TSTP Solution File: KLE146+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE146+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.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 02:15:33 EDT 2022
% Result : Theorem 1.04s 1.22s
% Output : CNFRefutation 1.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 23
% Syntax : Number of formulae : 116 ( 67 unt; 0 def)
% Number of atoms : 184 ( 154 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 140 ( 72 ~; 64 |; 1 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 227 ( 4 sgn 34 !; 1 ?)
% 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(infty_unfold1,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ) ).
fof(goals,conjecture,
! [X0] : leq(one,strong_iteration(X0)) ).
fof(subgoal_0,plain,
! [X0] : leq(one,strong_iteration(X0)),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0] : leq(one,strong_iteration(X0)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0] : ~ leq(one,strong_iteration(X0)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ leq(one,strong_iteration(skolemFOFtoCNF_X0)),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(canonicalize,[],[order]) ).
fof(normalize_0_3,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( ~ leq(A,B)
| addition(A,B) = B ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B] :
( addition(A,B) != B
| leq(A,B) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[additive_associativity]) ).
fof(normalize_0_7,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[idempotence]) ).
fof(normalize_0_9,plain,
! [A] : addition(A,A) = A,
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] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(canonicalize,[],[infty_unfold1]) ).
fof(normalize_0_13,plain,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(specialize,[],[normalize_0_12]) ).
cnf(refute_0_0,plain,
~ leq(one,strong_iteration(skolemFOFtoCNF_X0)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( addition(A,addition(X_109,A)) != addition(X_109,A)
| leq(A,addition(X_109,A)) ),
inference(subst,[],[refute_0_1:[bind(B,$fot(addition(X_109,A)))]]) ).
cnf(refute_0_3,plain,
addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
addition(addition(X_44,X_45),addition(X_44,X_45)) = addition(addition(addition(X_44,X_45),X_44),X_45),
inference(subst,[],[refute_0_3:[bind(A,$fot(addition(X_44,X_45))),bind(B,$fot(X_44)),bind(C,$fot(X_45))]]) ).
cnf(refute_0_5,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_6,plain,
addition(addition(X_44,X_45),addition(X_44,X_45)) = addition(X_44,X_45),
inference(subst,[],[refute_0_5:[bind(A,$fot(addition(X_44,X_45)))]]) ).
cnf(refute_0_7,plain,
( addition(addition(X_44,X_45),addition(X_44,X_45)) != addition(X_44,X_45)
| addition(addition(X_44,X_45),addition(X_44,X_45)) != addition(addition(addition(X_44,X_45),X_44),X_45)
| addition(X_44,X_45) = addition(addition(addition(X_44,X_45),X_44),X_45) ),
introduced(tautology,[equality,[$cnf( $equal(addition(addition(X_44,X_45),addition(X_44,X_45)),addition(addition(addition(X_44,X_45),X_44),X_45)) ),[0],$fot(addition(X_44,X_45))]]) ).
cnf(refute_0_8,plain,
( addition(addition(X_44,X_45),addition(X_44,X_45)) != addition(addition(addition(X_44,X_45),X_44),X_45)
| addition(X_44,X_45) = addition(addition(addition(X_44,X_45),X_44),X_45) ),
inference(resolve,[$cnf( $equal(addition(addition(X_44,X_45),addition(X_44,X_45)),addition(X_44,X_45)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
addition(X_44,X_45) = addition(addition(addition(X_44,X_45),X_44),X_45),
inference(resolve,[$cnf( $equal(addition(addition(X_44,X_45),addition(X_44,X_45)),addition(addition(addition(X_44,X_45),X_44),X_45)) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
addition(X_43,addition(X_44,X_45)) = addition(addition(X_43,X_44),X_45),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_43)),bind(B,$fot(X_44)),bind(C,$fot(X_45))]]) ).
cnf(refute_0_11,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_12,plain,
addition(X_45,X_44) = addition(X_44,X_45),
inference(subst,[],[refute_0_11:[bind(A,$fot(X_45)),bind(B,$fot(X_44))]]) ).
