TSTP Solution File: KLE008+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE008+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n014.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 05:25:33 EDT 2023
% Result : Theorem 1.64s 1.74s
% Output : CNFRefutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 28
% Syntax : Number of formulae : 159 ( 77 unt; 12 typ; 0 def)
% Number of atoms : 258 ( 139 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 189 ( 78 ~; 89 |; 13 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 5 ( 1 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 171 ( 7 sgn; 62 !; 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 ).
tff(decl_33,type,
esk4_0: $i ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(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(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_1) ).
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(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
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(goals,conjecture,
! [X4,X5,X6] :
( test(X6)
=> ( leq(X4,multiplication(X6,X5))
<=> ( leq(X4,X5)
& leq(multiplication(c(X6),X4),zero) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/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/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(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(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',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/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(c_0_16,plain,
! [X12] : addition(X12,zero) = X12,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_17,plain,
! [X7,X8] : addition(X7,X8) = addition(X8,X7),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_18,plain,
! [X33,X34] :
( ( multiplication(X33,X34) = zero
| ~ complement(X34,X33) )
& ( multiplication(X34,X33) = zero
| ~ complement(X34,X33) )
& ( addition(X33,X34) = one
| ~ complement(X34,X33) )
& ( multiplication(X33,X34) != zero
| multiplication(X34,X33) != zero
| addition(X33,X34) != one
| complement(X34,X33) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).
cnf(c_0_19,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_21,plain,
! [X25] : multiplication(X25,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
fof(c_0_22,plain,
! [X26] : multiplication(zero,X26) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_23,plain,
! [X29,X31,X32] :
( ( ~ test(X29)
| complement(esk1_1(X29),X29) )
& ( ~ complement(X32,X31)
| test(X31) ) ),
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_24,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_25,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_28,plain,
! [X35,X36] :
( ( c(X35) != X36
| complement(X35,X36)
| ~ test(X35) )
& ( ~ complement(X35,X36)
| c(X35) = X36
| ~ test(X35) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])]) ).
cnf(c_0_29,plain,
( test(X2)
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,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_24,c_0_25]),c_0_26]),c_0_27])])]) ).
cnf(c_0_31,plain,
( c(X1) = X2
| ~ complement(X1,X2)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_32,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_24,c_0_19]),c_0_27]),c_0_26])])]) ).
cnf(c_0_33,plain,
test(zero),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
fof(c_0_34,plain,
! [X17] : multiplication(X17,one) = X17,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_35,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_36,plain,
one = c(zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_37,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,plain,
( addition(X1,X2) = c(zero)
| ~ complement(X2,X1) ),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_37]) ).
fof(c_0_41,plain,
! [X19,X20,X21] : multiplication(X19,addition(X20,X21)) = addition(multiplication(X19,X20),multiplication(X19,X21)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_42,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_43,negated_conjecture,
~ ! [X4,X5,X6] :
( test(X6)
=> ( leq(X4,multiplication(X6,X5))
<=> ( leq(X4,X5)
& leq(multiplication(c(X6),X4),zero) ) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_44,plain,
multiplication(X1,c(zero)) = X1,
inference(rw,[status(thm)],[c_0_38,c_0_36]) ).
cnf(c_0_45,plain,
( addition(X1,c(X1)) = c(zero)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_20]) ).
cnf(c_0_46,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_47,plain,
( multiplication(X1,c(X1)) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_40]) ).
fof(c_0_48,plain,
! [X27,X28] :
( ( ~ leq(X27,X28)
| addition(X27,X28) = X28 )
& ( addition(X27,X28) != X28
| leq(X27,X28) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(c_0_49,negated_conjecture,
( test(esk4_0)
& ( ~ leq(esk2_0,multiplication(esk4_0,esk3_0))
| ~ leq(esk2_0,esk3_0)
| ~ leq(multiplication(c(esk4_0),esk2_0),zero) )
& ( leq(esk2_0,esk3_0)
| leq(esk2_0,multiplication(esk4_0,esk3_0)) )
& ( leq(multiplication(c(esk4_0),esk2_0),zero)
| leq(esk2_0,multiplication(esk4_0,esk3_0)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])])]) ).
cnf(c_0_50,plain,
( multiplication(X1,addition(X2,c(X2))) = X1
| ~ test(X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,plain,
( multiplication(X1,addition(X2,c(X1))) = multiplication(X1,X2)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_19]) ).
