TSTP Solution File: SYN551+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN551+2 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 : Thu Jul 21 09:03:57 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 33
% Syntax : Number of formulae : 139 ( 24 unt; 0 def)
% Number of atoms : 306 ( 304 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 311 ( 144 ~; 130 |; 6 &)
% ( 27 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-1 aty)
% Number of variables : 140 ( 0 sgn 38 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this_cute_thing,conjecture,
( ? [X] :
! [Y] :
( Y = f(g(Y))
<=> X = Y )
<=> ? [X] :
! [Y] :
( Y = g(f(Y))
<=> X = Y ) ) ).
fof(subgoal_0,plain,
( ? [X] :
! [Y] :
( Y = f(g(Y))
<=> X = Y )
=> ? [X] :
! [Y] :
( Y = g(f(Y))
<=> X = Y ) ),
inference(strip,[],[prove_this_cute_thing]) ).
fof(subgoal_1,plain,
( ? [X] :
! [Y] :
( Y = g(f(Y))
<=> X = Y )
=> ? [X] :
! [Y] :
( Y = f(g(Y))
<=> X = Y ) ),
inference(strip,[],[prove_this_cute_thing]) ).
fof(negate_0_0,plain,
~ ( ? [X] :
! [Y] :
( Y = f(g(Y))
<=> X = Y )
=> ? [X] :
! [Y] :
( Y = g(f(Y))
<=> X = Y ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ? [X] :
! [Y] :
( X != Y
<=> Y != f(g(Y)) )
& ! [X] :
? [Y] :
( X != Y
<=> Y = g(f(Y)) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [X] :
? [Y] :
( X != Y
<=> Y = g(f(Y)) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X] :
? [Y] :
( X != Y
<=> Y = g(f(Y)) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X] :
( X != skolemFOFtoCNF_Y(X)
<=> skolemFOFtoCNF_Y(X) = g(f(skolemFOFtoCNF_Y(X))) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X] :
( ( X != skolemFOFtoCNF_Y(X)
| skolemFOFtoCNF_Y(X) != g(f(skolemFOFtoCNF_Y(X))) )
& ( X = skolemFOFtoCNF_Y(X)
| skolemFOFtoCNF_Y(X) = g(f(skolemFOFtoCNF_Y(X))) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X] :
( X = skolemFOFtoCNF_Y(X)
| skolemFOFtoCNF_Y(X) = g(f(skolemFOFtoCNF_Y(X))) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [X] :
! [Y] :
( X != Y
<=> Y != f(g(Y)) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_7,plain,
! [Y] :
( Y != f(g(Y))
<=> skolemFOFtoCNF_X != Y ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [Y] :
( Y != f(g(Y))
<=> skolemFOFtoCNF_X != Y ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [Y] :
( ( Y != f(g(Y))
| skolemFOFtoCNF_X = Y )
& ( skolemFOFtoCNF_X != Y
| Y = f(g(Y)) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [Y] :
( Y != f(g(Y))
| skolemFOFtoCNF_X = Y ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X] :
( X != skolemFOFtoCNF_Y(X)
| skolemFOFtoCNF_Y(X) != g(f(skolemFOFtoCNF_Y(X))) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_12,plain,
! [Y] :
( skolemFOFtoCNF_X != Y
| Y = f(g(Y)) ),
inference(conjunct,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
( X = skolemFOFtoCNF_Y(X)
| skolemFOFtoCNF_Y(X) = g(f(skolemFOFtoCNF_Y(X))) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_1,plain,
( Y != f(g(Y))
| skolemFOFtoCNF_X = Y ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_2,plain,
( f(skolemFOFtoCNF_Y(X_2)) != f(g(f(skolemFOFtoCNF_Y(X_2))))
| skolemFOFtoCNF_X = f(skolemFOFtoCNF_Y(X_2)) ),
inference(subst,[],[refute_0_1:[bind(Y,$fot(f(skolemFOFtoCNF_Y(X_2))))]]) ).
cnf(refute_0_3,plain,
( X_2 = skolemFOFtoCNF_Y(X_2)
| skolemFOFtoCNF_Y(X_2) = g(f(skolemFOFtoCNF_Y(X_2))) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(X_2))]]) ).
cnf(refute_0_4,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_5,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_6,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( skolemFOFtoCNF_Y(X_2) != g(f(skolemFOFtoCNF_Y(X_2)))
| g(f(skolemFOFtoCNF_Y(X_2))) = skolemFOFtoCNF_Y(X_2) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(skolemFOFtoCNF_Y(X_2))),bind(Y0,$fot(g(f(skolemFOFtoCNF_Y(X_2)))))]]) ).