cnf(refute_0_13,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_14,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_15,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( addition(X_45,X_44) != addition(X_44,X_45)
| addition(X_44,X_45) = addition(X_45,X_44) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(addition(X_45,X_44))),bind(Y,$fot(addition(X_44,X_45)))]]) ).
cnf(refute_0_17,plain,
addition(X_44,X_45) = addition(X_45,X_44),
inference(resolve,[$cnf( $equal(addition(X_45,X_44),addition(X_44,X_45)) )],[refute_0_12,refute_0_16]) ).
cnf(refute_0_18,plain,
( addition(X_43,addition(X_44,X_45)) != addition(addition(X_43,X_44),X_45)
| addition(X_44,X_45) != addition(X_45,X_44)
| addition(X_43,addition(X_45,X_44)) = addition(addition(X_43,X_44),X_45) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_43,addition(X_44,X_45)),addition(addition(X_43,X_44),X_45)) ),[0,1],$fot(addition(X_45,X_44))]]) ).
cnf(refute_0_19,plain,
( addition(X_43,addition(X_44,X_45)) != addition(addition(X_43,X_44),X_45)
| addition(X_43,addition(X_45,X_44)) = addition(addition(X_43,X_44),X_45) ),
inference(resolve,[$cnf( $equal(addition(X_44,X_45),addition(X_45,X_44)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
addition(X_43,addition(X_45,X_44)) = addition(addition(X_43,X_44),X_45),
inference(resolve,[$cnf( $equal(addition(X_43,addition(X_44,X_45)),addition(addition(X_43,X_44),X_45)) )],[refute_0_10,refute_0_19]) ).
cnf(refute_0_21,plain,
( addition(A,addition(B,C)) != addition(addition(A,B),C)
| addition(addition(A,B),C) = addition(A,addition(B,C)) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(addition(A,addition(B,C)))),bind(Y,$fot(addition(addition(A,B),C)))]]) ).
cnf(refute_0_22,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(resolve,[$cnf( $equal(addition(A,addition(B,C)),addition(addition(A,B),C)) )],[refute_0_3,refute_0_21]) ).
cnf(refute_0_23,plain,
addition(addition(X_43,X_44),X_45) = addition(X_43,addition(X_44,X_45)),
inference(subst,[],[refute_0_22:[bind(A,$fot(X_43)),bind(B,$fot(X_44)),bind(C,$fot(X_45))]]) ).
cnf(refute_0_24,plain,
( addition(X_43,addition(X_45,X_44)) != addition(addition(X_43,X_44),X_45)
| addition(addition(X_43,X_44),X_45) != addition(X_43,addition(X_44,X_45))
| addition(X_43,addition(X_45,X_44)) = addition(X_43,addition(X_44,X_45)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(X_43,addition(X_45,X_44)),addition(X_43,addition(X_44,X_45))) ),[0],$fot(addition(addition(X_43,X_44),X_45))]]) ).
cnf(refute_0_25,plain,
( addition(X_43,addition(X_45,X_44)) != addition(addition(X_43,X_44),X_45)
| addition(X_43,addition(X_45,X_44)) = addition(X_43,addition(X_44,X_45)) ),
inference(resolve,[$cnf( $equal(addition(addition(X_43,X_44),X_45),addition(X_43,addition(X_44,X_45))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
addition(X_43,addition(X_45,X_44)) = addition(X_43,addition(X_44,X_45)),
inference(resolve,[$cnf( $equal(addition(X_43,addition(X_45,X_44)),addition(addition(X_43,X_44),X_45)) )],[refute_0_20,refute_0_25]) ).
cnf(refute_0_27,plain,
( addition(X_43,addition(X_45,X_44)) != addition(X_43,addition(X_44,X_45))
| addition(X_43,addition(X_44,X_45)) = addition(X_43,addition(X_45,X_44)) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(addition(X_43,addition(X_45,X_44)))),bind(Y,$fot(addition(X_43,addition(X_44,X_45))))]]) ).
