%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE166+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:35:51 PM UTC 2026
% Result : Theorem 23.02s 14.12s
% Output : CNFRefutation 23.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 18
% Syntax : Number of formulae : 159 ( 127 unt; 0 def)
% Number of atoms : 200 ( 135 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 71 ( 30 ~; 31 |; 3 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 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 : 214 ( 8 sgn 66 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
fof(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(goals,conjecture,
! [X4,X5] :
( leq(multiplication(X4,X5),multiplication(X5,strong_iteration(addition(X5,X4))))
=> ( multiplication(strong_iteration(addition(X5,X4)),zero) = zero
<=> addition(multiplication(strong_iteration(X5),zero),multiplication(strong_iteration(X4),zero)) = zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(infty_unfold1,axiom,
! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
fof(distributivity1,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity1) ).
fof(star_unfold2,axiom,
! [X1] : addition(one,multiplication(star(X1),X1)) = star(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_unfold2) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(star_unfold1,axiom,
! [X1] : addition(one,multiplication(X1,star(X1))) = star(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_unfold1) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity2) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).
fof(infty_coinduction,axiom,
! [X1,X2,X3] :
( leq(X3,addition(multiplication(X1,X3),X2))
=> leq(X3,multiplication(strong_iteration(X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
fof(star_induction1,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X1,X3),X2),X3)
=> leq(multiplication(star(X1),X2),X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_induction1) ).
fof(isolation,axiom,
! [X1] : strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',isolation) ).
fof(c_0_18,plain,
! [X44,X45,X46] : addition(X46,addition(X45,X44)) = addition(addition(X46,X45),X44),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_19,plain,
! [X48] : addition(X48,X48) = X48,
inference(variable_rename,[status(thm)],[idempotence]) ).
fof(c_0_20,negated_conjecture,
~ ! [X4,X5] :
( leq(multiplication(X4,X5),multiplication(X5,strong_iteration(addition(X5,X4))))
=> ( multiplication(strong_iteration(addition(X5,X4)),zero) = zero
<=> addition(multiplication(strong_iteration(X5),zero),multiplication(strong_iteration(X4),zero)) = zero ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_21,plain,
! [X69] : strong_iteration(X69) = addition(multiplication(X69,strong_iteration(X69)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
fof(c_0_22,plain,
! [X42,X43] : addition(X42,X43) = addition(X43,X42),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_23,plain,
! [X74,X75] :
( ( ~ leq(X74,X75)
| addition(X74,X75) = X75 )
& ( addition(X74,X75) != X75
| leq(X74,X75) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
cnf(c_0_24,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_26,plain,
! [X54,X55,X56] : multiplication(X54,addition(X55,X56)) = addition(multiplication(X54,X55),multiplication(X54,X56)),
inference(variable_rename,[status(thm)],[distributivity1]) ).
fof(c_0_27,plain,
! [X62] : addition(one,multiplication(star(X62),X62)) = star(X62),
inference(variable_rename,[status(thm)],[star_unfold2]) ).
fof(c_0_28,plain,
! [X52] : multiplication(X52,one) = X52,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_29,plain,
! [X61] : addition(one,multiplication(X61,star(X61))) = star(X61),
inference(variable_rename,[status(thm)],[star_unfold1]) ).
fof(c_0_30,plain,
! [X60] : multiplication(zero,X60) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_31,plain,
! [X47] : addition(X47,zero) = X47,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_32,negated_conjecture,
( leq(multiplication(esk1_0,esk2_0),multiplication(esk2_0,strong_iteration(addition(esk2_0,esk1_0))))
& ( multiplication(strong_iteration(addition(esk2_0,esk1_0)),zero) != zero
| addition(multiplication(strong_iteration(esk2_0),zero),multiplication(strong_iteration(esk1_0),zero)) != zero )
& ( multiplication(strong_iteration(addition(esk2_0,esk1_0)),zero) = zero
| addition(multiplication(strong_iteration(esk2_0),zero),multiplication(strong_iteration(esk1_0),zero)) = zero ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
fof(c_0_33,plain,
! [X57,X58,X59] : multiplication(addition(X57,X58),X59) = addition(multiplication(X57,X59),multiplication(X58,X59)),
inference(variable_rename,[status(thm)],[distributivity2]) ).