cnf(refute_0_8,plain,
( X_2 = skolemFOFtoCNF_Y(X_2)
| g(f(skolemFOFtoCNF_Y(X_2))) = skolemFOFtoCNF_Y(X_2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y(X_2),g(f(skolemFOFtoCNF_Y(X_2)))) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( f(skolemFOFtoCNF_Y(X_2)) != f(skolemFOFtoCNF_Y(X_2))
| g(f(skolemFOFtoCNF_Y(X_2))) != skolemFOFtoCNF_Y(X_2)
| f(skolemFOFtoCNF_Y(X_2)) = f(g(f(skolemFOFtoCNF_Y(X_2)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(skolemFOFtoCNF_Y(X_2)),f(g(f(skolemFOFtoCNF_Y(X_2))))) ),[1,0],$fot(skolemFOFtoCNF_Y(X_2))]]) ).
cnf(refute_0_10,plain,
( f(skolemFOFtoCNF_Y(X_2)) != f(skolemFOFtoCNF_Y(X_2))
| X_2 = skolemFOFtoCNF_Y(X_2)
| f(skolemFOFtoCNF_Y(X_2)) = f(g(f(skolemFOFtoCNF_Y(X_2)))) ),
inference(resolve,[$cnf( $equal(g(f(skolemFOFtoCNF_Y(X_2))),skolemFOFtoCNF_Y(X_2)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( f(skolemFOFtoCNF_Y(X_2)) != f(skolemFOFtoCNF_Y(X_2))
| X_2 = skolemFOFtoCNF_Y(X_2)
| skolemFOFtoCNF_X = f(skolemFOFtoCNF_Y(X_2)) ),
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_Y(X_2)),f(g(f(skolemFOFtoCNF_Y(X_2))))) )],[refute_0_10,refute_0_2]) ).
cnf(refute_0_12,plain,
f(skolemFOFtoCNF_Y(X_2)) = f(skolemFOFtoCNF_Y(X_2)),
introduced(tautology,[refl,[$fot(f(skolemFOFtoCNF_Y(X_2)))]]) ).
cnf(refute_0_13,plain,
( X_2 = skolemFOFtoCNF_Y(X_2)
| skolemFOFtoCNF_X = f(skolemFOFtoCNF_Y(X_2)) ),
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_Y(X_2)),f(skolemFOFtoCNF_Y(X_2))) )],[refute_0_12,refute_0_11]) ).
cnf(refute_0_14,plain,
( X = skolemFOFtoCNF_Y(X)
| skolemFOFtoCNF_X = f(skolemFOFtoCNF_Y(X)) ),
inference(subst,[],[refute_0_13:[bind(X_2,$fot(X))]]) ).
cnf(refute_0_15,plain,
( skolemFOFtoCNF_X != f(skolemFOFtoCNF_Y(X))
| f(skolemFOFtoCNF_Y(X)) = skolemFOFtoCNF_X ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(skolemFOFtoCNF_X)),bind(Y0,$fot(f(skolemFOFtoCNF_Y(X))))]]) ).
cnf(refute_0_16,plain,
( X = skolemFOFtoCNF_Y(X)
| f(skolemFOFtoCNF_Y(X)) = skolemFOFtoCNF_X ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y(X))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( f(skolemFOFtoCNF_Y(X)) != skolemFOFtoCNF_X
| skolemFOFtoCNF_Y(X) != g(f(skolemFOFtoCNF_Y(X)))
| skolemFOFtoCNF_Y(X) = g(skolemFOFtoCNF_X) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y(X),g(f(skolemFOFtoCNF_Y(X)))) ),[1,0],$fot(skolemFOFtoCNF_X)]]) ).
cnf(refute_0_18,plain,
( skolemFOFtoCNF_Y(X) != g(f(skolemFOFtoCNF_Y(X)))
| X = skolemFOFtoCNF_Y(X)
| skolemFOFtoCNF_Y(X) = g(skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_Y(X)),skolemFOFtoCNF_X) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( X = skolemFOFtoCNF_Y(X)
| skolemFOFtoCNF_Y(X) = g(skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y(X),g(f(skolemFOFtoCNF_Y(X)))) )],[refute_0_0,refute_0_18]) ).