cnf(refute_0_28,plain,
addition(X_43,addition(X_44,X_45)) = addition(X_43,addition(X_45,X_44)),
inference(resolve,[$cnf( $equal(addition(X_43,addition(X_45,X_44)),addition(X_43,addition(X_44,X_45))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
addition(X_45,addition(addition(X_44,X_45),X_44)) = addition(X_45,addition(X_44,addition(X_44,X_45))),
inference(subst,[],[refute_0_28:[bind(X_43,$fot(X_45)),bind(X_44,$fot(addition(X_44,X_45))),bind(X_45,$fot(X_44))]]) ).
cnf(refute_0_30,plain,
addition(A,addition(X_43,X_44)) = addition(addition(X_43,X_44),A),
inference(subst,[],[refute_0_11:[bind(B,$fot(addition(X_43,X_44)))]]) ).
cnf(refute_0_31,plain,
addition(X_43,addition(X_44,A)) = addition(addition(X_43,X_44),A),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_43)),bind(B,$fot(X_44)),bind(C,$fot(A))]]) ).
cnf(refute_0_32,plain,
( addition(X_43,addition(X_44,A)) != addition(addition(X_43,X_44),A)
| addition(addition(X_43,X_44),A) = addition(X_43,addition(X_44,A)) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(addition(X_43,addition(X_44,A)))),bind(Y,$fot(addition(addition(X_43,X_44),A)))]]) ).
cnf(refute_0_33,plain,
addition(addition(X_43,X_44),A) = addition(X_43,addition(X_44,A)),
inference(resolve,[$cnf( $equal(addition(X_43,addition(X_44,A)),addition(addition(X_43,X_44),A)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( addition(A,addition(X_43,X_44)) != addition(addition(X_43,X_44),A)
| addition(addition(X_43,X_44),A) != addition(X_43,addition(X_44,A))
| addition(A,addition(X_43,X_44)) = addition(X_43,addition(X_44,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(A,addition(X_43,X_44)),addition(X_43,addition(X_44,A))) ),[0],$fot(addition(addition(X_43,X_44),A))]]) ).
cnf(refute_0_35,plain,
( addition(A,addition(X_43,X_44)) != addition(addition(X_43,X_44),A)
| addition(A,addition(X_43,X_44)) = addition(X_43,addition(X_44,A)) ),
inference(resolve,[$cnf( $equal(addition(addition(X_43,X_44),A),addition(X_43,addition(X_44,A))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
addition(A,addition(X_43,X_44)) = addition(X_43,addition(X_44,A)),
inference(resolve,[$cnf( $equal(addition(A,addition(X_43,X_44)),addition(addition(X_43,X_44),A)) )],[refute_0_30,refute_0_35]) ).
cnf(refute_0_37,plain,
( addition(A,addition(X_43,X_44)) != addition(X_43,addition(X_44,A))
| addition(X_43,addition(X_44,A)) = addition(A,addition(X_43,X_44)) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(addition(A,addition(X_43,X_44)))),bind(Y,$fot(addition(X_43,addition(X_44,A))))]]) ).
cnf(refute_0_38,plain,
addition(X_43,addition(X_44,A)) = addition(A,addition(X_43,X_44)),
inference(resolve,[$cnf( $equal(addition(A,addition(X_43,X_44)),addition(X_43,addition(X_44,A))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
addition(addition(X_44,X_45),addition(X_44,X_45)) = addition(X_45,addition(addition(X_44,X_45),X_44)),
inference(subst,[],[refute_0_38:[bind(A,$fot(X_45)),bind(X_43,$fot(addition(X_44,X_45)))]]) ).
cnf(refute_0_40,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_41,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_15,refute_0_40]) ).
