TSTP Solution File: KLE150+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE150+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.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 02:15:35 EDT 2022
% Result : Theorem 1.94s 2.15s
% Output : CNFRefutation 1.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 35
% Syntax : Number of formulae : 184 ( 115 unt; 0 def)
% Number of atoms : 278 ( 223 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 196 ( 102 ~; 82 |; 5 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 241 ( 5 sgn 78 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A) ).
fof(additive_associativity,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) ).
fof(idempotence,axiom,
! [A] : addition(A,A) = A ).
fof(multiplicative_associativity,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ).
fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero ).
fof(star_unfold1,axiom,
! [A] : addition(one,multiplication(A,star(A))) = star(A) ).
fof(infty_unfold1,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) ).
fof(isolation,axiom,
! [A] : strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ) ).
fof(goals,conjecture,
! [X0] :
( leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero)))
& leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero))) ) ).
fof(subgoal_0,plain,
! [X0] : leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))),
inference(strip,[],[goals]) ).
fof(subgoal_1,plain,
! [X0] :
( leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero)))
=> leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero))) ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0] : leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0] : ~ leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ leq(strong_iteration(multiplication(skolemFOFtoCNF_X0,zero)),addition(one,multiplication(skolemFOFtoCNF_X0,zero))),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A] : addition(one,multiplication(A,star(A))) = star(A),
inference(canonicalize,[],[star_unfold1]) ).
fof(normalize_0_3,plain,
! [A] : addition(one,multiplication(A,star(A))) = star(A),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(canonicalize,[],[multiplicative_associativity]) ).
fof(normalize_0_5,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A] : multiplication(zero,A) = zero,
inference(canonicalize,[],[left_annihilation]) ).
fof(normalize_0_7,plain,
! [A] : multiplication(zero,A) = zero,
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(canonicalize,[],[infty_unfold1]) ).
fof(normalize_0_9,plain,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_11,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(canonicalize,[],[order]) ).
fof(normalize_0_13,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( ~ leq(A,B)
| addition(A,B) = B ) ),
inference(clausify,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,B] :
( addition(A,B) != B
| leq(A,B) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[idempotence]) ).
fof(normalize_0_17,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_0_16]) ).
cnf(refute_0_0,plain,
~ leq(strong_iteration(multiplication(skolemFOFtoCNF_X0,zero)),addition(one,multiplication(skolemFOFtoCNF_X0,zero))),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
addition(one,multiplication(A,star(A))) = star(A),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
addition(one,multiplication(multiplication(X_30,X_31),star(multiplication(X_30,X_31)))) = star(multiplication(X_30,X_31)),
inference(subst,[],[refute_0_1:[bind(A,$fot(multiplication(X_30,X_31)))]]) ).
cnf(refute_0_3,plain,
multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
multiplication(X_30,multiplication(X_31,star(multiplication(X_30,X_31)))) = multiplication(multiplication(X_30,X_31),star(multiplication(X_30,X_31))),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_30)),bind(B,$fot(X_31)),bind(C,$fot(star(multiplication(X_30,X_31))))]]) ).
cnf(refute_0_5,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_6,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_7,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( multiplication(X_30,multiplication(X_31,star(multiplication(X_30,X_31)))) != multiplication(multiplication(X_30,X_31),star(multiplication(X_30,X_31)))
| multiplication(multiplication(X_30,X_31),star(multiplication(X_30,X_31))) = multiplication(X_30,multiplication(X_31,star(multiplication(X_30,X_31)))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(multiplication(X_30,multiplication(X_31,star(multiplication(X_30,X_31)))))),bind(Y,$fot(multiplication(multiplication(X_30,X_31),star(multiplication(X_30,X_31)))))]]) ).
cnf(refute_0_9,plain,
multiplication(multiplication(X_30,X_31),star(multiplication(X_30,X_31))) = multiplication(X_30,multiplication(X_31,star(multiplication(X_30,X_31)))),
inference(resolve,[$cnf( $equal(multiplication(X_30,multiplication(X_31,star(multiplication(X_30,X_31)))),multiplication(multiplication(X_30,X_31),star(multiplication(X_30,X_31)))) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( addition(one,multiplication(multiplication(X_30,X_31),star(multiplication(X_30,X_31)))) != star(multiplication(X_30,X_31))
| multiplication(multiplication(X_30,X_31),star(multiplication(X_30,X_31))) != multiplication(X_30,multiplication(X_31,star(multiplication(X_30,X_31))))
| addition(one,multiplication(X_30,multiplication(X_31,star(multiplication(X_30,X_31))))) = star(multiplication(X_30,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(one,multiplication(multiplication(X_30,X_31),star(multiplication(X_30,X_31)))),star(multiplication(X_30,X_31))) ),[0,1],$fot(multiplication(X_30,multiplication(X_31,star(multiplication(X_30,X_31)))))]]) ).
cnf(refute_0_11,plain,
( addition(one,multiplication(multiplication(X_30,X_31),star(multiplication(X_30,X_31)))) != star(multiplication(X_30,X_31))
| addition(one,multiplication(X_30,multiplication(X_31,star(multiplication(X_30,X_31))))) = star(multiplication(X_30,X_31)) ),
inference(resolve,[$cnf( $equal(multiplication(multiplication(X_30,X_31),star(multiplication(X_30,X_31))),multiplication(X_30,multiplication(X_31,star(multiplication(X_30,X_31))))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
addition(one,multiplication(X_30,multiplication(X_31,star(multiplication(X_30,X_31))))) = star(multiplication(X_30,X_31)),
inference(resolve,[$cnf( $equal(addition(one,multiplication(multiplication(X_30,X_31),star(multiplication(X_30,X_31)))),star(multiplication(X_30,X_31))) )],[refute_0_2,refute_0_11]) ).
cnf(refute_0_13,plain,
addition(one,multiplication(X_227,multiplication(zero,star(multiplication(X_227,zero))))) = star(multiplication(X_227,zero)),
inference(subst,[],[refute_0_12:[bind(X_30,$fot(X_227)),bind(X_31,$fot(zero))]]) ).
cnf(refute_0_14,plain,
multiplication(zero,A) = zero,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_15,plain,
multiplication(zero,star(multiplication(X_227,zero))) = zero,
inference(subst,[],[refute_0_14:[bind(A,$fot(star(multiplication(X_227,zero))))]]) ).