cnf(refute_0_20,plain,
( g(skolemFOFtoCNF_X) = skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))
| skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)) = g(skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(g(skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_21,plain,
( skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)) != g(skolemFOFtoCNF_X)
| g(skolemFOFtoCNF_X) = skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))),bind(Y0,$fot(g(skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_22,plain,
g(skolemFOFtoCNF_X) = skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)),g(skolemFOFtoCNF_X)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( X != skolemFOFtoCNF_Y(X)
| skolemFOFtoCNF_Y(X) != g(f(skolemFOFtoCNF_Y(X))) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_24,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_25,plain,
( X != X
| X != skolemFOFtoCNF_Y(X)
| skolemFOFtoCNF_Y(X) = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(skolemFOFtoCNF_Y(X))]]) ).
cnf(refute_0_26,plain,
( X != skolemFOFtoCNF_Y(X)
| skolemFOFtoCNF_Y(X) = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( X != g(f(skolemFOFtoCNF_Y(X)))
| skolemFOFtoCNF_Y(X) != X
| skolemFOFtoCNF_Y(X) = g(f(skolemFOFtoCNF_Y(X))) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y(X),X) ),[1],$fot(g(f(skolemFOFtoCNF_Y(X))))]]) ).
cnf(refute_0_28,plain,
( X != g(f(skolemFOFtoCNF_Y(X)))
| X != skolemFOFtoCNF_Y(X)
| skolemFOFtoCNF_Y(X) = g(f(skolemFOFtoCNF_Y(X))) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y(X),X) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
f(skolemFOFtoCNF_Y(X)) = f(skolemFOFtoCNF_Y(X)),
introduced(tautology,[refl,[$fot(f(skolemFOFtoCNF_Y(X)))]]) ).
cnf(refute_0_30,plain,
( f(skolemFOFtoCNF_Y(X)) != f(skolemFOFtoCNF_Y(X))
| skolemFOFtoCNF_Y(X) != X
| f(skolemFOFtoCNF_Y(X)) = f(X) ),
introduced(tautology,[equality,[$cnf( $equal(f(skolemFOFtoCNF_Y(X)),f(skolemFOFtoCNF_Y(X))) ),[1,0],$fot(X)]]) ).
cnf(refute_0_31,plain,
( skolemFOFtoCNF_Y(X) != X
| f(skolemFOFtoCNF_Y(X)) = f(X) ),
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_Y(X)),f(skolemFOFtoCNF_Y(X))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( X != skolemFOFtoCNF_Y(X)
| f(skolemFOFtoCNF_Y(X)) = f(X) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y(X),X) )],[refute_0_26,refute_0_31]) ).
cnf(refute_0_33,plain,
g(f(skolemFOFtoCNF_Y(X))) = g(f(skolemFOFtoCNF_Y(X))),
introduced(tautology,[refl,[$fot(g(f(skolemFOFtoCNF_Y(X))))]]) ).
cnf(refute_0_34,plain,
( f(skolemFOFtoCNF_Y(X)) != f(X)
| g(f(skolemFOFtoCNF_Y(X))) != g(f(skolemFOFtoCNF_Y(X)))
| g(f(skolemFOFtoCNF_Y(X))) = g(f(X)) ),
introduced(tautology,[equality,[$cnf( $equal(g(f(skolemFOFtoCNF_Y(X))),g(f(skolemFOFtoCNF_Y(X)))) ),[1,0],$fot(f(X))]]) ).
cnf(refute_0_35,plain,
( f(skolemFOFtoCNF_Y(X)) != f(X)
| g(f(skolemFOFtoCNF_Y(X))) = g(f(X)) ),
inference(resolve,[$cnf( $equal(g(f(skolemFOFtoCNF_Y(X))),g(f(skolemFOFtoCNF_Y(X)))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( X != skolemFOFtoCNF_Y(X)
| g(f(skolemFOFtoCNF_Y(X))) = g(f(X)) ),
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_Y(X)),f(X)) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
( X != g(f(X))
| g(f(skolemFOFtoCNF_Y(X))) != g(f(X))
| X = g(f(skolemFOFtoCNF_Y(X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X,g(f(skolemFOFtoCNF_Y(X)))) ),[1],$fot(g(f(X)))]]) ).
cnf(refute_0_38,plain,
( X != g(f(X))
| X != skolemFOFtoCNF_Y(X)
| X = g(f(skolemFOFtoCNF_Y(X))) ),
inference(resolve,[$cnf( $equal(g(f(skolemFOFtoCNF_Y(X))),g(f(X))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
( X != g(f(X))
| X != skolemFOFtoCNF_Y(X)
| skolemFOFtoCNF_Y(X) = g(f(skolemFOFtoCNF_Y(X))) ),
inference(resolve,[$cnf( $equal(X,g(f(skolemFOFtoCNF_Y(X)))) )],[refute_0_38,refute_0_28]) ).
