TSTP Solution File: KLE014+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE014+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n018.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 05:25:38 EDT 2023
% Result : Theorem 33.15s 33.23s
% Output : CNFRefutation 33.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 28
% Syntax : Number of formulae : 326 ( 259 unt; 11 typ; 0 def)
% Number of atoms : 405 ( 282 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 153 ( 63 ~; 67 |; 14 &)
% ( 4 <=>; 5 =>; 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 : 315 ( 21 sgn; 63 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
addition: ( $i * $i ) > $i ).
tff(decl_23,type,
zero: $i ).
tff(decl_24,type,
multiplication: ( $i * $i ) > $i ).
tff(decl_25,type,
one: $i ).
tff(decl_26,type,
leq: ( $i * $i ) > $o ).
tff(decl_27,type,
test: $i > $o ).
tff(decl_28,type,
complement: ( $i * $i ) > $o ).
tff(decl_29,type,
c: $i > $i ).
tff(decl_30,type,
esk1_1: $i > $i ).
tff(decl_31,type,
esk2_0: $i ).
tff(decl_32,type,
esk3_0: $i ).
fof(test_3,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(goals,conjecture,
! [X4,X5] :
( ( test(X5)
& test(X4) )
=> ( leq(c(addition(X4,X5)),multiplication(c(X4),c(X5)))
& leq(multiplication(c(X4),c(X5)),c(addition(X4,X5))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(test_2,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( multiplication(X4,X5) = zero
& multiplication(X5,X4) = zero
& addition(X4,X5) = one ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(test_4,axiom,
! [X4] :
( ~ test(X4)
=> c(X4) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_4) ).
fof(c_0_17,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_18,negated_conjecture,
~ ! [X4,X5] :
( ( test(X5)
& test(X4) )
=> ( leq(c(addition(X4,X5)),multiplication(c(X4),c(X5)))
& leq(multiplication(c(X4),c(X5)),c(addition(X4,X5))) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_19,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_20,negated_conjecture,
( test(esk3_0)
& test(esk2_0)
& ( ~ leq(c(addition(esk2_0,esk3_0)),multiplication(c(esk2_0),c(esk3_0)))
| ~ leq(multiplication(c(esk2_0),c(esk3_0)),c(addition(esk2_0,esk3_0))) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
fof(c_0_21,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_22,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_23,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_24,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_25,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,negated_conjecture,
complement(esk3_0,c(esk3_0)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_27,plain,
! [X11] : addition(X11,zero) = X11,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_28,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_29,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_30,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
multiplication(esk3_0,c(esk3_0)) = zero,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_34,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_35,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_36,plain,
! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_37,plain,
! [X12] : addition(X12,X12) = X12,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_38,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_40,negated_conjecture,
multiplication(esk3_0,addition(X1,c(esk3_0))) = multiplication(esk3_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_41,negated_conjecture,
addition(esk3_0,c(esk3_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_26]),c_0_34]) ).
cnf(c_0_42,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,negated_conjecture,
complement(esk1_1(esk2_0),esk2_0),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
fof(c_0_46,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_47,negated_conjecture,
multiplication(esk3_0,esk3_0) = esk3_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_48,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_42]),c_0_34]) ).
cnf(c_0_49,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,negated_conjecture,
addition(esk2_0,esk1_1(esk2_0)) = one,
inference(spm,[status(thm)],[c_0_33,c_0_45]) ).
cnf(c_0_51,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_52,plain,
addition(multiplication(X1,X2),addition(multiplication(X1,X3),X4)) = addition(multiplication(X1,addition(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_43,c_0_30]) ).
cnf(c_0_53,negated_conjecture,
multiplication(esk3_0,addition(X1,one)) = multiplication(esk3_0,addition(X1,esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_47]),c_0_34]),c_0_48]) ).
cnf(c_0_54,negated_conjecture,
addition(esk2_0,one) = one,
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_55,plain,
( leq(multiplication(X1,X2),addition(multiplication(X1,X3),X4))
| addition(multiplication(X1,addition(X2,X3)),X4) != addition(multiplication(X1,X3),X4) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,negated_conjecture,
multiplication(esk3_0,addition(esk2_0,esk3_0)) = esk3_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_42]) ).
fof(c_0_57,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_58,negated_conjecture,
leq(multiplication(esk3_0,esk2_0),addition(esk3_0,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_47]),c_0_47])]) ).
cnf(c_0_59,plain,
( leq(X1,X2)
| addition(X2,X1) != X2 ),
inference(spm,[status(thm)],[c_0_51,c_0_34]) ).
cnf(c_0_60,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_61,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_62,negated_conjecture,
leq(multiplication(esk3_0,esk2_0),one),
inference(spm,[status(thm)],[c_0_58,c_0_41]) ).
fof(c_0_63,plain,
! [X13,X14,X15] : multiplication(X13,multiplication(X14,X15)) = multiplication(multiplication(X13,X14),X15),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_64,plain,
! [X17] : multiplication(one,X17) = X17,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_65,plain,
( leq(multiplication(X1,X2),multiplication(X3,X2))
| multiplication(addition(X3,X1),X2) != multiplication(X3,X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_66,negated_conjecture,
addition(one,multiplication(esk3_0,esk2_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_34]) ).
cnf(c_0_67,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_68,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_69,negated_conjecture,
complement(esk1_1(esk3_0),esk3_0),
inference(spm,[status(thm)],[c_0_38,c_0_23]) ).
cnf(c_0_70,negated_conjecture,
leq(multiplication(esk3_0,multiplication(esk2_0,X1)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),c_0_68]) ).
cnf(c_0_71,negated_conjecture,
addition(esk3_0,esk1_1(esk3_0)) = one,
inference(spm,[status(thm)],[c_0_33,c_0_69]) ).
cnf(c_0_72,negated_conjecture,
addition(X1,multiplication(esk3_0,multiplication(esk2_0,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_70]),c_0_34]) ).
cnf(c_0_73,negated_conjecture,
complement(esk2_0,c(esk2_0)),
inference(spm,[status(thm)],[c_0_22,c_0_39]) ).
cnf(c_0_74,plain,
( leq(multiplication(X1,X2),multiplication(X3,X2))
| multiplication(addition(X1,X3),X2) != multiplication(X3,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_60]) ).
cnf(c_0_75,negated_conjecture,
addition(esk3_0,one) = one,
inference(spm,[status(thm)],[c_0_49,c_0_71]) ).
cnf(c_0_76,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_68]),c_0_34]) ).
cnf(c_0_77,negated_conjecture,
multiplication(esk3_0,addition(one,multiplication(esk2_0,esk3_0))) = esk3_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_72]),c_0_34]) ).
cnf(c_0_78,negated_conjecture,
multiplication(esk3_0,multiplication(addition(esk2_0,esk3_0),X1)) = multiplication(esk3_0,X1),
inference(spm,[status(thm)],[c_0_67,c_0_56]) ).
cnf(c_0_79,negated_conjecture,
multiplication(addition(X1,esk3_0),c(esk3_0)) = multiplication(X1,c(esk3_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_31]),c_0_32]) ).
cnf(c_0_80,plain,
( multiplication(X1,X2) = zero
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_81,negated_conjecture,
multiplication(esk2_0,c(esk2_0)) = zero,
inference(spm,[status(thm)],[c_0_25,c_0_73]) ).
