TSTP Solution File: KLE023+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE023+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 : n024.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 05:25:42 EDT 2023
% Result : Theorem 23.54s 23.61s
% Output : CNFRefutation 23.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 28
% Syntax : Number of formulae : 181 ( 101 unt; 12 typ; 0 def)
% Number of atoms : 272 ( 153 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 185 ( 82 ~; 79 |; 14 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 5 ( 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 176 ( 3 sgn; 64 !; 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(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(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(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(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_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(goals,conjecture,
! [X4,X5,X6] :
( ( test(X5)
& test(X6) )
=> ( addition(multiplication(X5,X4),multiplication(X4,X6)) = multiplication(X4,X6)
=> addition(multiplication(X4,c(X6)),multiplication(c(X5),X4)) = multiplication(c(X5),X4) ) ),
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(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).
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(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(test_deMorgan2,axiom,
! [X4,X5] :
( ( test(X4)
& test(X5) )
=> c(multiplication(X4,X5)) = addition(c(X4),c(X5)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+2.ax',test_deMorgan2) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(c_0_16,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])])]) ).
fof(c_0_17,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_18,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_19,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_20,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_18]) ).
fof(c_0_22,plain,
! [X12] : addition(X12,zero) = X12,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_23,plain,
! [X7,X8] : addition(X7,X8) = addition(X8,X7),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_24,plain,
! [X9,X10,X11] : addition(X11,addition(X10,X9)) = addition(addition(X11,X10),X9),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_25,plain,
! [X13] : addition(X13,X13) = X13,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_26,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( multiplication(X1,c(X1)) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_30,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_31,plain,
! [X17] : multiplication(X17,one) = X17,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_32,negated_conjecture,
~ ! [X4,X5,X6] :
( ( test(X5)
& test(X6) )
=> ( addition(multiplication(X5,X4),multiplication(X4,X6)) = multiplication(X4,X6)
=> addition(multiplication(X4,c(X6)),multiplication(c(X5),X4)) = multiplication(c(X5),X4) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_33,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_35,plain,
! [X14,X15,X16] : multiplication(X14,multiplication(X15,X16)) = multiplication(multiplication(X14,X15),X16),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_36,plain,
( multiplication(X1,addition(X2,c(X1))) = multiplication(X1,X2)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_37,plain,
( addition(X1,c(X1)) = one
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_21]),c_0_30]) ).
cnf(c_0_38,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_39,negated_conjecture,
( test(esk3_0)
& test(esk4_0)
& addition(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)) = multiplication(esk2_0,esk4_0)
& addition(multiplication(esk2_0,c(esk4_0)),multiplication(c(esk3_0),esk2_0)) != multiplication(c(esk3_0),esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])]) ).
cnf(c_0_40,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_41,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,plain,
( multiplication(X1,X1) = X1
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_43,negated_conjecture,
test(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_44,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])]) ).
cnf(c_0_45,plain,
( addition(X1,one) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_37]) ).
cnf(c_0_46,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_47,plain,
( multiplication(X1,multiplication(X2,c(multiplication(X1,X2)))) = zero
| ~ test(multiplication(X1,X2)) ),
inference(spm,[status(thm)],[c_0_41,c_0_27]) ).
cnf(c_0_48,negated_conjecture,
multiplication(esk4_0,esk4_0) = esk4_0,
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_50,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_51,negated_conjecture,
addition(one,esk3_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_30]) ).
fof(c_0_52,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_53,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_47,c_0_48]),c_0_43])]) ).
cnf(c_0_54,negated_conjecture,
multiplication(esk4_0,multiplication(esk4_0,X1)) = multiplication(esk4_0,X1),
inference(spm,[status(thm)],[c_0_41,c_0_48]) ).
cnf(c_0_55,plain,
( leq(X1,X2)
| addition(X2,X1) != X2 ),
inference(spm,[status(thm)],[c_0_49,c_0_30]) ).
cnf(c_0_56,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_57,negated_conjecture,
addition(one,addition(esk3_0,X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_33,c_0_51]) ).
fof(c_0_58,plain,
! [X18] : multiplication(one,X18) = X18,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_59,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_30]) ).
cnf(c_0_60,plain,
( test(X2)
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_61,negated_conjecture,
multiplication(esk4_0,c(esk4_0)) = zero,
inference(rw,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_62,plain,
( leq(multiplication(X1,X2),multiplication(X3,X2))
| multiplication(addition(X3,X1),X2) != multiplication(X3,X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_63,negated_conjecture,
addition(one,c(esk3_0)) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_37]),c_0_34]),c_0_46])]) ).
