TSTP Solution File: KLE010+4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE010+4 : 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 : n029.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 1.05s 1.12s
% Output : CNFRefutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 30
% Syntax : Number of formulae : 241 ( 135 unt; 11 typ; 0 def)
% Number of atoms : 366 ( 236 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 260 ( 124 ~; 109 |; 16 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 7 ( 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 : 212 ( 14 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/sandbox2/benchmark/Axioms/KLE001+1.ax',test_3) ).
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(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(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_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(test_4,axiom,
! [X4] :
( ~ test(X4)
=> c(X4) = zero ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_4) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(test_deMorgan1,axiom,
! [X4,X5] :
( ( test(X4)
& test(X5) )
=> c(addition(X4,X5)) = multiplication(c(X4),c(X5)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+2.ax',test_deMorgan1) ).
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(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(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).
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(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,plain,
! [X11] : addition(X11,zero) = X11,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_21,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_22,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_23,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_24,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_25,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_27,plain,
! [X24] : multiplication(X24,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
fof(c_0_28,plain,
! [X25] : multiplication(zero,X25) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_29,plain,
( multiplication(X1,X2) = zero
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_23]) ).
fof(c_0_31,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_24])])]) ).
fof(c_0_32,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_33,plain,
( complement(X2,X1)
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero
| addition(X1,X2) != one ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_34,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_35,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,plain,
( multiplication(c(X1),X1) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_38,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,plain,
( test(X2)
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,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_33,c_0_34]),c_0_35]),c_0_36])])]) ).
cnf(c_0_41,negated_conjecture,
zero = multiplication(c(esk3_0),esk3_0),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
fof(c_0_42,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_43,plain,
( c(X1) = X2
| ~ complement(X1,X2)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_44,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_33,c_0_25]),c_0_36]),c_0_35])])]) ).
cnf(c_0_45,plain,
test(zero),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,plain,
( multiplication(c(X1),X1) = multiplication(c(esk3_0),esk3_0)
| ~ test(X1) ),
inference(rw,[status(thm)],[c_0_37,c_0_41]) ).
cnf(c_0_47,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_48,plain,
! [X4] :
( ~ test(X4)
=> c(X4) = zero ),
inference(fof_simplification,[status(thm)],[test_4]) ).
cnf(c_0_49,plain,
( c(multiplication(X1,X2)) = addition(c(X1),c(X2))
| ~ test(X1)
| ~ test(X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_50,plain,
! [X12] : addition(X12,X12) = X12,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_51,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_52,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_53,plain,
one = c(zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
cnf(c_0_54,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_55,negated_conjecture,
multiplication(c(esk3_0),esk3_0) = multiplication(c(esk2_0),esk2_0),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
fof(c_0_56,plain,
! [X36] :
( test(X36)
| c(X36) = zero ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])]) ).
fof(c_0_57,plain,
! [X13,X14,X15] : multiplication(X13,multiplication(X14,X15)) = multiplication(multiplication(X13,X14),X15),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_58,negated_conjecture,
( c(multiplication(X1,esk2_0)) = addition(c(X1),c(esk2_0))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_47]) ).
cnf(c_0_59,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_60,plain,
( c(addition(X1,X2)) = multiplication(c(X1),c(X2))
| ~ test(X1)
| ~ test(X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_61,plain,
( addition(X1,X2) = c(zero)
| ~ complement(X2,X1) ),
inference(rw,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_62,plain,
( multiplication(X1,X2) = multiplication(c(esk2_0),esk2_0)
| ~ complement(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_41]),c_0_55]) ).
cnf(c_0_63,plain,
( test(X1)
| c(X1) = zero ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_64,plain,
( test(c(X1))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_30]) ).
cnf(c_0_65,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_66,negated_conjecture,
c(multiplication(esk2_0,esk2_0)) = c(esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_47]),c_0_59]) ).
cnf(c_0_67,negated_conjecture,
( c(addition(X1,esk3_0)) = multiplication(c(X1),c(esk3_0))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_38]) ).
cnf(c_0_68,plain,
( addition(X1,X2) = c(multiplication(c(esk3_0),esk3_0))
| ~ complement(X2,X1) ),
inference(rw,[status(thm)],[c_0_61,c_0_41]) ).
cnf(c_0_69,plain,
( multiplication(X1,c(X1)) = multiplication(c(esk2_0),esk2_0)
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_30]) ).
cnf(c_0_70,plain,
test(c(X1)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_63]),c_0_64]) ).
fof(c_0_71,plain,
! [X17] : multiplication(one,X17) = X17,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_72,plain,
multiplication(c(esk3_0),multiplication(esk3_0,X1)) = multiplication(c(esk3_0),esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_41]),c_0_65]),c_0_41]) ).
cnf(c_0_73,negated_conjecture,
( complement(multiplication(esk2_0,esk2_0),c(esk2_0))
| ~ test(multiplication(esk2_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_30,c_0_66]) ).