cnf(c_0_82,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_34]) ).
cnf(c_0_83,negated_conjecture,
leq(multiplication(esk3_0,X1),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_68]) ).
cnf(c_0_84,negated_conjecture,
addition(one,multiplication(esk2_0,esk3_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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_43]),c_0_34]),c_0_76]),c_0_54]),c_0_68]),c_0_34]),c_0_75]),c_0_75]),c_0_68]) ).
cnf(c_0_85,negated_conjecture,
multiplication(esk3_0,multiplication(esk2_0,c(esk3_0))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_31]) ).
cnf(c_0_86,negated_conjecture,
multiplication(c(esk2_0),esk2_0) = zero,
inference(spm,[status(thm)],[c_0_80,c_0_73]) ).
cnf(c_0_87,negated_conjecture,
multiplication(esk2_0,addition(c(esk2_0),X1)) = multiplication(esk2_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_81]),c_0_82]) ).
cnf(c_0_88,negated_conjecture,
addition(X1,multiplication(esk3_0,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_83]),c_0_34]) ).
cnf(c_0_89,plain,
( test(X2)
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_90,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_34,c_0_43]) ).
cnf(c_0_91,negated_conjecture,
leq(multiplication(esk2_0,multiplication(esk3_0,X1)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_84]),c_0_67]),c_0_68]) ).
cnf(c_0_92,negated_conjecture,
multiplication(esk3_0,addition(esk3_0,multiplication(esk2_0,c(esk3_0)))) = esk3_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_85]),c_0_32]),c_0_53]),c_0_34]) ).
cnf(c_0_93,negated_conjecture,
multiplication(addition(c(esk2_0),X1),esk2_0) = multiplication(X1,esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_86]),c_0_82]) ).
cnf(c_0_94,plain,
addition(multiplication(X1,X2),multiplication(X3,multiplication(X4,X2))) = multiplication(addition(X1,multiplication(X3,X4)),X2),
inference(spm,[status(thm)],[c_0_60,c_0_67]) ).
cnf(c_0_95,negated_conjecture,
multiplication(esk2_0,multiplication(esk3_0,c(esk2_0))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_81]) ).
cnf(c_0_96,negated_conjecture,
multiplication(addition(esk2_0,X1),c(esk2_0)) = multiplication(X1,c(esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_81]),c_0_82]) ).
cnf(c_0_97,negated_conjecture,
addition(esk2_0,c(esk2_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_73]),c_0_34]) ).
cnf(c_0_98,negated_conjecture,
multiplication(esk2_0,addition(X1,c(esk2_0))) = multiplication(esk2_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_81]),c_0_32]) ).
cnf(c_0_99,negated_conjecture,
test(c(esk2_0)),
inference(spm,[status(thm)],[c_0_89,c_0_73]) ).
cnf(c_0_100,negated_conjecture,
leq(multiplication(X1,esk2_0),addition(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_54]),c_0_42]) ).
cnf(c_0_101,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_90,c_0_44]) ).
cnf(c_0_102,negated_conjecture,
leq(multiplication(esk2_0,esk3_0),addition(esk3_0,multiplication(esk2_0,c(esk3_0)))),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_103,plain,
addition(multiplication(X1,X2),addition(X3,multiplication(X1,X4))) = addition(X3,multiplication(X1,addition(X4,X2))),
inference(spm,[status(thm)],[c_0_90,c_0_30]) ).
cnf(c_0_104,negated_conjecture,
test(c(esk3_0)),
inference(spm,[status(thm)],[c_0_89,c_0_26]) ).
cnf(c_0_105,negated_conjecture,
addition(multiplication(X1,esk2_0),multiplication(addition(c(esk2_0),X1),X2)) = multiplication(addition(c(esk2_0),X1),addition(esk2_0,X2)),
inference(spm,[status(thm)],[c_0_30,c_0_93]) ).
cnf(c_0_106,negated_conjecture,
multiplication(addition(X1,multiplication(esk2_0,esk3_0)),c(esk2_0)) = multiplication(X1,c(esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_32]) ).
cnf(c_0_107,negated_conjecture,
multiplication(c(esk2_0),c(esk2_0)) = c(esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_68]) ).
cnf(c_0_108,negated_conjecture,
multiplication(esk2_0,esk2_0) = esk2_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_97]),c_0_42]) ).
cnf(c_0_109,negated_conjecture,
multiplication(addition(esk3_0,X1),c(esk3_0)) = multiplication(X1,c(esk3_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_31]),c_0_82]) ).
cnf(c_0_110,negated_conjecture,
complement(c(esk2_0),c(c(esk2_0))),
inference(spm,[status(thm)],[c_0_22,c_0_99]) ).
cnf(c_0_111,negated_conjecture,
leq(multiplication(X1,esk2_0),addition(X2,X1)),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_112,negated_conjecture,
addition(esk3_0,multiplication(esk2_0,c(esk3_0))) = addition(esk2_0,esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_102]),c_0_103]),c_0_34]),c_0_41]),c_0_42]),c_0_34]) ).
cnf(c_0_113,negated_conjecture,
multiplication(c(esk3_0),esk3_0) = zero,
inference(spm,[status(thm)],[c_0_80,c_0_26]) ).
cnf(c_0_114,negated_conjecture,
complement(c(esk3_0),c(c(esk3_0))),
inference(spm,[status(thm)],[c_0_22,c_0_104]) ).
cnf(c_0_115,plain,
( leq(addition(X1,X2),X3)
| addition(X1,addition(X2,X3)) != X3 ),
inference(spm,[status(thm)],[c_0_51,c_0_43]) ).
cnf(c_0_116,negated_conjecture,
addition(multiplication(esk2_0,multiplication(esk3_0,esk2_0)),c(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_105,c_0_106]),c_0_67]),c_0_107]),c_0_34]),c_0_97]),c_0_42]) ).
cnf(c_0_117,negated_conjecture,
multiplication(esk2_0,multiplication(esk2_0,X1)) = multiplication(esk2_0,X1),
inference(spm,[status(thm)],[c_0_67,c_0_108]) ).
cnf(c_0_118,negated_conjecture,
multiplication(esk3_0,addition(c(esk3_0),X1)) = multiplication(esk3_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_82]) ).
cnf(c_0_119,negated_conjecture,
multiplication(c(esk3_0),c(esk3_0)) = c(esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_41]),c_0_68]) ).
cnf(c_0_120,negated_conjecture,
addition(c(esk2_0),c(c(esk2_0))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_110]),c_0_34]) ).
cnf(c_0_121,negated_conjecture,
leq(multiplication(esk2_0,multiplication(c(esk3_0),esk2_0)),addition(esk2_0,esk3_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_67]) ).
cnf(c_0_122,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_30,c_0_113]),c_0_82]) ).
cnf(c_0_123,negated_conjecture,
multiplication(c(esk3_0),addition(X1,esk3_0)) = multiplication(c(esk3_0),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_113]),c_0_32]) ).
cnf(c_0_124,negated_conjecture,
addition(c(esk3_0),c(c(esk3_0))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_114]),c_0_34]) ).
fof(c_0_125,plain,
! [X25] : multiplication(zero,X25) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_126,plain,
( leq(addition(X1,multiplication(X2,X3)),multiplication(X2,X4))
| addition(X1,multiplication(X2,addition(X3,X4))) != multiplication(X2,X4) ),
inference(spm,[status(thm)],[c_0_115,c_0_30]) ).
cnf(c_0_127,negated_conjecture,
addition(X1,addition(c(esk2_0),multiplication(esk2_0,X1))) = addition(X1,c(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_98]),c_0_43]),c_0_54]),c_0_68]) ).
cnf(c_0_128,negated_conjecture,
multiplication(esk2_0,multiplication(esk3_0,esk2_0)) = multiplication(esk2_0,esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_116]),c_0_98]),c_0_117]),c_0_117]) ).