fof(c_0_52,plain,
! [X9,X10,X11] : addition(X11,addition(X10,X9)) = addition(addition(X11,X10),X9),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_53,plain,
! [X13] : addition(X13,X13) = X13,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_54,plain,
! [X14,X15,X16] : multiplication(X14,multiplication(X15,X16)) = multiplication(multiplication(X14,X15),X16),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_55,plain,
( multiplication(X1,X2) = zero
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_56,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_57,negated_conjecture,
( leq(multiplication(c(esk4_0),esk2_0),zero)
| leq(esk2_0,multiplication(esk4_0,esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_58,plain,
( multiplication(X1,X1) = X1
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_59,negated_conjecture,
test(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
fof(c_0_60,plain,
! [X18] : multiplication(one,X18) = X18,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_61,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_62,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_63,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_64,plain,
! [X22,X23,X24] : multiplication(addition(X22,X23),X24) = addition(multiplication(X22,X24),multiplication(X23,X24)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_65,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_66,plain,
( multiplication(c(X1),X1) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_40]) ).
cnf(c_0_67,negated_conjecture,
( multiplication(c(esk4_0),esk2_0) = zero
| leq(esk2_0,multiplication(esk4_0,esk3_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_19]) ).
cnf(c_0_68,negated_conjecture,
multiplication(esk4_0,esk4_0) = esk4_0,
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_69,negated_conjecture,
( leq(esk2_0,esk3_0)
| leq(esk2_0,multiplication(esk4_0,esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_70,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_71,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_72,plain,
( addition(X1,esk1_1(X1)) = c(zero)
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_63]) ).
cnf(c_0_73,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_74,plain,
( multiplication(c(X1),multiplication(X1,X2)) = zero
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_27]) ).
cnf(c_0_75,negated_conjecture,
( leq(esk2_0,multiplication(esk4_0,esk3_0))
| leq(zero,zero) ),
inference(spm,[status(thm)],[c_0_57,c_0_67]) ).
cnf(c_0_76,negated_conjecture,
multiplication(esk4_0,multiplication(esk4_0,X1)) = multiplication(esk4_0,X1),
inference(spm,[status(thm)],[c_0_65,c_0_68]) ).
cnf(c_0_77,negated_conjecture,
( addition(esk2_0,multiplication(esk4_0,esk3_0)) = multiplication(esk4_0,esk3_0)
| leq(esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_56,c_0_69]) ).
cnf(c_0_78,plain,
multiplication(c(zero),X1) = X1,
inference(rw,[status(thm)],[c_0_70,c_0_36]) ).
cnf(c_0_79,plain,
( addition(X1,c(zero)) = c(zero)
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_80,plain,
( test(c(X1))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_40]) ).
cnf(c_0_81,plain,
( multiplication(X1,multiplication(X2,c(multiplication(X1,X2)))) = zero
| ~ test(multiplication(X1,X2)) ),
inference(spm,[status(thm)],[c_0_65,c_0_47]) ).
cnf(c_0_82,negated_conjecture,
( multiplication(addition(X1,c(esk4_0)),esk2_0) = multiplication(X1,esk2_0)
| leq(esk2_0,multiplication(esk4_0,esk3_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_67]),c_0_19]) ).
cnf(c_0_83,negated_conjecture,
( ~ leq(esk2_0,multiplication(esk4_0,esk3_0))
| ~ leq(esk2_0,esk3_0)
| ~ leq(multiplication(c(esk4_0),esk2_0),zero) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_84,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_85,plain,
( multiplication(c(X1),addition(X2,multiplication(X1,X3))) = multiplication(c(X1),X2)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_74]),c_0_19]) ).
cnf(c_0_86,negated_conjecture,
( addition(esk2_0,multiplication(esk4_0,esk3_0)) = multiplication(esk4_0,esk3_0)
| leq(zero,zero) ),
inference(spm,[status(thm)],[c_0_56,c_0_75]) ).
cnf(c_0_87,negated_conjecture,
multiplication(c(esk4_0),multiplication(esk4_0,X1)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_76]),c_0_59])]) ).
cnf(c_0_88,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_20]),c_0_61]) ).
cnf(c_0_89,negated_conjecture,
( addition(esk2_0,multiplication(esk4_0,esk3_0)) = multiplication(esk4_0,esk3_0)
| addition(esk2_0,esk3_0) = esk3_0 ),
inference(spm,[status(thm)],[c_0_56,c_0_77]) ).
cnf(c_0_90,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,c(zero)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_78]),c_0_20]) ).
cnf(c_0_91,negated_conjecture,
addition(esk4_0,c(zero)) = c(zero),
inference(spm,[status(thm)],[c_0_79,c_0_59]) ).
cnf(c_0_92,plain,
( addition(c(X1),c(zero)) = c(zero)
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_93,negated_conjecture,
multiplication(esk4_0,multiplication(esk4_0,c(esk4_0))) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_68]),c_0_59])]) ).
cnf(c_0_94,negated_conjecture,
( multiplication(esk4_0,esk2_0) = esk2_0
| leq(esk2_0,multiplication(esk4_0,esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_45]),c_0_78]),c_0_59])]) ).
