TSTP Solution File: KLE145+2 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : KLE145+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n013.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 : 600s
% DateTime : Sun Jul 17 01:56:13 EDT 2022
% Result : Theorem 0.27s 7.46s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 19
% Syntax : Number of formulae : 121 ( 91 unt; 0 def)
% Number of atoms : 153 ( 89 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 62 ( 30 ~; 25 |; 3 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 215 ( 6 sgn 72 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(infty_coinduction,axiom,
! [X1,X2,X3] :
( leq(X3,addition(multiplication(X1,X3),X2))
=> leq(X3,multiplication(strong_iteration(X1),X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(star_unfold1,axiom,
! [X1] : addition(one,multiplication(X1,star(X1))) = star(X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_unfold1) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(infty_unfold1,axiom,
! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
fof(star_induction2,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X3,X1),X2),X3)
=> leq(multiplication(X2,star(X1)),X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_induction2) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).
fof(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
fof(distributivity2,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',distributivity2) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
fof(star_unfold2,axiom,
! [X1] : addition(one,multiplication(star(X1),X1)) = star(X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_unfold2) ).
fof(distributivity1,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',distributivity1) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).
fof(isolation,axiom,
! [X1] : strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',isolation) ).
fof(star_induction1,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X1,X3),X2),X3)
=> leq(multiplication(star(X1),X2),X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_induction1) ).
fof(goals,conjecture,
! [X4] :
( leq(star(strong_iteration(X4)),strong_iteration(X4))
& leq(strong_iteration(X4),star(strong_iteration(X4))) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals) ).
fof(c_0_19,plain,
! [X4,X5,X6] :
( ~ leq(X6,addition(multiplication(X4,X6),X5))
| leq(X6,multiplication(strong_iteration(X4),X5)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[infty_coinduction])]) ).
fof(c_0_20,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_21,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(multiplication(X2,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_22,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_23,plain,
! [X2] : addition(one,multiplication(X2,star(X2))) = star(X2),
inference(variable_rename,[status(thm)],[star_unfold1]) ).
fof(c_0_24,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_25,plain,
! [X2] : strong_iteration(X2) = addition(multiplication(X2,strong_iteration(X2)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
fof(c_0_26,plain,
! [X4,X5,X6] :
( ~ leq(addition(multiplication(X6,X4),X5),X6)
| leq(multiplication(X5,star(X4)),X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction2])]) ).
fof(c_0_27,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_28,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(X3,multiplication(X2,X1))) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,plain,
addition(one,multiplication(X1,star(X1))) = star(X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_31,plain,
! [X3,X4,X3,X4] :
( ( ~ leq(X3,X4)
| addition(X3,X4) = X4 )
& ( addition(X3,X4) != X4
| leq(X3,X4) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])])]) ).
fof(c_0_32,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[idempotence]) ).
cnf(c_0_33,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_34,plain,
! [X2] : multiplication(zero,X2) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_35,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_36,plain,
( leq(multiplication(X1,star(X2)),X3)
| ~ leq(addition(multiplication(X3,X2),X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,plain,
( leq(star(X1),strong_iteration(X1))
| ~ leq(star(X1),star(X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_39,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_33,c_0_22]) ).
cnf(c_0_42,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_43,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_44,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[distributivity2]) ).
fof(c_0_45,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_46,plain,
( leq(multiplication(X1,star(X2)),one)
| ~ leq(addition(X2,X1),one) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_47,plain,
leq(star(X1),strong_iteration(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
cnf(c_0_48,plain,
strong_iteration(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_49,plain,
star(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_42]),c_0_43]) ).
cnf(c_0_50,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_51,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_52,plain,
( leq(multiplication(X1,star(X1)),one)
| ~ leq(X1,one) ),
inference(spm,[status(thm)],[c_0_46,c_0_40]) ).
cnf(c_0_53,plain,
leq(one,one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_54,plain,
( leq(X1,multiplication(strong_iteration(X2),multiplication(X3,X1)))
| ~ leq(X1,multiplication(addition(X2,X3),X1)) ),
inference(spm,[status(thm)],[c_0_21,c_0_50]) ).
cnf(c_0_55,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_51,c_0_40]) ).
cnf(c_0_56,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_37]),c_0_22]) ).
cnf(c_0_57,plain,
( leq(multiplication(X1,star(one)),X2)
| ~ leq(addition(X2,X1),X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_30]) ).
cnf(c_0_58,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_59,plain,
leq(star(one),one),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_37]),c_0_53])]) ).
cnf(c_0_60,plain,
addition(one,star(one)) = star(one),
inference(spm,[status(thm)],[c_0_29,c_0_37]) ).
