TSTP Solution File: KLE009+4 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE009+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 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 : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 05:25:34 EDT 2023
% Result : Theorem 0.79s 0.89s
% Output : CNFRefutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 30
% Syntax : Number of formulae : 170 ( 90 unt; 11 typ; 0 def)
% Number of atoms : 265 ( 135 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 181 ( 75 ~; 79 |; 16 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 7 >; 4 *; 0 +; 0 <<)
% 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 : 160 ( 4 sgn; 71 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
addition: ( $i * $i ) > $i ).
tff(decl_23,type,
zero: $i ).
tff(decl_24,type,
multiplication: ( $i * $i ) > $i ).
tff(decl_25,type,
one: $i ).
tff(decl_26,type,
leq: ( $i * $i ) > $o ).
tff(decl_27,type,
test: $i > $o ).
tff(decl_28,type,
complement: ( $i * $i ) > $o ).
tff(decl_29,type,
c: $i > $i ).
tff(decl_30,type,
esk1_1: $i > $i ).
tff(decl_31,type,
esk2_0: $i ).
tff(decl_32,type,
esk3_0: $i ).
fof(test_3,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(goals,conjecture,
! [X4,X5] :
( ( test(X5)
& test(X4) )
=> ( leq(one,addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))))
& leq(addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))),one) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(test_2,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( multiplication(X4,X5) = zero
& multiplication(X5,X4) = zero
& addition(X4,X5) = one ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(test_deMorgan1,axiom,
! [X4,X5] :
( ( test(X4)
& test(X5) )
=> c(addition(X4,X5)) = multiplication(c(X4),c(X5)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+2.ax',test_deMorgan1) ).
fof(test_deMorgan2,axiom,
! [X4,X5] :
( ( test(X4)
& test(X5) )
=> c(multiplication(X4,X5)) = addition(c(X4),c(X5)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+2.ax',test_deMorgan2) ).
fof(test_4,axiom,
! [X4] :
( ~ test(X4)
=> c(X4) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_4) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(c_0_19,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_20,negated_conjecture,
~ ! [X4,X5] :
( ( test(X5)
& test(X4) )
=> ( leq(one,addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))))
& leq(addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))),one) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_21,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_22,negated_conjecture,
( test(esk3_0)
& test(esk2_0)
& ( ~ leq(one,addition(addition(addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))))
| ~ leq(addition(addition(addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))),one) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
fof(c_0_23,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_24,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_25,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_26,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_27,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])])])])]) ).
fof(c_0_28,plain,
! [X18,X19,X20] : multiplication(X18,addition(X19,X20)) = addition(multiplication(X18,X19),multiplication(X18,X20)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_29,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,negated_conjecture,
complement(esk3_0,c(esk3_0)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_32,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_33,plain,
( test(X2)
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,negated_conjecture,
addition(esk3_0,c(esk3_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_36,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_37,plain,
! [X13,X14,X15] : multiplication(X13,multiplication(X14,X15)) = multiplication(multiplication(X13,X14),X15),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_38,plain,
! [X17] : multiplication(one,X17) = X17,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_39,plain,
( multiplication(X1,X2) = zero
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_40,plain,
! [X24] : multiplication(X24,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_41,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_42,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_43,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_44,plain,
! [X37,X38] :
( ~ test(X37)
| ~ test(X38)
| c(addition(X37,X38)) = multiplication(c(X37),c(X38)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_deMorgan1])]) ).
cnf(c_0_45,plain,
( c(X1) = X2
| ~ complement(X1,X2)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_46,negated_conjecture,
test(c(esk3_0)),
inference(spm,[status(thm)],[c_0_33,c_0_30]) ).
cnf(c_0_47,plain,
( complement(X2,X1)
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero
| addition(X1,X2) != one ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_48,negated_conjecture,
addition(multiplication(X1,esk3_0),multiplication(X1,c(esk3_0))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_49,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_50,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_51,negated_conjecture,
multiplication(c(esk3_0),esk3_0) = zero,
inference(spm,[status(thm)],[c_0_39,c_0_30]) ).
cnf(c_0_52,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_53,negated_conjecture,
multiplication(esk3_0,c(esk3_0)) = zero,
inference(spm,[status(thm)],[c_0_41,c_0_30]) ).
cnf(c_0_54,plain,
( addition(X1,X2) = one
| ~ complement(X1,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_31]) ).
