%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN551+3 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 09:03:58 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 19
% Syntax : Number of formulae : 95 ( 28 unt; 0 def)
% Number of atoms : 212 ( 210 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 213 ( 96 ~; 76 |; 26 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 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 : 68 ( 0 sgn 32 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this_cute_thing,conjecture,
( ? [X] :
( X = f(g(X))
& ! [Y] :
( Y = f(g(Y))
=> Y = X ) )
<=> ? [X] :
( X = g(f(X))
& ! [Y] :
( Y = g(f(Y))
=> Y = X ) ) ) ).
fof(subgoal_0,plain,
( ? [X] :
( X = f(g(X))
& ! [Y] :
( Y = f(g(Y))
=> Y = X ) )
=> ? [X] :
( X = g(f(X))
& ! [Y] :
( Y = g(f(Y))
=> Y = X ) ) ),
inference(strip,[],[prove_this_cute_thing]) ).
fof(subgoal_1,plain,
( ? [X] :
( X = g(f(X))
& ! [Y] :
( Y = g(f(Y))
=> Y = X ) )
=> ? [X] :
( X = f(g(X))
& ! [Y] :
( Y = f(g(Y))
=> Y = X ) ) ),
inference(strip,[],[prove_this_cute_thing]) ).
fof(negate_0_0,plain,
~ ( ? [X] :
( X = f(g(X))
& ! [Y] :
( Y = f(g(Y))
=> Y = X ) )
=> ? [X] :
( X = g(f(X))
& ! [Y] :
( Y = g(f(Y))
=> Y = X ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ? [X] :
( X = f(g(X))
& ! [Y] :
( Y != f(g(Y))
| Y = X ) )
& ! [X] :
( X != g(f(X))
| ? [Y] :
( Y != X
& Y = g(f(Y)) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [X] :
( X != g(f(X))
| ? [Y] :
( Y != X
& Y = g(f(Y)) ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X] :
( X != g(f(X))
| ? [Y] :
( Y != X
& Y = g(f(Y)) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X] :
( ( X != g(f(X))
| skolemFOFtoCNF_Y(X) != X )
& ( X != g(f(X))
| skolemFOFtoCNF_Y(X) = g(f(skolemFOFtoCNF_Y(X))) ) ),
inference(clausify,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X] :
( X != g(f(X))
| skolemFOFtoCNF_Y(X) = g(f(skolemFOFtoCNF_Y(X))) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
? [X] :
( X = f(g(X))
& ! [Y] :
( Y != f(g(Y))
| Y = X ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_6,plain,
( skolemFOFtoCNF_X = f(g(skolemFOFtoCNF_X))
& ! [Y] :
( Y != f(g(Y))
| Y = skolemFOFtoCNF_X ) ),
inference(skolemize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
skolemFOFtoCNF_X = f(g(skolemFOFtoCNF_X)),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [Y] :
( Y != f(g(Y))
| Y = skolemFOFtoCNF_X ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_9,plain,
! [Y] :
( Y != f(g(Y))
| Y = skolemFOFtoCNF_X ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X] :
( X != g(f(X))
| skolemFOFtoCNF_Y(X) != X ),
inference(conjunct,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
( X != g(f(X))
| skolemFOFtoCNF_Y(X) = g(f(skolemFOFtoCNF_Y(X))) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
( g(skolemFOFtoCNF_X) != g(f(g(skolemFOFtoCNF_X)))
| skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)) = g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(g(skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_2,plain,
skolemFOFtoCNF_X = f(g(skolemFOFtoCNF_X)),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_4,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_5,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( skolemFOFtoCNF_X != f(g(skolemFOFtoCNF_X))
| f(g(skolemFOFtoCNF_X)) = skolemFOFtoCNF_X ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(skolemFOFtoCNF_X)),bind(Y0,$fot(f(g(skolemFOFtoCNF_X))))]]) ).
cnf(refute_0_7,plain,
f(g(skolemFOFtoCNF_X)) = skolemFOFtoCNF_X,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X,f(g(skolemFOFtoCNF_X))) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
( f(g(skolemFOFtoCNF_X)) != skolemFOFtoCNF_X
| g(skolemFOFtoCNF_X) != g(skolemFOFtoCNF_X)
| g(skolemFOFtoCNF_X) = g(f(g(skolemFOFtoCNF_X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(g(skolemFOFtoCNF_X),g(f(g(skolemFOFtoCNF_X)))) ),[1,0],$fot(skolemFOFtoCNF_X)]]) ).
cnf(refute_0_9,plain,
( g(skolemFOFtoCNF_X) != g(skolemFOFtoCNF_X)
| g(skolemFOFtoCNF_X) = g(f(g(skolemFOFtoCNF_X))) ),
inference(resolve,[$cnf( $equal(f(g(skolemFOFtoCNF_X)),skolemFOFtoCNF_X) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( g(skolemFOFtoCNF_X) != g(skolemFOFtoCNF_X)
| skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)) = g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))) ),
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_X),g(f(g(skolemFOFtoCNF_X)))) )],[refute_0_9,refute_0_1]) ).