cnf(c_0_61,plain,
( leq(X1,multiplication(strong_iteration(X2),multiplication(X3,X1)))
| addition(X1,multiplication(addition(X2,X3),X1)) != multiplication(addition(X2,X3),X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_39]) ).
cnf(c_0_62,plain,
addition(X1,multiplication(addition(X2,one),X1)) = multiplication(addition(X2,one),X1),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
fof(c_0_63,plain,
! [X2] : addition(one,multiplication(star(X2),X2)) = star(X2),
inference(variable_rename,[status(thm)],[star_unfold2]) ).
fof(c_0_64,plain,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[distributivity1]) ).
cnf(c_0_65,plain,
( leq(multiplication(X1,star(one)),X2)
| ~ leq(addition(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_57,c_0_22]) ).
cnf(c_0_66,plain,
star(one) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_22]),c_0_60]) ).
cnf(c_0_67,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(spm,[status(thm)],[c_0_50,c_0_37]) ).
cnf(c_0_68,plain,
leq(X1,multiplication(strong_iteration(X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_37]),c_0_62])]) ).
cnf(c_0_69,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
fof(c_0_70,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_71,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_72,plain,
( leq(X1,X2)
| ~ leq(addition(X1,X2),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66]),c_0_30]) ).
cnf(c_0_73,plain,
addition(X1,multiplication(addition(one,X2),X1)) = multiplication(addition(one,X2),X1),
inference(spm,[status(thm)],[c_0_55,c_0_67]) ).
cnf(c_0_74,plain,
leq(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_48]),c_0_37]) ).
cnf(c_0_75,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_55,c_0_69]) ).
cnf(c_0_76,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_77,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[c_0_71,c_0_30]) ).
cnf(c_0_78,plain,
leq(X1,multiplication(addition(one,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74])]) ).
cnf(c_0_79,plain,
addition(X1,multiplication(star(X2),X1)) = multiplication(star(X2),X1),
inference(spm,[status(thm)],[c_0_67,c_0_75]) ).
cnf(c_0_80,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_56,c_0_76]),c_0_22]) ).
cnf(c_0_81,plain,
addition(X1,multiplication(X1,multiplication(star(X2),X2))) = multiplication(X1,star(X2)),
inference(spm,[status(thm)],[c_0_77,c_0_69]) ).
cnf(c_0_82,plain,
addition(one,strong_iteration(X1)) = strong_iteration(X1),
inference(spm,[status(thm)],[c_0_55,c_0_41]) ).
cnf(c_0_83,plain,
addition(one,addition(multiplication(X1,star(X1)),X2)) = addition(star(X1),X2),
inference(spm,[status(thm)],[c_0_51,c_0_29]) ).
fof(c_0_84,plain,
! [X2] : strong_iteration(X2) = addition(star(X2),multiplication(strong_iteration(X2),zero)),
inference(variable_rename,[status(thm)],[isolation]) ).
fof(c_0_85,plain,
! [X4,X5,X6] :
( ~ leq(addition(multiplication(X4,X6),X5),X6)
| leq(multiplication(star(X4),X5),X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction1])]) ).
fof(c_0_86,negated_conjecture,
~ ! [X4] :
( leq(star(strong_iteration(X4)),strong_iteration(X4))
& leq(strong_iteration(X4),star(strong_iteration(X4))) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_87,plain,
leq(X1,multiplication(star(X2),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_30]) ).
cnf(c_0_88,plain,
multiplication(star(X1),X1) = multiplication(X1,star(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_29]) ).
cnf(c_0_89,plain,
addition(X1,multiplication(strong_iteration(X2),X1)) = multiplication(strong_iteration(X2),X1),
inference(spm,[status(thm)],[c_0_67,c_0_82]) ).
cnf(c_0_90,plain,
addition(star(X1),multiplication(X1,X2)) = addition(one,multiplication(X1,addition(star(X1),X2))),
inference(spm,[status(thm)],[c_0_83,c_0_71]) ).
cnf(c_0_91,plain,
strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_92,plain,
( leq(multiplication(star(X1),X2),X3)
| ~ leq(addition(multiplication(X1,X3),X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_93,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_55,c_0_22]) ).
fof(c_0_94,negated_conjecture,
( ~ leq(star(strong_iteration(esk1_0)),strong_iteration(esk1_0))
| ~ leq(strong_iteration(esk2_0),star(strong_iteration(esk2_0))) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_86])])])]) ).
cnf(c_0_95,plain,
leq(X1,multiplication(X1,star(X1))),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_96,plain,
multiplication(strong_iteration(X1),star(strong_iteration(X1))) = star(strong_iteration(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_40]),c_0_29]) ).
cnf(c_0_97,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_51]) ).