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_43,c_0_34]),c_0_43]) ).
cnf(c_0_130,negated_conjecture,
addition(multiplication(esk3_0,X1),multiplication(X2,addition(c(esk3_0),X1))) = multiplication(addition(esk3_0,X2),addition(c(esk3_0),X1)),
inference(spm,[status(thm)],[c_0_60,c_0_118]) ).
cnf(c_0_131,negated_conjecture,
multiplication(c(esk2_0),addition(X1,esk2_0)) = multiplication(c(esk2_0),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_86]),c_0_32]) ).
cnf(c_0_132,negated_conjecture,
multiplication(addition(X1,c(esk3_0)),esk3_0) = multiplication(X1,esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_113]),c_0_32]) ).
cnf(c_0_133,negated_conjecture,
addition(multiplication(esk2_0,X1),multiplication(X2,addition(X1,c(esk2_0)))) = multiplication(addition(esk2_0,X2),addition(X1,c(esk2_0))),
inference(spm,[status(thm)],[c_0_60,c_0_98]) ).
cnf(c_0_134,negated_conjecture,
multiplication(c(esk3_0),addition(c(esk3_0),X1)) = multiplication(c(esk3_0),addition(X1,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_119]),c_0_48]) ).
cnf(c_0_135,negated_conjecture,
addition(one,c(esk2_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_120]),c_0_34]) ).
cnf(c_0_136,plain,
addition(multiplication(X1,multiplication(X2,X3)),multiplication(X4,X3)) = multiplication(addition(multiplication(X1,X2),X4),X3),
inference(spm,[status(thm)],[c_0_60,c_0_67]) ).
cnf(c_0_137,plain,
( leq(multiplication(X1,X2),multiplication(X1,X3))
| multiplication(X1,addition(X3,X2)) != multiplication(X1,X3) ),
inference(spm,[status(thm)],[c_0_59,c_0_30]) ).
cnf(c_0_138,negated_conjecture,
addition(esk2_0,addition(esk3_0,multiplication(esk2_0,multiplication(c(esk3_0),esk2_0)))) = addition(esk2_0,esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_121]),c_0_34]),c_0_43]) ).
cnf(c_0_139,negated_conjecture,
multiplication(c(esk3_0),multiplication(esk2_0,c(esk3_0))) = multiplication(c(esk3_0),esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_112]),c_0_123]) ).
cnf(c_0_140,negated_conjecture,
addition(one,c(esk3_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_124]),c_0_34]) ).
cnf(c_0_141,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_142,negated_conjecture,
( leq(addition(X1,multiplication(X2,esk3_0)),X2)
| addition(X1,X2) != X2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_75]),c_0_42]),c_0_42]),c_0_42]) ).
cnf(c_0_143,negated_conjecture,
addition(multiplication(esk2_0,esk3_0),addition(multiplication(esk3_0,esk2_0),c(esk2_0))) = addition(multiplication(esk3_0,esk2_0),c(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_34]),c_0_129]) ).
cnf(c_0_144,negated_conjecture,
addition(esk2_0,addition(X1,c(esk2_0))) = addition(X1,one),
inference(spm,[status(thm)],[c_0_129,c_0_97]) ).
cnf(c_0_145,negated_conjecture,
multiplication(addition(esk3_0,c(esk2_0)),addition(esk2_0,c(esk3_0))) = addition(multiplication(esk3_0,esk2_0),multiplication(c(esk2_0),c(esk3_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_34]) ).
cnf(c_0_146,negated_conjecture,
addition(multiplication(X1,esk3_0),multiplication(addition(X1,c(esk3_0)),X2)) = multiplication(addition(X1,c(esk3_0)),addition(esk3_0,X2)),
inference(spm,[status(thm)],[c_0_30,c_0_132]) ).
cnf(c_0_147,negated_conjecture,
multiplication(addition(esk2_0,c(esk3_0)),addition(c(esk2_0),c(esk3_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_133,c_0_134]),c_0_34]),c_0_135]),c_0_42]),c_0_34]),c_0_76]),c_0_54]),c_0_68]),c_0_34]) ).
cnf(c_0_148,negated_conjecture,
addition(esk3_0,addition(X1,c(esk3_0))) = addition(X1,one),
inference(spm,[status(thm)],[c_0_129,c_0_41]) ).
cnf(c_0_149,negated_conjecture,
multiplication(addition(multiplication(X1,esk3_0),X2),esk3_0) = multiplication(addition(X1,X2),esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_47]),c_0_60]) ).
cnf(c_0_150,negated_conjecture,
addition(multiplication(esk2_0,esk3_0),multiplication(esk3_0,esk2_0)) = multiplication(esk3_0,esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_128]),c_0_34]),c_0_54]),c_0_68]) ).
cnf(c_0_151,negated_conjecture,
leq(multiplication(X1,c(esk2_0)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_135]),c_0_42]) ).
cnf(c_0_152,negated_conjecture,
multiplication(addition(esk3_0,multiplication(esk2_0,multiplication(c(esk3_0),esk2_0))),c(esk2_0)) = multiplication(esk3_0,c(esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_138]),c_0_96]) ).
cnf(c_0_153,negated_conjecture,
multiplication(addition(X1,multiplication(X2,esk2_0)),esk2_0) = multiplication(addition(X1,X2),esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_108]),c_0_60]) ).
cnf(c_0_154,negated_conjecture,
addition(multiplication(esk2_0,c(esk3_0)),multiplication(c(esk3_0),esk2_0)) = multiplication(esk2_0,c(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_139]),c_0_34]),c_0_140]),c_0_68]) ).
cnf(c_0_155,negated_conjecture,
multiplication(esk2_0,multiplication(esk3_0,multiplication(c(esk2_0),X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_95]),c_0_141]),c_0_67]) ).
cnf(c_0_156,negated_conjecture,
multiplication(esk2_0,addition(X1,one)) = multiplication(esk2_0,addition(X1,esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_108]),c_0_34]),c_0_48]) ).
cnf(c_0_157,negated_conjecture,
leq(esk3_0,addition(multiplication(esk3_0,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_142,c_0_143]),c_0_60]),c_0_144]),c_0_34]),c_0_66]),c_0_68]) ).
cnf(c_0_158,negated_conjecture,
addition(esk3_0,addition(multiplication(esk3_0,esk2_0),c(esk2_0))) = addition(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(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_48,c_0_145]),c_0_43]),c_0_43]),c_0_34]),c_0_140]),c_0_54]),c_0_42]),c_0_129]),c_0_48]),c_0_34]),c_0_140]),c_0_42]) ).