cnf(refute_0_16,plain,
( addition(one,multiplication(X_227,multiplication(zero,star(multiplication(X_227,zero))))) != star(multiplication(X_227,zero))
| multiplication(zero,star(multiplication(X_227,zero))) != zero
| addition(one,multiplication(X_227,zero)) = star(multiplication(X_227,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(one,multiplication(X_227,multiplication(zero,star(multiplication(X_227,zero))))),star(multiplication(X_227,zero))) ),[0,1,1],$fot(zero)]]) ).
cnf(refute_0_17,plain,
( addition(one,multiplication(X_227,multiplication(zero,star(multiplication(X_227,zero))))) != star(multiplication(X_227,zero))
| addition(one,multiplication(X_227,zero)) = star(multiplication(X_227,zero)) ),
inference(resolve,[$cnf( $equal(multiplication(zero,star(multiplication(X_227,zero))),zero) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
addition(one,multiplication(X_227,zero)) = star(multiplication(X_227,zero)),
inference(resolve,[$cnf( $equal(addition(one,multiplication(X_227,multiplication(zero,star(multiplication(X_227,zero))))),star(multiplication(X_227,zero))) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
addition(one,multiplication(skolemFOFtoCNF_X0,zero)) = star(multiplication(skolemFOFtoCNF_X0,zero)),
inference(subst,[],[refute_0_18:[bind(X_227,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_20,plain,
( addition(one,multiplication(skolemFOFtoCNF_X0,zero)) != star(multiplication(skolemFOFtoCNF_X0,zero))
| ~ leq(strong_iteration(multiplication(skolemFOFtoCNF_X0,zero)),star(multiplication(skolemFOFtoCNF_X0,zero)))
| leq(strong_iteration(multiplication(skolemFOFtoCNF_X0,zero)),addition(one,multiplication(skolemFOFtoCNF_X0,zero))) ),
introduced(tautology,[equality,[$cnf( ~ leq(strong_iteration(multiplication(skolemFOFtoCNF_X0,zero)),addition(one,multiplication(skolemFOFtoCNF_X0,zero))) ),[1],$fot(star(multiplication(skolemFOFtoCNF_X0,zero)))]]) ).
cnf(refute_0_21,plain,
( ~ leq(strong_iteration(multiplication(skolemFOFtoCNF_X0,zero)),star(multiplication(skolemFOFtoCNF_X0,zero)))
| leq(strong_iteration(multiplication(skolemFOFtoCNF_X0,zero)),addition(one,multiplication(skolemFOFtoCNF_X0,zero))) ),
inference(resolve,[$cnf( $equal(addition(one,multiplication(skolemFOFtoCNF_X0,zero)),star(multiplication(skolemFOFtoCNF_X0,zero))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
~ leq(strong_iteration(multiplication(skolemFOFtoCNF_X0,zero)),star(multiplication(skolemFOFtoCNF_X0,zero))),
inference(resolve,[$cnf( leq(strong_iteration(multiplication(skolemFOFtoCNF_X0,zero)),addition(one,multiplication(skolemFOFtoCNF_X0,zero))) )],[refute_0_21,refute_0_0]) ).
cnf(refute_0_23,plain,
strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_24,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_25,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_26,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
addition(multiplication(A,strong_iteration(A)),one) = addition(one,multiplication(A,strong_iteration(A))),
inference(subst,[],[refute_0_26:[bind(A,$fot(one)),bind(B,$fot(multiplication(A,strong_iteration(A))))]]) ).
cnf(refute_0_28,plain,
( addition(multiplication(A,strong_iteration(A)),one) != addition(one,multiplication(A,strong_iteration(A)))
| strong_iteration(A) != addition(multiplication(A,strong_iteration(A)),one)
| strong_iteration(A) = addition(one,multiplication(A,strong_iteration(A))) ),
introduced(tautology,[equality,[$cnf( $equal(strong_iteration(A),addition(multiplication(A,strong_iteration(A)),one)) ),[1],$fot(addition(one,multiplication(A,strong_iteration(A))))]]) ).
cnf(refute_0_29,plain,
( strong_iteration(A) != addition(multiplication(A,strong_iteration(A)),one)
| strong_iteration(A) = addition(one,multiplication(A,strong_iteration(A))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(A,strong_iteration(A)),one),addition(one,multiplication(A,strong_iteration(A)))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
strong_iteration(A) = addition(one,multiplication(A,strong_iteration(A))),
inference(resolve,[$cnf( $equal(strong_iteration(A),addition(multiplication(A,strong_iteration(A)),one)) )],[refute_0_23,refute_0_29]) ).
cnf(refute_0_31,plain,
strong_iteration(multiplication(X_30,X_31)) = addition(one,multiplication(multiplication(X_30,X_31),strong_iteration(multiplication(X_30,X_31)))),
inference(subst,[],[refute_0_30:[bind(A,$fot(multiplication(X_30,X_31)))]]) ).
cnf(refute_0_32,plain,
multiplication(X_30,multiplication(X_31,strong_iteration(multiplication(X_30,X_31)))) = multiplication(multiplication(X_30,X_31),strong_iteration(multiplication(X_30,X_31))),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_30)),bind(B,$fot(X_31)),bind(C,$fot(strong_iteration(multiplication(X_30,X_31))))]]) ).
cnf(refute_0_33,plain,
( multiplication(X_30,multiplication(X_31,strong_iteration(multiplication(X_30,X_31)))) != multiplication(multiplication(X_30,X_31),strong_iteration(multiplication(X_30,X_31)))
| multiplication(multiplication(X_30,X_31),strong_iteration(multiplication(X_30,X_31))) = multiplication(X_30,multiplication(X_31,strong_iteration(multiplication(X_30,X_31)))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(multiplication(X_30,multiplication(X_31,strong_iteration(multiplication(X_30,X_31)))))),bind(Y,$fot(multiplication(multiplication(X_30,X_31),strong_iteration(multiplication(X_30,X_31)))))]]) ).