cnf(c_0_55,negated_conjecture,
complement(esk1_1(esk2_0),esk2_0),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_56,plain,
( c(addition(X1,X2)) = multiplication(c(X1),c(X2))
| ~ test(X1)
| ~ test(X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_57,negated_conjecture,
( c(c(esk3_0)) = X1
| ~ complement(c(esk3_0),X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_58,negated_conjecture,
complement(c(esk3_0),esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_49])]),c_0_50]),c_0_50]),c_0_50]),c_0_51]),c_0_52]),c_0_50]),c_0_53]),c_0_52])]) ).
cnf(c_0_59,plain,
( complement(X1,X2)
| addition(X1,X2) != one
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero ),
inference(spm,[status(thm)],[c_0_47,c_0_31]) ).
cnf(c_0_60,negated_conjecture,
addition(esk2_0,esk1_1(esk2_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_31]) ).
cnf(c_0_61,negated_conjecture,
multiplication(esk2_0,esk1_1(esk2_0)) = zero,
inference(spm,[status(thm)],[c_0_39,c_0_55]) ).
cnf(c_0_62,negated_conjecture,
multiplication(esk1_1(esk2_0),esk2_0) = zero,
inference(spm,[status(thm)],[c_0_41,c_0_55]) ).
cnf(c_0_63,negated_conjecture,
( c(addition(X1,esk2_0)) = multiplication(c(X1),c(esk2_0))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_43]) ).
cnf(c_0_64,negated_conjecture,
c(c(esk3_0)) = esk3_0,
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_65,negated_conjecture,
complement(esk2_0,c(esk2_0)),
inference(spm,[status(thm)],[c_0_24,c_0_43]) ).
cnf(c_0_66,negated_conjecture,
( c(esk2_0) = X1
| ~ complement(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_43]) ).
cnf(c_0_67,negated_conjecture,
complement(esk2_0,esk1_1(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]),c_0_62])]) ).
fof(c_0_68,plain,
! [X39,X40] :
( ~ test(X39)
| ~ test(X40)
| c(multiplication(X39,X40)) = addition(c(X39),c(X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_deMorgan2])]) ).
cnf(c_0_69,negated_conjecture,
c(addition(esk2_0,c(esk3_0))) = multiplication(esk3_0,c(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_46]),c_0_31]),c_0_64]) ).
cnf(c_0_70,negated_conjecture,
test(c(esk2_0)),
inference(spm,[status(thm)],[c_0_33,c_0_65]) ).
cnf(c_0_71,negated_conjecture,
esk1_1(esk2_0) = c(esk2_0),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
fof(c_0_72,plain,
! [X4] :
( ~ test(X4)
=> c(X4) = zero ),
inference(fof_simplification,[status(thm)],[test_4]) ).
cnf(c_0_73,plain,
( c(multiplication(X1,X2)) = addition(c(X1),c(X2))
| ~ test(X1)
| ~ test(X2) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_74,negated_conjecture,
multiplication(c(esk2_0),esk3_0) = multiplication(esk3_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_56,c_0_69]),c_0_64]),c_0_46]),c_0_43])]) ).
cnf(c_0_75,negated_conjecture,
( c(c(esk2_0)) = X1
| ~ complement(c(esk2_0),X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_70]) ).
cnf(c_0_76,negated_conjecture,
complement(c(esk2_0),esk2_0),
inference(rw,[status(thm)],[c_0_55,c_0_71]) ).
fof(c_0_77,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])]) ).
fof(c_0_78,plain,
! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_79,plain,
! [X36] :
( test(X36)
| c(X36) = zero ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_72])]) ).
cnf(c_0_80,negated_conjecture,
c(multiplication(esk3_0,c(esk2_0))) = addition(c(esk3_0),c(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_73,c_0_74]),c_0_31]),c_0_25]),c_0_70])]) ).
cnf(c_0_81,negated_conjecture,
c(c(esk2_0)) = esk2_0,
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_82,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_83,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
fof(c_0_84,plain,
! [X12] : addition(X12,X12) = X12,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_85,plain,
( test(X1)
| c(X1) = zero ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_86,negated_conjecture,
c(multiplication(esk3_0,c(esk2_0))) = addition(esk2_0,c(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81]),c_0_31]) ).
fof(c_0_87,plain,
! [X11] : addition(X11,zero) = X11,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_88,plain,
( leq(X1,X2)
| addition(X2,X1) != X2 ),
inference(spm,[status(thm)],[c_0_82,c_0_31]) ).