cnf(c_0_159,negated_conjecture,
addition(multiplication(esk2_0,esk3_0),c(esk3_0)) = addition(esk2_0,c(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_148]),c_0_34]),c_0_135]),c_0_42]) ).
cnf(c_0_160,negated_conjecture,
multiplication(esk3_0,multiplication(esk2_0,esk3_0)) = multiplication(esk2_0,esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_67]),c_0_76]),c_0_75]),c_0_68]) ).
cnf(c_0_161,negated_conjecture,
leq(multiplication(esk3_0,c(esk2_0)),addition(esk3_0,multiplication(esk2_0,multiplication(c(esk3_0),esk2_0)))),
inference(spm,[status(thm)],[c_0_151,c_0_152]) ).
cnf(c_0_162,negated_conjecture,
multiplication(esk2_0,multiplication(c(esk3_0),esk2_0)) = multiplication(c(esk3_0),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_153,c_0_154]),c_0_67]),c_0_34]),c_0_76]),c_0_54]),c_0_68]) ).
cnf(c_0_163,negated_conjecture,
multiplication(esk2_0,addition(esk2_0,multiplication(esk3_0,multiplication(c(esk2_0),X1)))) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_155]),c_0_32]),c_0_156]),c_0_34]) ).
cnf(c_0_164,negated_conjecture,
multiplication(c(esk2_0),multiplication(esk2_0,X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_86]),c_0_141]) ).
cnf(c_0_165,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_61,c_0_157]),c_0_158]) ).
cnf(c_0_166,negated_conjecture,
multiplication(esk3_0,esk2_0) = multiplication(esk2_0,esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_159]),c_0_40]),c_0_160]) ).
cnf(c_0_167,negated_conjecture,
leq(multiplication(esk3_0,c(esk2_0)),addition(esk3_0,multiplication(c(esk3_0),esk2_0))),
inference(spm,[status(thm)],[c_0_161,c_0_162]) ).
cnf(c_0_168,negated_conjecture,
multiplication(esk2_0,addition(esk2_0,multiplication(esk3_0,c(esk2_0)))) = esk2_0,
inference(spm,[status(thm)],[c_0_163,c_0_42]) ).
cnf(c_0_169,negated_conjecture,
multiplication(c(esk2_0),addition(multiplication(esk2_0,X1),X2)) = multiplication(c(esk2_0),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_164]),c_0_82]) ).
cnf(c_0_170,negated_conjecture,
addition(multiplication(esk2_0,esk3_0),c(esk2_0)) = addition(esk3_0,c(esk2_0)),
inference(rw,[status(thm)],[c_0_165,c_0_166]) ).
cnf(c_0_171,negated_conjecture,
addition(esk3_0,addition(multiplication(esk3_0,c(esk2_0)),multiplication(c(esk3_0),esk2_0))) = addition(esk3_0,multiplication(c(esk3_0),esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_167]),c_0_129]) ).
cnf(c_0_172,plain,
( complement(X2,X1)
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero
| addition(X1,X2) != one ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_173,negated_conjecture,
leq(multiplication(esk3_0,esk2_0),addition(esk2_0,multiplication(esk3_0,c(esk2_0)))),
inference(spm,[status(thm)],[c_0_70,c_0_168]) ).
cnf(c_0_174,negated_conjecture,
addition(multiplication(c(esk3_0),X1),multiplication(X2,addition(esk3_0,X1))) = multiplication(addition(c(esk3_0),X2),addition(esk3_0,X1)),
inference(spm,[status(thm)],[c_0_60,c_0_122]) ).
cnf(c_0_175,negated_conjecture,
multiplication(c(esk2_0),addition(esk3_0,c(esk2_0))) = c(esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_107]) ).
cnf(c_0_176,negated_conjecture,
multiplication(addition(multiplication(esk3_0,c(esk2_0)),multiplication(c(esk3_0),esk2_0)),c(esk3_0)) = multiplication(c(esk3_0),esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_171]),c_0_109]),c_0_67]),c_0_139]) ).
cnf(c_0_177,plain,
( complement(X1,addition(X2,X3))
| addition(X2,addition(X3,X1)) != one
| multiplication(X1,addition(X2,X3)) != zero
| multiplication(addition(X2,X3),X1) != zero ),
inference(spm,[status(thm)],[c_0_172,c_0_43]) ).
cnf(c_0_178,negated_conjecture,
multiplication(c(esk2_0),addition(esk2_0,X1)) = multiplication(c(esk2_0),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_86]),c_0_82]) ).
cnf(c_0_179,negated_conjecture,
addition(esk2_0,multiplication(esk3_0,c(esk2_0))) = addition(esk2_0,esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_173]),c_0_103]),c_0_34]),c_0_97]),c_0_42]) ).
cnf(c_0_180,negated_conjecture,
multiplication(addition(c(esk2_0),c(esk3_0)),addition(esk3_0,c(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(spm,[status(thm)],[c_0_174,c_0_175]),c_0_34]),c_0_76]),c_0_34]),c_0_140]),c_0_68]),c_0_34]) ).
cnf(c_0_181,negated_conjecture,
multiplication(esk3_0,multiplication(esk3_0,X1)) = multiplication(esk3_0,X1),
inference(spm,[status(thm)],[c_0_67,c_0_47]) ).
cnf(c_0_182,negated_conjecture,
leq(multiplication(esk3_0,multiplication(c(esk2_0),c(esk3_0))),multiplication(c(esk3_0),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(spm,[status(thm)],[c_0_74,c_0_176]),c_0_67]),c_0_67]),c_0_139]),c_0_67]),c_0_139])]) ).
cnf(c_0_183,negated_conjecture,
multiplication(esk3_0,multiplication(c(esk3_0),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_31]),c_0_141]) ).
cnf(c_0_184,plain,
( complement(multiplication(X1,X2),addition(X3,multiplication(X1,X4)))
| multiplication(X1,multiplication(X2,addition(X3,multiplication(X1,X4)))) != zero
| multiplication(addition(X3,multiplication(X1,X4)),multiplication(X1,X2)) != zero
| addition(X3,multiplication(X1,addition(X4,X2))) != one ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_30]),c_0_67]) ).
cnf(c_0_185,negated_conjecture,
multiplication(addition(esk2_0,X1),multiplication(esk3_0,c(esk2_0))) = multiplication(X1,multiplication(esk3_0,c(esk2_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_95]),c_0_82]) ).
cnf(c_0_186,negated_conjecture,
multiplication(c(esk2_0),multiplication(esk3_0,c(esk2_0))) = multiplication(c(esk2_0),esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_179]),c_0_178]) ).
cnf(c_0_187,negated_conjecture,
addition(c(esk2_0),multiplication(c(esk3_0),esk2_0)) = addition(c(esk2_0),c(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_180]),c_0_34]),c_0_144]),c_0_75]),c_0_42]) ).
cnf(c_0_188,negated_conjecture,
multiplication(esk2_0,multiplication(c(esk2_0),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_81]),c_0_141]) ).
cnf(c_0_189,negated_conjecture,
multiplication(esk3_0,addition(X1,multiplication(esk3_0,X2))) = multiplication(esk3_0,addition(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_181]),c_0_30]) ).