cnf(refute_0_34,plain,
multiplication(multiplication(X_30,X_31),strong_iteration(multiplication(X_30,X_31))) = multiplication(X_30,multiplication(X_31,strong_iteration(multiplication(X_30,X_31)))),
inference(resolve,[$cnf( $equal(multiplication(X_30,multiplication(X_31,strong_iteration(multiplication(X_30,X_31)))),multiplication(multiplication(X_30,X_31),strong_iteration(multiplication(X_30,X_31)))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( multiplication(multiplication(X_30,X_31),strong_iteration(multiplication(X_30,X_31))) != multiplication(X_30,multiplication(X_31,strong_iteration(multiplication(X_30,X_31))))
| strong_iteration(multiplication(X_30,X_31)) != addition(one,multiplication(multiplication(X_30,X_31),strong_iteration(multiplication(X_30,X_31))))
| strong_iteration(multiplication(X_30,X_31)) = addition(one,multiplication(X_30,multiplication(X_31,strong_iteration(multiplication(X_30,X_31))))) ),
introduced(tautology,[equality,[$cnf( $equal(strong_iteration(multiplication(X_30,X_31)),addition(one,multiplication(multiplication(X_30,X_31),strong_iteration(multiplication(X_30,X_31))))) ),[1,1],$fot(multiplication(X_30,multiplication(X_31,strong_iteration(multiplication(X_30,X_31)))))]]) ).
cnf(refute_0_36,plain,
( strong_iteration(multiplication(X_30,X_31)) != addition(one,multiplication(multiplication(X_30,X_31),strong_iteration(multiplication(X_30,X_31))))
| strong_iteration(multiplication(X_30,X_31)) = addition(one,multiplication(X_30,multiplication(X_31,strong_iteration(multiplication(X_30,X_31))))) ),
inference(resolve,[$cnf( $equal(multiplication(multiplication(X_30,X_31),strong_iteration(multiplication(X_30,X_31))),multiplication(X_30,multiplication(X_31,strong_iteration(multiplication(X_30,X_31))))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
strong_iteration(multiplication(X_30,X_31)) = addition(one,multiplication(X_30,multiplication(X_31,strong_iteration(multiplication(X_30,X_31))))),
inference(resolve,[$cnf( $equal(strong_iteration(multiplication(X_30,X_31)),addition(one,multiplication(multiplication(X_30,X_31),strong_iteration(multiplication(X_30,X_31))))) )],[refute_0_31,refute_0_36]) ).
cnf(refute_0_38,plain,
strong_iteration(multiplication(X_240,zero)) = addition(one,multiplication(X_240,multiplication(zero,strong_iteration(multiplication(X_240,zero))))),
inference(subst,[],[refute_0_37:[bind(X_30,$fot(X_240)),bind(X_31,$fot(zero))]]) ).
cnf(refute_0_39,plain,
multiplication(zero,strong_iteration(multiplication(X_240,zero))) = zero,
inference(subst,[],[refute_0_14:[bind(A,$fot(strong_iteration(multiplication(X_240,zero))))]]) ).
cnf(refute_0_40,plain,
( multiplication(zero,strong_iteration(multiplication(X_240,zero))) != zero
| strong_iteration(multiplication(X_240,zero)) != addition(one,multiplication(X_240,multiplication(zero,strong_iteration(multiplication(X_240,zero)))))
| strong_iteration(multiplication(X_240,zero)) = addition(one,multiplication(X_240,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(strong_iteration(multiplication(X_240,zero)),addition(one,multiplication(X_240,multiplication(zero,strong_iteration(multiplication(X_240,zero)))))) ),[1,1,1],$fot(zero)]]) ).
cnf(refute_0_41,plain,
( strong_iteration(multiplication(X_240,zero)) != addition(one,multiplication(X_240,multiplication(zero,strong_iteration(multiplication(X_240,zero)))))
| strong_iteration(multiplication(X_240,zero)) = addition(one,multiplication(X_240,zero)) ),
inference(resolve,[$cnf( $equal(multiplication(zero,strong_iteration(multiplication(X_240,zero))),zero) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
strong_iteration(multiplication(X_240,zero)) = addition(one,multiplication(X_240,zero)),
inference(resolve,[$cnf( $equal(strong_iteration(multiplication(X_240,zero)),addition(one,multiplication(X_240,multiplication(zero,strong_iteration(multiplication(X_240,zero)))))) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
addition(one,multiplication(X_240,zero)) = star(multiplication(X_240,zero)),
inference(subst,[],[refute_0_18:[bind(X_227,$fot(X_240))]]) ).
cnf(refute_0_44,plain,
( addition(one,multiplication(X_240,zero)) != star(multiplication(X_240,zero))
| strong_iteration(multiplication(X_240,zero)) != addition(one,multiplication(X_240,zero))
| strong_iteration(multiplication(X_240,zero)) = star(multiplication(X_240,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(strong_iteration(multiplication(X_240,zero)),addition(one,multiplication(X_240,zero))) ),[1],$fot(star(multiplication(X_240,zero)))]]) ).
cnf(refute_0_45,plain,
( strong_iteration(multiplication(X_240,zero)) != addition(one,multiplication(X_240,zero))
| strong_iteration(multiplication(X_240,zero)) = star(multiplication(X_240,zero)) ),
inference(resolve,[$cnf( $equal(addition(one,multiplication(X_240,zero)),star(multiplication(X_240,zero))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
strong_iteration(multiplication(X_240,zero)) = star(multiplication(X_240,zero)),
inference(resolve,[$cnf( $equal(strong_iteration(multiplication(X_240,zero)),addition(one,multiplication(X_240,zero))) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
strong_iteration(multiplication(skolemFOFtoCNF_X0,zero)) = star(multiplication(skolemFOFtoCNF_X0,zero)),
inference(subst,[],[refute_0_46:[bind(X_240,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_48,plain,
( strong_iteration(multiplication(skolemFOFtoCNF_X0,zero)) != star(multiplication(skolemFOFtoCNF_X0,zero))
| ~ leq(star(multiplication(skolemFOFtoCNF_X0,zero)),star(multiplication(skolemFOFtoCNF_X0,zero)))
| leq(strong_iteration(multiplication(skolemFOFtoCNF_X0,zero)),star(multiplication(skolemFOFtoCNF_X0,zero))) ),
introduced(tautology,[equality,[$cnf( ~ leq(strong_iteration(multiplication(skolemFOFtoCNF_X0,zero)),star(multiplication(skolemFOFtoCNF_X0,zero))) ),[0],$fot(star(multiplication(skolemFOFtoCNF_X0,zero)))]]) ).