cnf(c_0_64,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_65,plain,
( multiplication(X1,addition(c(X1),X2)) = multiplication(X1,X2)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_59]) ).
cnf(c_0_66,plain,
( test(c(X1))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_21]) ).
fof(c_0_67,plain,
! [X40,X41] :
( ~ test(X40)
| ~ test(X41)
| c(multiplication(X40,X41)) = addition(c(X40),c(X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_deMorgan2])]) ).
cnf(c_0_68,negated_conjecture,
multiplication(esk4_0,addition(c(esk4_0),X1)) = multiplication(esk4_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_61]),c_0_59]) ).
cnf(c_0_69,negated_conjecture,
leq(multiplication(c(esk3_0),X1),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).
cnf(c_0_70,plain,
( multiplication(X1,c(c(X1))) = X1
| ~ test(X1) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_37]),c_0_38]),c_0_66]) ).
cnf(c_0_71,negated_conjecture,
addition(one,esk4_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_43]),c_0_30]) ).
cnf(c_0_72,plain,
( c(multiplication(X1,X2)) = addition(c(X1),c(X2))
| ~ test(X1)
| ~ test(X2) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_73,negated_conjecture,
( multiplication(esk4_0,c(c(esk4_0))) = esk4_0
| ~ test(c(esk4_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_37]),c_0_38]) ).
cnf(c_0_74,negated_conjecture,
( leq(c(esk3_0),c(c(c(esk3_0))))
| ~ test(c(esk3_0)) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_75,negated_conjecture,
addition(one,addition(esk4_0,X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_33,c_0_71]) ).
cnf(c_0_76,plain,
( leq(c(X1),c(X2))
| c(multiplication(X2,X1)) != c(X2)
| ~ test(X1)
| ~ test(X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_72]) ).
cnf(c_0_77,negated_conjecture,
multiplication(esk4_0,c(c(esk4_0))) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_66]),c_0_43])]) ).
cnf(c_0_78,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_79,negated_conjecture,
leq(c(esk3_0),c(c(c(esk3_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_66]),c_0_46])]) ).
cnf(c_0_80,negated_conjecture,
addition(one,c(esk4_0)) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_37]),c_0_34]),c_0_43])]) ).
cnf(c_0_81,negated_conjecture,
( leq(c(c(c(esk4_0))),c(esk4_0))
| ~ test(c(c(esk4_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_43])]) ).
cnf(c_0_82,negated_conjecture,
addition(c(esk3_0),c(c(c(esk3_0)))) = c(c(c(esk3_0))),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_83,negated_conjecture,
leq(multiplication(c(esk4_0),X1),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_80]),c_0_64]) ).
cnf(c_0_84,negated_conjecture,
( leq(c(c(c(esk4_0))),c(esk4_0))
| ~ test(c(esk4_0)) ),
inference(spm,[status(thm)],[c_0_81,c_0_66]) ).
cnf(c_0_85,negated_conjecture,
( c(multiplication(esk3_0,c(c(esk3_0)))) = c(c(c(esk3_0)))
| ~ test(c(c(esk3_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_82]),c_0_46])]) ).
cnf(c_0_86,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_64]),c_0_30]) ).
cnf(c_0_87,negated_conjecture,
( leq(c(esk4_0),c(c(c(esk4_0))))
| ~ test(c(esk4_0)) ),
inference(spm,[status(thm)],[c_0_83,c_0_70]) ).
cnf(c_0_88,negated_conjecture,
leq(c(c(c(esk4_0))),c(esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_66]),c_0_43])]) ).
cnf(c_0_89,negated_conjecture,
( c(multiplication(esk3_0,c(c(esk3_0)))) = c(c(c(esk3_0)))
| ~ test(c(esk3_0)) ),
inference(spm,[status(thm)],[c_0_85,c_0_66]) ).
cnf(c_0_90,negated_conjecture,
addition(esk4_0,c(c(esk4_0))) = c(c(esk4_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_77]),c_0_30]),c_0_71]),c_0_64]),c_0_30]) ).
cnf(c_0_91,negated_conjecture,
leq(c(esk4_0),c(c(c(esk4_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_66]),c_0_43])]) ).