cnf(refute_0_40,plain,
( X != g(f(X))
| X != skolemFOFtoCNF_Y(X) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y(X),g(f(skolemFOFtoCNF_Y(X)))) )],[refute_0_39,refute_0_23]) ).
cnf(refute_0_41,plain,
( g(skolemFOFtoCNF_X) != g(f(g(skolemFOFtoCNF_X)))
| g(skolemFOFtoCNF_X) != skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_40:[bind(X,$fot(g(skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_42,plain,
( skolemFOFtoCNF_X != Y
| Y = f(g(Y)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_43,plain,
( skolemFOFtoCNF_X != skolemFOFtoCNF_X
| skolemFOFtoCNF_X = f(g(skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_42:[bind(Y,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_44,plain,
skolemFOFtoCNF_X = skolemFOFtoCNF_X,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_X)]]) ).
cnf(refute_0_45,plain,
skolemFOFtoCNF_X = f(g(skolemFOFtoCNF_X)),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_44,refute_0_43]) ).
cnf(refute_0_46,plain,
( skolemFOFtoCNF_X != f(g(skolemFOFtoCNF_X))
| f(g(skolemFOFtoCNF_X)) = skolemFOFtoCNF_X ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(skolemFOFtoCNF_X)),bind(Y0,$fot(f(g(skolemFOFtoCNF_X))))]]) ).
cnf(refute_0_47,plain,
f(g(skolemFOFtoCNF_X)) = skolemFOFtoCNF_X,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X,f(g(skolemFOFtoCNF_X))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( f(g(skolemFOFtoCNF_X)) != skolemFOFtoCNF_X
| g(skolemFOFtoCNF_X) != g(skolemFOFtoCNF_X)
| g(skolemFOFtoCNF_X) = g(f(g(skolemFOFtoCNF_X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(g(skolemFOFtoCNF_X),g(f(g(skolemFOFtoCNF_X)))) ),[1,0],$fot(skolemFOFtoCNF_X)]]) ).
cnf(refute_0_49,plain,
( g(skolemFOFtoCNF_X) != g(skolemFOFtoCNF_X)
| g(skolemFOFtoCNF_X) = g(f(g(skolemFOFtoCNF_X))) ),
inference(resolve,[$cnf( $equal(f(g(skolemFOFtoCNF_X)),skolemFOFtoCNF_X) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
( g(skolemFOFtoCNF_X) != g(skolemFOFtoCNF_X)
| g(skolemFOFtoCNF_X) != skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_X),g(f(g(skolemFOFtoCNF_X)))) )],[refute_0_49,refute_0_41]) ).
cnf(refute_0_51,plain,
g(skolemFOFtoCNF_X) = g(skolemFOFtoCNF_X),
introduced(tautology,[refl,[$fot(g(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_52,plain,
g(skolemFOFtoCNF_X) != skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)),
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_X),g(skolemFOFtoCNF_X)) )],[refute_0_51,refute_0_50]) ).
cnf(refute_0_53,plain,
$false,
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_X),skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))) )],[refute_0_22,refute_0_52]) ).
fof(negate_1_0,plain,
~ ( ? [X] :
! [Y] :
( Y = g(f(Y))
<=> X = Y )
=> ? [X] :
! [Y] :
( Y = f(g(Y))
<=> X = Y ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
( ? [X] :
! [Y] :
( X != Y
<=> Y != g(f(Y)) )
& ! [X] :
? [Y] :
( X != Y
<=> Y = f(g(Y)) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
! [X] :
? [Y] :
( X != Y
<=> Y = f(g(Y)) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [X] :
? [Y] :
( X != Y
<=> Y = f(g(Y)) ),
inference(specialize,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [X] :
( X != skolemFOFtoCNF_Y_1(X)
<=> skolemFOFtoCNF_Y_1(X) = f(g(skolemFOFtoCNF_Y_1(X))) ),
inference(skolemize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [X] :
( ( X != skolemFOFtoCNF_Y_1(X)
| skolemFOFtoCNF_Y_1(X) != f(g(skolemFOFtoCNF_Y_1(X))) )
& ( X = skolemFOFtoCNF_Y_1(X)
| skolemFOFtoCNF_Y_1(X) = f(g(skolemFOFtoCNF_Y_1(X))) ) ),
inference(clausify,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [X] :
( X = skolemFOFtoCNF_Y_1(X)
| skolemFOFtoCNF_Y_1(X) = f(g(skolemFOFtoCNF_Y_1(X))) ),
inference(conjunct,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
? [X] :
! [Y] :
( X != Y
<=> Y != g(f(Y)) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_7,plain,
! [Y] :
( Y != g(f(Y))
<=> skolemFOFtoCNF_X_1 != Y ),
inference(skolemize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [Y] :
( Y != g(f(Y))
<=> skolemFOFtoCNF_X_1 != Y ),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [Y] :
( ( Y != g(f(Y))
| skolemFOFtoCNF_X_1 = Y )
& ( skolemFOFtoCNF_X_1 != Y
| Y = g(f(Y)) ) ),
inference(clausify,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [Y] :
( Y != g(f(Y))
| skolemFOFtoCNF_X_1 = Y ),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [X] :
( X != skolemFOFtoCNF_Y_1(X)
| skolemFOFtoCNF_Y_1(X) != f(g(skolemFOFtoCNF_Y_1(X))) ),
inference(conjunct,[],[normalize_1_4]) ).
