TSTP Solution File: KLE010+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE010+2 : 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 : n002.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 05:25:35 EDT 2023
% Result : Theorem 0.20s 0.64s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 26
% Syntax : Number of formulae : 133 ( 77 unt; 11 typ; 0 def)
% Number of atoms : 199 ( 112 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 142 ( 65 ~; 56 |; 14 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 9 ( 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 : 147 ( 5 sgn; 58 !; 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/sandbox2/benchmark/Axioms/KLE001+1.ax',test_3) ).
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/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/sandbox2/benchmark/Axioms/KLE001+1.ax',test_2) ).
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(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(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
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_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(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(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).
fof(c_0_15,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_16,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]) ).
cnf(c_0_17,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_18,negated_conjecture,
( test(esk3_0)
& test(esk2_0)
& ( ~ leq(one,addition(addition(addition(addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0)),multiplication(esk2_0,esk3_0)),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))))
| ~ leq(addition(addition(addition(addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0)),multiplication(esk2_0,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_16])])]) ).
fof(c_0_19,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_20,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_21,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
( multiplication(X1,X2) = zero
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,negated_conjecture,
complement(esk3_0,c(esk3_0)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
zero = multiplication(c(esk3_0),esk3_0),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
( multiplication(X1,X2) = multiplication(c(esk3_0),esk3_0)
| ~ complement(X1,X2) ),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,negated_conjecture,
multiplication(c(esk3_0),esk3_0) = multiplication(esk3_0,c(esk3_0)),
inference(spm,[status(thm)],[c_0_26,c_0_23]) ).
cnf(c_0_28,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,plain,
( multiplication(X1,X2) = multiplication(esk3_0,c(esk3_0))
| ~ complement(X2,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_25]),c_0_27]) ).
cnf(c_0_30,negated_conjecture,
complement(esk2_0,c(esk2_0)),
inference(spm,[status(thm)],[c_0_20,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
multiplication(esk3_0,c(esk3_0)) = multiplication(c(esk2_0),esk2_0),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
fof(c_0_32,plain,
! [X11] : addition(X11,zero) = X11,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_33,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_34,plain,
( multiplication(X1,X2) = multiplication(c(esk2_0),esk2_0)
| ~ complement(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_31]) ).
cnf(c_0_35,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_37,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_38,plain,
! [X25] : multiplication(zero,X25) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_39,negated_conjecture,
multiplication(c(esk2_0),esk2_0) = multiplication(esk2_0,c(esk2_0)),
inference(spm,[status(thm)],[c_0_34,c_0_30]) ).
fof(c_0_40,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_41,plain,
addition(X1,multiplication(c(esk2_0),esk2_0)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_25]),c_0_27]),c_0_31]) ).
fof(c_0_42,plain,
! [X17] : multiplication(one,X17) = X17,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_43,negated_conjecture,
one = addition(esk3_0,c(esk3_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_23]),c_0_37]) ).
cnf(c_0_44,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_45,plain,
! [X13,X14,X15] : multiplication(X13,multiplication(X14,X15)) = multiplication(multiplication(X13,X14),X15),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_46,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_47,plain,
( multiplication(X1,X2) = multiplication(esk2_0,c(esk2_0))
| ~ complement(X2,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_31]),c_0_39]) ).
cnf(c_0_48,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_49,plain,
addition(multiplication(c(esk2_0),esk2_0),X1) = X1,
inference(spm,[status(thm)],[c_0_37,c_0_41]) ).
cnf(c_0_50,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_51,plain,
( addition(X1,X2) = addition(esk3_0,c(esk3_0))
| ~ complement(X2,X1) ),
inference(rw,[status(thm)],[c_0_36,c_0_43]) ).
cnf(c_0_52,plain,
multiplication(multiplication(esk3_0,c(esk3_0)),X1) = multiplication(esk3_0,c(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_25]),c_0_25]),c_0_27]),c_0_27]) ).