cnf(c_0_74,plain,
( c(X1) = multiplication(c(esk3_0),esk3_0)
| test(X1) ),
inference(rw,[status(thm)],[c_0_63,c_0_41]) ).
cnf(c_0_75,negated_conjecture,
c(addition(esk2_0,esk3_0)) = multiplication(c(esk2_0),c(esk3_0)),
inference(spm,[status(thm)],[c_0_67,c_0_47]) ).
cnf(c_0_76,plain,
( addition(X1,X2) = c(multiplication(c(esk2_0),esk2_0))
| ~ complement(X2,X1) ),
inference(rw,[status(thm)],[c_0_68,c_0_55]) ).
cnf(c_0_77,negated_conjecture,
multiplication(c(esk2_0),esk2_0) = multiplication(esk2_0,c(esk2_0)),
inference(spm,[status(thm)],[c_0_69,c_0_47]) ).
cnf(c_0_78,negated_conjecture,
c(multiplication(c(X1),esk2_0)) = addition(c(esk2_0),c(c(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_70]),c_0_26]) ).
cnf(c_0_79,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_80,plain,
test(multiplication(c(esk3_0),esk3_0)),
inference(rw,[status(thm)],[c_0_45,c_0_41]) ).
cnf(c_0_81,plain,
multiplication(c(esk3_0),multiplication(esk3_0,X1)) = multiplication(c(esk2_0),esk2_0),
inference(rw,[status(thm)],[c_0_72,c_0_55]) ).
cnf(c_0_82,negated_conjecture,
( multiplication(c(esk2_0),esk2_0) = multiplication(esk2_0,multiplication(esk2_0,c(esk2_0)))
| ~ test(multiplication(esk2_0,esk2_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_73]),c_0_65]) ).
cnf(c_0_83,plain,
( c(X1) = multiplication(c(esk2_0),esk2_0)
| test(X1) ),
inference(rw,[status(thm)],[c_0_74,c_0_55]) ).
cnf(c_0_84,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_31]) ).
fof(c_0_85,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_86,negated_conjecture,
( complement(addition(esk2_0,esk3_0),multiplication(c(esk2_0),c(esk3_0)))
| ~ test(addition(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_30,c_0_75]) ).
cnf(c_0_87,plain,
( addition(X1,X2) = c(multiplication(esk2_0,c(esk2_0)))
| ~ complement(X2,X1) ),
inference(rw,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_88,negated_conjecture,
c(multiplication(esk2_0,c(esk2_0))) = addition(c(esk2_0),c(c(esk2_0))),
inference(spm,[status(thm)],[c_0_78,c_0_77]) ).
cnf(c_0_89,plain,
multiplication(c(zero),X1) = X1,
inference(rw,[status(thm)],[c_0_79,c_0_53]) ).
cnf(c_0_90,plain,
test(multiplication(c(esk2_0),esk2_0)),
inference(rw,[status(thm)],[c_0_80,c_0_55]) ).
cnf(c_0_91,plain,
multiplication(c(esk2_0),multiplication(esk2_0,X1)) = multiplication(c(esk2_0),esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_81]),c_0_65]),c_0_65]),c_0_72]),c_0_55]) ).
cnf(c_0_92,negated_conjecture,
( multiplication(c(esk2_0),esk2_0) = multiplication(esk2_0,multiplication(esk2_0,c(esk2_0)))
| multiplication(c(esk2_0),esk2_0) = c(esk2_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_66]) ).
cnf(c_0_93,plain,
multiplication(X1,multiplication(c(esk3_0),esk3_0)) = multiplication(c(esk3_0),esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_41]),c_0_41]) ).
cnf(c_0_94,plain,
c(one) = zero,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_40]),c_0_63]) ).
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_84,c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_96,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_97,negated_conjecture,
( zero = multiplication(addition(esk2_0,esk3_0),multiplication(c(esk2_0),c(esk3_0)))
| ~ test(addition(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_54,c_0_86]) ).
cnf(c_0_98,plain,
( addition(X1,X2) = addition(c(esk2_0),c(c(esk2_0)))
| ~ complement(X2,X1) ),
inference(rw,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_99,negated_conjecture,
multiplication(c(multiplication(c(esk3_0),esk3_0)),X1) = X1,
inference(spm,[status(thm)],[c_0_89,c_0_41]) ).
cnf(c_0_100,negated_conjecture,
addition(c(esk2_0),c(multiplication(c(esk2_0),esk2_0))) = c(multiplication(c(esk2_0),esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_90]),c_0_65]),c_0_91]),c_0_26]) ).
cnf(c_0_101,negated_conjecture,
( multiplication(c(esk2_0),esk2_0) = c(esk2_0)
| multiplication(esk2_0,multiplication(esk2_0,c(esk2_0))) != c(esk2_0) ),
inference(ef,[status(thm)],[c_0_92]) ).