fof(normalize_1_12,plain,
! [Y] :
( skolemFOFtoCNF_X_1 != Y
| Y = g(f(Y)) ),
inference(conjunct,[],[normalize_1_9]) ).
cnf(refute_1_0,plain,
( X = skolemFOFtoCNF_Y_1(X)
| skolemFOFtoCNF_Y_1(X) = f(g(skolemFOFtoCNF_Y_1(X))) ),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_1,plain,
( Y != g(f(Y))
| skolemFOFtoCNF_X_1 = Y ),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_2,plain,
( g(skolemFOFtoCNF_Y_1(X_6)) != g(f(g(skolemFOFtoCNF_Y_1(X_6))))
| skolemFOFtoCNF_X_1 = g(skolemFOFtoCNF_Y_1(X_6)) ),
inference(subst,[],[refute_1_1:[bind(Y,$fot(g(skolemFOFtoCNF_Y_1(X_6))))]]) ).
cnf(refute_1_3,plain,
( X_6 = skolemFOFtoCNF_Y_1(X_6)
| skolemFOFtoCNF_Y_1(X_6) = f(g(skolemFOFtoCNF_Y_1(X_6))) ),
inference(subst,[],[refute_1_0:[bind(X,$fot(X_6))]]) ).
cnf(refute_1_4,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_1_5,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_1_6,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_1_4,refute_1_5]) ).
cnf(refute_1_7,plain,
( skolemFOFtoCNF_Y_1(X_6) != f(g(skolemFOFtoCNF_Y_1(X_6)))
| f(g(skolemFOFtoCNF_Y_1(X_6))) = skolemFOFtoCNF_Y_1(X_6) ),
inference(subst,[],[refute_1_6:[bind(X0,$fot(skolemFOFtoCNF_Y_1(X_6))),bind(Y0,$fot(f(g(skolemFOFtoCNF_Y_1(X_6)))))]]) ).
cnf(refute_1_8,plain,
( X_6 = skolemFOFtoCNF_Y_1(X_6)
| f(g(skolemFOFtoCNF_Y_1(X_6))) = skolemFOFtoCNF_Y_1(X_6) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1(X_6),f(g(skolemFOFtoCNF_Y_1(X_6)))) )],[refute_1_3,refute_1_7]) ).
cnf(refute_1_9,plain,
( f(g(skolemFOFtoCNF_Y_1(X_6))) != skolemFOFtoCNF_Y_1(X_6)
| g(skolemFOFtoCNF_Y_1(X_6)) != g(skolemFOFtoCNF_Y_1(X_6))
| g(skolemFOFtoCNF_Y_1(X_6)) = g(f(g(skolemFOFtoCNF_Y_1(X_6)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(g(skolemFOFtoCNF_Y_1(X_6)),g(f(g(skolemFOFtoCNF_Y_1(X_6))))) ),[1,0],$fot(skolemFOFtoCNF_Y_1(X_6))]]) ).
cnf(refute_1_10,plain,
( g(skolemFOFtoCNF_Y_1(X_6)) != g(skolemFOFtoCNF_Y_1(X_6))
| X_6 = skolemFOFtoCNF_Y_1(X_6)
| g(skolemFOFtoCNF_Y_1(X_6)) = g(f(g(skolemFOFtoCNF_Y_1(X_6)))) ),
inference(resolve,[$cnf( $equal(f(g(skolemFOFtoCNF_Y_1(X_6))),skolemFOFtoCNF_Y_1(X_6)) )],[refute_1_8,refute_1_9]) ).