cnf(c_0_53,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_54,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_55,plain,
( multiplication(X1,esk1_1(X1)) = multiplication(esk2_0,c(esk2_0))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_56,plain,
addition(multiplication(esk2_0,c(esk2_0)),X1) = X1,
inference(rw,[status(thm)],[c_0_49,c_0_39]) ).
cnf(c_0_57,plain,
multiplication(addition(esk3_0,c(esk3_0)),X1) = X1,
inference(rw,[status(thm)],[c_0_50,c_0_43]) ).
cnf(c_0_58,negated_conjecture,
addition(esk3_0,c(esk3_0)) = addition(esk2_0,c(esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_30]),c_0_37]) ).
fof(c_0_59,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_60,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_61,plain,
multiplication(esk3_0,multiplication(c(esk3_0),X1)) = multiplication(c(esk2_0),esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_53]),c_0_31]) ).
cnf(c_0_62,plain,
( multiplication(addition(X1,X2),esk1_1(X1)) = multiplication(X2,esk1_1(X1))
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]) ).
cnf(c_0_63,plain,
multiplication(addition(esk2_0,c(esk2_0)),X1) = X1,
inference(rw,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_64,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_65,plain,
( addition(X1,X2) = addition(esk2_0,c(esk2_0))
| ~ complement(X2,X1) ),
inference(rw,[status(thm)],[c_0_51,c_0_58]) ).
cnf(c_0_66,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_67,plain,
addition(X1,multiplication(esk2_0,c(esk2_0))) = X1,
inference(rw,[status(thm)],[c_0_41,c_0_39]) ).
cnf(c_0_68,plain,
multiplication(esk3_0,multiplication(c(esk3_0),X1)) = multiplication(esk2_0,c(esk2_0)),
inference(rw,[status(thm)],[c_0_61,c_0_39]) ).
cnf(c_0_69,negated_conjecture,
multiplication(c(esk3_0),esk1_1(esk3_0)) = esk1_1(esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_58]),c_0_63]),c_0_21])]) ).
fof(c_0_70,plain,
! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_71,plain,
! [X12] : addition(X12,X12) = X12,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_72,plain,
( test(X2)
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_73,plain,
( multiplication(X1,addition(esk1_1(X1),X2)) = multiplication(X1,X2)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_55]),c_0_56]) ).
cnf(c_0_74,plain,
( addition(X1,esk1_1(X1)) = addition(esk2_0,c(esk2_0))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_48]) ).
cnf(c_0_75,plain,
multiplication(X1,addition(esk2_0,c(esk2_0))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_43]),c_0_58]) ).
cnf(c_0_76,plain,
( multiplication(addition(X1,X2),esk1_1(X2)) = multiplication(X1,esk1_1(X2))
| ~ test(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_67]) ).
cnf(c_0_77,negated_conjecture,
multiplication(esk3_0,esk1_1(esk3_0)) = multiplication(esk2_0,c(esk2_0)),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_78,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_79,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_80,negated_conjecture,
test(c(esk3_0)),
inference(spm,[status(thm)],[c_0_72,c_0_23]) ).
cnf(c_0_81,plain,
( c(X1) = X2
| ~ complement(X1,X2)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_82,plain,
( multiplication(X1,esk1_1(esk1_1(X1))) = X1
| ~ test(esk1_1(X1))
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]) ).
cnf(c_0_83,plain,
( multiplication(X1,esk1_1(esk1_1(X1))) = esk1_1(esk1_1(X1))
| ~ test(esk1_1(X1))
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_74]),c_0_63]) ).
cnf(c_0_84,negated_conjecture,
multiplication(esk3_0,addition(esk1_1(esk3_0),X1)) = multiplication(esk3_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_77]),c_0_56]) ).
cnf(c_0_85,negated_conjecture,
multiplication(c(esk3_0),esk3_0) = multiplication(c(esk2_0),esk2_0),
inference(rw,[status(thm)],[c_0_27,c_0_31]) ).
cnf(c_0_86,negated_conjecture,
( ~ leq(one,addition(addition(addition(addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0)),multiplication(esk2_0,esk3_0)),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))))
| ~ leq(addition(addition(addition(addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0)),multiplication(esk2_0,esk3_0)),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))),one) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_87,plain,
multiplication(esk2_0,addition(c(esk2_0),X1)) = multiplication(esk2_0,X1),
inference(spm,[status(thm)],[c_0_64,c_0_56]) ).