cnf(refute_0_49,plain,
( ~ leq(star(multiplication(skolemFOFtoCNF_X0,zero)),star(multiplication(skolemFOFtoCNF_X0,zero)))
| leq(strong_iteration(multiplication(skolemFOFtoCNF_X0,zero)),star(multiplication(skolemFOFtoCNF_X0,zero))) ),
inference(resolve,[$cnf( $equal(strong_iteration(multiplication(skolemFOFtoCNF_X0,zero)),star(multiplication(skolemFOFtoCNF_X0,zero))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
~ leq(star(multiplication(skolemFOFtoCNF_X0,zero)),star(multiplication(skolemFOFtoCNF_X0,zero))),
inference(resolve,[$cnf( leq(strong_iteration(multiplication(skolemFOFtoCNF_X0,zero)),star(multiplication(skolemFOFtoCNF_X0,zero))) )],[refute_0_49,refute_0_22]) ).
cnf(refute_0_51,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_52,plain,
( addition(X_97,X_97) != X_97
| leq(X_97,X_97) ),
inference(subst,[],[refute_0_51:[bind(A,$fot(X_97)),bind(B,$fot(X_97))]]) ).
cnf(refute_0_53,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_54,plain,
addition(X_97,X_97) = X_97,
inference(subst,[],[refute_0_53:[bind(A,$fot(X_97))]]) ).
cnf(refute_0_55,plain,
( X_97 != X_97
| addition(X_97,X_97) != X_97
| addition(X_97,X_97) = X_97 ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_97,X_97),X_97) ),[0,0],$fot(X_97)]]) ).
cnf(refute_0_56,plain,
( X_97 != X_97
| addition(X_97,X_97) = X_97 ),
inference(resolve,[$cnf( $equal(addition(X_97,X_97),X_97) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
( X_97 != X_97
| leq(X_97,X_97) ),
inference(resolve,[$cnf( $equal(addition(X_97,X_97),X_97) )],[refute_0_56,refute_0_52]) ).
cnf(refute_0_58,plain,
X_97 = X_97,
introduced(tautology,[refl,[$fot(X_97)]]) ).
cnf(refute_0_59,plain,
leq(X_97,X_97),
inference(resolve,[$cnf( $equal(X_97,X_97) )],[refute_0_58,refute_0_57]) ).
cnf(refute_0_60,plain,
leq(star(multiplication(skolemFOFtoCNF_X0,zero)),star(multiplication(skolemFOFtoCNF_X0,zero))),
inference(subst,[],[refute_0_59:[bind(X_97,$fot(star(multiplication(skolemFOFtoCNF_X0,zero))))]]) ).
cnf(refute_0_61,plain,
$false,
inference(resolve,[$cnf( leq(star(multiplication(skolemFOFtoCNF_X0,zero)),star(multiplication(skolemFOFtoCNF_X0,zero))) )],[refute_0_60,refute_0_50]) ).
fof(negate_1_0,plain,
~ ! [X0] :
( leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero)))
=> leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero))) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [X0] :
( ~ leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero)))
& leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ~ leq(addition(one,multiplication(skolemFOFtoCNF_X0_1,zero)),strong_iteration(multiplication(skolemFOFtoCNF_X0_1,zero)))
& leq(strong_iteration(multiplication(skolemFOFtoCNF_X0_1,zero)),addition(one,multiplication(skolemFOFtoCNF_X0_1,zero))) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
~ leq(addition(one,multiplication(skolemFOFtoCNF_X0_1,zero)),strong_iteration(multiplication(skolemFOFtoCNF_X0_1,zero))),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A] : addition(one,multiplication(A,star(A))) = star(A),
inference(canonicalize,[],[star_unfold1]) ).
fof(normalize_1_4,plain,
! [A] : addition(one,multiplication(A,star(A))) = star(A),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(canonicalize,[],[multiplicative_associativity]) ).
fof(normalize_1_6,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(specialize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A] : multiplication(zero,A) = zero,
inference(canonicalize,[],[left_annihilation]) ).
fof(normalize_1_8,plain,
! [A] : multiplication(zero,A) = zero,
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(canonicalize,[],[order]) ).
fof(normalize_1_10,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(specialize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( ~ leq(A,B)
| addition(A,B) = B ) ),
inference(clausify,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
! [A,B] :
( addition(A,B) != B
| leq(A,B) ),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[additive_associativity]) ).
fof(normalize_1_14,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(specialize,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
! [A] : strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)),
inference(canonicalize,[],[isolation]) ).
fof(normalize_1_16,plain,
! [A] : strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)),
inference(specialize,[],[normalize_1_15]) ).
fof(normalize_1_17,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_1_18,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_1_17]) ).
fof(normalize_1_19,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[idempotence]) ).
fof(normalize_1_20,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_1_19]) ).
cnf(refute_1_0,plain,
~ leq(addition(one,multiplication(skolemFOFtoCNF_X0_1,zero)),strong_iteration(multiplication(skolemFOFtoCNF_X0_1,zero))),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
addition(one,multiplication(A,star(A))) = star(A),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_2,plain,
addition(one,multiplication(multiplication(X_254,X_255),star(multiplication(X_254,X_255)))) = star(multiplication(X_254,X_255)),
inference(subst,[],[refute_1_1:[bind(A,$fot(multiplication(X_254,X_255)))]]) ).
cnf(refute_1_3,plain,
multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_4,plain,
multiplication(X_254,multiplication(X_255,star(multiplication(X_254,X_255)))) = multiplication(multiplication(X_254,X_255),star(multiplication(X_254,X_255))),
inference(subst,[],[refute_1_3:[bind(A,$fot(X_254)),bind(B,$fot(X_255)),bind(C,$fot(star(multiplication(X_254,X_255))))]]) ).
cnf(refute_1_5,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_6,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_7,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_5,refute_1_6]) ).
cnf(refute_1_8,plain,
( multiplication(X_254,multiplication(X_255,star(multiplication(X_254,X_255)))) != multiplication(multiplication(X_254,X_255),star(multiplication(X_254,X_255)))
| multiplication(multiplication(X_254,X_255),star(multiplication(X_254,X_255))) = multiplication(X_254,multiplication(X_255,star(multiplication(X_254,X_255)))) ),
inference(subst,[],[refute_1_7:[bind(X,$fot(multiplication(X_254,multiplication(X_255,star(multiplication(X_254,X_255)))))),bind(Y,$fot(multiplication(multiplication(X_254,X_255),star(multiplication(X_254,X_255)))))]]) ).