cnf(c_0_190,negated_conjecture,
addition(multiplication(c(esk3_0),esk2_0),multiplication(esk3_0,multiplication(c(esk2_0),c(esk3_0)))) = multiplication(c(esk3_0),esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_182]),c_0_34]) ).
cnf(c_0_191,negated_conjecture,
multiplication(esk3_0,addition(multiplication(c(esk3_0),X1),X2)) = multiplication(esk3_0,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_183]),c_0_82]) ).
cnf(c_0_192,negated_conjecture,
( complement(multiplication(X1,c(esk3_0)),addition(X2,multiplication(X1,esk3_0)))
| multiplication(X1,multiplication(c(esk3_0),addition(X2,multiplication(X1,esk3_0)))) != zero
| multiplication(addition(X2,multiplication(X1,esk3_0)),multiplication(X1,c(esk3_0))) != zero
| addition(X2,X1) != one ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_41]),c_0_42]) ).
cnf(c_0_193,negated_conjecture,
multiplication(c(esk2_0),esk3_0) = multiplication(esk3_0,c(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_97]),c_0_68]),c_0_186]) ).
cnf(c_0_194,negated_conjecture,
multiplication(c(esk3_0),esk2_0) = multiplication(esk2_0,c(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_187]),c_0_87]),c_0_162]) ).
cnf(c_0_195,negated_conjecture,
multiplication(addition(esk2_0,X1),multiplication(c(esk2_0),X2)) = multiplication(X1,multiplication(c(esk2_0),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_188]),c_0_82]) ).
cnf(c_0_196,negated_conjecture,
multiplication(esk3_0,multiplication(c(esk2_0),c(esk3_0))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_190]),c_0_183]),c_0_191]) ).
cnf(c_0_197,negated_conjecture,
complement(multiplication(c(esk2_0),c(esk3_0)),addition(esk2_0,esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(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_192,c_0_97]),c_0_193]),c_0_179]),c_0_193]),c_0_179]),c_0_123]),c_0_194]),c_0_164]),c_0_193]),c_0_179]),c_0_195]),c_0_196])]) ).
cnf(c_0_198,negated_conjecture,
multiplication(addition(X1,one),esk2_0) = multiplication(addition(esk2_0,X1),esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_108]),c_0_76]) ).
cnf(c_0_199,negated_conjecture,
test(addition(esk2_0,esk3_0)),
inference(spm,[status(thm)],[c_0_89,c_0_197]) ).
cnf(c_0_200,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_51,c_0_49]) ).
cnf(c_0_201,negated_conjecture,
addition(esk3_0,multiplication(esk2_0,addition(esk2_0,c(esk3_0)))) = addition(esk2_0,esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_156]),c_0_42]),c_0_34]),c_0_34]),c_0_34]),c_0_140]),c_0_42]) ).
cnf(c_0_202,negated_conjecture,
multiplication(addition(esk2_0,esk3_0),esk2_0) = esk2_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_75]),c_0_68]) ).
cnf(c_0_203,negated_conjecture,
complement(addition(esk2_0,esk3_0),c(addition(esk2_0,esk3_0))),
inference(spm,[status(thm)],[c_0_22,c_0_199]) ).
cnf(c_0_204,plain,
leq(X1,addition(X2,addition(X3,X1))),
inference(spm,[status(thm)],[c_0_200,c_0_90]) ).
cnf(c_0_205,negated_conjecture,
multiplication(c(esk3_0),multiplication(esk2_0,addition(esk2_0,c(esk3_0)))) = multiplication(c(esk3_0),esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_201]),c_0_123]) ).
cnf(c_0_206,negated_conjecture,
addition(esk2_0,multiplication(addition(esk2_0,esk3_0),X1)) = multiplication(addition(esk2_0,esk3_0),addition(esk2_0,X1)),
inference(spm,[status(thm)],[c_0_30,c_0_202]) ).
cnf(c_0_207,negated_conjecture,
multiplication(addition(esk2_0,esk3_0),c(addition(esk2_0,esk3_0))) = zero,
inference(spm,[status(thm)],[c_0_25,c_0_203]) ).
cnf(c_0_208,negated_conjecture,
leq(multiplication(esk2_0,c(esk3_0)),addition(X1,addition(esk2_0,esk3_0))),
inference(spm,[status(thm)],[c_0_204,c_0_112]) ).
cnf(c_0_209,negated_conjecture,
addition(multiplication(c(esk3_0),esk2_0),multiplication(esk2_0,addition(esk2_0,c(esk3_0)))) = multiplication(esk2_0,addition(esk2_0,c(esk3_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_205]),c_0_34]),c_0_140]),c_0_68]),c_0_34]) ).
cnf(c_0_210,plain,
( leq(multiplication(X1,X2),multiplication(X1,X3))
| multiplication(X1,addition(X2,X3)) != multiplication(X1,X3) ),
inference(spm,[status(thm)],[c_0_51,c_0_30]) ).
cnf(c_0_211,negated_conjecture,
multiplication(addition(esk2_0,esk3_0),addition(esk2_0,c(addition(esk2_0,esk3_0)))) = esk2_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_207]),c_0_32]) ).
cnf(c_0_212,negated_conjecture,
multiplication(esk3_0,addition(X1,addition(c(esk3_0),X2))) = multiplication(esk3_0,addition(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_118]),c_0_30]) ).
cnf(c_0_213,negated_conjecture,
addition(esk3_0,addition(c(esk3_0),X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_43,c_0_41]) ).
cnf(c_0_214,negated_conjecture,
leq(multiplication(esk2_0,c(esk3_0)),addition(esk2_0,addition(esk3_0,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_34]),c_0_43]) ).
cnf(c_0_215,negated_conjecture,
leq(addition(multiplication(esk2_0,esk3_0),multiplication(c(esk3_0),esk2_0)),multiplication(esk2_0,addition(esk2_0,c(esk3_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_209]),c_0_67]),c_0_132]),c_0_117]),c_0_34]) ).
cnf(c_0_216,negated_conjecture,
leq(multiplication(X1,esk2_0),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_210,c_0_54]),c_0_42]) ).
cnf(c_0_217,negated_conjecture,
multiplication(esk3_0,addition(esk2_0,c(addition(esk2_0,esk3_0)))) = multiplication(esk2_0,esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_211]),c_0_166]) ).
cnf(c_0_218,negated_conjecture,
addition(esk2_0,addition(one,X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_43,c_0_54]) ).
cnf(c_0_219,negated_conjecture,
multiplication(esk3_0,addition(one,X1)) = multiplication(esk3_0,addition(esk3_0,X1)),
inference(spm,[status(thm)],[c_0_212,c_0_213]) ).
cnf(c_0_220,plain,
( leq(X1,addition(X2,X3))
| addition(X2,addition(X3,X1)) != addition(X2,X3) ),
inference(spm,[status(thm)],[c_0_59,c_0_43]) ).
cnf(c_0_221,negated_conjecture,
leq(multiplication(esk2_0,c(esk3_0)),one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_41]),c_0_54]) ).
cnf(c_0_222,plain,
addition(multiplication(X1,X2),addition(multiplication(X3,X2),X4)) = addition(multiplication(addition(X1,X3),X2),X4),
inference(spm,[status(thm)],[c_0_43,c_0_60]) ).