cnf(c_0_102,plain,
multiplication(X1,multiplication(c(esk2_0),esk2_0)) = multiplication(c(esk2_0),esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_55]),c_0_55]) ).
cnf(c_0_103,plain,
c(c(zero)) = zero,
inference(rw,[status(thm)],[c_0_94,c_0_53]) ).
cnf(c_0_104,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),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)))),one) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_105,negated_conjecture,
( multiplication(c(esk3_0),esk3_0) = multiplication(addition(esk2_0,esk3_0),multiplication(c(esk2_0),c(esk3_0)))
| ~ test(addition(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_97,c_0_41]) ).
fof(c_0_106,plain,
! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_107,plain,
( addition(X1,c(X1)) = addition(c(esk2_0),c(c(esk2_0)))
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_30]),c_0_26]) ).
cnf(c_0_108,negated_conjecture,
multiplication(c(multiplication(c(esk2_0),esk2_0)),X1) = X1,
inference(spm,[status(thm)],[c_0_99,c_0_55]) ).
cnf(c_0_109,negated_conjecture,
( addition(c(esk2_0),c(c(esk2_0))) = c(c(esk2_0))
| multiplication(esk2_0,multiplication(esk2_0,c(esk2_0))) != c(esk2_0) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_110,plain,
multiplication(X1,multiplication(esk2_0,c(esk2_0))) = multiplication(esk2_0,c(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_77]),c_0_77]) ).
cnf(c_0_111,plain,
c(c(multiplication(c(esk3_0),esk3_0))) = multiplication(c(esk3_0),esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_41]),c_0_41]) ).
cnf(c_0_112,negated_conjecture,
( ~ leq(c(zero),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)))),c(zero)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_53]),c_0_53]) ).
cnf(c_0_113,negated_conjecture,
( multiplication(c(esk3_0),esk3_0) = multiplication(addition(esk2_0,esk3_0),multiplication(c(esk2_0),c(esk3_0)))
| multiplication(c(esk3_0),esk3_0) = multiplication(c(esk2_0),c(esk3_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_74]),c_0_75]) ).
cnf(c_0_114,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_115,negated_conjecture,
addition(c(esk2_0),c(c(esk2_0))) = addition(esk3_0,c(esk3_0)),
inference(spm,[status(thm)],[c_0_107,c_0_38]) ).
cnf(c_0_116,negated_conjecture,
( c(multiplication(X1,esk3_0)) = addition(c(X1),c(esk3_0))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_38]) ).
cnf(c_0_117,negated_conjecture,
multiplication(addition(c(esk2_0),c(c(esk2_0))),X1) = X1,
inference(rw,[status(thm)],[c_0_108,c_0_78]) ).
cnf(c_0_118,negated_conjecture,
( addition(c(esk2_0),c(c(esk2_0))) = c(c(esk2_0))
| multiplication(esk2_0,c(esk2_0)) != c(esk2_0) ),
inference(rw,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_119,plain,
c(c(multiplication(c(esk2_0),esk2_0))) = multiplication(c(esk2_0),esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_55]),c_0_55]) ).
cnf(c_0_120,negated_conjecture,
( ~ leq(c(multiplication(c(esk3_0),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)))),c(multiplication(c(esk3_0),esk3_0))) ),
inference(spm,[status(thm)],[c_0_112,c_0_41]) ).
cnf(c_0_121,negated_conjecture,
( multiplication(c(esk3_0),esk3_0) = multiplication(c(esk2_0),c(esk3_0))
| multiplication(addition(esk2_0,esk3_0),multiplication(c(esk2_0),c(esk3_0))) != multiplication(c(esk2_0),c(esk3_0)) ),
inference(ef,[status(thm)],[c_0_113]) ).
cnf(c_0_122,plain,
addition(multiplication(c(esk3_0),esk3_0),X1) = X1,
inference(rw,[status(thm)],[c_0_34,c_0_41]) ).
cnf(c_0_123,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_114,c_0_59]) ).
cnf(c_0_124,plain,
( addition(X1,c(X1)) = addition(esk3_0,c(esk3_0))
| ~ test(X1) ),
inference(rw,[status(thm)],[c_0_107,c_0_115]) ).
cnf(c_0_125,negated_conjecture,
c(multiplication(c(X1),esk3_0)) = addition(c(esk3_0),c(c(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_70]),c_0_26]) ).
cnf(c_0_126,negated_conjecture,
( multiplication(c(c(esk2_0)),X1) = X1
| multiplication(esk2_0,c(esk2_0)) != c(esk2_0) ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_127,negated_conjecture,
( c(c(c(esk2_0))) = c(esk2_0)
| multiplication(esk2_0,multiplication(esk2_0,c(esk2_0))) != c(esk2_0) ),
inference(spm,[status(thm)],[c_0_119,c_0_101]) ).