cnf(c_0_89,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_31,c_0_83]) ).
cnf(c_0_90,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_91,negated_conjecture,
complement(esk1_1(esk3_0),esk3_0),
inference(spm,[status(thm)],[c_0_42,c_0_25]) ).
cnf(c_0_92,plain,
( leq(addition(X1,X2),X3)
| addition(X1,addition(X2,X3)) != X3 ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_93,negated_conjecture,
( addition(esk2_0,c(esk3_0)) = zero
| test(multiplication(esk3_0,c(esk2_0))) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_94,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_95,plain,
( leq(addition(X1,X2),X3)
| addition(X2,addition(X3,X1)) != X3 ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_96,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_83,c_0_90]) ).
cnf(c_0_97,negated_conjecture,
addition(esk3_0,esk1_1(esk3_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_91]),c_0_31]) ).
fof(c_0_98,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_99,negated_conjecture,
( ~ leq(one,addition(addition(addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))))
| ~ leq(addition(addition(addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))),one) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_100,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_101,negated_conjecture,
( test(multiplication(esk3_0,c(esk2_0)))
| leq(addition(esk2_0,c(esk3_0)),c(esk3_0)) ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94])]),c_0_31]) ).
cnf(c_0_102,negated_conjecture,
( test(multiplication(esk3_0,c(esk2_0)))
| leq(addition(esk2_0,c(esk3_0)),esk2_0) ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_93]),c_0_94])]),c_0_31]) ).
cnf(c_0_103,plain,
( multiplication(c(X1),c(X1)) = c(X1)
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_90]) ).
cnf(c_0_104,negated_conjecture,
addition(one,esk3_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_31]) ).
cnf(c_0_105,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_106,negated_conjecture,
addition(one,esk2_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_60]),c_0_31]) ).
cnf(c_0_107,negated_conjecture,
( ~ leq(one,addition(multiplication(esk2_0,esk3_0),addition(multiplication(esk2_0,c(esk3_0)),addition(multiplication(c(esk2_0),esk3_0),multiplication(c(esk2_0),c(esk3_0))))))
| ~ leq(addition(multiplication(esk2_0,esk3_0),addition(multiplication(esk2_0,c(esk3_0)),addition(multiplication(c(esk2_0),esk3_0),multiplication(c(esk2_0),c(esk3_0))))),one) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_83]),c_0_83]),c_0_83]),c_0_83]) ).
cnf(c_0_108,negated_conjecture,
( addition(esk2_0,c(esk3_0)) = c(esk3_0)
| test(multiplication(esk3_0,c(esk2_0))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_83]),c_0_90]) ).
cnf(c_0_109,negated_conjecture,
( addition(esk2_0,c(esk3_0)) = esk2_0
| test(multiplication(esk3_0,c(esk2_0))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_102]),c_0_83]),c_0_31]),c_0_96]) ).
cnf(c_0_110,negated_conjecture,
multiplication(c(c(esk2_0)),c(c(esk2_0))) = c(c(esk2_0)),
inference(spm,[status(thm)],[c_0_103,c_0_70]) ).
cnf(c_0_111,negated_conjecture,
addition(one,addition(esk3_0,X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_83,c_0_104]) ).
cnf(c_0_112,negated_conjecture,
addition(X1,multiplication(esk2_0,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_50]),c_0_50]) ).
cnf(c_0_113,negated_conjecture,
( ~ leq(one,addition(multiplication(esk2_0,esk3_0),addition(c(esk2_0),multiplication(esk2_0,c(esk3_0)))))
| ~ leq(addition(multiplication(esk2_0,esk3_0),addition(c(esk2_0),multiplication(esk2_0,c(esk3_0)))),one) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_48]),c_0_31]),c_0_31]) ).
cnf(c_0_114,negated_conjecture,
( c(esk3_0) = esk2_0
| test(multiplication(esk3_0,c(esk2_0))) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_115,negated_conjecture,
multiplication(esk2_0,esk2_0) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_81]),c_0_81]),c_0_81]) ).
cnf(c_0_116,negated_conjecture,
addition(esk2_0,c(esk2_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_65]),c_0_31]) ).
cnf(c_0_117,negated_conjecture,
addition(one,multiplication(esk2_0,esk3_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_104]) ).
cnf(c_0_118,plain,
leq(X1,X1),
inference(spm,[status(thm)],[c_0_82,c_0_90]) ).
