TSTP Solution File: KLE166+1 by Enigma---0.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : KLE166+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n025.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 01:50:41 EDT 2022
% Result : Theorem 87.58s 12.27s
% Output : CNFRefutation 87.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 19
% Syntax : Number of formulae : 204 ( 152 unt; 0 def)
% Number of atoms : 263 ( 169 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 98 ( 39 ~; 48 |; 3 &)
% ( 3 <=>; 5 =>; 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 : 261 ( 19 sgn 72 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',goals) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).
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(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(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(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
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(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_unfold2,axiom,
! [X1] : addition(one,multiplication(star(X1),X1)) = star(X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_unfold2) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
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(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(star_unfold1,axiom,
! [X1] : addition(one,multiplication(X1,star(X1))) = star(X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_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(c_0_19,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_20,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_19])])]) ).
fof(c_0_21,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_22,plain,
! [X38,X39] :
( ( ~ leq(X38,X39)
| addition(X38,X39) = X39 )
& ( addition(X38,X39) != X39
| leq(X38,X39) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
cnf(c_0_23,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_20]) ).
cnf(c_0_24,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_25,plain,
! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_26,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
leq(multiplication(esk1_0,esk2_0),multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0)))),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_28,plain,
! [X33] : strong_iteration(X33) = addition(multiplication(X33,strong_iteration(X33)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
cnf(c_0_29,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,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_26,c_0_27]) ).
cnf(c_0_31,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_32,plain,
! [X21,X22,X23] : multiplication(addition(X21,X22),X23) = addition(multiplication(X21,X23),multiplication(X22,X23)),
inference(variable_rename,[status(thm)],[distributivity2]) ).
cnf(c_0_33,negated_conjecture,
addition(multiplication(esk1_0,esk2_0),addition(multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0))),X1)) = addition(multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0))),X1),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_24,c_0_29]) ).
cnf(c_0_35,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_31,c_0_24]) ).
cnf(c_0_36,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_38,negated_conjecture,
addition(multiplication(esk1_0,esk2_0),addition(X1,addition(X2,multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0)))))) = addition(X1,addition(X2,multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0))))),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,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_35,c_0_36]) ).
fof(c_0_40,plain,
! [X12] : addition(X12,X12) = X12,
inference(variable_rename,[status(thm)],[idempotence]) ).
cnf(c_0_41,plain,
( leq(addition(X1,X2),X3)
| addition(X1,addition(X2,X3)) != X3 ),
inference(spm,[status(thm)],[c_0_37,c_0_29]) ).
cnf(c_0_42,negated_conjecture,
addition(multiplication(esk1_0,esk2_0),strong_iteration(addition(esk1_0,esk2_0))) = strong_iteration(addition(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_44,negated_conjecture,
( leq(addition(X1,multiplication(esk1_0,esk2_0)),strong_iteration(addition(esk1_0,esk2_0)))
| addition(X1,strong_iteration(addition(esk1_0,esk2_0))) != strong_iteration(addition(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,plain,
addition(one,addition(multiplication(X1,strong_iteration(X1)),X2)) = addition(strong_iteration(X1),X2),
inference(spm,[status(thm)],[c_0_29,c_0_35]) ).
cnf(c_0_46,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_29,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
( leq(addition(X1,multiplication(esk1_0,esk2_0)),strong_iteration(addition(esk1_0,esk2_0)))
| addition(strong_iteration(addition(esk1_0,esk2_0)),X1) != strong_iteration(addition(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_44,c_0_24]) ).
cnf(c_0_48,plain,
addition(strong_iteration(X1),multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_43]),c_0_35]) ).
cnf(c_0_49,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_37,c_0_46]) ).
cnf(c_0_50,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_36]),c_0_29]),c_0_24]),c_0_30]) ).
cnf(c_0_51,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_24]),c_0_29]) ).
cnf(c_0_52,plain,
addition(one,strong_iteration(X1)) = strong_iteration(X1),
inference(spm,[status(thm)],[c_0_46,c_0_35]) ).