cnf(refute_0_42,plain,
( addition(X_45,addition(addition(X_44,X_45),X_44)) != addition(X_45,addition(X_44,addition(X_44,X_45)))
| addition(addition(X_44,X_45),addition(X_44,X_45)) != addition(X_45,addition(addition(X_44,X_45),X_44))
| addition(addition(X_44,X_45),addition(X_44,X_45)) = addition(X_45,addition(X_44,addition(X_44,X_45))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(addition(addition(X_44,X_45),addition(X_44,X_45)))),bind(Y,$fot(addition(X_45,addition(addition(X_44,X_45),X_44)))),bind(Z,$fot(addition(X_45,addition(X_44,addition(X_44,X_45)))))]]) ).
cnf(refute_0_43,plain,
( addition(X_45,addition(addition(X_44,X_45),X_44)) != addition(X_45,addition(X_44,addition(X_44,X_45)))
| addition(addition(X_44,X_45),addition(X_44,X_45)) = addition(X_45,addition(X_44,addition(X_44,X_45))) ),
inference(resolve,[$cnf( $equal(addition(addition(X_44,X_45),addition(X_44,X_45)),addition(X_45,addition(addition(X_44,X_45),X_44))) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
addition(addition(X_44,X_45),addition(X_44,X_45)) = addition(X_45,addition(X_44,addition(X_44,X_45))),
inference(resolve,[$cnf( $equal(addition(X_45,addition(addition(X_44,X_45),X_44)),addition(X_45,addition(X_44,addition(X_44,X_45)))) )],[refute_0_29,refute_0_43]) ).
cnf(refute_0_45,plain,
addition(addition(addition(X_44,X_45),X_44),X_45) = addition(addition(X_44,X_45),addition(X_44,X_45)),
inference(subst,[],[refute_0_22:[bind(A,$fot(addition(X_44,X_45))),bind(B,$fot(X_44)),bind(C,$fot(X_45))]]) ).
cnf(refute_0_46,plain,
( addition(addition(X_44,X_45),addition(X_44,X_45)) != addition(X_45,addition(X_44,addition(X_44,X_45)))
| addition(addition(addition(X_44,X_45),X_44),X_45) != addition(addition(X_44,X_45),addition(X_44,X_45))
| addition(addition(addition(X_44,X_45),X_44),X_45) = addition(X_45,addition(X_44,addition(X_44,X_45))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(addition(addition(addition(X_44,X_45),X_44),X_45))),bind(Y,$fot(addition(addition(X_44,X_45),addition(X_44,X_45)))),bind(Z,$fot(addition(X_45,addition(X_44,addition(X_44,X_45)))))]]) ).
cnf(refute_0_47,plain,
( addition(addition(X_44,X_45),addition(X_44,X_45)) != addition(X_45,addition(X_44,addition(X_44,X_45)))
| addition(addition(addition(X_44,X_45),X_44),X_45) = addition(X_45,addition(X_44,addition(X_44,X_45))) ),
inference(resolve,[$cnf( $equal(addition(addition(addition(X_44,X_45),X_44),X_45),addition(addition(X_44,X_45),addition(X_44,X_45))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
addition(addition(addition(X_44,X_45),X_44),X_45) = addition(X_45,addition(X_44,addition(X_44,X_45))),
inference(resolve,[$cnf( $equal(addition(addition(X_44,X_45),addition(X_44,X_45)),addition(X_45,addition(X_44,addition(X_44,X_45)))) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
( addition(X_44,X_45) != addition(addition(addition(X_44,X_45),X_44),X_45)
| addition(addition(addition(X_44,X_45),X_44),X_45) != addition(X_45,addition(X_44,addition(X_44,X_45)))
| addition(X_44,X_45) = addition(X_45,addition(X_44,addition(X_44,X_45))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(X_44,X_45),addition(X_45,addition(X_44,addition(X_44,X_45)))) ),[0],$fot(addition(addition(addition(X_44,X_45),X_44),X_45))]]) ).