cnf(c_0_119,negated_conjecture,
test(multiplication(esk3_0,c(esk2_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_113,c_0_114]),c_0_31]),c_0_115]),c_0_116]),c_0_31]),c_0_117]),c_0_118]),c_0_31]),c_0_115]),c_0_116]),c_0_31]),c_0_117]),c_0_118])]) ).
cnf(c_0_120,negated_conjecture,
( c(multiplication(X1,esk3_0)) = addition(c(X1),c(esk3_0))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_25]) ).
cnf(c_0_121,negated_conjecture,
( c(addition(X1,esk3_0)) = multiplication(c(X1),c(esk3_0))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_25]) ).
cnf(c_0_122,negated_conjecture,
complement(multiplication(esk3_0,c(esk2_0)),addition(esk2_0,c(esk3_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_119]),c_0_80]),c_0_81]),c_0_31]) ).
cnf(c_0_123,plain,
( addition(X1,addition(X2,X3)) = X3
| ~ leq(addition(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_100,c_0_83]) ).
cnf(c_0_124,negated_conjecture,
c(multiplication(esk2_0,esk3_0)) = addition(c(esk2_0),c(esk3_0)),
inference(spm,[status(thm)],[c_0_120,c_0_43]) ).
cnf(c_0_125,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_94,c_0_31]) ).
cnf(c_0_126,negated_conjecture,
c(addition(esk2_0,esk3_0)) = multiplication(c(esk2_0),c(esk3_0)),
inference(spm,[status(thm)],[c_0_121,c_0_43]) ).
cnf(c_0_127,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_31]),c_0_83]) ).
cnf(c_0_128,negated_conjecture,
test(addition(esk2_0,c(esk3_0))),
inference(spm,[status(thm)],[c_0_33,c_0_122]) ).
cnf(c_0_129,plain,
( addition(X1,X2) = X2
| ~ leq(addition(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_123,c_0_90]) ).
cnf(c_0_130,negated_conjecture,
( addition(c(esk2_0),c(esk3_0)) = zero
| test(multiplication(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_85,c_0_124]) ).
cnf(c_0_131,plain,
leq(zero,X1),
inference(spm,[status(thm)],[c_0_82,c_0_125]) ).
cnf(c_0_132,negated_conjecture,
( c(multiplication(X1,c(esk2_0))) = addition(c(X1),c(c(esk2_0)))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_70]) ).
cnf(c_0_133,negated_conjecture,
multiplication(c(esk3_0),c(esk2_0)) = multiplication(c(esk2_0),c(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_25]),c_0_31]),c_0_126]) ).
cnf(c_0_134,negated_conjecture,
addition(esk2_0,addition(multiplication(esk3_0,c(esk2_0)),c(esk3_0))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_122]),c_0_127]) ).
cnf(c_0_135,negated_conjecture,
addition(multiplication(esk3_0,c(esk2_0)),c(esk3_0)) = addition(c(esk2_0),c(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_128]),c_0_105]),c_0_51]),c_0_94]),c_0_124]),c_0_69]) ).
cnf(c_0_136,negated_conjecture,
( c(esk3_0) = zero
| test(multiplication(esk2_0,esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_131])]) ).
cnf(c_0_137,negated_conjecture,
( c(multiplication(X1,c(esk2_0))) = addition(esk2_0,c(X1))
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_132,c_0_81]),c_0_31]) ).
cnf(c_0_138,negated_conjecture,
multiplication(esk2_0,c(esk2_0)) = zero,
inference(spm,[status(thm)],[c_0_41,c_0_65]) ).
cnf(c_0_139,negated_conjecture,
c(multiplication(c(esk2_0),c(esk3_0))) = addition(esk3_0,c(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_73,c_0_133]),c_0_64]),c_0_70]),c_0_46])]) ).
fof(c_0_140,plain,
! [X25] : multiplication(zero,X25) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_141,negated_conjecture,
( leq(one,X1)
| addition(esk2_0,addition(multiplication(esk3_0,c(esk2_0)),addition(c(esk3_0),X1))) != X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_134]),c_0_83]) ).
cnf(c_0_142,negated_conjecture,
( multiplication(esk3_0,c(esk2_0)) = c(esk2_0)
| test(multiplication(esk2_0,esk3_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_94]),c_0_94]) ).