cnf(c_0_223,negated_conjecture,
addition(multiplication(esk3_0,X1),multiplication(X2,addition(X1,c(esk3_0)))) = multiplication(addition(esk3_0,X2),addition(X1,c(esk3_0))),
inference(spm,[status(thm)],[c_0_60,c_0_40]) ).
cnf(c_0_224,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_215]),c_0_43]),c_0_209]),c_0_30]),c_0_148]),c_0_54]),c_0_42]) ).
fof(c_0_225,plain,
! [X24] : multiplication(X24,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_226,negated_conjecture,
leq(multiplication(X1,multiplication(X2,esk2_0)),multiplication(X1,X2)),
inference(spm,[status(thm)],[c_0_216,c_0_67]) ).
cnf(c_0_227,negated_conjecture,
multiplication(esk3_0,addition(esk3_0,c(addition(esk2_0,esk3_0)))) = esk3_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_217]),c_0_76]),c_0_54]),c_0_68]),c_0_43]),c_0_34]),c_0_218]),c_0_219]) ).
cnf(c_0_228,negated_conjecture,
addition(esk3_0,multiplication(X1,addition(esk2_0,esk3_0))) = multiplication(addition(esk3_0,X1),addition(esk2_0,esk3_0)),
inference(spm,[status(thm)],[c_0_60,c_0_56]) ).
cnf(c_0_229,negated_conjecture,
multiplication(c(addition(esk2_0,esk3_0)),addition(esk2_0,esk3_0)) = zero,
inference(spm,[status(thm)],[c_0_80,c_0_203]) ).
cnf(c_0_230,negated_conjecture,
leq(multiplication(c(esk3_0),esk2_0),addition(X1,multiplication(esk2_0,c(esk3_0)))),
inference(spm,[status(thm)],[c_0_220,c_0_154]) ).
cnf(c_0_231,negated_conjecture,
addition(one,multiplication(esk2_0,c(esk3_0))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_221]),c_0_34]) ).
cnf(c_0_232,negated_conjecture,
addition(multiplication(addition(X1,esk2_0),esk2_0),X2) = addition(esk2_0,addition(multiplication(X1,esk2_0),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_222,c_0_108]),c_0_129]) ).
cnf(c_0_233,negated_conjecture,
addition(multiplication(addition(esk3_0,X1),X2),multiplication(X1,c(esk3_0))) = multiplication(addition(esk3_0,X1),addition(X2,c(esk3_0))),
inference(spm,[status(thm)],[c_0_30,c_0_109]) ).
cnf(c_0_234,negated_conjecture,
multiplication(addition(esk2_0,esk3_0),addition(esk2_0,c(esk3_0))) = 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_223,c_0_224]),c_0_34]),c_0_76]),c_0_75]),c_0_68]),c_0_34]) ).
cnf(c_0_235,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_225]) ).
cnf(c_0_236,plain,
addition(multiplication(X1,X2),addition(X3,multiplication(X4,X2))) = addition(X3,multiplication(addition(X4,X1),X2)),
inference(spm,[status(thm)],[c_0_90,c_0_60]) ).
cnf(c_0_237,negated_conjecture,
leq(multiplication(esk3_0,multiplication(addition(esk3_0,c(addition(esk2_0,esk3_0))),esk2_0)),esk3_0),
inference(spm,[status(thm)],[c_0_226,c_0_227]) ).
cnf(c_0_238,negated_conjecture,
multiplication(addition(esk3_0,c(addition(esk2_0,esk3_0))),addition(esk2_0,esk3_0)) = esk3_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_228,c_0_229]),c_0_32]) ).
cnf(c_0_239,negated_conjecture,
leq(multiplication(c(esk3_0),esk2_0),one),
inference(spm,[status(thm)],[c_0_230,c_0_231]) ).
cnf(c_0_240,negated_conjecture,
addition(esk2_0,addition(multiplication(esk3_0,esk2_0),multiplication(esk2_0,c(esk3_0)))) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_232,c_0_233]),c_0_34]),c_0_234]) ).
cnf(c_0_241,negated_conjecture,
multiplication(addition(multiplication(X1,esk2_0),X2),c(esk2_0)) = multiplication(X2,c(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_81]),c_0_235]),c_0_82]) ).
cnf(c_0_242,negated_conjecture,
multiplication(esk2_0,multiplication(addition(c(esk2_0),X1),X2)) = multiplication(esk2_0,multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_87]),c_0_67]) ).
cnf(c_0_243,negated_conjecture,
multiplication(addition(X1,one),esk3_0) = multiplication(addition(X1,esk3_0),esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_47]),c_0_34]),c_0_76]) ).
cnf(c_0_244,plain,
( leq(multiplication(X1,multiplication(X2,X3)),multiplication(X1,addition(X4,multiplication(X5,X3))))
| multiplication(X1,addition(X4,multiplication(addition(X5,X2),X3))) != multiplication(X1,addition(X4,multiplication(X5,X3))) ),
inference(spm,[status(thm)],[c_0_210,c_0_236]) ).
cnf(c_0_245,negated_conjecture,
multiplication(esk3_0,addition(esk3_0,multiplication(addition(esk3_0,c(addition(esk2_0,esk3_0))),esk2_0))) = esk3_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_237]),c_0_34]),c_0_48]),c_0_34]),c_0_219]) ).
cnf(c_0_246,negated_conjecture,
leq(multiplication(addition(esk3_0,c(addition(esk2_0,esk3_0))),esk2_0),esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_238]),c_0_202]) ).
cnf(c_0_247,negated_conjecture,
addition(one,multiplication(c(esk3_0),esk2_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_239]),c_0_34]) ).
cnf(c_0_248,negated_conjecture,
multiplication(esk2_0,multiplication(c(esk3_0),c(esk2_0))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_240]),c_0_81]),c_0_241]),c_0_67]) ).
cnf(c_0_249,negated_conjecture,
multiplication(esk2_0,multiplication(addition(esk3_0,c(esk2_0)),esk3_0)) = multiplication(esk2_0,esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_242,c_0_243]),c_0_34]),c_0_68]) ).
cnf(c_0_250,negated_conjecture,
leq(multiplication(esk3_0,multiplication(c(addition(esk2_0,esk3_0)),esk2_0)),esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244,c_0_245]),c_0_48]),c_0_54]),c_0_42]),c_0_47]),c_0_48]),c_0_54]),c_0_42]),c_0_47])]) ).
cnf(c_0_251,plain,
( leq(multiplication(X1,X2),addition(X3,multiplication(X4,X2)))
| addition(X3,multiplication(addition(X4,X1),X2)) != addition(X3,multiplication(X4,X2)) ),
inference(spm,[status(thm)],[c_0_220,c_0_60]) ).
cnf(c_0_252,negated_conjecture,
addition(esk3_0,multiplication(addition(esk3_0,c(addition(esk2_0,esk3_0))),esk2_0)) = esk3_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_246]),c_0_34]) ).
cnf(c_0_253,negated_conjecture,
leq(multiplication(c(esk3_0),multiplication(esk2_0,X1)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_247]),c_0_67]),c_0_68]) ).