cnf(c_0_53,plain,
leq(X1,addition(X2,addition(X3,X1))),
inference(spm,[status(thm)],[c_0_49,c_0_34]) ).
cnf(c_0_54,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_26,c_0_50]),c_0_29]),c_0_24]),c_0_51]) ).
fof(c_0_55,plain,
! [X17] : multiplication(one,X17) = X17,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_56,plain,
! [X13,X14,X15] : multiplication(X13,multiplication(X14,X15)) = multiplication(multiplication(X13,X14),X15),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_57,plain,
! [X11] : addition(X11,zero) = X11,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_58,plain,
! [X27,X28,X29] :
( ~ leq(addition(multiplication(X27,X29),X28),X29)
| leq(multiplication(star(X27),X28),X29) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction1])]) ).
cnf(c_0_59,plain,
( leq(addition(X1,one),strong_iteration(X2))
| addition(X1,strong_iteration(X2)) != strong_iteration(X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_52]) ).
cnf(c_0_60,negated_conjecture,
leq(multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0))),strong_iteration(addition(esk1_0,esk2_0))),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_61,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_62,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_63,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_20]) ).
cnf(c_0_64,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_57]) ).
fof(c_0_65,plain,
! [X37] : strong_iteration(X37) = addition(star(X37),multiplication(strong_iteration(X37),zero)),
inference(variable_rename,[status(thm)],[isolation]) ).
cnf(c_0_66,plain,
( leq(multiplication(star(X1),X3),X2)
| ~ leq(addition(multiplication(X1,X2),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
fof(c_0_67,plain,
! [X26] : addition(one,multiplication(star(X26),X26)) = star(X26),
inference(variable_rename,[status(thm)],[star_unfold2]) ).
cnf(c_0_68,plain,
( leq(addition(X1,one),strong_iteration(X2))
| addition(strong_iteration(X2),X1) != strong_iteration(X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_24]) ).
cnf(c_0_69,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_26,c_0_60]),c_0_24]) ).
fof(c_0_70,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_71,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_36,c_0_35]),c_0_61]),c_0_62]) ).
cnf(c_0_72,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_63,c_0_24]),c_0_24]) ).
cnf(c_0_73,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_64,c_0_24]) ).
cnf(c_0_74,plain,
strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
fof(c_0_75,plain,
! [X24] : multiplication(zero,X24) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_76,plain,
( leq(multiplication(star(X1),multiplication(X1,X2)),X2)
| ~ leq(multiplication(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_66,c_0_43]) ).
cnf(c_0_77,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_78,plain,
( leq(multiplication(star(X1),X2),X3)
| ~ leq(addition(X2,multiplication(X1,X3)),X3) ),
inference(spm,[status(thm)],[c_0_66,c_0_24]) ).
cnf(c_0_79,negated_conjecture,
leq(addition(one,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_68,c_0_69]),c_0_24]) ).
cnf(c_0_80,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_70]) ).
fof(c_0_81,plain,
! [X18,X19,X20] : multiplication(X18,addition(X19,X20)) = addition(multiplication(X18,X19),multiplication(X18,X20)),
inference(variable_rename,[status(thm)],[distributivity1]) ).
cnf(c_0_82,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_34,c_0_43]) ).
cnf(c_0_83,negated_conjecture,
( addition(multiplication(strong_iteration(esk1_0),zero),multiplication(strong_iteration(esk2_0),zero)) = zero
| addition(multiplication(esk1_0,zero),multiplication(esk2_0,zero)) = zero ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_36]),c_0_73]) ).
cnf(c_0_84,plain,
addition(multiplication(strong_iteration(X1),zero),star(X1)) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_74,c_0_24]) ).
cnf(c_0_85,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_86,negated_conjecture,
leq(multiplication(star(esk2_0),multiplication(esk2_0,strong_iteration(addition(esk1_0,esk2_0)))),strong_iteration(addition(esk1_0,esk2_0))),
inference(spm,[status(thm)],[c_0_76,c_0_60]) ).