cnf(c_0_143,negated_conjecture,
addition(esk2_0,multiplication(esk3_0,c(esk2_0))) = addition(esk2_0,esk3_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(spm,[status(thm)],[c_0_137,c_0_128]),c_0_105]),c_0_138]),c_0_133]),c_0_125]),c_0_139]),c_0_81]),c_0_31]),c_0_69]) ).
cnf(c_0_144,negated_conjecture,
( c(esk2_0) = zero
| test(multiplication(esk2_0,esk3_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_130]),c_0_94]) ).
cnf(c_0_145,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_146,negated_conjecture,
leq(esk2_0,one),
inference(spm,[status(thm)],[c_0_88,c_0_106]) ).
cnf(c_0_147,negated_conjecture,
( leq(one,X1)
| addition(esk2_0,addition(multiplication(esk3_0,c(esk2_0)),addition(X1,c(esk3_0)))) != X1 ),
inference(spm,[status(thm)],[c_0_141,c_0_31]) ).
cnf(c_0_148,negated_conjecture,
( addition(esk2_0,c(esk3_0)) = esk2_0
| test(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(spm,[status(thm)],[c_0_73,c_0_142]),c_0_81]),c_0_81]),c_0_31]),c_0_70]),c_0_25])]) ).
cnf(c_0_149,negated_conjecture,
( addition(esk2_0,esk3_0) = esk2_0
| test(multiplication(esk2_0,esk3_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_52]),c_0_94]) ).
cnf(c_0_150,negated_conjecture,
( test(multiplication(esk2_0,esk3_0))
| ~ leq(one,esk2_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(spm,[status(thm)],[c_0_107,c_0_144]),c_0_145]),c_0_145]),c_0_90]),c_0_94]),c_0_48]),c_0_145]),c_0_145]),c_0_90]),c_0_94]),c_0_48]),c_0_146])]) ).
cnf(c_0_151,negated_conjecture,
( ~ leq(one,addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,c(esk3_0)),multiplication(c(esk2_0),c(esk3_0))))))
| ~ leq(addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,c(esk3_0)),multiplication(c(esk2_0),c(esk3_0))))),one) ),
inference(spm,[status(thm)],[c_0_107,c_0_127]) ).
cnf(c_0_152,negated_conjecture,
addition(multiplication(esk2_0,X1),multiplication(c(esk2_0),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_116]),c_0_50]) ).
cnf(c_0_153,negated_conjecture,
test(multiplication(esk2_0,esk3_0)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_31]),c_0_143]),c_0_96]),c_0_149]),c_0_150]) ).
cnf(c_0_154,negated_conjecture,
( ~ leq(one,addition(multiplication(esk2_0,esk3_0),addition(multiplication(esk3_0,c(esk2_0)),c(esk3_0))))
| ~ leq(addition(multiplication(esk2_0,esk3_0),addition(multiplication(esk3_0,c(esk2_0)),c(esk3_0))),one) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_74]),c_0_74]) ).
cnf(c_0_155,negated_conjecture,
complement(multiplication(esk2_0,esk3_0),addition(c(esk2_0),c(esk3_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_153]),c_0_124]) ).
cnf(c_0_156,negated_conjecture,
( ~ leq(one,addition(multiplication(esk2_0,esk3_0),addition(c(esk2_0),c(esk3_0))))
| ~ leq(addition(multiplication(esk2_0,esk3_0),addition(c(esk2_0),c(esk3_0))),one) ),
inference(spm,[status(thm)],[c_0_154,c_0_135]) ).
cnf(c_0_157,negated_conjecture,
addition(multiplication(esk2_0,esk3_0),addition(c(esk2_0),c(esk3_0))) = one,
inference(spm,[status(thm)],[c_0_54,c_0_155]) ).
cnf(c_0_158,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_156,c_0_157]),c_0_118]),c_0_157]),c_0_118])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE009+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.17/0.33 % Computer : n026.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Aug 29 12:50:50 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.79/0.89 % Version : CSE_E---1.5
% 0.79/0.89 % Problem : theBenchmark.p
% 0.79/0.89 % Proof found
% 0.79/0.89 % SZS status Theorem for theBenchmark.p
% 0.79/0.89 % SZS output start Proof
% See solution above
% 0.88/0.90 % Total time : 0.312000 s
% 0.88/0.90 % SZS output end Proof
% 0.88/0.90 % Total time : 0.315000 s
%------------------------------------------------------------------------------