cnf(c_0_34,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_35,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_36,plain,
! [X53] : multiplication(one,X53) = X53,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_37,plain,
! [X49,X50,X51] : multiplication(X49,multiplication(X50,X51)) = multiplication(multiplication(X49,X50),X51),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_38,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_39,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_40,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_41,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_42,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_43,plain,
addition(one,multiplication(X1,star(X1))) = star(X1),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_44,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_45,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_46,plain,
! [X70,X71,X72] :
( ~ leq(X72,addition(multiplication(X70,X72),X71))
| leq(X72,multiplication(strong_iteration(X70),X71)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[infty_coinduction])]) ).
cnf(c_0_47,negated_conjecture,
( multiplication(strong_iteration(addition(esk2_0,esk1_0)),zero) = zero
| addition(multiplication(strong_iteration(esk2_0),zero),multiplication(strong_iteration(esk1_0),zero)) = zero ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_48,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_49,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_50,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_51,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_52,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_53,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_35,c_0_24]) ).
cnf(c_0_54,plain,
addition(X1,multiplication(X1,multiplication(star(X2),X2))) = multiplication(X1,star(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_55,plain,
star(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_56,negated_conjecture,
leq(multiplication(esk1_0,esk2_0),multiplication(esk2_0,strong_iteration(addition(esk2_0,esk1_0)))),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_57,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(multiplication(X2,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_58,negated_conjecture,
( addition(multiplication(strong_iteration(esk1_0),zero),multiplication(strong_iteration(esk2_0),zero)) = zero
| multiplication(strong_iteration(addition(esk1_0,esk2_0)),zero) = zero ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_35]),c_0_35]) ).
cnf(c_0_59,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_45,c_0_35]) ).
cnf(c_0_60,plain,
addition(X1,multiplication(X2,multiplication(strong_iteration(X2),X1))) = multiplication(strong_iteration(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_51]) ).
cnf(c_0_61,plain,
leq(X1,addition(X2,addition(X3,X1))),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_62,plain,
addition(X1,multiplication(X1,zero)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_50]),c_0_42]) ).
cnf(c_0_63,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_64,negated_conjecture,
leq(multiplication(esk1_0,esk2_0),multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0)))),
inference(rw,[status(thm)],[c_0_56,c_0_35]) ).
cnf(c_0_65,negated_conjecture,
( addition(multiplication(strong_iteration(esk1_0),zero),multiplication(strong_iteration(esk2_0),zero)) = zero
| leq(X1,zero)
| ~ leq(X1,addition(multiplication(esk1_0,X1),multiplication(esk2_0,X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_48]),c_0_24]),c_0_45]) ).
cnf(c_0_66,plain,
multiplication(X1,multiplication(strong_iteration(X1),zero)) = multiplication(strong_iteration(X1),zero),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
fof(c_0_67,plain,
! [X63,X64,X65] :
( ~ leq(addition(multiplication(X63,X65),X64),X65)
| leq(multiplication(star(X63),X64),X65) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction1])]) ).
fof(c_0_68,plain,
! [X73] : strong_iteration(X73) = addition(star(X73),multiplication(strong_iteration(X73),zero)),
inference(variable_rename,[status(thm)],[isolation]) ).
cnf(c_0_69,plain,
leq(multiplication(X1,zero),addition(X2,X1)),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_70,negated_conjecture,
addition(multiplication(esk1_0,esk2_0),multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0)))) = multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0))),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_71,plain,
( addition(X1,addition(X2,X3)) = X3
| ~ leq(addition(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_63,c_0_24]) ).
cnf(c_0_72,negated_conjecture,
( addition(multiplication(strong_iteration(esk1_0),zero),multiplication(strong_iteration(esk2_0),zero)) = zero
| leq(multiplication(strong_iteration(esk2_0),zero),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_35]),c_0_52])]) ).
cnf(c_0_73,plain,
( leq(multiplication(star(X1),X3),X2)
| ~ leq(addition(multiplication(X1,X2),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_74,plain,
addition(one,addition(multiplication(X1,strong_iteration(X1)),X2)) = addition(strong_iteration(X1),X2),
inference(spm,[status(thm)],[c_0_24,c_0_49]) ).
cnf(c_0_75,plain,
strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_76,plain,
addition(one,strong_iteration(X1)) = strong_iteration(X1),
inference(spm,[status(thm)],[c_0_39,c_0_49]) ).