cnf(c_0_98,plain,
addition(multiplication(strong_iteration(X1),zero),star(X1)) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_91,c_0_22]) ).
cnf(c_0_99,plain,
addition(multiplication(X1,multiplication(X2,X3)),multiplication(X4,X3)) = multiplication(addition(multiplication(X1,X2),X4),X3),
inference(spm,[status(thm)],[c_0_50,c_0_76]) ).
cnf(c_0_100,plain,
( leq(multiplication(star(X1),addition(X2,multiplication(X1,X3))),X3)
| ~ leq(addition(X2,multiplication(X1,X3)),X3) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_101,plain,
addition(multiplication(X1,addition(X2,X3)),X4) = addition(multiplication(X1,X2),addition(multiplication(X1,X3),X4)),
inference(spm,[status(thm)],[c_0_51,c_0_71]) ).
cnf(c_0_102,plain,
multiplication(star(X1),multiplication(X1,X2)) = multiplication(X1,multiplication(star(X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_88]),c_0_76]) ).
cnf(c_0_103,plain,
addition(X1,multiplication(X2,multiplication(star(X2),X1))) = multiplication(star(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_29]),c_0_76]) ).
cnf(c_0_104,negated_conjecture,
( ~ leq(strong_iteration(esk2_0),star(strong_iteration(esk2_0)))
| ~ leq(star(strong_iteration(esk1_0)),strong_iteration(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_105,plain,
leq(strong_iteration(X1),star(strong_iteration(X1))),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_106,plain,
( leq(multiplication(star(X1),X2),X3)
| addition(X3,addition(multiplication(X1,X3),X2)) != X3 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_39]),c_0_51]),c_0_97]) ).
cnf(c_0_107,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_22]),c_0_51]) ).
cnf(c_0_108,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_30]),c_0_22]) ).
cnf(c_0_109,plain,
addition(multiplication(strong_iteration(X1),zero),addition(star(X1),X2)) = addition(strong_iteration(X1),X2),
inference(spm,[status(thm)],[c_0_51,c_0_98]) ).
cnf(c_0_110,plain,
addition(X1,multiplication(X1,strong_iteration(X2))) = multiplication(X1,strong_iteration(X2)),
inference(spm,[status(thm)],[c_0_77,c_0_82]) ).
cnf(c_0_111,plain,
addition(multiplication(X1,zero),multiplication(X2,X3)) = multiplication(addition(multiplication(X1,zero),X2),X3),
inference(spm,[status(thm)],[c_0_99,c_0_42]) ).
cnf(c_0_112,plain,
( multiplication(star(X1),addition(X2,X3)) = X3
| ~ leq(addition(X2,multiplication(X1,X3)),X3) ),
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_58,c_0_100]),c_0_101]),c_0_102]),c_0_22]),c_0_103]),c_0_71]) ).
cnf(c_0_113,negated_conjecture,
~ leq(star(strong_iteration(esk1_0)),strong_iteration(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_105])]) ).
cnf(c_0_114,plain,
( leq(star(X1),X2)
| addition(X2,addition(one,multiplication(X1,X2))) != X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_30]),c_0_22]) ).
cnf(c_0_115,plain,
addition(X1,addition(X2,multiplication(X1,X3))) = addition(X2,multiplication(X1,addition(X3,one))),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_116,plain,
addition(strong_iteration(X1),multiplication(star(X1),strong_iteration(X2))) = multiplication(strong_iteration(X1),strong_iteration(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_111]),c_0_98]) ).
cnf(c_0_117,plain,
multiplication(star(X1),strong_iteration(X1)) = strong_iteration(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_41]),c_0_82]),c_0_74])]) ).
cnf(c_0_118,negated_conjecture,
addition(one,multiplication(strong_iteration(esk1_0),strong_iteration(esk1_0))) != strong_iteration(esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_115]),c_0_22]),c_0_82]) ).
cnf(c_0_119,plain,
multiplication(strong_iteration(X1),strong_iteration(X1)) = strong_iteration(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_116]),c_0_75]),c_0_117]) ).
cnf(c_0_120,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_119]),c_0_82])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KLE145+2 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : run_ET %s %d
% 0.12/0.34 % Computer : n013.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 : 600
% 0.12/0.34 % DateTime : Thu Jun 16 07:47:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.27/7.46 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.27/7.46 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.27/7.46 # Preprocessing time : 0.015 s
% 0.27/7.46
% 0.27/7.46 # Proof found!