cnf(refute_1_9,plain,
multiplication(multiplication(X_254,X_255),star(multiplication(X_254,X_255))) = multiplication(X_254,multiplication(X_255,star(multiplication(X_254,X_255)))),
inference(resolve,[$cnf( $equal(multiplication(X_254,multiplication(X_255,star(multiplication(X_254,X_255)))),multiplication(multiplication(X_254,X_255),star(multiplication(X_254,X_255)))) )],[refute_1_4,refute_1_8]) ).
cnf(refute_1_10,plain,
( addition(one,multiplication(multiplication(X_254,X_255),star(multiplication(X_254,X_255)))) != star(multiplication(X_254,X_255))
| multiplication(multiplication(X_254,X_255),star(multiplication(X_254,X_255))) != multiplication(X_254,multiplication(X_255,star(multiplication(X_254,X_255))))
| addition(one,multiplication(X_254,multiplication(X_255,star(multiplication(X_254,X_255))))) = star(multiplication(X_254,X_255)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(one,multiplication(multiplication(X_254,X_255),star(multiplication(X_254,X_255)))),star(multiplication(X_254,X_255))) ),[0,1],$fot(multiplication(X_254,multiplication(X_255,star(multiplication(X_254,X_255)))))]]) ).
cnf(refute_1_11,plain,
( addition(one,multiplication(multiplication(X_254,X_255),star(multiplication(X_254,X_255)))) != star(multiplication(X_254,X_255))
| addition(one,multiplication(X_254,multiplication(X_255,star(multiplication(X_254,X_255))))) = star(multiplication(X_254,X_255)) ),
inference(resolve,[$cnf( $equal(multiplication(multiplication(X_254,X_255),star(multiplication(X_254,X_255))),multiplication(X_254,multiplication(X_255,star(multiplication(X_254,X_255))))) )],[refute_1_9,refute_1_10]) ).
cnf(refute_1_12,plain,
addition(one,multiplication(X_254,multiplication(X_255,star(multiplication(X_254,X_255))))) = star(multiplication(X_254,X_255)),
inference(resolve,[$cnf( $equal(addition(one,multiplication(multiplication(X_254,X_255),star(multiplication(X_254,X_255)))),star(multiplication(X_254,X_255))) )],[refute_1_2,refute_1_11]) ).
cnf(refute_1_13,plain,
addition(one,multiplication(X_281,multiplication(zero,star(multiplication(X_281,zero))))) = star(multiplication(X_281,zero)),
inference(subst,[],[refute_1_12:[bind(X_254,$fot(X_281)),bind(X_255,$fot(zero))]]) ).
cnf(refute_1_14,plain,
multiplication(zero,A) = zero,
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_15,plain,
multiplication(zero,star(multiplication(X_281,zero))) = zero,
inference(subst,[],[refute_1_14:[bind(A,$fot(star(multiplication(X_281,zero))))]]) ).
cnf(refute_1_16,plain,
( addition(one,multiplication(X_281,multiplication(zero,star(multiplication(X_281,zero))))) != star(multiplication(X_281,zero))
| multiplication(zero,star(multiplication(X_281,zero))) != zero
| addition(one,multiplication(X_281,zero)) = star(multiplication(X_281,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(one,multiplication(X_281,multiplication(zero,star(multiplication(X_281,zero))))),star(multiplication(X_281,zero))) ),[0,1,1],$fot(zero)]]) ).
cnf(refute_1_17,plain,
( addition(one,multiplication(X_281,multiplication(zero,star(multiplication(X_281,zero))))) != star(multiplication(X_281,zero))
| addition(one,multiplication(X_281,zero)) = star(multiplication(X_281,zero)) ),
inference(resolve,[$cnf( $equal(multiplication(zero,star(multiplication(X_281,zero))),zero) )],[refute_1_15,refute_1_16]) ).
cnf(refute_1_18,plain,
addition(one,multiplication(X_281,zero)) = star(multiplication(X_281,zero)),
inference(resolve,[$cnf( $equal(addition(one,multiplication(X_281,multiplication(zero,star(multiplication(X_281,zero))))),star(multiplication(X_281,zero))) )],[refute_1_13,refute_1_17]) ).
cnf(refute_1_19,plain,
addition(one,multiplication(skolemFOFtoCNF_X0_1,zero)) = star(multiplication(skolemFOFtoCNF_X0_1,zero)),
inference(subst,[],[refute_1_18:[bind(X_281,$fot(skolemFOFtoCNF_X0_1))]]) ).
cnf(refute_1_20,plain,
( addition(one,multiplication(skolemFOFtoCNF_X0_1,zero)) != star(multiplication(skolemFOFtoCNF_X0_1,zero))
| ~ leq(star(multiplication(skolemFOFtoCNF_X0_1,zero)),strong_iteration(multiplication(skolemFOFtoCNF_X0_1,zero)))
| leq(addition(one,multiplication(skolemFOFtoCNF_X0_1,zero)),strong_iteration(multiplication(skolemFOFtoCNF_X0_1,zero))) ),
introduced(tautology,[equality,[$cnf( ~ leq(addition(one,multiplication(skolemFOFtoCNF_X0_1,zero)),strong_iteration(multiplication(skolemFOFtoCNF_X0_1,zero))) ),[0],$fot(star(multiplication(skolemFOFtoCNF_X0_1,zero)))]]) ).
cnf(refute_1_21,plain,
( ~ leq(star(multiplication(skolemFOFtoCNF_X0_1,zero)),strong_iteration(multiplication(skolemFOFtoCNF_X0_1,zero)))
| leq(addition(one,multiplication(skolemFOFtoCNF_X0_1,zero)),strong_iteration(multiplication(skolemFOFtoCNF_X0_1,zero))) ),
inference(resolve,[$cnf( $equal(addition(one,multiplication(skolemFOFtoCNF_X0_1,zero)),star(multiplication(skolemFOFtoCNF_X0_1,zero))) )],[refute_1_19,refute_1_20]) ).