cnf(refute_0_50,plain,
( addition(X_44,X_45) != addition(addition(addition(X_44,X_45),X_44),X_45)
| addition(X_44,X_45) = addition(X_45,addition(X_44,addition(X_44,X_45))) ),
inference(resolve,[$cnf( $equal(addition(addition(addition(X_44,X_45),X_44),X_45),addition(X_45,addition(X_44,addition(X_44,X_45)))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
addition(X_44,X_45) = addition(X_45,addition(X_44,addition(X_44,X_45))),
inference(resolve,[$cnf( $equal(addition(X_44,X_45),addition(addition(addition(X_44,X_45),X_44),X_45)) )],[refute_0_9,refute_0_50]) ).
cnf(refute_0_52,plain,
addition(X_44,addition(X_44,X_45)) = addition(addition(X_44,X_44),X_45),
inference(subst,[],[refute_0_3:[bind(A,$fot(X_44)),bind(B,$fot(X_44)),bind(C,$fot(X_45))]]) ).
cnf(refute_0_53,plain,
addition(X_44,X_44) = X_44,
inference(subst,[],[refute_0_5:[bind(A,$fot(X_44))]]) ).
cnf(refute_0_54,plain,
( addition(X_44,X_44) != X_44
| addition(X_44,addition(X_44,X_45)) != addition(addition(X_44,X_44),X_45)
| addition(X_44,addition(X_44,X_45)) = addition(X_44,X_45) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_44,addition(X_44,X_45)),addition(addition(X_44,X_44),X_45)) ),[1,0],$fot(X_44)]]) ).
cnf(refute_0_55,plain,
( addition(X_44,addition(X_44,X_45)) != addition(addition(X_44,X_44),X_45)
| addition(X_44,addition(X_44,X_45)) = addition(X_44,X_45) ),
inference(resolve,[$cnf( $equal(addition(X_44,X_44),X_44) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
addition(X_44,addition(X_44,X_45)) = addition(X_44,X_45),
inference(resolve,[$cnf( $equal(addition(X_44,addition(X_44,X_45)),addition(addition(X_44,X_44),X_45)) )],[refute_0_52,refute_0_55]) ).
cnf(refute_0_57,plain,
addition(X_45,addition(X_44,addition(X_44,X_45))) = addition(X_45,addition(X_44,addition(X_44,X_45))),
introduced(tautology,[refl,[$fot(addition(X_45,addition(X_44,addition(X_44,X_45))))]]) ).
cnf(refute_0_58,plain,
( addition(X_44,addition(X_44,X_45)) != addition(X_44,X_45)
| addition(X_45,addition(X_44,addition(X_44,X_45))) != addition(X_45,addition(X_44,addition(X_44,X_45)))
| addition(X_45,addition(X_44,addition(X_44,X_45))) = addition(X_45,addition(X_44,X_45)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_45,addition(X_44,addition(X_44,X_45))),addition(X_45,addition(X_44,addition(X_44,X_45)))) ),[1,1],$fot(addition(X_44,X_45))]]) ).
cnf(refute_0_59,plain,
( addition(X_44,addition(X_44,X_45)) != addition(X_44,X_45)
| addition(X_45,addition(X_44,addition(X_44,X_45))) = addition(X_45,addition(X_44,X_45)) ),
inference(resolve,[$cnf( $equal(addition(X_45,addition(X_44,addition(X_44,X_45))),addition(X_45,addition(X_44,addition(X_44,X_45)))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
addition(X_45,addition(X_44,addition(X_44,X_45))) = addition(X_45,addition(X_44,X_45)),
inference(resolve,[$cnf( $equal(addition(X_44,addition(X_44,X_45)),addition(X_44,X_45)) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
( addition(X_44,X_45) != addition(X_45,addition(X_44,addition(X_44,X_45)))
| addition(X_45,addition(X_44,addition(X_44,X_45))) != addition(X_45,addition(X_44,X_45))
| addition(X_44,X_45) = addition(X_45,addition(X_44,X_45)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(X_44,X_45),addition(X_45,addition(X_44,X_45))) ),[0],$fot(addition(X_45,addition(X_44,addition(X_44,X_45))))]]) ).