cnf(c_0_254,negated_conjecture,
multiplication(esk2_0,addition(esk2_0,multiplication(c(esk3_0),c(esk2_0)))) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_248]),c_0_32]),c_0_156]),c_0_34]) ).
cnf(c_0_255,negated_conjecture,
addition(multiplication(X1,c(esk3_0)),multiplication(addition(esk3_0,X1),X2)) = multiplication(addition(esk3_0,X1),addition(c(esk3_0),X2)),
inference(spm,[status(thm)],[c_0_30,c_0_109]) ).
cnf(c_0_256,negated_conjecture,
multiplication(addition(esk3_0,c(esk2_0)),esk3_0) = esk3_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_249]),c_0_60]),c_0_43]),c_0_34]),c_0_97]),c_0_75]),c_0_68]),c_0_54]),c_0_68]) ).
cnf(c_0_257,negated_conjecture,
( leq(multiplication(c(esk3_0),X1),multiplication(esk3_0,X1))
| multiplication(esk3_0,X1) != X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_41]),c_0_68]) ).
cnf(c_0_258,negated_conjecture,
multiplication(esk3_0,addition(esk3_0,multiplication(c(addition(esk2_0,esk3_0)),esk2_0))) = esk3_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_250]),c_0_34]),c_0_48]),c_0_53]),c_0_34]) ).
cnf(c_0_259,negated_conjecture,
leq(multiplication(c(addition(esk2_0,esk3_0)),esk2_0),esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_251,c_0_252]),c_0_48]),c_0_54]),c_0_42]),c_0_48]),c_0_54]),c_0_42])]) ).
cnf(c_0_260,negated_conjecture,
leq(multiplication(c(esk3_0),esk2_0),addition(esk2_0,multiplication(c(esk3_0),c(esk2_0)))),
inference(spm,[status(thm)],[c_0_253,c_0_254]) ).
cnf(c_0_261,negated_conjecture,
addition(esk3_0,multiplication(c(esk2_0),c(esk3_0))) = addition(esk3_0,c(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_255,c_0_256]),c_0_34]),c_0_34]),c_0_41]),c_0_42]) ).
cnf(c_0_262,negated_conjecture,
( leq(multiplication(c(esk3_0),multiplication(c(addition(esk2_0,esk3_0)),esk2_0)),esk3_0)
| addition(esk3_0,multiplication(c(addition(esk2_0,esk3_0)),esk2_0)) != esk3_0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_257,c_0_258]),c_0_122]) ).
cnf(c_0_263,negated_conjecture,
addition(esk3_0,multiplication(c(addition(esk2_0,esk3_0)),esk2_0)) = esk3_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_259]),c_0_34]) ).
cnf(c_0_264,negated_conjecture,
addition(esk2_0,multiplication(c(esk3_0),c(esk2_0))) = addition(esk2_0,c(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_260]),c_0_103]),c_0_34]),c_0_97]),c_0_42]) ).
cnf(c_0_265,negated_conjecture,
multiplication(c(esk3_0),multiplication(c(esk2_0),c(esk3_0))) = multiplication(c(esk3_0),c(esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_261]),c_0_122]) ).
fof(c_0_266,plain,
! [X4] :
( ~ test(X4)
=> c(X4) = zero ),
inference(fof_simplification,[status(thm)],[test_4]) ).
cnf(c_0_267,negated_conjecture,
multiplication(addition(X1,one),esk2_0) = multiplication(addition(X1,esk2_0),esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_108]),c_0_34]),c_0_76]) ).
cnf(c_0_268,negated_conjecture,
leq(multiplication(c(esk3_0),multiplication(c(addition(esk2_0,esk3_0)),esk2_0)),esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_262,c_0_263])]) ).
cnf(c_0_269,plain,
addition(X1,multiplication(X2,multiplication(X3,X1))) = multiplication(addition(one,multiplication(X2,X3)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_67]),c_0_34]) ).
cnf(c_0_270,negated_conjecture,
addition(esk2_0,addition(esk3_0,c(addition(esk2_0,esk3_0)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_203]),c_0_34]),c_0_43]) ).
cnf(c_0_271,negated_conjecture,
multiplication(c(esk2_0),multiplication(c(esk3_0),c(esk2_0))) = multiplication(c(esk2_0),c(esk3_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_264]),c_0_178]) ).
cnf(c_0_272,negated_conjecture,
addition(multiplication(c(esk2_0),c(esk3_0)),multiplication(c(esk3_0),c(esk2_0))) = multiplication(c(esk2_0),c(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_265]),c_0_34]),c_0_140]),c_0_68]) ).
fof(c_0_273,plain,
! [X36] :
( test(X36)
| c(X36) = zero ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_266])]) ).
cnf(c_0_274,negated_conjecture,
multiplication(addition(esk2_0,addition(esk3_0,X1)),esk2_0) = multiplication(addition(X1,esk2_0),esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_202]),c_0_76]),c_0_43]),c_0_267]) ).
cnf(c_0_275,negated_conjecture,
addition(esk3_0,multiplication(c(esk3_0),multiplication(c(addition(esk2_0,esk3_0)),esk2_0))) = esk3_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_268]),c_0_34]) ).
cnf(c_0_276,negated_conjecture,
multiplication(addition(one,multiplication(X1,X2)),esk2_0) = multiplication(addition(esk2_0,multiplication(X1,X2)),esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_108]),c_0_269]) ).
cnf(c_0_277,negated_conjecture,
multiplication(c(esk3_0),multiplication(addition(esk3_0,X1),X2)) = multiplication(c(esk3_0),multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_122]),c_0_67]) ).
cnf(c_0_278,negated_conjecture,
multiplication(addition(esk3_0,c(addition(esk2_0,esk3_0))),c(esk2_0)) = c(esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_270]),c_0_68]) ).
cnf(c_0_279,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_271]),c_0_34]),c_0_135]),c_0_68]),c_0_34]),c_0_272]) ).
cnf(c_0_280,plain,
( test(X1)
| c(X1) = zero ),
inference(split_conjunct,[status(thm)],[c_0_273]) ).
cnf(c_0_281,plain,
( leq(addition(X1,X2),X3)
| addition(X2,addition(X3,X1)) != X3 ),
inference(spm,[status(thm)],[c_0_59,c_0_90]) ).
cnf(c_0_282,negated_conjecture,
addition(multiplication(addition(esk2_0,X1),X2),multiplication(X1,c(esk2_0))) = multiplication(addition(esk2_0,X1),addition(X2,c(esk2_0))),
inference(spm,[status(thm)],[c_0_30,c_0_96]) ).
cnf(c_0_283,negated_conjecture,
multiplication(addition(esk2_0,multiplication(c(esk3_0),c(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(spm,[status(thm)],[c_0_274,c_0_275]),c_0_202]),c_0_34]),c_0_269]),c_0_276]),c_0_67]),c_0_108]) ).
cnf(c_0_284,negated_conjecture,
multiplication(c(esk3_0),multiplication(c(addition(esk2_0,esk3_0)),c(esk2_0))) = multiplication(c(esk2_0),c(esk3_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_277,c_0_278]),c_0_279]) ).