cnf(refute_1_22,plain,
~ leq(star(multiplication(skolemFOFtoCNF_X0_1,zero)),strong_iteration(multiplication(skolemFOFtoCNF_X0_1,zero))),
inference(resolve,[$cnf( leq(addition(one,multiplication(skolemFOFtoCNF_X0_1,zero)),strong_iteration(multiplication(skolemFOFtoCNF_X0_1,zero))) )],[refute_1_21,refute_1_0]) ).
cnf(refute_1_23,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_24,plain,
( addition(star(X_286),strong_iteration(X_286)) != strong_iteration(X_286)
| leq(star(X_286),strong_iteration(X_286)) ),
inference(subst,[],[refute_1_23:[bind(A,$fot(star(X_286))),bind(B,$fot(strong_iteration(X_286)))]]) ).
cnf(refute_1_25,plain,
addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_26,plain,
addition(star(A),addition(multiplication(strong_iteration(A),zero),X_259)) = addition(addition(star(A),multiplication(strong_iteration(A),zero)),X_259),
inference(subst,[],[refute_1_25:[bind(A,$fot(star(A))),bind(B,$fot(multiplication(strong_iteration(A),zero))),bind(C,$fot(X_259))]]) ).
cnf(refute_1_27,plain,
strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_28,plain,
( strong_iteration(A) != addition(star(A),multiplication(strong_iteration(A),zero))
| addition(star(A),multiplication(strong_iteration(A),zero)) = strong_iteration(A) ),
inference(subst,[],[refute_1_7:[bind(X,$fot(strong_iteration(A))),bind(Y,$fot(addition(star(A),multiplication(strong_iteration(A),zero))))]]) ).
cnf(refute_1_29,plain,
addition(star(A),multiplication(strong_iteration(A),zero)) = strong_iteration(A),
inference(resolve,[$cnf( $equal(strong_iteration(A),addition(star(A),multiplication(strong_iteration(A),zero))) )],[refute_1_27,refute_1_28]) ).
cnf(refute_1_30,plain,
( addition(star(A),addition(multiplication(strong_iteration(A),zero),X_259)) != addition(addition(star(A),multiplication(strong_iteration(A),zero)),X_259)
| addition(star(A),multiplication(strong_iteration(A),zero)) != strong_iteration(A)
| addition(star(A),addition(multiplication(strong_iteration(A),zero),X_259)) = addition(strong_iteration(A),X_259) ),
introduced(tautology,[equality,[$cnf( $equal(addition(star(A),addition(multiplication(strong_iteration(A),zero),X_259)),addition(addition(star(A),multiplication(strong_iteration(A),zero)),X_259)) ),[1,0],$fot(strong_iteration(A))]]) ).
cnf(refute_1_31,plain,
( addition(star(A),addition(multiplication(strong_iteration(A),zero),X_259)) != addition(addition(star(A),multiplication(strong_iteration(A),zero)),X_259)
| addition(star(A),addition(multiplication(strong_iteration(A),zero),X_259)) = addition(strong_iteration(A),X_259) ),
inference(resolve,[$cnf( $equal(addition(star(A),multiplication(strong_iteration(A),zero)),strong_iteration(A)) )],[refute_1_29,refute_1_30]) ).
cnf(refute_1_32,plain,
addition(star(A),addition(multiplication(strong_iteration(A),zero),X_259)) = addition(strong_iteration(A),X_259),
inference(resolve,[$cnf( $equal(addition(star(A),addition(multiplication(strong_iteration(A),zero),X_259)),addition(addition(star(A),multiplication(strong_iteration(A),zero)),X_259)) )],[refute_1_26,refute_1_31]) ).
cnf(refute_1_33,plain,
addition(star(X_267),addition(multiplication(strong_iteration(X_267),zero),X_268)) = addition(strong_iteration(X_267),X_268),
inference(subst,[],[refute_1_32:[bind(A,$fot(X_267)),bind(X_259,$fot(X_268))]]) ).
cnf(refute_1_34,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_35,plain,
addition(X_268,multiplication(strong_iteration(X_267),zero)) = addition(multiplication(strong_iteration(X_267),zero),X_268),
inference(subst,[],[refute_1_34:[bind(A,$fot(X_268)),bind(B,$fot(multiplication(strong_iteration(X_267),zero)))]]) ).
cnf(refute_1_36,plain,
( addition(X_268,multiplication(strong_iteration(X_267),zero)) != addition(multiplication(strong_iteration(X_267),zero),X_268)
| addition(multiplication(strong_iteration(X_267),zero),X_268) = addition(X_268,multiplication(strong_iteration(X_267),zero)) ),
inference(subst,[],[refute_1_7:[bind(X,$fot(addition(X_268,multiplication(strong_iteration(X_267),zero)))),bind(Y,$fot(addition(multiplication(strong_iteration(X_267),zero),X_268)))]]) ).
cnf(refute_1_37,plain,
addition(multiplication(strong_iteration(X_267),zero),X_268) = addition(X_268,multiplication(strong_iteration(X_267),zero)),
inference(resolve,[$cnf( $equal(addition(X_268,multiplication(strong_iteration(X_267),zero)),addition(multiplication(strong_iteration(X_267),zero),X_268)) )],[refute_1_35,refute_1_36]) ).
cnf(refute_1_38,plain,
( addition(multiplication(strong_iteration(X_267),zero),X_268) != addition(X_268,multiplication(strong_iteration(X_267),zero))
| addition(star(X_267),addition(multiplication(strong_iteration(X_267),zero),X_268)) != addition(strong_iteration(X_267),X_268)
| addition(star(X_267),addition(X_268,multiplication(strong_iteration(X_267),zero))) = addition(strong_iteration(X_267),X_268) ),
introduced(tautology,[equality,[$cnf( $equal(addition(star(X_267),addition(multiplication(strong_iteration(X_267),zero),X_268)),addition(strong_iteration(X_267),X_268)) ),[0,1],$fot(addition(X_268,multiplication(strong_iteration(X_267),zero)))]]) ).
cnf(refute_1_39,plain,
( addition(star(X_267),addition(multiplication(strong_iteration(X_267),zero),X_268)) != addition(strong_iteration(X_267),X_268)
| addition(star(X_267),addition(X_268,multiplication(strong_iteration(X_267),zero))) = addition(strong_iteration(X_267),X_268) ),
inference(resolve,[$cnf( $equal(addition(multiplication(strong_iteration(X_267),zero),X_268),addition(X_268,multiplication(strong_iteration(X_267),zero))) )],[refute_1_37,refute_1_38]) ).