cnf(c_0_87,plain,
addition(X1,multiplication(star(X2),multiplication(X2,X1))) = multiplication(star(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_77]),c_0_61]),c_0_62]) ).
cnf(c_0_88,negated_conjecture,
leq(star(esk2_0),strong_iteration(addition(esk1_0,esk2_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]) ).
cnf(c_0_89,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_90,negated_conjecture,
( addition(multiplication(esk1_0,zero),multiplication(esk2_0,zero)) = zero
| multiplication(strong_iteration(esk2_0),zero) = zero ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_64]) ).
cnf(c_0_91,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_36,c_0_84]),c_0_62]),c_0_85]) ).
cnf(c_0_92,negated_conjecture,
multiplication(star(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_26,c_0_86]),c_0_24]),c_0_87]) ).
cnf(c_0_93,plain,
addition(multiplication(strong_iteration(X1),zero),addition(X2,star(X1))) = addition(X2,strong_iteration(X1)),
inference(spm,[status(thm)],[c_0_51,c_0_84]) ).
cnf(c_0_94,negated_conjecture,
addition(strong_iteration(addition(esk1_0,esk2_0)),star(esk2_0)) = strong_iteration(addition(esk1_0,esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_88]),c_0_24]) ).
cnf(c_0_95,plain,
addition(multiplication(strong_iteration(X1),zero),addition(star(X1),X2)) = addition(strong_iteration(X1),X2),
inference(spm,[status(thm)],[c_0_29,c_0_84]) ).
cnf(c_0_96,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_89,c_0_35]),c_0_80]) ).
cnf(c_0_97,negated_conjecture,
( addition(multiplication(esk1_0,zero),multiplication(esk2_0,zero)) = zero
| multiplication(esk2_0,zero) = zero ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_90]),c_0_73]) ).
cnf(c_0_98,plain,
addition(multiplication(X1,zero),multiplication(X1,X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_89,c_0_73]) ).
fof(c_0_99,plain,
! [X34,X35,X36] :
( ~ leq(X36,addition(multiplication(X34,X36),X35))
| leq(X36,multiplication(strong_iteration(X34),X35)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[infty_coinduction])]) ).
cnf(c_0_100,negated_conjecture,
multiplication(strong_iteration(esk2_0),strong_iteration(addition(esk1_0,esk2_0))) = addition(multiplication(strong_iteration(esk2_0),zero),strong_iteration(addition(esk1_0,esk2_0))),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_101,negated_conjecture,
addition(multiplication(strong_iteration(esk2_0),zero),strong_iteration(addition(esk1_0,esk2_0))) = addition(strong_iteration(esk2_0),strong_iteration(addition(esk1_0,esk2_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_24]) ).
cnf(c_0_102,plain,
leq(X1,X1),
inference(spm,[status(thm)],[c_0_37,c_0_43]) ).
cnf(c_0_103,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_95,c_0_96]),c_0_91]) ).
fof(c_0_104,plain,
! [X25] : addition(one,multiplication(X25,star(X25))) = star(X25),
inference(variable_rename,[status(thm)],[star_unfold1]) ).
cnf(c_0_105,negated_conjecture,
multiplication(esk2_0,zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_97]),c_0_64])]) ).
cnf(c_0_106,plain,
leq(multiplication(X1,zero),multiplication(X1,X2)),
inference(spm,[status(thm)],[c_0_37,c_0_98]) ).
cnf(c_0_107,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(multiplication(X2,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_108,negated_conjecture,
multiplication(strong_iteration(esk2_0),strong_iteration(addition(esk1_0,esk2_0))) = addition(strong_iteration(esk2_0),strong_iteration(addition(esk1_0,esk2_0))),
inference(rw,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_109,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_78,c_0_48]),c_0_102])]) ).