cnf(c_0_77,negated_conjecture,
leq(multiplication(esk2_0,multiplication(strong_iteration(addition(esk1_0,esk2_0)),zero)),multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_51]) ).
cnf(c_0_78,plain,
( addition(X1,X2) = X2
| ~ leq(addition(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_25]) ).
cnf(c_0_79,negated_conjecture,
( addition(multiplication(strong_iteration(esk1_0),zero),multiplication(strong_iteration(esk2_0),zero)) = zero
| multiplication(strong_iteration(esk2_0),zero) = zero ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_72]),c_0_45]) ).
cnf(c_0_80,plain,
leq(zero,X1),
inference(spm,[status(thm)],[c_0_38,c_0_59]) ).
cnf(c_0_81,plain,
( leq(multiplication(star(X1),X2),X3)
| ~ leq(addition(X2,multiplication(X1,X3)),X3) ),
inference(spm,[status(thm)],[c_0_73,c_0_35]) ).
cnf(c_0_82,plain,
addition(strong_iteration(X1),multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_25]),c_0_49]) ).
cnf(c_0_83,plain,
leq(X1,X1),
inference(spm,[status(thm)],[c_0_38,c_0_25]) ).
cnf(c_0_84,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_39,c_0_41]) ).
cnf(c_0_85,plain,
addition(multiplication(strong_iteration(X1),zero),star(X1)) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_75,c_0_35]) ).
cnf(c_0_86,plain,
addition(one,addition(X1,multiplication(X2,strong_iteration(X2)))) = addition(strong_iteration(X2),X1),
inference(spm,[status(thm)],[c_0_74,c_0_35]) ).
cnf(c_0_87,plain,
addition(X1,multiplication(X1,strong_iteration(X2))) = multiplication(X1,strong_iteration(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_76]),c_0_42]) ).
cnf(c_0_88,plain,
leq(X1,addition(X2,X1)),
inference(spm,[status(thm)],[c_0_52,c_0_35]) ).
cnf(c_0_89,plain,
addition(one,addition(multiplication(X1,strong_iteration(addition(X1,X2))),addition(multiplication(X2,strong_iteration(addition(X1,X2))),X3))) = addition(strong_iteration(addition(X1,X2)),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_48]),c_0_24]) ).
cnf(c_0_90,negated_conjecture,
addition(multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0))),multiplication(esk2_0,multiplication(strong_iteration(addition(esk1_0,esk2_0)),zero))) = multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_77]),c_0_35]) ).
cnf(c_0_91,plain,
addition(one,addition(multiplication(X1,strong_iteration(addition(X1,X2))),multiplication(X2,strong_iteration(addition(X1,X2))))) = strong_iteration(addition(X1,X2)),
inference(spm,[status(thm)],[c_0_49,c_0_48]) ).
cnf(c_0_92,negated_conjecture,
multiplication(strong_iteration(esk2_0),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80])]) ).
cnf(c_0_93,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_53,c_0_25]) ).
cnf(c_0_94,plain,
addition(X1,multiplication(X1,multiplication(X2,strong_iteration(X2)))) = multiplication(X1,strong_iteration(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_49]),c_0_42]) ).
cnf(c_0_95,plain,
leq(multiplication(star(X1),strong_iteration(X1)),strong_iteration(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83])]) ).
cnf(c_0_96,plain,
addition(X1,multiplication(star(X2),X1)) = multiplication(star(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_84]),c_0_50]) ).
cnf(c_0_97,plain,
addition(multiplication(strong_iteration(X1),zero),addition(star(X1),X2)) = addition(strong_iteration(X1),X2),
inference(spm,[status(thm)],[c_0_24,c_0_85]) ).
cnf(c_0_98,plain,
addition(multiplication(strong_iteration(X1),zero),multiplication(star(X1),X2)) = multiplication(strong_iteration(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_85]),c_0_51]),c_0_44]) ).
cnf(c_0_99,plain,
( leq(X1,addition(multiplication(strong_iteration(X2),X3),multiplication(strong_iteration(X2),X4)))
| ~ leq(X1,addition(X4,addition(multiplication(X2,X1),X3))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_53]),c_0_40]) ).
cnf(c_0_100,plain,
strong_iteration(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_44]),c_0_45]) ).
cnf(c_0_101,plain,
leq(addition(X1,X2),addition(X1,addition(X2,X3))),
inference(spm,[status(thm)],[c_0_52,c_0_24]) ).