cnf(c_0_128,negated_conjecture,
( multiplication(addition(esk2_0,esk3_0),multiplication(c(esk2_0),c(esk3_0))) != multiplication(c(esk2_0),c(esk3_0))
| ~ leq(c(multiplication(c(esk2_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)))),c(multiplication(c(esk2_0),c(esk3_0)))) ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_129,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_26]),c_0_114]) ).
cnf(c_0_130,negated_conjecture,
( multiplication(c(esk2_0),esk2_0) = c(esk2_0)
| multiplication(esk2_0,c(esk2_0)) != c(esk2_0) ),
inference(rw,[status(thm)],[c_0_101,c_0_110]) ).
cnf(c_0_131,plain,
addition(multiplication(c(esk2_0),esk2_0),X1) = X1,
inference(rw,[status(thm)],[c_0_122,c_0_55]) ).
fof(c_0_132,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_133,negated_conjecture,
addition(c(esk3_0),c(multiplication(c(esk2_0),esk2_0))) = c(multiplication(c(esk2_0),esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_90]),c_0_65]),c_0_91]),c_0_26]) ).
cnf(c_0_134,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_123,c_0_26]) ).
cnf(c_0_135,negated_conjecture,
addition(esk3_0,c(esk3_0)) = addition(esk2_0,c(esk2_0)),
inference(spm,[status(thm)],[c_0_124,c_0_47]) ).
cnf(c_0_136,negated_conjecture,
( addition(c(esk3_0),c(c(c(esk2_0)))) = c(esk3_0)
| multiplication(esk2_0,c(esk2_0)) != c(esk2_0) ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_137,negated_conjecture,
( c(c(c(esk2_0))) = c(esk2_0)
| multiplication(esk2_0,c(esk2_0)) != c(esk2_0) ),
inference(rw,[status(thm)],[c_0_127,c_0_110]) ).
cnf(c_0_138,negated_conjecture,
( multiplication(addition(esk2_0,esk3_0),multiplication(c(esk2_0),c(esk3_0))) != multiplication(c(esk2_0),c(esk3_0))
| ~ leq(c(multiplication(c(esk2_0),c(esk3_0))),addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(c(esk2_0),c(esk3_0)),multiplication(addition(esk3_0,c(esk3_0)),esk2_0)))))
| ~ leq(addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(c(esk2_0),c(esk3_0)),multiplication(addition(esk3_0,c(esk3_0)),esk2_0)))),c(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(rw,[status(thm)],[c_0_128,c_0_129]),c_0_129]),c_0_129]),c_0_129]),c_0_129]),c_0_129]) ).
cnf(c_0_139,negated_conjecture,
( multiplication(c(esk2_0),X1) = multiplication(esk2_0,c(esk2_0))
| multiplication(esk2_0,c(esk2_0)) != c(esk2_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_130]),c_0_91]),c_0_77]) ).
cnf(c_0_140,plain,
addition(multiplication(esk2_0,c(esk2_0)),X1) = X1,
inference(rw,[status(thm)],[c_0_131,c_0_77]) ).
cnf(c_0_141,negated_conjecture,
multiplication(addition(esk3_0,c(esk3_0)),X1) = X1,
inference(rw,[status(thm)],[c_0_117,c_0_115]) ).
cnf(c_0_142,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_132]) ).
cnf(c_0_143,plain,
( c(multiplication(X1,c(X2))) = addition(c(X1),c(c(X2)))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_70]) ).
cnf(c_0_144,negated_conjecture,
addition(c(esk3_0),c(multiplication(esk2_0,c(esk2_0)))) = c(multiplication(esk2_0,c(esk2_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_77]),c_0_77]) ).
cnf(c_0_145,negated_conjecture,
addition(esk2_0,addition(c(esk2_0),c(esk3_0))) = addition(esk2_0,c(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_26]),c_0_114]) ).
cnf(c_0_146,negated_conjecture,
( addition(c(esk2_0),c(esk3_0)) = c(esk3_0)
| multiplication(esk2_0,c(esk2_0)) != c(esk2_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_26]) ).
cnf(c_0_147,negated_conjecture,
( c(addition(X1,esk2_0)) = multiplication(c(X1),c(esk2_0))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_47]) ).
cnf(c_0_148,negated_conjecture,
( multiplication(esk2_0,c(esk2_0)) != c(esk2_0)
| ~ leq(addition(c(esk2_0),c(c(esk2_0))),addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),multiplication(addition(esk3_0,c(esk3_0)),esk2_0))))
| ~ leq(addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),multiplication(addition(esk3_0,c(esk3_0)),esk2_0))),addition(c(esk2_0),c(c(esk2_0)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_110]),c_0_140]),c_0_140])]),c_0_88]),c_0_88]) ).
cnf(c_0_149,negated_conjecture,
multiplication(addition(esk2_0,c(esk2_0)),X1) = X1,
inference(rw,[status(thm)],[c_0_141,c_0_135]) ).