cnf(c_0_88,negated_conjecture,
test(c(esk2_0)),
inference(spm,[status(thm)],[c_0_72,c_0_30]) ).
cnf(c_0_89,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_90,negated_conjecture,
complement(c(esk3_0),c(c(esk3_0))),
inference(spm,[status(thm)],[c_0_20,c_0_80]) ).
cnf(c_0_91,plain,
( c(esk1_1(X1)) = X1
| ~ test(esk1_1(X1))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_48]) ).
cnf(c_0_92,plain,
( esk1_1(esk1_1(X1)) = X1
| ~ test(esk1_1(X1))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_93,negated_conjecture,
( multiplication(esk3_0,esk1_1(esk1_1(esk3_0))) = esk3_0
| ~ test(esk1_1(esk3_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_74]),c_0_75]) ).
cnf(c_0_94,negated_conjecture,
multiplication(c(esk3_0),esk3_0) = multiplication(esk2_0,c(esk2_0)),
inference(rw,[status(thm)],[c_0_85,c_0_39]) ).
cnf(c_0_95,negated_conjecture,
( ~ leq(one,addition(multiplication(c(esk2_0),c(esk3_0)),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,esk3_0),addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0))))))
| ~ leq(addition(multiplication(c(esk2_0),c(esk3_0)),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,esk3_0),addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0))))),one) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_37]),c_0_37]),c_0_37]),c_0_37]),c_0_37]),c_0_37]) ).
cnf(c_0_96,plain,
multiplication(esk2_0,esk1_1(c(esk2_0))) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_74]),c_0_75]),c_0_88])]) ).
cnf(c_0_97,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_89,c_0_37]) ).
cnf(c_0_98,negated_conjecture,
addition(c(esk3_0),c(c(esk3_0))) = addition(esk2_0,c(esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_90]),c_0_37]) ).
cnf(c_0_99,plain,
( esk1_1(X1) = c(X1)
| ~ test(esk1_1(X1))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_100,negated_conjecture,
( esk1_1(esk1_1(esk3_0)) = esk3_0
| ~ test(esk1_1(esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_83]),c_0_21])]) ).
cnf(c_0_101,negated_conjecture,
multiplication(c(esk3_0),addition(esk3_0,X1)) = multiplication(c(esk3_0),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_94]),c_0_56]) ).
cnf(c_0_102,negated_conjecture,
( ~ leq(addition(esk3_0,c(esk3_0)),addition(multiplication(c(esk2_0),c(esk3_0)),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,esk3_0),multiplication(addition(esk3_0,c(esk3_0)),esk2_0)))))
| ~ leq(addition(multiplication(c(esk2_0),c(esk3_0)),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,esk3_0),multiplication(addition(esk3_0,c(esk3_0)),esk2_0)))),addition(esk3_0,c(esk3_0))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_43]),c_0_54]),c_0_54]),c_0_43]) ).
fof(c_0_103,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_104,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(esk2_0,addition(c(esk2_0),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_75]),c_0_78]) ).
cnf(c_0_105,plain,
esk1_1(c(esk2_0)) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_76]),c_0_96]),c_0_88])]) ).
cnf(c_0_106,negated_conjecture,
addition(esk2_0,addition(c(esk2_0),c(c(esk3_0)))) = addition(esk2_0,c(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_37]),c_0_78]) ).
cnf(c_0_107,negated_conjecture,
( c(esk1_1(esk3_0)) = esk3_0
| ~ test(esk1_1(esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_21])]) ).
cnf(c_0_108,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(spm,[status(thm)],[c_0_101,c_0_74]),c_0_75]),c_0_69]),c_0_21])]) ).