cnf(c_0_110,plain,
multiplication(star(X1),strong_iteration(X1)) = multiplication(strong_iteration(X1),strong_iteration(X1)),
inference(spm,[status(thm)],[c_0_87,c_0_103]) ).
fof(c_0_111,plain,
! [X30,X31,X32] :
( ~ leq(addition(multiplication(X32,X30),X31),X32)
| leq(multiplication(X31,star(X30)),X32) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction2])]) ).
cnf(c_0_112,plain,
addition(one,multiplication(X1,star(X1))) = star(X1),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_113,negated_conjecture,
( leq(multiplication(star(esk2_0),X1),zero)
| ~ leq(X1,zero) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_105]),c_0_73]) ).
cnf(c_0_114,negated_conjecture,
( addition(multiplication(strong_iteration(esk1_0),zero),multiplication(strong_iteration(esk2_0),zero)) = zero
| leq(multiplication(strong_iteration(addition(esk1_0,esk2_0)),zero),zero) ),
inference(spm,[status(thm)],[c_0_106,c_0_72]) ).
cnf(c_0_115,plain,
( leq(X1,multiplication(strong_iteration(addition(X2,X3)),X4))
| ~ leq(X1,addition(multiplication(X2,X1),addition(multiplication(X3,X1),X4))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_36]),c_0_29]) ).
cnf(c_0_116,negated_conjecture,
addition(multiplication(esk2_0,strong_iteration(esk2_0)),strong_iteration(addition(esk1_0,esk2_0))) = addition(strong_iteration(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_71,c_0_108]),c_0_89]),c_0_51]),c_0_69]) ).
cnf(c_0_117,plain,
leq(multiplication(strong_iteration(X1),strong_iteration(X1)),strong_iteration(X1)),
inference(rw,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_118,plain,
addition(X1,multiplication(strong_iteration(X2),X1)) = multiplication(strong_iteration(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_52]),c_0_61]) ).
cnf(c_0_119,plain,
( leq(multiplication(X3,star(X2)),X1)
| ~ leq(addition(multiplication(X1,X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_120,plain,
addition(one,addition(multiplication(X1,star(addition(X1,X2))),multiplication(X2,star(addition(X1,X2))))) = star(addition(X1,X2)),
inference(spm,[status(thm)],[c_0_112,c_0_36]) ).
cnf(c_0_121,plain,
addition(one,addition(multiplication(X1,star(X1)),X2)) = addition(star(X1),X2),
inference(spm,[status(thm)],[c_0_29,c_0_112]) ).
cnf(c_0_122,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_46,c_0_77]) ).
cnf(c_0_123,negated_conjecture,
( addition(multiplication(strong_iteration(esk1_0),zero),multiplication(strong_iteration(esk2_0),zero)) = zero
| leq(multiplication(star(esk2_0),multiplication(strong_iteration(addition(esk1_0,esk2_0)),zero)),zero) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_124,negated_conjecture,
leq(strong_iteration(esk2_0),multiplication(strong_iteration(addition(X1,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_115,c_0_116]),c_0_51]),c_0_49])]) ).
cnf(c_0_125,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_26,c_0_117]),c_0_24]),c_0_118]) ).
cnf(c_0_126,plain,
( leq(multiplication(X1,multiplication(X2,star(X2))),X1)
| ~ leq(multiplication(X1,X2),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_43]),c_0_62]) ).
cnf(c_0_127,plain,
multiplication(strong_iteration(X1),star(strong_iteration(X1))) = star(strong_iteration(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_48]),c_0_62]),c_0_121]),c_0_71]) ).
cnf(c_0_128,plain,
addition(one,addition(X1,multiplication(X2,star(X2)))) = addition(X1,star(X2)),
inference(spm,[status(thm)],[c_0_51,c_0_112]) ).
cnf(c_0_129,plain,
addition(X1,multiplication(X1,star(X2))) = multiplication(X1,star(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_122]),c_0_80]) ).