cnf(refute_1_40,plain,
addition(star(X_267),addition(X_268,multiplication(strong_iteration(X_267),zero))) = addition(strong_iteration(X_267),X_268),
inference(resolve,[$cnf( $equal(addition(star(X_267),addition(multiplication(strong_iteration(X_267),zero),X_268)),addition(strong_iteration(X_267),X_268)) )],[refute_1_33,refute_1_39]) ).
cnf(refute_1_41,plain,
addition(star(X_286),addition(strong_iteration(X_286),multiplication(strong_iteration(X_286),zero))) = addition(strong_iteration(X_286),strong_iteration(X_286)),
inference(subst,[],[refute_1_40:[bind(X_267,$fot(X_286)),bind(X_268,$fot(strong_iteration(X_286)))]]) ).
cnf(refute_1_42,plain,
addition(star(X_267),addition(multiplication(strong_iteration(X_267),zero),multiplication(strong_iteration(X_267),zero))) = addition(strong_iteration(X_267),multiplication(strong_iteration(X_267),zero)),
inference(subst,[],[refute_1_32:[bind(A,$fot(X_267)),bind(X_259,$fot(multiplication(strong_iteration(X_267),zero)))]]) ).
cnf(refute_1_43,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_1_20]) ).
cnf(refute_1_44,plain,
addition(multiplication(strong_iteration(X_267),zero),multiplication(strong_iteration(X_267),zero)) = multiplication(strong_iteration(X_267),zero),
inference(subst,[],[refute_1_43:[bind(A,$fot(multiplication(strong_iteration(X_267),zero)))]]) ).
cnf(refute_1_45,plain,
( addition(multiplication(strong_iteration(X_267),zero),multiplication(strong_iteration(X_267),zero)) != multiplication(strong_iteration(X_267),zero)
| addition(star(X_267),addition(multiplication(strong_iteration(X_267),zero),multiplication(strong_iteration(X_267),zero))) != addition(strong_iteration(X_267),multiplication(strong_iteration(X_267),zero))
| addition(star(X_267),multiplication(strong_iteration(X_267),zero)) = addition(strong_iteration(X_267),multiplication(strong_iteration(X_267),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(star(X_267),addition(multiplication(strong_iteration(X_267),zero),multiplication(strong_iteration(X_267),zero))),addition(strong_iteration(X_267),multiplication(strong_iteration(X_267),zero))) ),[0,1],$fot(multiplication(strong_iteration(X_267),zero))]]) ).
cnf(refute_1_46,plain,
( addition(star(X_267),addition(multiplication(strong_iteration(X_267),zero),multiplication(strong_iteration(X_267),zero))) != addition(strong_iteration(X_267),multiplication(strong_iteration(X_267),zero))
| addition(star(X_267),multiplication(strong_iteration(X_267),zero)) = addition(strong_iteration(X_267),multiplication(strong_iteration(X_267),zero)) ),
inference(resolve,[$cnf( $equal(addition(multiplication(strong_iteration(X_267),zero),multiplication(strong_iteration(X_267),zero)),multiplication(strong_iteration(X_267),zero)) )],[refute_1_44,refute_1_45]) ).
cnf(refute_1_47,plain,
addition(star(X_267),multiplication(strong_iteration(X_267),zero)) = addition(strong_iteration(X_267),multiplication(strong_iteration(X_267),zero)),
inference(resolve,[$cnf( $equal(addition(star(X_267),addition(multiplication(strong_iteration(X_267),zero),multiplication(strong_iteration(X_267),zero))),addition(strong_iteration(X_267),multiplication(strong_iteration(X_267),zero))) )],[refute_1_42,refute_1_46]) ).
cnf(refute_1_48,plain,
addition(star(X_267),multiplication(strong_iteration(X_267),zero)) = strong_iteration(X_267),
inference(subst,[],[refute_1_29:[bind(A,$fot(X_267))]]) ).
cnf(refute_1_49,plain,
( addition(star(X_267),multiplication(strong_iteration(X_267),zero)) != addition(strong_iteration(X_267),multiplication(strong_iteration(X_267),zero))
| addition(star(X_267),multiplication(strong_iteration(X_267),zero)) != strong_iteration(X_267)
| strong_iteration(X_267) = addition(strong_iteration(X_267),multiplication(strong_iteration(X_267),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(star(X_267),multiplication(strong_iteration(X_267),zero)),addition(strong_iteration(X_267),multiplication(strong_iteration(X_267),zero))) ),[0],$fot(strong_iteration(X_267))]]) ).
cnf(refute_1_50,plain,
( addition(star(X_267),multiplication(strong_iteration(X_267),zero)) != addition(strong_iteration(X_267),multiplication(strong_iteration(X_267),zero))
| strong_iteration(X_267) = addition(strong_iteration(X_267),multiplication(strong_iteration(X_267),zero)) ),
inference(resolve,[$cnf( $equal(addition(star(X_267),multiplication(strong_iteration(X_267),zero)),strong_iteration(X_267)) )],[refute_1_48,refute_1_49]) ).
cnf(refute_1_51,plain,
strong_iteration(X_267) = addition(strong_iteration(X_267),multiplication(strong_iteration(X_267),zero)),
inference(resolve,[$cnf( $equal(addition(star(X_267),multiplication(strong_iteration(X_267),zero)),addition(strong_iteration(X_267),multiplication(strong_iteration(X_267),zero))) )],[refute_1_47,refute_1_50]) ).
cnf(refute_1_52,plain,
strong_iteration(X_286) = addition(strong_iteration(X_286),multiplication(strong_iteration(X_286),zero)),
inference(subst,[],[refute_1_51:[bind(X_267,$fot(X_286))]]) ).
cnf(refute_1_53,plain,
( strong_iteration(X_286) != addition(strong_iteration(X_286),multiplication(strong_iteration(X_286),zero))
| addition(strong_iteration(X_286),multiplication(strong_iteration(X_286),zero)) = strong_iteration(X_286) ),
inference(subst,[],[refute_1_7:[bind(X,$fot(strong_iteration(X_286))),bind(Y,$fot(addition(strong_iteration(X_286),multiplication(strong_iteration(X_286),zero))))]]) ).