cnf(c_0_92,negated_conjecture,
addition(c(esk4_0),c(c(c(esk4_0)))) = c(esk4_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_88]),c_0_30]) ).
cnf(c_0_93,negated_conjecture,
c(multiplication(esk3_0,c(c(esk3_0)))) = c(c(c(esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_66]),c_0_46])]) ).
cnf(c_0_94,negated_conjecture,
( multiplication(c(esk4_0),c(c(esk4_0))) = multiplication(c(esk4_0),esk4_0)
| ~ test(c(esk4_0)) ),
inference(spm,[status(thm)],[c_0_36,c_0_90]) ).
cnf(c_0_95,negated_conjecture,
c(c(c(esk4_0))) = c(esk4_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_91]),c_0_92]) ).
cnf(c_0_96,negated_conjecture,
c(c(c(esk3_0))) = c(esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_70]),c_0_46])]) ).
cnf(c_0_97,plain,
( addition(c(X1),c(X2)) = c(multiplication(X2,X1))
| ~ test(X1)
| ~ test(X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_72]) ).
cnf(c_0_98,negated_conjecture,
multiplication(c(esk4_0),c(c(esk4_0))) = multiplication(c(esk4_0),esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_66]),c_0_43])]) ).
cnf(c_0_99,negated_conjecture,
( complement(c(c(esk4_0)),c(esk4_0))
| ~ test(c(c(esk4_0))) ),
inference(spm,[status(thm)],[c_0_21,c_0_95]) ).
cnf(c_0_100,negated_conjecture,
c(multiplication(esk3_0,c(c(esk3_0)))) = c(esk3_0),
inference(rw,[status(thm)],[c_0_93,c_0_96]) ).
cnf(c_0_101,negated_conjecture,
( c(multiplication(c(c(esk4_0)),esk4_0)) = c(esk4_0)
| ~ test(c(c(esk4_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_92]),c_0_43])]) ).
cnf(c_0_102,negated_conjecture,
( multiplication(c(esk4_0),esk4_0) = zero
| ~ test(c(esk4_0)) ),
inference(spm,[status(thm)],[c_0_27,c_0_98]) ).
cnf(c_0_103,negated_conjecture,
( complement(c(c(esk4_0)),c(esk4_0))
| ~ test(c(esk4_0)) ),
inference(spm,[status(thm)],[c_0_99,c_0_66]) ).
cnf(c_0_104,negated_conjecture,
( test(c(esk3_0))
| ~ test(multiplication(esk3_0,c(c(esk3_0)))) ),
inference(spm,[status(thm)],[c_0_66,c_0_100]) ).
cnf(c_0_105,plain,
( multiplication(X1,X2) = zero
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_106,negated_conjecture,
( c(multiplication(c(c(esk4_0)),esk4_0)) = c(esk4_0)
| ~ test(c(esk4_0)) ),
inference(spm,[status(thm)],[c_0_101,c_0_66]) ).
cnf(c_0_107,negated_conjecture,
multiplication(c(esk4_0),esk4_0) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_66]),c_0_43])]) ).
cnf(c_0_108,negated_conjecture,
complement(c(c(esk4_0)),c(esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_66]),c_0_43])]) ).
cnf(c_0_109,negated_conjecture,
( complement(c(c(esk3_0)),c(esk3_0))
| ~ test(c(c(esk3_0))) ),
inference(spm,[status(thm)],[c_0_21,c_0_96]) ).
cnf(c_0_110,negated_conjecture,
test(c(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_70]),c_0_46])]) ).
cnf(c_0_111,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_112,plain,
( multiplication(c(X1),X1) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_105,c_0_21]) ).
cnf(c_0_113,negated_conjecture,
c(multiplication(c(c(esk4_0)),esk4_0)) = c(esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_66]),c_0_43])]) ).
cnf(c_0_114,negated_conjecture,
multiplication(addition(c(esk4_0),X1),esk4_0) = multiplication(X1,esk4_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_107]),c_0_59]) ).
cnf(c_0_115,negated_conjecture,
test(c(esk4_0)),
inference(spm,[status(thm)],[c_0_60,c_0_108]) ).
cnf(c_0_116,negated_conjecture,
complement(c(c(esk3_0)),c(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_66]),c_0_110])]) ).
cnf(c_0_117,plain,
( c(X1) = X2
| ~ complement(X1,X2)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_118,plain,
( complement(c(X1),X1)
| ~ test(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_37]),c_0_27]),c_0_112]) ).