cnf(refute_1_11,plain,
( g(skolemFOFtoCNF_Y_1(X_6)) != g(skolemFOFtoCNF_Y_1(X_6))
| X_6 = skolemFOFtoCNF_Y_1(X_6)
| skolemFOFtoCNF_X_1 = g(skolemFOFtoCNF_Y_1(X_6)) ),
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_Y_1(X_6)),g(f(g(skolemFOFtoCNF_Y_1(X_6))))) )],[refute_1_10,refute_1_2]) ).
cnf(refute_1_12,plain,
g(skolemFOFtoCNF_Y_1(X_6)) = g(skolemFOFtoCNF_Y_1(X_6)),
introduced(tautology,[refl,[$fot(g(skolemFOFtoCNF_Y_1(X_6)))]]) ).
cnf(refute_1_13,plain,
( X_6 = skolemFOFtoCNF_Y_1(X_6)
| skolemFOFtoCNF_X_1 = g(skolemFOFtoCNF_Y_1(X_6)) ),
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_Y_1(X_6)),g(skolemFOFtoCNF_Y_1(X_6))) )],[refute_1_12,refute_1_11]) ).
cnf(refute_1_14,plain,
( X = skolemFOFtoCNF_Y_1(X)
| skolemFOFtoCNF_X_1 = g(skolemFOFtoCNF_Y_1(X)) ),
inference(subst,[],[refute_1_13:[bind(X_6,$fot(X))]]) ).
cnf(refute_1_15,plain,
( skolemFOFtoCNF_X_1 != g(skolemFOFtoCNF_Y_1(X))
| g(skolemFOFtoCNF_Y_1(X)) = skolemFOFtoCNF_X_1 ),
inference(subst,[],[refute_1_6:[bind(X0,$fot(skolemFOFtoCNF_X_1)),bind(Y0,$fot(g(skolemFOFtoCNF_Y_1(X))))]]) ).
cnf(refute_1_16,plain,
( X = skolemFOFtoCNF_Y_1(X)
| g(skolemFOFtoCNF_Y_1(X)) = skolemFOFtoCNF_X_1 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_1,g(skolemFOFtoCNF_Y_1(X))) )],[refute_1_14,refute_1_15]) ).
cnf(refute_1_17,plain,
( g(skolemFOFtoCNF_Y_1(X)) != skolemFOFtoCNF_X_1
| skolemFOFtoCNF_Y_1(X) != f(g(skolemFOFtoCNF_Y_1(X)))
| skolemFOFtoCNF_Y_1(X) = f(skolemFOFtoCNF_X_1) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y_1(X),f(g(skolemFOFtoCNF_Y_1(X)))) ),[1,0],$fot(skolemFOFtoCNF_X_1)]]) ).
cnf(refute_1_18,plain,
( skolemFOFtoCNF_Y_1(X) != f(g(skolemFOFtoCNF_Y_1(X)))
| X = skolemFOFtoCNF_Y_1(X)
| skolemFOFtoCNF_Y_1(X) = f(skolemFOFtoCNF_X_1) ),
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_Y_1(X)),skolemFOFtoCNF_X_1) )],[refute_1_16,refute_1_17]) ).
cnf(refute_1_19,plain,
( X = skolemFOFtoCNF_Y_1(X)
| skolemFOFtoCNF_Y_1(X) = f(skolemFOFtoCNF_X_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1(X),f(g(skolemFOFtoCNF_Y_1(X)))) )],[refute_1_0,refute_1_18]) ).
cnf(refute_1_20,plain,
( f(skolemFOFtoCNF_X_1) = skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))
| skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)) = f(skolemFOFtoCNF_X_1) ),
inference(subst,[],[refute_1_19:[bind(X,$fot(f(skolemFOFtoCNF_X_1)))]]) ).
cnf(refute_1_21,plain,
( skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)) != f(skolemFOFtoCNF_X_1)
| f(skolemFOFtoCNF_X_1) = skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)) ),
inference(subst,[],[refute_1_6:[bind(X0,$fot(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))),bind(Y0,$fot(f(skolemFOFtoCNF_X_1)))]]) ).
cnf(refute_1_22,plain,
f(skolemFOFtoCNF_X_1) = skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)),f(skolemFOFtoCNF_X_1)) )],[refute_1_20,refute_1_21]) ).
cnf(refute_1_23,plain,
( X != skolemFOFtoCNF_Y_1(X)
| skolemFOFtoCNF_Y_1(X) != f(g(skolemFOFtoCNF_Y_1(X))) ),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_24,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_25,plain,
( X != X
| X != skolemFOFtoCNF_Y_1(X)
| skolemFOFtoCNF_Y_1(X) = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(skolemFOFtoCNF_Y_1(X))]]) ).