cnf(c_0_130,negated_conjecture,
( addition(multiplication(strong_iteration(esk1_0),zero),multiplication(strong_iteration(esk2_0),zero)) = zero
| multiplication(star(esk2_0),multiplication(strong_iteration(addition(esk1_0,esk2_0)),zero)) = zero ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_123]),c_0_64]) ).
cnf(c_0_131,negated_conjecture,
leq(strong_iteration(esk2_0),strong_iteration(addition(esk1_0,esk2_0))),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_132,plain,
leq(star(strong_iteration(X1)),strong_iteration(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_117]),c_0_127]),c_0_127]) ).
cnf(c_0_133,plain,
addition(X1,star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_112]) ).
cnf(c_0_134,plain,
leq(X1,addition(X2,X1)),
inference(spm,[status(thm)],[c_0_49,c_0_24]) ).
cnf(c_0_135,plain,
addition(X1,multiplication(star(multiplication(X2,X3)),multiplication(X2,multiplication(X3,X1)))) = multiplication(star(multiplication(X2,X3)),X1),
inference(spm,[status(thm)],[c_0_87,c_0_62]) ).
cnf(c_0_136,negated_conjecture,
( multiplication(strong_iteration(esk2_0),multiplication(strong_iteration(addition(esk1_0,esk2_0)),zero)) = multiplication(strong_iteration(esk2_0),zero)
| addition(multiplication(strong_iteration(esk1_0),zero),multiplication(strong_iteration(esk2_0),zero)) = zero ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_130]),c_0_64]) ).
cnf(c_0_137,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_26,c_0_131]) ).
cnf(c_0_138,plain,
star(strong_iteration(X1)) = strong_iteration(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_132]),c_0_24]),c_0_133]) ).
cnf(c_0_139,plain,
leq(X1,multiplication(strong_iteration(X2),X1)),
inference(spm,[status(thm)],[c_0_107,c_0_134]) ).
cnf(c_0_140,negated_conjecture,
( multiplication(strong_iteration(addition(esk1_0,esk2_0)),multiplication(strong_iteration(esk2_0),zero)) = multiplication(strong_iteration(addition(esk1_0,esk2_0)),zero)
| addition(multiplication(strong_iteration(esk1_0),zero),multiplication(strong_iteration(esk2_0),zero)) = zero ),
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_135,c_0_136]),c_0_100]),c_0_101]),c_0_137]),c_0_138]),c_0_73]),c_0_100]),c_0_101]),c_0_137]),c_0_138]) ).
cnf(c_0_141,plain,
leq(X1,addition(X2,addition(X1,X3))),
inference(spm,[status(thm)],[c_0_49,c_0_34]) ).
cnf(c_0_142,negated_conjecture,
( addition(multiplication(strong_iteration(esk1_0),zero),multiplication(strong_iteration(esk2_0),zero)) = zero
| leq(multiplication(strong_iteration(esk2_0),zero),multiplication(strong_iteration(addition(esk1_0,esk2_0)),zero)) ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_143,negated_conjecture,
leq(multiplication(esk1_0,strong_iteration(addition(esk1_0,esk2_0))),strong_iteration(addition(esk1_0,esk2_0))),
inference(spm,[status(thm)],[c_0_141,c_0_54]) ).
cnf(c_0_144,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(spm,[status(thm)],[c_0_142,c_0_72]) ).
cnf(c_0_145,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_26,c_0_143]),c_0_24]) ).
cnf(c_0_146,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_26,c_0_144]),c_0_64]) ).
cnf(c_0_147,negated_conjecture,
leq(addition(one,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_68,c_0_145]),c_0_24]) ).
cnf(c_0_148,plain,
multiplication(X1,multiplication(strong_iteration(X1),zero)) = multiplication(strong_iteration(X1),zero),
inference(spm,[status(thm)],[c_0_73,c_0_71]) ).
cnf(c_0_149,negated_conjecture,
multiplication(strong_iteration(esk2_0),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_146]),c_0_64])]) ).