cnf(refute_1_54,plain,
addition(strong_iteration(X_286),multiplication(strong_iteration(X_286),zero)) = strong_iteration(X_286),
inference(resolve,[$cnf( $equal(strong_iteration(X_286),addition(strong_iteration(X_286),multiplication(strong_iteration(X_286),zero))) )],[refute_1_52,refute_1_53]) ).
cnf(refute_1_55,plain,
( addition(star(X_286),addition(strong_iteration(X_286),multiplication(strong_iteration(X_286),zero))) != addition(strong_iteration(X_286),strong_iteration(X_286))
| addition(strong_iteration(X_286),multiplication(strong_iteration(X_286),zero)) != strong_iteration(X_286)
| addition(star(X_286),strong_iteration(X_286)) = addition(strong_iteration(X_286),strong_iteration(X_286)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(star(X_286),addition(strong_iteration(X_286),multiplication(strong_iteration(X_286),zero))),addition(strong_iteration(X_286),strong_iteration(X_286))) ),[0,1],$fot(strong_iteration(X_286))]]) ).
cnf(refute_1_56,plain,
( addition(star(X_286),addition(strong_iteration(X_286),multiplication(strong_iteration(X_286),zero))) != addition(strong_iteration(X_286),strong_iteration(X_286))
| addition(star(X_286),strong_iteration(X_286)) = addition(strong_iteration(X_286),strong_iteration(X_286)) ),
inference(resolve,[$cnf( $equal(addition(strong_iteration(X_286),multiplication(strong_iteration(X_286),zero)),strong_iteration(X_286)) )],[refute_1_54,refute_1_55]) ).
cnf(refute_1_57,plain,
addition(star(X_286),strong_iteration(X_286)) = addition(strong_iteration(X_286),strong_iteration(X_286)),
inference(resolve,[$cnf( $equal(addition(star(X_286),addition(strong_iteration(X_286),multiplication(strong_iteration(X_286),zero))),addition(strong_iteration(X_286),strong_iteration(X_286))) )],[refute_1_41,refute_1_56]) ).
cnf(refute_1_58,plain,
addition(strong_iteration(X_286),strong_iteration(X_286)) = strong_iteration(X_286),
inference(subst,[],[refute_1_43:[bind(A,$fot(strong_iteration(X_286)))]]) ).
cnf(refute_1_59,plain,
( addition(star(X_286),strong_iteration(X_286)) != addition(strong_iteration(X_286),strong_iteration(X_286))
| addition(strong_iteration(X_286),strong_iteration(X_286)) != strong_iteration(X_286)
| addition(star(X_286),strong_iteration(X_286)) = strong_iteration(X_286) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(star(X_286),strong_iteration(X_286)),strong_iteration(X_286)) ),[0],$fot(addition(strong_iteration(X_286),strong_iteration(X_286)))]]) ).
cnf(refute_1_60,plain,
( addition(star(X_286),strong_iteration(X_286)) != addition(strong_iteration(X_286),strong_iteration(X_286))
| addition(star(X_286),strong_iteration(X_286)) = strong_iteration(X_286) ),
inference(resolve,[$cnf( $equal(addition(strong_iteration(X_286),strong_iteration(X_286)),strong_iteration(X_286)) )],[refute_1_58,refute_1_59]) ).
cnf(refute_1_61,plain,
addition(star(X_286),strong_iteration(X_286)) = strong_iteration(X_286),
inference(resolve,[$cnf( $equal(addition(star(X_286),strong_iteration(X_286)),addition(strong_iteration(X_286),strong_iteration(X_286))) )],[refute_1_57,refute_1_60]) ).
cnf(refute_1_62,plain,
( addition(star(X_286),strong_iteration(X_286)) != strong_iteration(X_286)
| strong_iteration(X_286) != strong_iteration(X_286)
| addition(star(X_286),strong_iteration(X_286)) = strong_iteration(X_286) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(star(X_286),strong_iteration(X_286)),strong_iteration(X_286)) ),[0],$fot(strong_iteration(X_286))]]) ).
cnf(refute_1_63,plain,
( strong_iteration(X_286) != strong_iteration(X_286)
| addition(star(X_286),strong_iteration(X_286)) = strong_iteration(X_286) ),
inference(resolve,[$cnf( $equal(addition(star(X_286),strong_iteration(X_286)),strong_iteration(X_286)) )],[refute_1_61,refute_1_62]) ).
cnf(refute_1_64,plain,
( strong_iteration(X_286) != strong_iteration(X_286)
| leq(star(X_286),strong_iteration(X_286)) ),
inference(resolve,[$cnf( $equal(addition(star(X_286),strong_iteration(X_286)),strong_iteration(X_286)) )],[refute_1_63,refute_1_24]) ).
cnf(refute_1_65,plain,
strong_iteration(X_286) = strong_iteration(X_286),
introduced(tautology,[refl,[$fot(strong_iteration(X_286))]]) ).
cnf(refute_1_66,plain,
leq(star(X_286),strong_iteration(X_286)),
inference(resolve,[$cnf( $equal(strong_iteration(X_286),strong_iteration(X_286)) )],[refute_1_65,refute_1_64]) ).
cnf(refute_1_67,plain,
leq(star(multiplication(skolemFOFtoCNF_X0_1,zero)),strong_iteration(multiplication(skolemFOFtoCNF_X0_1,zero))),
inference(subst,[],[refute_1_66:[bind(X_286,$fot(multiplication(skolemFOFtoCNF_X0_1,zero)))]]) ).
cnf(refute_1_68,plain,
$false,
inference(resolve,[$cnf( leq(star(multiplication(skolemFOFtoCNF_X0_1,zero)),strong_iteration(multiplication(skolemFOFtoCNF_X0_1,zero))) )],[refute_1_67,refute_1_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : KLE150+2 : TPTP v8.1.0. Released v4.0.0.
% 0.05/0.10 % Command : metis --show proof --show saturation %s
% 0.08/0.29 % Computer : n032.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 600
% 0.08/0.29 % DateTime : Thu Jun 16 08:28:59 EDT 2022
% 0.08/0.29 % CPUTime :
% 0.08/0.29 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.94/2.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.94/2.15
% 1.94/2.15 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.94/2.16
%------------------------------------------------------------------------------