cnf(refute_1_26,plain,
( X != skolemFOFtoCNF_Y_1(X)
| skolemFOFtoCNF_Y_1(X) = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_24,refute_1_25]) ).
cnf(refute_1_27,plain,
( X != f(g(skolemFOFtoCNF_Y_1(X)))
| skolemFOFtoCNF_Y_1(X) != X
| skolemFOFtoCNF_Y_1(X) = f(g(skolemFOFtoCNF_Y_1(X))) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y_1(X),X) ),[1],$fot(f(g(skolemFOFtoCNF_Y_1(X))))]]) ).
cnf(refute_1_28,plain,
( X != f(g(skolemFOFtoCNF_Y_1(X)))
| X != skolemFOFtoCNF_Y_1(X)
| skolemFOFtoCNF_Y_1(X) = f(g(skolemFOFtoCNF_Y_1(X))) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1(X),X) )],[refute_1_26,refute_1_27]) ).
cnf(refute_1_29,plain,
g(skolemFOFtoCNF_Y_1(X)) = g(skolemFOFtoCNF_Y_1(X)),
introduced(tautology,[refl,[$fot(g(skolemFOFtoCNF_Y_1(X)))]]) ).
cnf(refute_1_30,plain,
( g(skolemFOFtoCNF_Y_1(X)) != g(skolemFOFtoCNF_Y_1(X))
| skolemFOFtoCNF_Y_1(X) != X
| g(skolemFOFtoCNF_Y_1(X)) = g(X) ),
introduced(tautology,[equality,[$cnf( $equal(g(skolemFOFtoCNF_Y_1(X)),g(skolemFOFtoCNF_Y_1(X))) ),[1,0],$fot(X)]]) ).
cnf(refute_1_31,plain,
( skolemFOFtoCNF_Y_1(X) != X
| g(skolemFOFtoCNF_Y_1(X)) = g(X) ),
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_Y_1(X)),g(skolemFOFtoCNF_Y_1(X))) )],[refute_1_29,refute_1_30]) ).
cnf(refute_1_32,plain,
( X != skolemFOFtoCNF_Y_1(X)
| g(skolemFOFtoCNF_Y_1(X)) = g(X) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1(X),X) )],[refute_1_26,refute_1_31]) ).
cnf(refute_1_33,plain,
f(g(skolemFOFtoCNF_Y_1(X))) = f(g(skolemFOFtoCNF_Y_1(X))),
introduced(tautology,[refl,[$fot(f(g(skolemFOFtoCNF_Y_1(X))))]]) ).
cnf(refute_1_34,plain,
( f(g(skolemFOFtoCNF_Y_1(X))) != f(g(skolemFOFtoCNF_Y_1(X)))
| g(skolemFOFtoCNF_Y_1(X)) != g(X)
| f(g(skolemFOFtoCNF_Y_1(X))) = f(g(X)) ),
introduced(tautology,[equality,[$cnf( $equal(f(g(skolemFOFtoCNF_Y_1(X))),f(g(skolemFOFtoCNF_Y_1(X)))) ),[1,0],$fot(g(X))]]) ).
cnf(refute_1_35,plain,
( g(skolemFOFtoCNF_Y_1(X)) != g(X)
| f(g(skolemFOFtoCNF_Y_1(X))) = f(g(X)) ),
inference(resolve,[$cnf( $equal(f(g(skolemFOFtoCNF_Y_1(X))),f(g(skolemFOFtoCNF_Y_1(X)))) )],[refute_1_33,refute_1_34]) ).
cnf(refute_1_36,plain,
( X != skolemFOFtoCNF_Y_1(X)
| f(g(skolemFOFtoCNF_Y_1(X))) = f(g(X)) ),
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_Y_1(X)),g(X)) )],[refute_1_32,refute_1_35]) ).
cnf(refute_1_37,plain,
( X != f(g(X))
| f(g(skolemFOFtoCNF_Y_1(X))) != f(g(X))
| X = f(g(skolemFOFtoCNF_Y_1(X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X,f(g(skolemFOFtoCNF_Y_1(X)))) ),[1],$fot(f(g(X)))]]) ).
cnf(refute_1_38,plain,
( X != f(g(X))
| X != skolemFOFtoCNF_Y_1(X)
| X = f(g(skolemFOFtoCNF_Y_1(X))) ),
inference(resolve,[$cnf( $equal(f(g(skolemFOFtoCNF_Y_1(X))),f(g(X))) )],[refute_1_36,refute_1_37]) ).