cnf(c_0_119,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_120,negated_conjecture,
( addition(c(esk4_0),multiplication(c(c(esk4_0)),esk4_0)) = one
| ~ test(multiplication(c(c(esk4_0)),esk4_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_113]),c_0_30]) ).
cnf(c_0_121,negated_conjecture,
multiplication(c(c(esk4_0)),esk4_0) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_37]),c_0_64]),c_0_115])]) ).
cnf(c_0_122,negated_conjecture,
addition(c(esk3_0),c(c(esk3_0))) = one,
inference(spm,[status(thm)],[c_0_29,c_0_116]) ).
cnf(c_0_123,plain,
( c(c(X1)) = X1
| ~ test(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_66]) ).
cnf(c_0_124,plain,
( addition(X1,esk1_1(X1)) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_119]) ).
cnf(c_0_125,plain,
( multiplication(addition(X1,X2),c(X2)) = multiplication(X1,c(X2))
| ~ test(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_27]),c_0_28]) ).
cnf(c_0_126,negated_conjecture,
addition(esk4_0,c(esk4_0)) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_121]),c_0_30]),c_0_121]),c_0_43])]) ).
cnf(c_0_127,negated_conjecture,
addition(esk3_0,c(esk3_0)) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_30]),c_0_46])]) ).
cnf(c_0_128,negated_conjecture,
multiplication(esk3_0,c(c(esk3_0))) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_122]),c_0_38]),c_0_46])]) ).
cnf(c_0_129,negated_conjecture,
addition(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)) = multiplication(esk2_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_130,plain,
( multiplication(X1,esk1_1(c(X1))) = X1
| ~ test(X1) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_124]),c_0_38]),c_0_66]) ).
cnf(c_0_131,negated_conjecture,
c(c(esk4_0)) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_64]),c_0_77]),c_0_115])]) ).
cnf(c_0_132,negated_conjecture,
c(c(esk3_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_125,c_0_127]),c_0_64]),c_0_128]),c_0_110])]) ).
cnf(c_0_133,negated_conjecture,
addition(multiplication(esk2_0,esk4_0),multiplication(esk3_0,esk2_0)) = multiplication(esk2_0,esk4_0),
inference(rw,[status(thm)],[c_0_129,c_0_30]) ).
cnf(c_0_134,negated_conjecture,
multiplication(c(esk4_0),esk1_1(esk4_0)) = c(esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_115])]) ).
cnf(c_0_135,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_30,c_0_33]) ).
cnf(c_0_136,negated_conjecture,
multiplication(c(esk3_0),esk1_1(esk3_0)) = c(esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_132]),c_0_110])]) ).
cnf(c_0_137,negated_conjecture,
addition(multiplication(esk2_0,esk4_0),addition(multiplication(esk3_0,esk2_0),X1)) = addition(multiplication(esk2_0,esk4_0),X1),
inference(spm,[status(thm)],[c_0_33,c_0_133]) ).
cnf(c_0_138,plain,
( addition(X1,addition(c(X1),X2)) = addition(one,X2)
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_37]) ).
cnf(c_0_139,negated_conjecture,
addition(c(esk4_0),esk1_1(esk4_0)) = esk1_1(esk4_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_134]),c_0_30]),c_0_30]),c_0_80]),c_0_64]) ).
cnf(c_0_140,negated_conjecture,
addition(one,esk1_1(esk4_0)) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_124]),c_0_34]),c_0_43])]) ).
cnf(c_0_141,plain,
( addition(X1,addition(c(X1),X2)) = addition(X2,one)
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_135,c_0_37]) ).
cnf(c_0_142,negated_conjecture,
addition(c(esk3_0),esk1_1(esk3_0)) = esk1_1(esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_136]),c_0_30]),c_0_30]),c_0_63]),c_0_64]) ).
cnf(c_0_143,negated_conjecture,
addition(one,esk1_1(esk3_0)) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_124]),c_0_34]),c_0_46])]) ).
fof(c_0_144,plain,
! [X25] : multiplication(X25,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_145,negated_conjecture,
addition(multiplication(esk2_0,esk4_0),multiplication(addition(esk3_0,X1),esk2_0)) = addition(multiplication(esk2_0,esk4_0),multiplication(X1,esk2_0)),
inference(spm,[status(thm)],[c_0_137,c_0_56]) ).