cnf(c_0_150,plain,
( leq(addition(X1,X2),zero)
| addition(X1,X2) != zero ),
inference(spm,[status(thm)],[c_0_41,c_0_64]) ).
cnf(c_0_151,plain,
addition(one,addition(multiplication(star(addition(X1,X2)),X1),multiplication(star(addition(X1,X2)),X2))) = star(addition(X1,X2)),
inference(spm,[status(thm)],[c_0_77,c_0_89]) ).
cnf(c_0_152,negated_conjecture,
leq(star(esk1_0),strong_iteration(addition(esk1_0,esk2_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_147]),c_0_80]) ).
cnf(c_0_153,plain,
addition(X1,multiplication(X1,multiplication(star(X2),X2))) = multiplication(X1,star(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_77]),c_0_80]) ).
cnf(c_0_154,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_36,c_0_112]),c_0_61]),c_0_62]) ).
cnf(c_0_155,plain,
leq(multiplication(strong_iteration(X1),zero),multiplication(strong_iteration(addition(X1,X2)),X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_148]),c_0_49])]) ).
cnf(c_0_156,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_72,c_0_149]),c_0_64]) ).
cnf(c_0_157,plain,
( leq(multiplication(X1,X2),zero)
| multiplication(X1,X2) != zero ),
inference(spm,[status(thm)],[c_0_150,c_0_98]) ).
cnf(c_0_158,plain,
addition(star(addition(X1,X2)),addition(multiplication(star(addition(X1,X2)),X1),multiplication(star(addition(X1,X2)),X2))) = star(addition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_151]),c_0_29]),c_0_24]),c_0_51]) ).
cnf(c_0_159,negated_conjecture,
addition(star(esk1_0),strong_iteration(addition(esk1_0,esk2_0))) = strong_iteration(addition(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_26,c_0_152]) ).
cnf(c_0_160,plain,
multiplication(star(X1),X1) = multiplication(X1,star(X1)),
inference(spm,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_161,negated_conjecture,
leq(multiplication(strong_iteration(esk1_0),zero),zero),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_157]) ).
cnf(c_0_162,plain,
( leq(X1,addition(X2,X3))
| addition(X3,addition(X1,X2)) != addition(X2,X3) ),
inference(spm,[status(thm)],[c_0_37,c_0_34]) ).
cnf(c_0_163,negated_conjecture,
addition(multiplication(esk2_0,strong_iteration(esk2_0)),strong_iteration(addition(esk1_0,esk2_0))) = strong_iteration(addition(esk1_0,esk2_0)),
inference(rw,[status(thm)],[c_0_116,c_0_137]) ).
cnf(c_0_164,plain,
addition(X1,X2) = addition(X2,X1),
c_0_24 ).
cnf(c_0_165,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
c_0_29 ).
cnf(c_0_166,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
c_0_62 ).
cnf(c_0_167,plain,
addition(multiplication(X1,multiplication(strong_iteration(X2),zero)),multiplication(X1,star(X2))) = multiplication(X1,strong_iteration(X2)),
inference(spm,[status(thm)],[c_0_89,c_0_84]) ).
cnf(c_0_168,negated_conjecture,
multiplication(strong_iteration(addition(esk1_0,esk2_0)),star(esk1_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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_138]),c_0_138]),c_0_160]),c_0_127]),c_0_138]),c_0_24]),c_0_129]),c_0_129]),c_0_138]) ).
cnf(c_0_169,plain,
leq(one,addition(strong_iteration(X1),X2)),
inference(spm,[status(thm)],[c_0_49,c_0_45]) ).
cnf(c_0_170,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_36,c_0_30]),c_0_62]),c_0_62]),c_0_62]) ).
cnf(c_0_171,negated_conjecture,
multiplication(strong_iteration(esk1_0),zero) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_161]),c_0_64]) ).
cnf(c_0_172,negated_conjecture,
leq(multiplication(esk2_0,strong_iteration(esk2_0)),addition(strong_iteration(addition(esk1_0,esk2_0)),X1)),
inference(ar,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_163]),c_0_164,c_0_165,c_0_166]) ).