cnf(c_0_95,negated_conjecture,
( multiplication(c(esk4_0),esk2_0) != zero
| ~ leq(esk2_0,multiplication(esk4_0,esk3_0))
| ~ leq(esk2_0,esk3_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_19]) ).
cnf(c_0_96,negated_conjecture,
( multiplication(c(esk4_0),esk2_0) = zero
| leq(zero,zero) ),
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_59])]) ).
cnf(c_0_97,negated_conjecture,
( addition(esk2_0,addition(X1,multiplication(esk4_0,esk3_0))) = addition(X1,multiplication(esk4_0,esk3_0))
| addition(esk2_0,esk3_0) = esk3_0 ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_98,negated_conjecture,
addition(X1,multiplication(esk4_0,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_78]) ).
cnf(c_0_99,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(c(zero),X2),X1),
inference(spm,[status(thm)],[c_0_73,c_0_78]) ).
cnf(c_0_100,plain,
( addition(c(zero),c(X1)) = c(zero)
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_92]) ).
cnf(c_0_101,negated_conjecture,
multiplication(esk4_0,c(esk4_0)) = zero,
inference(rw,[status(thm)],[c_0_93,c_0_76]) ).
cnf(c_0_102,negated_conjecture,
( addition(esk2_0,multiplication(esk4_0,esk3_0)) = multiplication(esk4_0,esk3_0)
| multiplication(esk4_0,esk2_0) = esk2_0 ),
inference(spm,[status(thm)],[c_0_56,c_0_94]) ).
cnf(c_0_103,negated_conjecture,
( leq(zero,zero)
| ~ leq(esk2_0,esk3_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_75]) ).
cnf(c_0_104,negated_conjecture,
addition(esk2_0,esk3_0) = esk3_0,
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_105,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(c(zero),X2)),
inference(spm,[status(thm)],[c_0_46,c_0_44]) ).
cnf(c_0_106,plain,
( addition(X1,multiplication(c(X2),X1)) = X1
| ~ test(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_78]) ).
cnf(c_0_107,negated_conjecture,
multiplication(addition(esk4_0,X1),c(esk4_0)) = multiplication(X1,c(esk4_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_101]),c_0_25]) ).
cnf(c_0_108,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_20,c_0_61]) ).
cnf(c_0_109,negated_conjecture,
( multiplication(c(esk4_0),esk2_0) = zero
| multiplication(esk4_0,esk2_0) = esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_102]),c_0_87]),c_0_59])]) ).
cnf(c_0_110,negated_conjecture,
leq(zero,zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_84]),c_0_104])]) ).
cnf(c_0_111,plain,
( addition(X1,multiplication(X1,c(X2))) = X1
| ~ test(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_44]),c_0_44]) ).
cnf(c_0_112,negated_conjecture,
multiplication(esk1_1(esk4_0),c(esk4_0)) = c(esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_72]),c_0_78]),c_0_59])]) ).
cnf(c_0_113,plain,
( addition(X1,addition(c(X1),X2)) = addition(X2,c(zero))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_108,c_0_45]) ).
cnf(c_0_114,negated_conjecture,
addition(esk4_0,addition(X1,c(zero))) = addition(X1,c(zero)),
inference(spm,[status(thm)],[c_0_88,c_0_91]) ).
cnf(c_0_115,plain,
( multiplication(X1,esk1_1(X1)) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_63]) ).
cnf(c_0_116,plain,
( multiplication(esk1_1(X1),X1) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_63]) ).
cnf(c_0_117,negated_conjecture,
( multiplication(esk4_0,esk2_0) = esk2_0
| ~ leq(esk2_0,esk3_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_109]),c_0_110])]),c_0_94]) ).
cnf(c_0_118,plain,
( complement(X1,X2)
| addition(X2,X1) != c(zero)
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero ),
inference(rw,[status(thm)],[c_0_24,c_0_36]) ).
cnf(c_0_119,plain,
( addition(X1,addition(X2,esk1_1(X1))) = addition(X2,c(zero))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_88,c_0_72]) ).
cnf(c_0_120,negated_conjecture,
addition(c(esk4_0),esk1_1(esk4_0)) = esk1_1(esk4_0),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_59])]),c_0_20]) ).
cnf(c_0_121,negated_conjecture,
addition(c(zero),c(esk4_0)) = c(zero),
inference(cn,[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_20]),c_0_62]),c_0_59])]) ).
cnf(c_0_122,plain,
( multiplication(X1,multiplication(X2,esk1_1(multiplication(X1,X2)))) = zero
| ~ test(multiplication(X1,X2)) ),
inference(spm,[status(thm)],[c_0_65,c_0_115]) ).