cnf(c_0_146,plain,
( multiplication(esk1_1(X1),X1) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_119]) ).
cnf(c_0_147,plain,
( multiplication(addition(X1,X2),c(X1)) = multiplication(X2,c(X1))
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_27]),c_0_59]) ).
cnf(c_0_148,negated_conjecture,
addition(esk4_0,esk1_1(esk4_0)) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_140]),c_0_43])]) ).
cnf(c_0_149,negated_conjecture,
addition(esk3_0,esk1_1(esk3_0)) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_30]),c_0_143]),c_0_46])]) ).
cnf(c_0_150,plain,
( leq(multiplication(X1,X2),multiplication(X1,X3))
| multiplication(X1,addition(X3,X2)) != multiplication(X1,X3) ),
inference(spm,[status(thm)],[c_0_55,c_0_26]) ).
cnf(c_0_151,plain,
addition(multiplication(X1,multiplication(X2,X3)),multiplication(X4,X3)) = multiplication(addition(multiplication(X1,X2),X4),X3),
inference(spm,[status(thm)],[c_0_56,c_0_41]) ).
cnf(c_0_152,plain,
( multiplication(X1,esk1_1(X1)) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_105,c_0_119]) ).
cnf(c_0_153,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_144]) ).
cnf(c_0_154,negated_conjecture,
addition(multiplication(esk2_0,esk4_0),multiplication(esk1_1(esk3_0),esk2_0)) = addition(esk2_0,multiplication(esk2_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_124]),c_0_64]),c_0_30]),c_0_46])]) ).
cnf(c_0_155,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_38]),c_0_30]) ).
cnf(c_0_156,plain,
( multiplication(esk1_1(X1),addition(X1,X2)) = multiplication(esk1_1(X1),X2)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_146]),c_0_59]) ).
cnf(c_0_157,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_147,c_0_148]),c_0_64]),c_0_43])]) ).
cnf(c_0_158,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_147,c_0_149]),c_0_64]),c_0_46])]) ).
cnf(c_0_159,negated_conjecture,
leq(multiplication(X1,c(esk4_0)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_80]),c_0_38]) ).
cnf(c_0_160,plain,
( multiplication(addition(multiplication(X1,X2),X3),esk1_1(X2)) = multiplication(X3,esk1_1(X2))
| ~ test(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_153]),c_0_59]) ).
cnf(c_0_161,negated_conjecture,
addition(multiplication(esk2_0,esk4_0),multiplication(esk1_1(esk3_0),esk2_0)) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_154,c_0_155]),c_0_30]),c_0_71]),c_0_38]) ).
cnf(c_0_162,negated_conjecture,
esk1_1(esk4_0) = c(esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_126]),c_0_38]),c_0_157]),c_0_43])]) ).
cnf(c_0_163,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_156,c_0_127]),c_0_38]),c_0_158]),c_0_46])]) ).
cnf(c_0_164,negated_conjecture,
leq(multiplication(X1,multiplication(X2,c(esk4_0))),multiplication(X1,X2)),
inference(spm,[status(thm)],[c_0_159,c_0_41]) ).
cnf(c_0_165,negated_conjecture,
multiplication(c(esk3_0),multiplication(esk2_0,c(esk4_0))) = multiplication(esk2_0,c(esk4_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_160,c_0_161]),c_0_162]),c_0_163]),c_0_162]),c_0_41]),c_0_43])]) ).
cnf(c_0_166,negated_conjecture,
leq(multiplication(esk2_0,c(esk4_0)),multiplication(c(esk3_0),esk2_0)),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_167,negated_conjecture,
addition(multiplication(esk2_0,c(esk4_0)),multiplication(c(esk3_0),esk2_0)) != multiplication(c(esk3_0),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_168,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_166]),c_0_167]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : KLE023+2 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.30 % Computer : n024.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Aug 29 10:56:08 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.15/0.52 start to proof: theBenchmark
% 23.54/23.61 % Version : CSE_E---1.5
% 23.54/23.61 % Problem : theBenchmark.p
% 23.54/23.61 % Proof found
% 23.54/23.61 % SZS status Theorem for theBenchmark.p
% 23.54/23.61 % SZS output start Proof
% See solution above
% 23.54/23.62 % Total time : 23.081000 s
% 23.54/23.62 % SZS output end Proof
% 23.54/23.62 % Total time : 23.085000 s
%------------------------------------------------------------------------------