cnf(c_0_102,plain,
addition(X1,strong_iteration(X1)) = strong_iteration(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_49]),c_0_35]) ).
cnf(c_0_103,plain,
leq(addition(multiplication(X1,strong_iteration(X1)),X2),addition(strong_iteration(X1),X2)),
inference(spm,[status(thm)],[c_0_88,c_0_74]) ).
cnf(c_0_104,negated_conjecture,
addition(strong_iteration(addition(esk1_0,esk2_0)),multiplication(esk2_0,multiplication(strong_iteration(addition(esk1_0,esk2_0)),zero))) = strong_iteration(addition(esk1_0,esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]) ).
cnf(c_0_105,negated_conjecture,
( multiplication(strong_iteration(esk1_0),zero) = zero
| leq(X1,zero)
| ~ leq(X1,addition(multiplication(esk1_0,X1),multiplication(esk2_0,X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_92]),c_0_45]) ).
cnf(c_0_106,plain,
( X1 = zero
| ~ leq(X1,zero) ),
inference(spm,[status(thm)],[c_0_78,c_0_45]) ).
cnf(c_0_107,plain,
addition(multiplication(X1,strong_iteration(X2)),multiplication(X1,multiplication(X2,strong_iteration(X2)))) = multiplication(X1,strong_iteration(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_35]) ).
cnf(c_0_108,plain,
multiplication(star(X1),strong_iteration(X1)) = strong_iteration(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_95]),c_0_35]),c_0_96]) ).
cnf(c_0_109,plain,
addition(strong_iteration(X1),multiplication(star(X1),multiplication(X2,strong_iteration(X2)))) = multiplication(strong_iteration(X1),strong_iteration(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_94]),c_0_98]) ).
cnf(c_0_110,plain,
( leq(X1,addition(X2,X3))
| ~ leq(X1,addition(X3,X2)) ),
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_99,c_0_44]),c_0_100]),c_0_50]),c_0_100]),c_0_50]),c_0_59]) ).
cnf(c_0_111,plain,
leq(addition(X1,X2),addition(X1,strong_iteration(X2))),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_112,negated_conjecture,
leq(addition(multiplication(esk1_0,strong_iteration(addition(esk1_0,esk2_0))),multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0)))),strong_iteration(addition(esk1_0,esk2_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_48]),c_0_24]),c_0_90]) ).
cnf(c_0_113,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_35]),c_0_24]) ).
cnf(c_0_114,plain,
addition(X1,multiplication(X2,multiplication(star(X2),X1))) = multiplication(star(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_43]),c_0_50]),c_0_51]) ).
cnf(c_0_115,negated_conjecture,
multiplication(strong_iteration(esk1_0),zero) = zero,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_66]),c_0_52])]),c_0_106]) ).
cnf(c_0_116,negated_conjecture,
addition(multiplication(esk1_0,multiplication(esk2_0,X1)),multiplication(esk2_0,multiplication(strong_iteration(addition(esk1_0,esk2_0)),X1))) = multiplication(esk2_0,multiplication(strong_iteration(addition(esk1_0,esk2_0)),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_70]),c_0_51]),c_0_51]),c_0_51]) ).
cnf(c_0_117,plain,
multiplication(strong_iteration(X1),strong_iteration(X1)) = strong_iteration(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109]) ).
cnf(c_0_118,plain,
leq(addition(X1,X2),addition(strong_iteration(X2),X1)),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_119,negated_conjecture,
addition(strong_iteration(addition(esk1_0,esk2_0)),addition(multiplication(esk1_0,strong_iteration(addition(esk1_0,esk2_0))),multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0))))) = strong_iteration(addition(esk1_0,esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_112]),c_0_24]),c_0_35]),c_0_113]) ).
cnf(c_0_120,plain,
multiplication(star(X1),X1) = multiplication(X1,star(X1)),
inference(spm,[status(thm)],[c_0_54,c_0_114]) ).
cnf(c_0_121,negated_conjecture,
star(esk1_0) = strong_iteration(esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_115]),c_0_59]) ).
cnf(c_0_122,negated_conjecture,
addition(multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0))),multiplication(esk1_0,multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0))))) = multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_35]) ).
cnf(c_0_123,plain,
( leq(addition(multiplication(star(X1),X2),multiplication(star(X1),X3)),X4)
| ~ leq(addition(X3,addition(multiplication(X1,X4),X2)),X4) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_53]),c_0_40]) ).