fof(c_0_150,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_151,negated_conjecture,
multiplication(esk3_0,c(esk3_0)) = multiplication(c(esk2_0),esk2_0),
inference(spm,[status(thm)],[c_0_69,c_0_38]) ).
cnf(c_0_152,plain,
multiplication(X1,c(zero)) = X1,
inference(rw,[status(thm)],[c_0_142,c_0_53]) ).
fof(c_0_153,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_154,negated_conjecture,
( addition(multiplication(c(esk2_0),c(esk3_0)),multiplication(X1,esk3_0)) = multiplication(addition(c(esk3_0),X1),esk3_0)
| multiplication(addition(esk2_0,esk3_0),multiplication(c(esk2_0),c(esk3_0))) != multiplication(c(esk2_0),c(esk3_0)) ),
inference(spm,[status(thm)],[c_0_96,c_0_121]) ).
cnf(c_0_155,negated_conjecture,
c(multiplication(esk2_0,c(X1))) = addition(c(esk2_0),c(c(X1))),
inference(spm,[status(thm)],[c_0_143,c_0_47]) ).
cnf(c_0_156,negated_conjecture,
addition(c(esk2_0),addition(c(esk3_0),c(c(esk2_0)))) = addition(c(esk2_0),c(c(esk2_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_144,c_0_88]),c_0_129]),c_0_88]) ).
cnf(c_0_157,plain,
multiplication(addition(esk2_0,X1),c(esk2_0)) = multiplication(X1,c(esk2_0)),
inference(spm,[status(thm)],[c_0_96,c_0_140]) ).
cnf(c_0_158,negated_conjecture,
( addition(esk2_0,c(esk3_0)) = addition(esk2_0,c(esk2_0))
| multiplication(esk2_0,c(esk2_0)) != c(esk2_0) ),
inference(spm,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_159,negated_conjecture,
multiplication(c(esk2_0),c(esk2_0)) = c(esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_47]),c_0_59]) ).
cnf(c_0_160,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_147,c_0_38]),c_0_26]),c_0_75]) ).
cnf(c_0_161,negated_conjecture,
( multiplication(esk2_0,c(esk2_0)) != c(esk2_0)
| ~ leq(addition(esk2_0,c(esk2_0)),addition(esk2_0,esk3_0))
| ~ leq(addition(esk2_0,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_148,c_0_115]),c_0_115]),c_0_135]),c_0_141]),c_0_26]),c_0_129]),c_0_96]),c_0_149]),c_0_141]),c_0_26]),c_0_129]),c_0_96]),c_0_149]),c_0_135]) ).
cnf(c_0_162,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_150]) ).
cnf(c_0_163,negated_conjecture,
addition(esk2_0,addition(esk3_0,c(esk2_0))) = addition(esk2_0,c(esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_135]),c_0_129]) ).
cnf(c_0_164,negated_conjecture,
multiplication(esk3_0,c(esk3_0)) = multiplication(esk2_0,c(esk2_0)),
inference(rw,[status(thm)],[c_0_151,c_0_77]) ).
cnf(c_0_165,negated_conjecture,
multiplication(esk2_0,multiplication(c(esk2_0),X1)) = multiplication(esk2_0,c(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_77]),c_0_65]),c_0_91]),c_0_77]) ).
cnf(c_0_166,negated_conjecture,
multiplication(X1,c(multiplication(c(esk3_0),esk3_0))) = X1,
inference(spm,[status(thm)],[c_0_152,c_0_41]) ).
cnf(c_0_167,negated_conjecture,
c(multiplication(esk3_0,esk2_0)) = addition(c(esk2_0),c(esk3_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_38]),c_0_26]) ).
cnf(c_0_168,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_153]) ).
cnf(c_0_169,negated_conjecture,
( addition(esk3_0,multiplication(c(esk2_0),c(esk3_0))) = esk3_0
| multiplication(addition(esk2_0,esk3_0),multiplication(c(esk2_0),c(esk3_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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_89]),c_0_26]),c_0_41]),c_0_55]),c_0_77]),c_0_155]),c_0_129]),c_0_156]),c_0_117]) ).
cnf(c_0_170,negated_conjecture,
( multiplication(c(esk2_0),c(esk3_0)) = c(esk2_0)
| multiplication(esk2_0,c(esk2_0)) != c(esk2_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_157]),c_0_159]),c_0_160]) ).
cnf(c_0_171,negated_conjecture,
( addition(esk2_0,c(esk2_0)) != addition(esk2_0,esk3_0)
| multiplication(esk2_0,c(esk2_0)) != c(esk2_0)
| ~ leq(addition(esk2_0,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(spm,[status(thm)],[c_0_161,c_0_162]),c_0_114]),c_0_26]),c_0_114]),c_0_163]),c_0_123]) ).
cnf(c_0_172,negated_conjecture,
multiplication(esk3_0,multiplication(c(esk3_0),X1)) = multiplication(esk2_0,c(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_164]),c_0_65]),c_0_165]) ).