% 0.27/7.46 # SZS status Theorem
% 0.27/7.46 # SZS output start CNFRefutation
% See solution above
% 0.27/7.46 # Proof object total steps : 121
% 0.27/7.46 # Proof object clause steps : 82
% 0.27/7.46 # Proof object formula steps : 39
% 0.27/7.46 # Proof object conjectures : 7
% 0.27/7.46 # Proof object clause conjectures : 4
% 0.27/7.46 # Proof object formula conjectures : 3
% 0.27/7.46 # Proof object initial clauses used : 20
% 0.27/7.46 # Proof object initial formulas used : 19
% 0.27/7.46 # Proof object generating inferences : 57
% 0.27/7.46 # Proof object simplifying inferences : 52
% 0.27/7.46 # Training examples: 0 positive, 0 negative
% 0.27/7.46 # Parsed axioms : 19
% 0.27/7.46 # Removed by relevancy pruning/SinE : 0
% 0.27/7.46 # Initial clauses : 20
% 0.27/7.46 # Removed in clause preprocessing : 0
% 0.27/7.46 # Initial clauses in saturation : 20
% 0.27/7.46 # Processed clauses : 16852
% 0.27/7.46 # ...of these trivial : 929
% 0.27/7.46 # ...subsumed : 14052
% 0.27/7.46 # ...remaining for further processing : 1871
% 0.27/7.46 # Other redundant clauses eliminated : 1
% 0.27/7.46 # Clauses deleted for lack of memory : 183596
% 0.27/7.46 # Backward-subsumed : 102
% 0.27/7.46 # Backward-rewritten : 207
% 0.27/7.46 # Generated clauses : 391043
% 0.27/7.46 # ...of the previous two non-trivial : 338020
% 0.27/7.46 # Contextual simplify-reflections : 1325
% 0.27/7.46 # Paramodulations : 391039
% 0.27/7.46 # Factorizations : 0
% 0.27/7.46 # Equation resolutions : 4
% 0.27/7.46 # Current number of processed clauses : 1562
% 0.27/7.46 # Positive orientable unit clauses : 360
% 0.27/7.46 # Positive unorientable unit clauses: 61
% 0.27/7.46 # Negative unit clauses : 92
% 0.27/7.46 # Non-unit-clauses : 1049
% 0.27/7.46 # Current number of unprocessed clauses: 108521
% 0.27/7.46 # ...number of literals in the above : 208741
% 0.27/7.46 # Current number of archived formulas : 0
% 0.27/7.46 # Current number of archived clauses : 309
% 0.27/7.46 # Clause-clause subsumption calls (NU) : 145682
% 0.27/7.46 # Rec. Clause-clause subsumption calls : 142989
% 0.27/7.46 # Non-unit clause-clause subsumptions : 5664
% 0.27/7.46 # Unit Clause-clause subsumption calls : 10385
% 0.27/7.46 # Rewrite failures with RHS unbound : 0
% 0.27/7.46 # BW rewrite match attempts : 6324
% 0.27/7.46 # BW rewrite match successes : 604
% 0.27/7.46 # Condensation attempts : 0
% 0.27/7.46 # Condensation successes : 0
% 0.27/7.46 # Termbank termtop insertions : 6841880
% 0.27/7.46
% 0.27/7.46 # -------------------------------------------------
% 0.27/7.46 # User time : 6.777 s
% 0.27/7.46 # System time : 0.111 s
% 0.27/7.46 # Total time : 6.888 s
% 0.27/7.46 # Maximum resident set size: 153740 pages
% 0.27/23.42 eprover: CPU time limit exceeded, terminating
% 0.27/23.43 eprover: CPU time limit exceeded, terminating
% 0.27/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.43 eprover: No such file or directory
% 0.27/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.44 eprover: No such file or directory
% 0.27/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.44 eprover: No such file or directory
% 0.27/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.45 eprover: No such file or directory
% 0.27/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.45 eprover: No such file or directory
% 0.27/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.45 eprover: No such file or directory
% 0.27/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.45 eprover: No such file or directory
% 0.27/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.46 eprover: No such file or directory
% 0.27/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.46 eprover: No such file or directory
% 0.27/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.46 eprover: No such file or directory
% 0.27/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.46 eprover: No such file or directory
% 0.27/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.46 eprover: No such file or directory
% 0.27/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.47 eprover: No such file or directory
% 0.27/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.47 eprover: No such file or directory
% 0.27/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.47 eprover: No such file or directory
% 0.27/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.47 eprover: No such file or directory
% 0.27/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.48 eprover: No such file or directory
% 0.27/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.48 eprover: No such file or directory
% 0.27/23.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.49 eprover: No such file or directory
% 0.27/23.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.49 eprover: No such file or directory
% 0.27/23.50 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.50 eprover: No such file or directory
% 0.27/23.50 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.50 eprover: No such file or directory
%------------------------------------------------------------------------------