_0,X1),
inference(spm,[status(thm)],[c_0_37,c_0_43]) ).
cnf(c_0_121,negated_conjecture,
multiplication(esk2_0,multiplication(esk3_0,c(esk2_0))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_90]),c_0_49]) ).
cnf(c_0_122,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_123,plain,
( addition(multiplication(X1,X2),multiplication(X1,esk1_1(X2))) = X1
| ~ test(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_68]),c_0_53]) ).
cnf(c_0_124,negated_conjecture,
complement(addition(multiplication(esk3_0,c(esk2_0)),c(esk3_0)),multiplication(esk2_0,esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_117]),c_0_25]),c_0_37]),c_0_118]),c_0_119]),c_0_96]),c_0_49]),c_0_37]),c_0_52]),c_0_120]),c_0_87]),c_0_35]),c_0_121])]) ).
cnf(c_0_125,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_122,c_0_67]) ).
cnf(c_0_126,negated_conjecture,
( multiplication(c(esk2_0),esk1_1(multiplication(esk2_0,X1))) = c(esk2_0)
| ~ test(multiplication(esk2_0,X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_118]),c_0_49]) ).
cnf(c_0_127,negated_conjecture,
test(multiplication(esk2_0,esk3_0)),
inference(spm,[status(thm)],[c_0_50,c_0_124]) ).
cnf(c_0_128,plain,
( multiplication(X1,esk1_1(X1)) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_64]) ).
cnf(c_0_129,plain,
( c(X1) = X2
| ~ complement(X1,X2)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_130,negated_conjecture,
complement(multiplication(esk2_0,esk3_0),addition(multiplication(esk3_0,c(esk2_0)),c(esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_117]),c_0_37]),c_0_52]),c_0_120]),c_0_87]),c_0_35]),c_0_121]),c_0_25]),c_0_37]),c_0_118]),c_0_119]),c_0_96]),c_0_49])]) ).
cnf(c_0_131,plain,
( leq(multiplication(X1,X2),X2)
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_125,c_0_33]) ).
cnf(c_0_132,negated_conjecture,
multiplication(c(esk2_0),esk1_1(multiplication(esk2_0,esk3_0))) = c(esk2_0),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_133,plain,
( complement(X1,esk1_1(X1))
| ~ test(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_68]),c_0_103]),c_0_128]) ).
cnf(c_0_134,negated_conjecture,
( c(multiplication(esk2_0,esk3_0)) = addition(multiplication(esk3_0,c(esk2_0)),c(esk3_0))
| ~ test(multiplication(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_135,negated_conjecture,
leq(c(esk2_0),esk1_1(multiplication(esk2_0,esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_100])]) ).
cnf(c_0_136,plain,
( esk1_1(X1) = c(X1)
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_129,c_0_133]) ).
cnf(c_0_137,negated_conjecture,
c(multiplication(esk2_0,esk3_0)) = addition(multiplication(esk3_0,c(esk2_0)),c(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_127])]) ).
cnf(c_0_138,negated_conjecture,
c(multiplication(esk2_0,esk3_0)) != addition(c(esk2_0),c(esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_139,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_140,negated_conjecture,
leq(c(esk2_0),addition(multiplication(esk3_0,c(esk2_0)),c(esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_137]),c_0_127])]) ).
cnf(c_0_141,negated_conjecture,
addition(X1,addition(multiplication(esk3_0,X1),X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_62,c_0_88]) ).
cnf(c_0_142,negated_conjecture,
addition(multiplication(esk3_0,c(esk2_0)),c(esk3_0)) != addition(c(esk2_0),c(esk3_0)),
inference(rw,[status(thm)],[c_0_138,c_0_137]) ).
cnf(c_0_143,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_141]),c_0_142]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE016+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : enigmatic-eprover.py %s %d 1
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 16 12:06:58 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.20/0.44 # ENIGMATIC: Selected SinE mode:
% 0.20/0.45 # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.20/0.45 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.20/0.45 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 13.73/3.15 # ENIGMATIC: Solved by autoschedule:
% 13.73/3.15 # No SInE strategy applied
% 13.73/3.15 # Trying AutoSched0 for 150 seconds
% 13.73/3.15 # AutoSched0-Mode selected heuristic G_E___208_B00_00_F1_SE_CS_SP_PS_S083N
% 13.73/3.15 # and selection function SelectCQArNT.
% 13.73/3.15 #
% 13.73/3.15 # Preprocessing time : 0.024 s
% 13.73/3.15 # Presaturation interreduction done
% 13.73/3.15
% 13.73/3.15 # Proof found!
% 13.73/3.15 # SZS status Theorem
% 13.73/3.15 # SZS output start CNFRefutation
% See solution above
% 13.73/3.15 # Training examples: 0 positive, 0 negative
% 13.73/3.15
% 13.73/3.15 # -------------------------------------------------
% 13.73/3.15 # User time : 0.709 s
% 13.73/3.15 # System time : 0.031 s
% 13.73/3.15 # Total time : 0.740 s
% 13.73/3.15 # Maximum resident set size: 7120 pages
% 13.73/3.15
%------------------------------------------------------------------------------