cnf(c_0_173,plain,
addition(X1,multiplication(c(esk3_0),esk3_0)) = X1,
inference(rw,[status(thm)],[c_0_25,c_0_41]) ).
cnf(c_0_174,negated_conjecture,
multiplication(X1,c(multiplication(c(esk2_0),esk2_0))) = X1,
inference(spm,[status(thm)],[c_0_166,c_0_55]) ).
cnf(c_0_175,plain,
( multiplication(X1,X2) = multiplication(esk2_0,c(esk2_0))
| ~ complement(X1,X2) ),
inference(rw,[status(thm)],[c_0_62,c_0_77]) ).
cnf(c_0_176,negated_conjecture,
( complement(multiplication(esk3_0,esk2_0),addition(c(esk2_0),c(esk3_0)))
| ~ test(multiplication(esk3_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_30,c_0_167]) ).
cnf(c_0_177,plain,
multiplication(esk2_0,addition(c(esk2_0),X1)) = multiplication(esk2_0,X1),
inference(spm,[status(thm)],[c_0_168,c_0_140]) ).
cnf(c_0_178,negated_conjecture,
( addition(esk3_0,c(esk2_0)) = esk3_0
| multiplication(esk3_0,c(esk2_0)) != c(esk2_0)
| multiplication(esk2_0,c(esk2_0)) != c(esk2_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_157]) ).
cnf(c_0_179,negated_conjecture,
( addition(esk2_0,c(esk2_0)) != addition(esk2_0,esk3_0)
| multiplication(esk2_0,c(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(spm,[status(thm)],[c_0_171,c_0_162]),c_0_114]),c_0_129]),c_0_163]),c_0_123])]) ).
cnf(c_0_180,negated_conjecture,
multiplication(esk3_0,multiplication(c(esk2_0),c(esk3_0))) = multiplication(esk2_0,c(esk2_0)),
inference(spm,[status(thm)],[c_0_172,c_0_160]) ).
cnf(c_0_181,plain,
multiplication(addition(c(esk2_0),X1),esk2_0) = multiplication(X1,esk2_0),
inference(spm,[status(thm)],[c_0_96,c_0_131]) ).
cnf(c_0_182,plain,
addition(X1,multiplication(c(esk2_0),esk2_0)) = X1,
inference(rw,[status(thm)],[c_0_173,c_0_55]) ).
cnf(c_0_183,negated_conjecture,
multiplication(X1,addition(c(esk2_0),c(c(esk2_0)))) = X1,
inference(rw,[status(thm)],[c_0_174,c_0_78]) ).
cnf(c_0_184,negated_conjecture,
( multiplication(esk3_0,multiplication(esk2_0,c(esk3_0))) = multiplication(esk2_0,c(esk2_0))
| ~ test(multiplication(esk3_0,esk2_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_176]),c_0_65]),c_0_177]) ).
cnf(c_0_185,plain,
( c(X1) = multiplication(esk2_0,c(esk2_0))
| test(X1) ),
inference(rw,[status(thm)],[c_0_83,c_0_77]) ).
cnf(c_0_186,negated_conjecture,
( multiplication(esk3_0,c(esk2_0)) != c(esk2_0)
| multiplication(esk2_0,c(esk2_0)) != c(esk2_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_178]),c_0_179]) ).
cnf(c_0_187,negated_conjecture,
( multiplication(esk3_0,c(esk2_0)) = multiplication(esk2_0,c(esk2_0))
| multiplication(esk2_0,c(esk2_0)) != c(esk2_0) ),
inference(spm,[status(thm)],[c_0_180,c_0_170]) ).
cnf(c_0_188,negated_conjecture,
addition(c(esk2_0),c(multiplication(c(esk2_0),c(esk3_0)))) = addition(c(esk2_0),c(c(esk2_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_75]),c_0_165]),c_0_155]) ).
cnf(c_0_189,negated_conjecture,
multiplication(c(c(esk2_0)),esk2_0) = esk2_0,
inference(spm,[status(thm)],[c_0_181,c_0_117]) ).
cnf(c_0_190,plain,
multiplication(addition(X1,c(esk2_0)),esk2_0) = multiplication(X1,esk2_0),
inference(spm,[status(thm)],[c_0_96,c_0_182]) ).
cnf(c_0_191,negated_conjecture,
multiplication(X1,addition(esk3_0,c(esk3_0))) = X1,
inference(rw,[status(thm)],[c_0_183,c_0_115]) ).
cnf(c_0_192,negated_conjecture,
( multiplication(esk3_0,multiplication(esk2_0,c(esk3_0))) = multiplication(esk2_0,c(esk2_0))
| addition(c(esk2_0),c(esk3_0)) = multiplication(esk2_0,c(esk2_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_185]),c_0_167]) ).
cnf(c_0_193,plain,
addition(X1,multiplication(esk2_0,c(esk2_0))) = X1,
inference(rw,[status(thm)],[c_0_182,c_0_77]) ).