cnf(c_0_109,negated_conjecture,
( ~ leq(addition(esk2_0,c(esk2_0)),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,esk3_0),addition(multiplication(addition(esk2_0,c(esk2_0)),esk2_0),multiplication(c(esk2_0),c(esk3_0))))))
| ~ leq(addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,esk3_0),addition(multiplication(addition(esk2_0,c(esk2_0)),esk2_0),multiplication(c(esk2_0),c(esk3_0))))),addition(esk2_0,c(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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_58]),c_0_58]),c_0_37]),c_0_78]),c_0_78]),c_0_58]),c_0_37]),c_0_78]),c_0_78]),c_0_58]) ).
cnf(c_0_110,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_111,plain,
addition(X1,multiplication(X1,esk2_0)) = X1,
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_104,c_0_74]),c_0_105]),c_0_89]),c_0_75]),c_0_88])]) ).
cnf(c_0_112,negated_conjecture,
addition(X1,multiplication(X1,c(c(esk3_0)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_106]),c_0_75]) ).
cnf(c_0_113,negated_conjecture,
c(c(esk3_0)) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_108]),c_0_108]),c_0_80])]) ).
cnf(c_0_114,negated_conjecture,
( addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,esk3_0),addition(multiplication(addition(esk2_0,c(esk2_0)),esk2_0),addition(esk2_0,addition(c(esk2_0),multiplication(c(esk2_0),c(esk3_0))))))) != addition(esk2_0,c(esk2_0))
| ~ leq(addition(esk2_0,c(esk2_0)),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,esk3_0),addition(multiplication(addition(esk2_0,c(esk2_0)),esk2_0),multiplication(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_109,c_0_110]),c_0_78]),c_0_78]),c_0_78]),c_0_37]),c_0_78]) ).
cnf(c_0_115,plain,
addition(X1,addition(multiplication(X1,esk2_0),X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_78,c_0_111]) ).
cnf(c_0_116,negated_conjecture,
addition(X1,multiplication(X1,esk3_0)) = X1,
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_117,negated_conjecture,
( addition(esk2_0,addition(c(esk2_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,esk3_0),addition(multiplication(addition(esk2_0,c(esk2_0)),esk2_0),multiplication(c(esk2_0),c(esk3_0))))))) != addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,esk3_0),addition(multiplication(addition(esk2_0,c(esk2_0)),esk2_0),multiplication(c(esk2_0),c(esk3_0)))))
| addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,esk3_0),addition(multiplication(addition(esk2_0,c(esk2_0)),esk2_0),addition(esk2_0,addition(c(esk2_0),multiplication(c(esk2_0),c(esk3_0))))))) != addition(esk2_0,c(esk2_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_110]),c_0_78]) ).
cnf(c_0_118,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_37]),c_0_78]) ).
cnf(c_0_119,negated_conjecture,
addition(X1,multiplication(X1,multiplication(esk2_0,esk3_0))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_111]),c_0_53]) ).
cnf(c_0_120,negated_conjecture,
addition(esk2_0,addition(multiplication(esk2_0,esk3_0),c(esk2_0))) != addition(esk2_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(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_117,c_0_118]),c_0_63]),c_0_118]),c_0_64]),c_0_58]),c_0_75]),c_0_118]),c_0_118]),c_0_97]),c_0_89]),c_0_118]),c_0_63]),c_0_118]),c_0_64]),c_0_58]),c_0_75]),c_0_118]),c_0_118]),c_0_63]),c_0_89]),c_0_118]),c_0_118]),c_0_64]),c_0_58]),c_0_75]),c_0_79]),c_0_118])]) ).
cnf(c_0_121,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_63]),c_0_78]),c_0_37]),c_0_120]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KLE010+2 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 12:37:50 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.55 start to proof: theBenchmark
% 0.20/0.64 % Version : CSE_E---1.5
% 0.20/0.64 % Problem : theBenchmark.p
% 0.20/0.64 % Proof found
% 0.20/0.64 % SZS status Theorem for theBenchmark.p
% 0.20/0.64 % SZS output start Proof
% See solution above
% 0.20/0.65 % Total time : 0.082000 s
% 0.20/0.65 % SZS output end Proof
% 0.20/0.65 % Total time : 0.085000 s
%------------------------------------------------------------------------------