cnf(c_0_123,plain,
( multiplication(esk1_1(X1),multiplication(X1,X2)) = zero
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_116]),c_0_27]) ).
cnf(c_0_124,negated_conjecture,
multiplication(esk4_0,esk2_0) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_84]),c_0_104])]) ).
cnf(c_0_125,plain,
( complement(X1,X2)
| addition(X1,X2) != c(zero)
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero ),
inference(spm,[status(thm)],[c_0_118,c_0_20]) ).
cnf(c_0_126,negated_conjecture,
addition(esk4_0,esk1_1(esk4_0)) = c(zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_20]),c_0_121]),c_0_59])]) ).
cnf(c_0_127,negated_conjecture,
multiplication(esk4_0,esk1_1(esk4_0)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_122]),c_0_68]),c_0_68]),c_0_59])]) ).
cnf(c_0_128,negated_conjecture,
multiplication(esk1_1(esk4_0),esk4_0) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_68]),c_0_59])]) ).
cnf(c_0_129,negated_conjecture,
multiplication(c(esk4_0),esk2_0) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_124]),c_0_59])]) ).
cnf(c_0_130,negated_conjecture,
complement(esk4_0,esk1_1(esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_127]),c_0_128])]) ).
cnf(c_0_131,negated_conjecture,
( ~ leq(esk2_0,multiplication(esk4_0,esk3_0))
| ~ leq(esk2_0,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_129])]) ).
cnf(c_0_132,negated_conjecture,
( multiplication(addition(c(esk4_0),X1),esk2_0) = multiplication(X1,esk2_0)
| leq(esk2_0,multiplication(esk4_0,esk3_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_67]),c_0_25]) ).
cnf(c_0_133,negated_conjecture,
esk1_1(esk4_0) = c(esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_130]),c_0_59])]) ).
cnf(c_0_134,negated_conjecture,
test(esk1_1(esk4_0)),
inference(spm,[status(thm)],[c_0_29,c_0_130]) ).
cnf(c_0_135,negated_conjecture,
( addition(esk2_0,multiplication(esk4_0,esk3_0)) != multiplication(esk4_0,esk3_0)
| ~ leq(esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_131,c_0_84]) ).
cnf(c_0_136,negated_conjecture,
( multiplication(c(c(esk4_0)),esk2_0) = esk2_0
| leq(esk2_0,multiplication(esk4_0,esk3_0))
| ~ test(c(esk4_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_45]),c_0_78]) ).
cnf(c_0_137,negated_conjecture,
complement(c(esk4_0),esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_133]),c_0_59])]) ).
cnf(c_0_138,negated_conjecture,
test(c(esk4_0)),
inference(rw,[status(thm)],[c_0_134,c_0_133]) ).
cnf(c_0_139,negated_conjecture,
addition(esk2_0,multiplication(esk4_0,esk3_0)) != multiplication(esk4_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_84]),c_0_104])]) ).
cnf(c_0_140,negated_conjecture,
( addition(esk2_0,multiplication(c(c(esk4_0)),X1)) = multiplication(c(c(esk4_0)),addition(esk2_0,X1))
| leq(esk2_0,multiplication(esk4_0,esk3_0))
| ~ test(c(esk4_0)) ),
inference(spm,[status(thm)],[c_0_46,c_0_136]) ).
cnf(c_0_141,negated_conjecture,
c(c(esk4_0)) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_137]),c_0_138])]) ).
cnf(c_0_142,negated_conjecture,
leq(esk2_0,esk3_0),
inference(sr,[status(thm)],[c_0_77,c_0_139]) ).
cnf(c_0_143,negated_conjecture,
( addition(esk2_0,multiplication(esk4_0,X1)) = multiplication(esk4_0,addition(esk2_0,X1))
| leq(esk2_0,multiplication(esk4_0,esk3_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_140,c_0_138])]),c_0_141]),c_0_141]) ).
cnf(c_0_144,negated_conjecture,
~ leq(esk2_0,multiplication(esk4_0,esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_131,c_0_142])]) ).
cnf(c_0_145,negated_conjecture,
addition(esk2_0,multiplication(esk4_0,X1)) = multiplication(esk4_0,addition(esk2_0,X1)),
inference(sr,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_146,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_145]),c_0_104])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE008+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n014.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 : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 11:56:15 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.55 start to proof: theBenchmark
% 1.64/1.74 % Version : CSE_E---1.5
% 1.64/1.74 % Problem : theBenchmark.p
% 1.64/1.74 % Proof found
% 1.64/1.74 % SZS status Theorem for theBenchmark.p
% 1.64/1.74 % SZS output start Proof
% See solution above
% 1.64/1.75 % Total time : 1.177000 s
% 1.64/1.75 % SZS output end Proof
% 1.64/1.75 % Total time : 1.181000 s
%------------------------------------------------------------------------------