cnf(c_0_194,negated_conjecture,
multiplication(esk2_0,c(esk2_0)) != c(esk2_0),
inference(spm,[status(thm)],[c_0_186,c_0_187]) ).
cnf(c_0_195,negated_conjecture,
addition(c(esk2_0),c(multiplication(c(esk2_0),c(esk3_0)))) = addition(esk2_0,c(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_188,c_0_115]),c_0_135]) ).
cnf(c_0_196,negated_conjecture,
multiplication(c(multiplication(c(esk2_0),c(esk3_0))),esk2_0) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_188]),c_0_181]),c_0_189]) ).
cnf(c_0_197,negated_conjecture,
multiplication(esk2_0,c(c(esk2_0))) = esk2_0,
inference(spm,[status(thm)],[c_0_177,c_0_183]) ).
cnf(c_0_198,negated_conjecture,
( ~ leq(c(multiplication(c(esk2_0),esk2_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)))),c(multiplication(c(esk2_0),esk2_0))) ),
inference(spm,[status(thm)],[c_0_120,c_0_55]) ).
cnf(c_0_199,plain,
addition(multiplication(X1,esk2_0),multiplication(addition(X1,c(esk2_0)),X2)) = multiplication(addition(X1,c(esk2_0)),addition(esk2_0,X2)),
inference(spm,[status(thm)],[c_0_168,c_0_190]) ).
cnf(c_0_200,negated_conjecture,
multiplication(addition(esk3_0,c(esk2_0)),c(esk2_0)) = c(esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_163]),c_0_157]),c_0_159]) ).
cnf(c_0_201,negated_conjecture,
multiplication(X1,addition(esk2_0,c(esk2_0))) = X1,
inference(rw,[status(thm)],[c_0_191,c_0_135]) ).
cnf(c_0_202,plain,
addition(multiplication(X1,X2),multiplication(X3,multiplication(X4,X2))) = multiplication(addition(X1,multiplication(X3,X4)),X2),
inference(spm,[status(thm)],[c_0_96,c_0_65]) ).
cnf(c_0_203,negated_conjecture,
multiplication(esk3_0,multiplication(esk2_0,c(esk3_0))) = multiplication(esk2_0,c(esk2_0)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_192]),c_0_193]),c_0_194]) ).
cnf(c_0_204,negated_conjecture,
multiplication(esk2_0,esk2_0) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_195]),c_0_190]),c_0_196]) ).
cnf(c_0_205,plain,
addition(multiplication(X1,addition(X2,X3)),X4) = addition(multiplication(X1,X2),addition(multiplication(X1,X3),X4)),
inference(spm,[status(thm)],[c_0_114,c_0_168]) ).
cnf(c_0_206,negated_conjecture,
multiplication(esk2_0,addition(c(esk3_0),c(c(esk2_0)))) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_156]),c_0_177]),c_0_197]) ).
cnf(c_0_207,negated_conjecture,
( ~ leq(c(multiplication(c(esk2_0),esk2_0)),addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(c(esk2_0),c(esk3_0)),multiplication(addition(esk3_0,c(esk3_0)),esk2_0)))))
| ~ leq(addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(c(esk2_0),c(esk3_0)),multiplication(addition(esk3_0,c(esk3_0)),esk2_0)))),c(multiplication(c(esk2_0),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)],[c_0_198,c_0_129]),c_0_129]),c_0_129]),c_0_129]),c_0_129]),c_0_129]) ).
cnf(c_0_208,plain,
multiplication(esk2_0,addition(X1,c(esk2_0))) = multiplication(esk2_0,X1),
inference(spm,[status(thm)],[c_0_168,c_0_193]) ).
cnf(c_0_209,negated_conjecture,
addition(multiplication(esk3_0,esk2_0),c(esk2_0)) = addition(esk3_0,c(esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_200]),c_0_201]) ).
cnf(c_0_210,plain,
addition(multiplication(addition(X1,X2),X3),X4) = addition(multiplication(X1,X3),addition(multiplication(X2,X3),X4)),
inference(spm,[status(thm)],[c_0_114,c_0_96]) ).
cnf(c_0_211,negated_conjecture,
multiplication(addition(X1,multiplication(esk3_0,esk2_0)),c(esk3_0)) = multiplication(X1,c(esk3_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_203]),c_0_193]) ).
cnf(c_0_212,negated_conjecture,
addition(esk2_0,multiplication(X1,esk2_0)) = multiplication(addition(esk2_0,X1),esk2_0),
inference(spm,[status(thm)],[c_0_96,c_0_204]) ).
cnf(c_0_213,negated_conjecture,
addition(esk2_0,addition(multiplication(esk2_0,c(esk3_0)),X1)) = addition(esk2_0,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_206]),c_0_197]),c_0_129]) ).