cnf(c_0_285,negated_conjecture,
addition(esk2_0,multiplication(c(esk2_0),c(esk3_0))) = addition(esk2_0,c(esk3_0)),
inference(rw,[status(thm)],[c_0_264,c_0_279]) ).
cnf(c_0_286,plain,
( c(X1) = zero
| complement(X1,c(X1)) ),
inference(spm,[status(thm)],[c_0_22,c_0_280]) ).
cnf(c_0_287,plain,
( leq(addition(multiplication(X1,X2),X3),X2)
| addition(X3,multiplication(addition(X1,one),X2)) != X2 ),
inference(spm,[status(thm)],[c_0_281,c_0_76]) ).
cnf(c_0_288,negated_conjecture,
addition(esk2_0,multiplication(c(esk3_0),c(addition(esk2_0,esk3_0)))) = addition(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_282,c_0_283]),c_0_67]),c_0_284]),c_0_285]),c_0_97]),c_0_42]) ).
cnf(c_0_289,negated_conjecture,
addition(X1,addition(c(esk3_0),multiplication(esk3_0,X1))) = addition(X1,c(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_40]),c_0_43]),c_0_75]),c_0_68]) ).
cnf(c_0_290,negated_conjecture,
multiplication(esk3_0,addition(esk3_0,multiplication(c(esk2_0),c(esk3_0)))) = esk3_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_196]),c_0_32]),c_0_53]),c_0_34]) ).
cnf(c_0_291,negated_conjecture,
addition(esk3_0,addition(X1,one)) = addition(X1,one),
inference(spm,[status(thm)],[c_0_129,c_0_75]) ).
cnf(c_0_292,negated_conjecture,
multiplication(esk2_0,addition(esk2_0,esk3_0)) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_75]),c_0_42]),c_0_34]) ).
cnf(c_0_293,plain,
( multiplication(X1,c(X1)) = zero
| c(X1) = zero ),
inference(spm,[status(thm)],[c_0_25,c_0_286]) ).
cnf(c_0_294,negated_conjecture,
( leq(addition(multiplication(esk3_0,X1),X2),X1)
| addition(X2,X1) != X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_287,c_0_75]),c_0_68]) ).
cnf(c_0_295,negated_conjecture,
multiplication(c(esk2_0),multiplication(c(esk3_0),c(addition(esk2_0,esk3_0)))) = multiplication(c(esk2_0),c(esk3_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_288]),c_0_178]) ).
cnf(c_0_296,negated_conjecture,
addition(one,multiplication(c(esk2_0),c(esk3_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)],[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_289,c_0_290]),c_0_34]),c_0_41]),c_0_43]),c_0_291]),c_0_43]),c_0_34]),c_0_76]),c_0_34]),c_0_135]),c_0_68]),c_0_41]),c_0_34]) ).
cnf(c_0_297,negated_conjecture,
multiplication(esk2_0,multiplication(addition(esk2_0,esk3_0),X1)) = multiplication(esk2_0,X1),
inference(spm,[status(thm)],[c_0_67,c_0_292]) ).
cnf(c_0_298,negated_conjecture,
( multiplication(esk3_0,c(addition(esk2_0,esk3_0))) = zero
| c(addition(esk2_0,esk3_0)) = zero ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_293]),c_0_235]) ).
cnf(c_0_299,negated_conjecture,
( leq(addition(multiplication(esk3_0,X1),X2),X1)
| addition(X1,X2) != X1 ),
inference(spm,[status(thm)],[c_0_294,c_0_34]) ).
cnf(c_0_300,negated_conjecture,
addition(c(addition(esk2_0,esk3_0)),multiplication(c(esk2_0),c(esk3_0))) = c(addition(esk2_0,esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_269,c_0_295]),c_0_296]),c_0_68]) ).
cnf(c_0_301,negated_conjecture,
multiplication(esk3_0,c(addition(esk2_0,esk3_0))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_207]),c_0_235]) ).
cnf(c_0_302,negated_conjecture,
( multiplication(esk2_0,c(addition(esk2_0,esk3_0))) = zero
| c(addition(esk2_0,esk3_0)) = zero ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_297,c_0_293]),c_0_235]) ).
cnf(c_0_303,negated_conjecture,
( multiplication(addition(esk3_0,X1),c(addition(esk2_0,esk3_0))) = multiplication(X1,c(addition(esk2_0,esk3_0)))
| c(addition(esk2_0,esk3_0)) = zero ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_298]),c_0_82]) ).
cnf(c_0_304,negated_conjecture,
( ~ leq(c(addition(esk2_0,esk3_0)),multiplication(c(esk2_0),c(esk3_0)))
| ~ leq(multiplication(c(esk2_0),c(esk3_0)),c(addition(esk2_0,esk3_0))) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_305,negated_conjecture,
leq(multiplication(c(esk2_0),c(esk3_0)),c(addition(esk2_0,esk3_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_299,c_0_300]),c_0_301]),c_0_82]) ).
cnf(c_0_306,negated_conjecture,
( multiplication(addition(esk2_0,X1),c(addition(esk2_0,esk3_0))) = multiplication(X1,c(addition(esk2_0,esk3_0)))
| c(addition(esk2_0,esk3_0)) = zero ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_302]),c_0_82]) ).
cnf(c_0_307,negated_conjecture,
( multiplication(c(esk3_0),c(addition(esk2_0,esk3_0))) = c(addition(esk2_0,esk3_0))
| c(addition(esk2_0,esk3_0)) = zero ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_303,c_0_41]),c_0_68]) ).
cnf(c_0_308,negated_conjecture,
~ leq(c(addition(esk2_0,esk3_0)),multiplication(c(esk2_0),c(esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_304,c_0_305])]) ).
cnf(c_0_309,negated_conjecture,
( multiplication(c(esk2_0),c(addition(esk2_0,esk3_0))) = c(addition(esk2_0,esk3_0))
| c(addition(esk2_0,esk3_0)) = zero ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_306,c_0_97]),c_0_68]) ).
cnf(c_0_310,negated_conjecture,
( multiplication(c(esk2_0),c(addition(esk2_0,esk3_0))) = multiplication(c(esk2_0),c(esk3_0))
| c(addition(esk2_0,esk3_0)) = zero ),
inference(spm,[status(thm)],[c_0_295,c_0_307]) ).
cnf(c_0_311,negated_conjecture,
multiplication(c(esk2_0),c(esk3_0)) != c(addition(esk2_0,esk3_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_300]),c_0_308]) ).
cnf(c_0_312,negated_conjecture,
c(addition(esk2_0,esk3_0)) = zero,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_309,c_0_310]),c_0_311]) ).
cnf(c_0_313,plain,
leq(zero,X1),
inference(spm,[status(thm)],[c_0_51,c_0_82]) ).
cnf(c_0_314,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_308,c_0_312]),c_0_313])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE014+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 12:03:17 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 33.15/33.23 % Version : CSE_E---1.5
% 33.15/33.23 % Problem : theBenchmark.p
% 33.15/33.23 % Proof found
% 33.15/33.23 % SZS status Theorem for theBenchmark.p
% 33.15/33.23 % SZS output start Proof
% See solution above
% 33.15/33.24 % Total time : 32.647000 s
% 33.15/33.24 % SZS output end Proof
% 33.15/33.24 % Total time : 32.652000 s
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