cnf(refute_0_62,plain,
( addition(X_44,X_45) != addition(X_45,addition(X_44,addition(X_44,X_45)))
| addition(X_44,X_45) = addition(X_45,addition(X_44,X_45)) ),
inference(resolve,[$cnf( $equal(addition(X_45,addition(X_44,addition(X_44,X_45))),addition(X_45,addition(X_44,X_45))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
addition(X_44,X_45) = addition(X_45,addition(X_44,X_45)),
inference(resolve,[$cnf( $equal(addition(X_44,X_45),addition(X_45,addition(X_44,addition(X_44,X_45)))) )],[refute_0_51,refute_0_62]) ).
cnf(refute_0_64,plain,
addition(X_109,A) = addition(A,addition(X_109,A)),
inference(subst,[],[refute_0_63:[bind(X_44,$fot(X_109)),bind(X_45,$fot(A))]]) ).
cnf(refute_0_65,plain,
( addition(X_109,A) != addition(A,addition(X_109,A))
| addition(A,addition(X_109,A)) = addition(X_109,A) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(addition(X_109,A))),bind(Y,$fot(addition(A,addition(X_109,A))))]]) ).
cnf(refute_0_66,plain,
addition(A,addition(X_109,A)) = addition(X_109,A),
inference(resolve,[$cnf( $equal(addition(X_109,A),addition(A,addition(X_109,A))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
( addition(A,addition(X_109,A)) != addition(X_109,A)
| addition(X_109,A) != addition(X_109,A)
| addition(A,addition(X_109,A)) = addition(X_109,A) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(A,addition(X_109,A)),addition(X_109,A)) ),[0],$fot(addition(X_109,A))]]) ).
cnf(refute_0_68,plain,
( addition(X_109,A) != addition(X_109,A)
| addition(A,addition(X_109,A)) = addition(X_109,A) ),
inference(resolve,[$cnf( $equal(addition(A,addition(X_109,A)),addition(X_109,A)) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
( addition(X_109,A) != addition(X_109,A)
| leq(A,addition(X_109,A)) ),
inference(resolve,[$cnf( $equal(addition(A,addition(X_109,A)),addition(X_109,A)) )],[refute_0_68,refute_0_2]) ).
cnf(refute_0_70,plain,
addition(X_109,A) = addition(X_109,A),
introduced(tautology,[refl,[$fot(addition(X_109,A))]]) ).
cnf(refute_0_71,plain,
leq(A,addition(X_109,A)),
inference(resolve,[$cnf( $equal(addition(X_109,A),addition(X_109,A)) )],[refute_0_70,refute_0_69]) ).
cnf(refute_0_72,plain,
leq(X_115,addition(X_116,X_115)),
inference(subst,[],[refute_0_71:[bind(A,$fot(X_115)),bind(X_109,$fot(X_116))]]) ).
cnf(refute_0_73,plain,
addition(X_115,X_116) = addition(X_116,X_115),
inference(subst,[],[refute_0_11:[bind(A,$fot(X_115)),bind(B,$fot(X_116))]]) ).
cnf(refute_0_74,plain,
( addition(X_115,X_116) != addition(X_116,X_115)
| addition(X_116,X_115) = addition(X_115,X_116) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(addition(X_115,X_116))),bind(Y,$fot(addition(X_116,X_115)))]]) ).
cnf(refute_0_75,plain,
addition(X_116,X_115) = addition(X_115,X_116),
inference(resolve,[$cnf( $equal(addition(X_115,X_116),addition(X_116,X_115)) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
( addition(X_116,X_115) != addition(X_115,X_116)
| ~ leq(X_115,addition(X_116,X_115))
| leq(X_115,addition(X_115,X_116)) ),
introduced(tautology,[equality,[$cnf( leq(X_115,addition(X_116,X_115)) ),[1],$fot(addition(X_115,X_116))]]) ).