cnf(c_0_124,negated_conjecture,
leq(addition(esk1_0,addition(multiplication(esk1_0,strong_iteration(addition(esk1_0,esk2_0))),multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0))))),strong_iteration(addition(esk1_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_118,c_0_119]),c_0_24]),c_0_53]),c_0_35]),c_0_113]),c_0_87]),c_0_113]) ).
cnf(c_0_125,negated_conjecture,
multiplication(strong_iteration(esk1_0),esk1_0) = multiplication(esk1_0,strong_iteration(esk1_0)),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_126,negated_conjecture,
leq(multiplication(strong_iteration(esk1_0),multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0)))),multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_122]),c_0_121]),c_0_83])]) ).
cnf(c_0_127,plain,
addition(X1,multiplication(strong_iteration(X2),X1)) = multiplication(strong_iteration(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_76]),c_0_50]) ).
cnf(c_0_128,plain,
addition(X1,addition(X2,addition(X3,X1))) = addition(X2,addition(X3,X1)),
inference(spm,[status(thm)],[c_0_39,c_0_53]) ).
cnf(c_0_129,plain,
addition(X1,addition(X2,addition(X1,X3))) = addition(X2,addition(X1,X3)),
inference(spm,[status(thm)],[c_0_39,c_0_53]) ).
cnf(c_0_130,negated_conjecture,
leq(addition(multiplication(esk1_0,strong_iteration(esk1_0)),multiplication(strong_iteration(esk1_0),multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0))))),strong_iteration(addition(esk1_0,esk2_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_121]),c_0_121]),c_0_125]),c_0_35]) ).
cnf(c_0_131,negated_conjecture,
multiplication(strong_iteration(esk1_0),multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0)))) = multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_126]),c_0_35]),c_0_127]) ).
cnf(c_0_132,negated_conjecture,
addition(strong_iteration(addition(esk1_0,esk2_0)),multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0)))) = strong_iteration(addition(esk1_0,esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_119]),c_0_35]) ).
cnf(c_0_133,negated_conjecture,
star(esk2_0) = strong_iteration(esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_92]),c_0_59]) ).
cnf(c_0_134,negated_conjecture,
addition(strong_iteration(addition(esk1_0,esk2_0)),multiplication(esk1_0,strong_iteration(addition(esk1_0,esk2_0)))) = strong_iteration(addition(esk1_0,esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_119]),c_0_35]) ).
cnf(c_0_135,negated_conjecture,
leq(addition(multiplication(esk1_0,strong_iteration(esk1_0)),multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0)))),strong_iteration(addition(esk1_0,esk2_0))),
inference(rw,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_136,negated_conjecture,
leq(multiplication(strong_iteration(esk2_0),strong_iteration(addition(esk1_0,esk2_0))),strong_iteration(addition(esk1_0,esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_132]),c_0_133]),c_0_83])]) ).
cnf(c_0_137,negated_conjecture,
leq(multiplication(strong_iteration(esk1_0),strong_iteration(addition(esk1_0,esk2_0))),strong_iteration(addition(esk1_0,esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_134]),c_0_121]),c_0_83])]) ).
cnf(c_0_138,negated_conjecture,
leq(multiplication(strong_iteration(esk2_0),multiplication(esk1_0,strong_iteration(esk1_0))),strong_iteration(addition(esk1_0,esk2_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_135]),c_0_133]) ).
cnf(c_0_139,negated_conjecture,
multiplication(strong_iteration(esk2_0),strong_iteration(addition(esk1_0,esk2_0))) = strong_iteration(addition(esk1_0,esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_136]),c_0_35]),c_0_127]) ).
cnf(c_0_140,plain,
addition(X1,addition(multiplication(X1,multiplication(X2,strong_iteration(addition(X2,X3)))),multiplication(X1,multiplication(X3,strong_iteration(addition(X2,X3)))))) = multiplication(X1,strong_iteration(addition(X2,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_48]),c_0_40]) ).
cnf(c_0_141,negated_conjecture,
multiplication(strong_iteration(esk1_0),multiplication(esk1_0,X1)) = multiplication(esk1_0,multiplication(strong_iteration(esk1_0),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_125]),c_0_51]) ).