cnf(c_0_173,negated_conjecture,
addition(strong_iteration(addition(esk1_0,esk2_0)),multiplication(strong_iteration(addition(esk1_0,esk2_0)),multiplication(strong_iteration(esk1_0),zero))) = multiplication(strong_iteration(addition(esk1_0,esk2_0)),strong_iteration(esk1_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_24]) ).
cnf(c_0_174,plain,
leq(one,addition(X1,strong_iteration(X2))),
inference(spm,[status(thm)],[c_0_169,c_0_24]) ).
cnf(c_0_175,plain,
star(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_85]),c_0_64]) ).
cnf(c_0_176,negated_conjecture,
( leq(multiplication(star(esk1_0),multiplication(esk2_0,multiplication(strong_iteration(addition(esk1_0,esk2_0)),X1))),multiplication(esk2_0,X1))
| ~ leq(multiplication(esk2_0,multiplication(strong_iteration(addition(esk1_0,esk2_0)),X1)),multiplication(esk2_0,X1)) ),
inference(spm,[status(thm)],[c_0_66,c_0_170]) ).
cnf(c_0_177,negated_conjecture,
star(esk1_0) = strong_iteration(esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_171]),c_0_73]) ).
cnf(c_0_178,negated_conjecture,
leq(multiplication(esk2_0,strong_iteration(esk2_0)),multiplication(strong_iteration(addition(esk1_0,esk2_0)),strong_iteration(esk1_0))),
inference(spm,[status(thm)],[c_0_172,c_0_173]) ).
cnf(c_0_179,plain,
leq(one,multiplication(strong_iteration(X1),strong_iteration(X2))),
inference(spm,[status(thm)],[c_0_107,c_0_174]) ).
cnf(c_0_180,plain,
addition(X1,multiplication(X1,zero)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_175]),c_0_61]),c_0_80]) ).
cnf(c_0_181,negated_conjecture,
( leq(multiplication(strong_iteration(esk1_0),multiplication(esk2_0,multiplication(strong_iteration(addition(esk1_0,esk2_0)),X1))),multiplication(esk2_0,X1))
| ~ leq(multiplication(esk2_0,multiplication(strong_iteration(addition(esk1_0,esk2_0)),X1)),multiplication(esk2_0,X1)) ),
inference(rw,[status(thm)],[c_0_176,c_0_177]) ).
cnf(c_0_182,negated_conjecture,
addition(multiplication(esk2_0,strong_iteration(esk2_0)),multiplication(strong_iteration(addition(esk1_0,esk2_0)),strong_iteration(esk1_0))) = multiplication(strong_iteration(addition(esk1_0,esk2_0)),strong_iteration(esk1_0)),
inference(spm,[status(thm)],[c_0_26,c_0_178]) ).
cnf(c_0_183,plain,
addition(one,multiplication(strong_iteration(X1),strong_iteration(X2))) = multiplication(strong_iteration(X1),strong_iteration(X2)),
inference(spm,[status(thm)],[c_0_26,c_0_179]) ).
cnf(c_0_184,negated_conjecture,
multiplication(strong_iteration(addition(esk1_0,esk2_0)),strong_iteration(esk1_0)) = strong_iteration(addition(esk1_0,esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_173,c_0_171]),c_0_180]) ).
cnf(c_0_185,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(spm,[status(thm)],[c_0_181,c_0_125]),c_0_102])]) ).
cnf(c_0_186,plain,
( leq(multiplication(X1,star(X2)),X3)
| ~ leq(addition(X1,multiplication(X3,X2)),X3) ),
inference(spm,[status(thm)],[c_0_119,c_0_24]) ).
cnf(c_0_187,negated_conjecture,
addition(strong_iteration(esk2_0),multiplication(strong_iteration(addition(esk1_0,esk2_0)),strong_iteration(esk1_0))) = multiplication(strong_iteration(addition(esk1_0,esk2_0)),strong_iteration(esk1_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_182]),c_0_183]) ).