cnf(refute_0_77,plain,
( ~ leq(X_115,addition(X_116,X_115))
| leq(X_115,addition(X_115,X_116)) ),
inference(resolve,[$cnf( $equal(addition(X_116,X_115),addition(X_115,X_116)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
leq(X_115,addition(X_115,X_116)),
inference(resolve,[$cnf( leq(X_115,addition(X_116,X_115)) )],[refute_0_72,refute_0_77]) ).
cnf(refute_0_79,plain,
leq(one,addition(one,multiplication(A,strong_iteration(A)))),
inference(subst,[],[refute_0_78:[bind(X_115,$fot(one)),bind(X_116,$fot(multiplication(A,strong_iteration(A))))]]) ).
cnf(refute_0_80,plain,
strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_81,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_82,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_11,refute_0_81]) ).
cnf(refute_0_83,plain,
addition(multiplication(A,strong_iteration(A)),one) = addition(one,multiplication(A,strong_iteration(A))),
inference(subst,[],[refute_0_82:[bind(A,$fot(one)),bind(B,$fot(multiplication(A,strong_iteration(A))))]]) ).
cnf(refute_0_84,plain,
( addition(multiplication(A,strong_iteration(A)),one) != addition(one,multiplication(A,strong_iteration(A)))
| strong_iteration(A) != addition(multiplication(A,strong_iteration(A)),one)
| strong_iteration(A) = addition(one,multiplication(A,strong_iteration(A))) ),
introduced(tautology,[equality,[$cnf( $equal(strong_iteration(A),addition(multiplication(A,strong_iteration(A)),one)) ),[1],$fot(addition(one,multiplication(A,strong_iteration(A))))]]) ).
cnf(refute_0_85,plain,
( strong_iteration(A) != addition(multiplication(A,strong_iteration(A)),one)
| strong_iteration(A) = addition(one,multiplication(A,strong_iteration(A))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(A,strong_iteration(A)),one),addition(one,multiplication(A,strong_iteration(A)))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
strong_iteration(A) = addition(one,multiplication(A,strong_iteration(A))),
inference(resolve,[$cnf( $equal(strong_iteration(A),addition(multiplication(A,strong_iteration(A)),one)) )],[refute_0_80,refute_0_85]) ).
cnf(refute_0_87,plain,
( strong_iteration(A) != addition(one,multiplication(A,strong_iteration(A)))
| addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(strong_iteration(A))),bind(Y,$fot(addition(one,multiplication(A,strong_iteration(A)))))]]) ).
cnf(refute_0_88,plain,
addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A),
inference(resolve,[$cnf( $equal(strong_iteration(A),addition(one,multiplication(A,strong_iteration(A)))) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
( addition(one,multiplication(A,strong_iteration(A))) != strong_iteration(A)
| ~ leq(one,addition(one,multiplication(A,strong_iteration(A))))
| leq(one,strong_iteration(A)) ),
introduced(tautology,[equality,[$cnf( leq(one,addition(one,multiplication(A,strong_iteration(A)))) ),[1],$fot(strong_iteration(A))]]) ).
cnf(refute_0_90,plain,
( ~ leq(one,addition(one,multiplication(A,strong_iteration(A))))
| leq(one,strong_iteration(A)) ),
inference(resolve,[$cnf( $equal(addition(one,multiplication(A,strong_iteration(A))),strong_iteration(A)) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
leq(one,strong_iteration(A)),
inference(resolve,[$cnf( leq(one,addition(one,multiplication(A,strong_iteration(A)))) )],[refute_0_79,refute_0_90]) ).
cnf(refute_0_92,plain,
leq(one,strong_iteration(skolemFOFtoCNF_X0)),
inference(subst,[],[refute_0_91:[bind(A,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_93,plain,
$false,
inference(resolve,[$cnf( leq(one,strong_iteration(skolemFOFtoCNF_X0)) )],[refute_0_92,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KLE146+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 16 16:30:26 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.22/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.04/1.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.04/1.22
% 1.04/1.22 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.04/1.23
%------------------------------------------------------------------------------