cnf(c_0_142,negated_conjecture,
multiplication(strong_iteration(esk1_0),strong_iteration(addition(esk1_0,esk2_0))) = strong_iteration(addition(esk1_0,esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_137]),c_0_35]),c_0_127]) ).
cnf(c_0_143,negated_conjecture,
( multiplication(strong_iteration(addition(esk2_0,esk1_0)),zero) != zero
| addition(multiplication(strong_iteration(esk2_0),zero),multiplication(strong_iteration(esk1_0),zero)) != zero ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_144,plain,
addition(X1,addition(multiplication(X1,multiplication(X2,strong_iteration(X2))),X3)) = addition(multiplication(X1,strong_iteration(X2)),X3),
inference(spm,[status(thm)],[c_0_24,c_0_94]) ).
cnf(c_0_145,negated_conjecture,
addition(multiplication(strong_iteration(esk2_0),multiplication(esk1_0,strong_iteration(esk1_0))),strong_iteration(addition(esk1_0,esk2_0))) = strong_iteration(addition(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_63,c_0_138]) ).
cnf(c_0_146,negated_conjecture,
addition(strong_iteration(esk2_0),strong_iteration(addition(esk1_0,esk2_0))) = strong_iteration(addition(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_87,c_0_139]) ).
cnf(c_0_147,negated_conjecture,
addition(strong_iteration(esk1_0),addition(multiplication(esk1_0,strong_iteration(addition(esk1_0,esk2_0))),multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0))))) = strong_iteration(addition(esk1_0,esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_131]),c_0_141]),c_0_142]),c_0_142]) ).
cnf(c_0_148,negated_conjecture,
( addition(multiplication(strong_iteration(esk1_0),zero),multiplication(strong_iteration(esk2_0),zero)) != zero
| multiplication(strong_iteration(addition(esk1_0,esk2_0)),zero) != zero ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_143,c_0_35]),c_0_35]) ).
cnf(c_0_149,plain,
( addition(X1,X2) = X1
| ~ leq(X2,X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_35]) ).
cnf(c_0_150,negated_conjecture,
addition(multiplication(strong_iteration(esk2_0),strong_iteration(esk1_0)),strong_iteration(addition(esk1_0,esk2_0))) = strong_iteration(addition(esk1_0,esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_146]) ).
cnf(c_0_151,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(X3,multiplication(X2,X1))) ),
inference(spm,[status(thm)],[c_0_57,c_0_35]) ).
cnf(c_0_152,negated_conjecture,
leq(strong_iteration(addition(esk1_0,esk2_0)),addition(strong_iteration(esk1_0),multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_147]),c_0_131]),c_0_117]),c_0_35]),c_0_83])]) ).
cnf(c_0_153,negated_conjecture,
( multiplication(strong_iteration(addition(esk1_0,esk2_0)),zero) != zero
| multiplication(strong_iteration(esk1_0),zero) != zero ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_148,c_0_92]),c_0_45]) ).
cnf(c_0_154,negated_conjecture,
( strong_iteration(addition(esk1_0,esk2_0)) = multiplication(strong_iteration(esk2_0),strong_iteration(esk1_0))
| ~ leq(strong_iteration(addition(esk1_0,esk2_0)),multiplication(strong_iteration(esk2_0),strong_iteration(esk1_0))) ),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_155,negated_conjecture,
leq(strong_iteration(addition(esk1_0,esk2_0)),multiplication(strong_iteration(esk2_0),strong_iteration(esk1_0))),
inference(spm,[status(thm)],[c_0_151,c_0_152]) ).
cnf(c_0_156,negated_conjecture,
multiplication(strong_iteration(addition(esk1_0,esk2_0)),zero) != zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_153,c_0_115])]) ).
cnf(c_0_157,negated_conjecture,
strong_iteration(addition(esk1_0,esk2_0)) = multiplication(strong_iteration(esk2_0),strong_iteration(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_154,c_0_155])]) ).
cnf(c_0_158,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_156,c_0_157]),c_0_51]),c_0_115]),c_0_92])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE166+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.34 % Computer : n029.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon May 4 20:32:59 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 23.02/14.12 % Version : CSE_E---1.7
% 23.02/14.12 % Problem : theBenchmark.p
% 23.02/14.12 % SZS status Theorem for theBenchmark.p
% 23.02/14.12 % SZS output start CNFRefutation
% See solution above
% 23.10/14.24 % Total time : 10.385s
%------------------------------------------------------------------------------