cnf(c_0_188,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_20]) ).
cnf(c_0_189,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_107,c_0_34]),c_0_89]) ).
cnf(c_0_190,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(spm,[status(thm)],[c_0_71,c_0_184]),c_0_36]) ).
cnf(c_0_191,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_26,c_0_185]),c_0_24]),c_0_118]) ).
cnf(c_0_192,negated_conjecture,
( leq(multiplication(strong_iteration(esk2_0),strong_iteration(esk1_0)),strong_iteration(addition(esk1_0,esk2_0)))
| ~ leq(multiplication(strong_iteration(addition(esk1_0,esk2_0)),strong_iteration(esk1_0)),strong_iteration(addition(esk1_0,esk2_0))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_187]),c_0_138]) ).
cnf(c_0_193,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_188,c_0_24]),c_0_24]) ).
cnf(c_0_194,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(X3,multiplication(X2,X1))) ),
inference(spm,[status(thm)],[c_0_107,c_0_24]) ).
cnf(c_0_195,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_189,c_0_190]),c_0_191]),c_0_125]),c_0_24]),c_0_102])]) ).
cnf(c_0_196,negated_conjecture,
leq(multiplication(strong_iteration(esk2_0),strong_iteration(esk1_0)),strong_iteration(addition(esk1_0,esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_192,c_0_184]),c_0_102])]) ).
cnf(c_0_197,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_193,c_0_149]),c_0_64]) ).
cnf(c_0_198,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_194,c_0_195]) ).
cnf(c_0_199,plain,
addition(X1,multiplication(X2,X3)) = addition(multiplication(X2,X3),addition(X1,multiplication(X2,zero))),
inference(spm,[status(thm)],[c_0_34,c_0_98]) ).
cnf(c_0_200,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(spm,[status(thm)],[c_0_26,c_0_196]) ).
cnf(c_0_201,negated_conjecture,
multiplication(strong_iteration(addition(esk1_0,esk2_0)),zero) != zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_197,c_0_171])]) ).
cnf(c_0_202,negated_conjecture,
strong_iteration(addition(esk1_0,esk2_0)) = multiplication(strong_iteration(esk2_0),strong_iteration(esk1_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_26,c_0_198]),c_0_199]),c_0_24]),c_0_149]),c_0_73]),c_0_200]) ).
cnf(c_0_203,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_201,c_0_202]),c_0_62]),c_0_171]),c_0_149])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KLE166+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : enigmatic-eprover.py %s %d 1
% 0.12/0.34 % Computer : n025.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 11:06:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.45 # ENIGMATIC: Selected SinE mode:
% 0.19/0.46 # Parsing /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.19/0.46 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.19/0.46 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 87.58/12.27 # ENIGMATIC: Solved by autoschedule:
% 87.58/12.27 # No SInE strategy applied
% 87.58/12.27 # Trying AutoSched0 for 150 seconds
% 87.58/12.27 # AutoSched0-Mode selected heuristic G_E___208_B00_00_F1_SE_CS_SP_PS_S071I
% 87.58/12.27 # and selection function SelectCQArEqLast.
% 87.58/12.27 #
% 87.58/12.27 # Preprocessing time : 0.014 s
% 87.58/12.27 # Presaturation interreduction done
% 87.58/12.27
% 87.58/12.27 # Proof found!
% 87.58/12.27 # SZS status Theorem
% 87.58/12.27 # SZS output start CNFRefutation
% See solution above
% 87.58/12.27 # Training examples: 1 positive, 36 negative
% 87.58/12.27
% 87.58/12.27 # -------------------------------------------------
% 87.58/12.27 # User time : 9.723 s
% 87.58/12.27 # System time : 0.296 s
% 87.58/12.27 # Total time : 10.019 s
% 87.58/12.27 # Maximum resident set size: 7120 pages
% 87.58/12.27
%------------------------------------------------------------------------------