cnf(refute_1_39,plain,
( X != f(g(X))
| X != skolemFOFtoCNF_Y_1(X)
| skolemFOFtoCNF_Y_1(X) = f(g(skolemFOFtoCNF_Y_1(X))) ),
inference(resolve,[$cnf( $equal(X,f(g(skolemFOFtoCNF_Y_1(X)))) )],[refute_1_38,refute_1_28]) ).
cnf(refute_1_40,plain,
( X != f(g(X))
| X != skolemFOFtoCNF_Y_1(X) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1(X),f(g(skolemFOFtoCNF_Y_1(X)))) )],[refute_1_39,refute_1_23]) ).
cnf(refute_1_41,plain,
( f(skolemFOFtoCNF_X_1) != f(g(f(skolemFOFtoCNF_X_1)))
| f(skolemFOFtoCNF_X_1) != skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)) ),
inference(subst,[],[refute_1_40:[bind(X,$fot(f(skolemFOFtoCNF_X_1)))]]) ).
cnf(refute_1_42,plain,
( skolemFOFtoCNF_X_1 != Y
| Y = g(f(Y)) ),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_43,plain,
( skolemFOFtoCNF_X_1 != skolemFOFtoCNF_X_1
| skolemFOFtoCNF_X_1 = g(f(skolemFOFtoCNF_X_1)) ),
inference(subst,[],[refute_1_42:[bind(Y,$fot(skolemFOFtoCNF_X_1))]]) ).
cnf(refute_1_44,plain,
skolemFOFtoCNF_X_1 = skolemFOFtoCNF_X_1,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_X_1)]]) ).
cnf(refute_1_45,plain,
skolemFOFtoCNF_X_1 = g(f(skolemFOFtoCNF_X_1)),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_1,skolemFOFtoCNF_X_1) )],[refute_1_44,refute_1_43]) ).
cnf(refute_1_46,plain,
( skolemFOFtoCNF_X_1 != g(f(skolemFOFtoCNF_X_1))
| g(f(skolemFOFtoCNF_X_1)) = skolemFOFtoCNF_X_1 ),
inference(subst,[],[refute_1_6:[bind(X0,$fot(skolemFOFtoCNF_X_1)),bind(Y0,$fot(g(f(skolemFOFtoCNF_X_1))))]]) ).
cnf(refute_1_47,plain,
g(f(skolemFOFtoCNF_X_1)) = skolemFOFtoCNF_X_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_1,g(f(skolemFOFtoCNF_X_1))) )],[refute_1_45,refute_1_46]) ).
cnf(refute_1_48,plain,
( f(skolemFOFtoCNF_X_1) != f(skolemFOFtoCNF_X_1)
| g(f(skolemFOFtoCNF_X_1)) != skolemFOFtoCNF_X_1
| f(skolemFOFtoCNF_X_1) = f(g(f(skolemFOFtoCNF_X_1))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(skolemFOFtoCNF_X_1),f(g(f(skolemFOFtoCNF_X_1)))) ),[1,0],$fot(skolemFOFtoCNF_X_1)]]) ).
cnf(refute_1_49,plain,
( f(skolemFOFtoCNF_X_1) != f(skolemFOFtoCNF_X_1)
| f(skolemFOFtoCNF_X_1) = f(g(f(skolemFOFtoCNF_X_1))) ),
inference(resolve,[$cnf( $equal(g(f(skolemFOFtoCNF_X_1)),skolemFOFtoCNF_X_1) )],[refute_1_47,refute_1_48]) ).
cnf(refute_1_50,plain,
( f(skolemFOFtoCNF_X_1) != f(skolemFOFtoCNF_X_1)
| f(skolemFOFtoCNF_X_1) != skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)) ),
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_X_1),f(g(f(skolemFOFtoCNF_X_1)))) )],[refute_1_49,refute_1_41]) ).
cnf(refute_1_51,plain,
f(skolemFOFtoCNF_X_1) = f(skolemFOFtoCNF_X_1),
introduced(tautology,[refl,[$fot(f(skolemFOFtoCNF_X_1))]]) ).
cnf(refute_1_52,plain,
f(skolemFOFtoCNF_X_1) != skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)),
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_X_1),f(skolemFOFtoCNF_X_1)) )],[refute_1_51,refute_1_50]) ).
cnf(refute_1_53,plain,
$false,
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_X_1),skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))) )],[refute_1_22,refute_1_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN551+2 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 13:21:13 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37
%------------------------------------------------------------------------------