cnf(c_0_214,negated_conjecture,
addition(esk2_0,multiplication(esk2_0,X1)) = multiplication(esk2_0,addition(esk2_0,X1)),
inference(spm,[status(thm)],[c_0_168,c_0_204]) ).
cnf(c_0_215,negated_conjecture,
( ~ leq(addition(c(esk2_0),c(c(esk2_0))),addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(c(esk2_0),c(esk3_0)),multiplication(addition(esk3_0,c(esk3_0)),esk2_0)))))
| ~ leq(addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(c(esk2_0),c(esk3_0)),multiplication(addition(esk3_0,c(esk3_0)),esk2_0)))),addition(c(esk2_0),c(c(esk2_0)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_207,c_0_78]),c_0_78]) ).
cnf(c_0_216,negated_conjecture,
multiplication(esk2_0,multiplication(esk3_0,esk2_0)) = multiplication(esk2_0,esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_209]),c_0_208]) ).
cnf(c_0_217,plain,
addition(multiplication(X1,X2),addition(multiplication(c(esk2_0),X2),multiplication(X1,esk2_0))) = multiplication(addition(X1,c(esk2_0)),addition(X2,esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_190]),c_0_210]) ).
cnf(c_0_218,negated_conjecture,
multiplication(addition(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))) = multiplication(esk2_0,c(esk3_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_212]),c_0_65]) ).
cnf(c_0_219,plain,
multiplication(c(esk2_0),multiplication(esk2_0,X1)) = multiplication(esk2_0,c(esk2_0)),
inference(rw,[status(thm)],[c_0_91,c_0_77]) ).
cnf(c_0_220,negated_conjecture,
multiplication(esk2_0,addition(esk2_0,c(esk3_0))) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_213]),c_0_59]),c_0_26]),c_0_214]) ).
cnf(c_0_221,negated_conjecture,
addition(esk2_0,addition(X1,multiplication(esk2_0,c(esk3_0)))) = addition(esk2_0,X1),
inference(spm,[status(thm)],[c_0_213,c_0_26]) ).
cnf(c_0_222,negated_conjecture,
( ~ leq(addition(esk2_0,c(esk2_0)),addition(esk2_0,addition(multiplication(esk2_0,esk3_0),c(esk2_0))))
| ~ leq(addition(esk2_0,addition(multiplication(esk2_0,esk3_0),c(esk2_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)],[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_215,c_0_115]),c_0_115]),c_0_135]),c_0_141]),c_0_26]),c_0_129]),c_0_168]),c_0_191]),c_0_129]),c_0_141]),c_0_26]),c_0_129]),c_0_168]),c_0_191]),c_0_129]),c_0_135]) ).
cnf(c_0_223,negated_conjecture,
multiplication(esk2_0,multiplication(addition(esk2_0,esk3_0),esk2_0)) = multiplication(esk2_0,addition(esk2_0,esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_216]),c_0_214]),c_0_212]) ).
cnf(c_0_224,negated_conjecture,
multiplication(addition(esk2_0,esk3_0),esk2_0) = 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_218]),c_0_219]),c_0_140]),c_0_114]),c_0_163]),c_0_26]),c_0_214]),c_0_220]),c_0_190]),c_0_204]),c_0_26]),c_0_210]),c_0_204]),c_0_221]),c_0_212]) ).
cnf(c_0_225,negated_conjecture,
( addition(esk2_0,addition(multiplication(esk2_0,esk3_0),c(esk2_0))) != addition(esk2_0,c(esk2_0))
| ~ leq(addition(esk2_0,c(esk2_0)),addition(esk2_0,addition(multiplication(esk2_0,esk3_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(spm,[status(thm)],[c_0_222,c_0_162]),c_0_114]),c_0_114]),c_0_134]),c_0_129]),c_0_123]) ).
cnf(c_0_226,negated_conjecture,
multiplication(esk2_0,addition(esk2_0,esk3_0)) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_223,c_0_224]),c_0_204]) ).
cnf(c_0_227,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(spm,[status(thm)],[c_0_225,c_0_162]),c_0_114]),c_0_129]),c_0_134]),c_0_123])]) ).
cnf(c_0_228,negated_conjecture,
addition(esk2_0,addition(multiplication(esk2_0,esk3_0),X1)) = addition(esk2_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_226]),c_0_204]) ).
cnf(c_0_229,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_227,c_0_228])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE010+4 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 12:00:56 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.46/0.58 start to proof: theBenchmark
% 1.05/1.12 % Version : CSE_E---1.5
% 1.05/1.12 % Problem : theBenchmark.p
% 1.05/1.12 % Proof found
% 1.05/1.12 % SZS status Theorem for theBenchmark.p
% 1.05/1.12 % SZS output start Proof
% See solution above
% 1.11/1.13 % Total time : 0.537000 s
% 1.11/1.13 % SZS output end Proof
% 1.11/1.13 % Total time : 0.541000 s
%------------------------------------------------------------------------------