cnf(refute_0_11,plain,
g(skolemFOFtoCNF_X) = g(skolemFOFtoCNF_X),
introduced(tautology,[refl,[$fot(g(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_12,plain,
skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)) = g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))),
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_X),g(skolemFOFtoCNF_X)) )],[refute_0_11,refute_0_10]) ).
cnf(refute_0_13,plain,
( Y != f(g(Y))
| Y = skolemFOFtoCNF_X ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_14,plain,
( f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))) != f(g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))))
| f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))) = skolemFOFtoCNF_X ),
inference(subst,[],[refute_0_13:[bind(Y,$fot(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))))]]) ).
cnf(refute_0_15,plain,
( skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)) != g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))))
| g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))) = skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))),bind(Y0,$fot(g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))))))]]) ).
cnf(refute_0_16,plain,
g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))) = skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)),g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))))) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
( f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))) != f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))
| g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))) != skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))
| f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))) = f(g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))),f(g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))))) ),[1,0],$fot(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_18,plain,
( f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))) != f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))
| f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))) = f(g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))))) ),
inference(resolve,[$cnf( $equal(g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))),skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))) != f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))
| f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))) = skolemFOFtoCNF_X ),
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))),f(g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))))) )],[refute_0_18,refute_0_14]) ).
cnf(refute_0_20,plain,
f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))) = f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))),
introduced(tautology,[refl,[$fot(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))))]]) ).
cnf(refute_0_21,plain,
f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))) = skolemFOFtoCNF_X,
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))),f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))) )],[refute_0_20,refute_0_19]) ).
cnf(refute_0_22,plain,
g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))) = g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))),
introduced(tautology,[refl,[$fot(g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))))]]) ).
cnf(refute_0_23,plain,
( f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))) != skolemFOFtoCNF_X
| g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))) != g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))))
| g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))) = g(skolemFOFtoCNF_X) ),
introduced(tautology,[equality,[$cnf( $equal(g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))),g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))))) ),[1,0],$fot(skolemFOFtoCNF_X)]]) ).
cnf(refute_0_24,plain,
( f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))) != skolemFOFtoCNF_X
| g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))) = g(skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( $equal(g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))),g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))) = g(skolemFOFtoCNF_X),
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))),skolemFOFtoCNF_X) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
( g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))) != g(skolemFOFtoCNF_X)
| skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)) != g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))))
| skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)) = g(skolemFOFtoCNF_X) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)),g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))))) ),[1],$fot(g(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_27,plain,
( skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)) != g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))))
| skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)) = g(skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( $equal(g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)))),g(skolemFOFtoCNF_X)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)) = g(skolemFOFtoCNF_X),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)),g(f(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X))))) )],[refute_0_12,refute_0_27]) ).
cnf(refute_0_29,plain,
( X != g(f(X))
| skolemFOFtoCNF_Y(X) != X ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_30,plain,
( g(skolemFOFtoCNF_X) != g(f(g(skolemFOFtoCNF_X)))
| skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)) != g(skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(g(skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_31,plain,
( g(skolemFOFtoCNF_X) != g(skolemFOFtoCNF_X)
| skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)) != g(skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_X),g(f(g(skolemFOFtoCNF_X)))) )],[refute_0_9,refute_0_30]) ).
cnf(refute_0_32,plain,
skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)) != g(skolemFOFtoCNF_X),
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_X),g(skolemFOFtoCNF_X)) )],[refute_0_11,refute_0_31]) ).
cnf(refute_0_33,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y(g(skolemFOFtoCNF_X)),g(skolemFOFtoCNF_X)) )],[refute_0_28,refute_0_32]) ).
fof(negate_1_0,plain,
~ ( ? [X] :
( X = g(f(X))
& ! [Y] :
( Y = g(f(Y))
=> Y = X ) )
=> ? [X] :
( X = f(g(X))
& ! [Y] :
( Y = f(g(Y))
=> Y = X ) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
( ? [X] :
( X = g(f(X))
& ! [Y] :
( Y != g(f(Y))
| Y = X ) )
& ! [X] :
( X != f(g(X))
| ? [Y] :
( Y != X
& Y = f(g(Y)) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
! [X] :
( X != f(g(X))
| ? [Y] :
( Y != X
& Y = f(g(Y)) ) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [X] :
( X != f(g(X))
| ? [Y] :
( Y != X
& Y = f(g(Y)) ) ),
inference(specialize,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [X] :
( ( X != f(g(X))
| skolemFOFtoCNF_Y_1(X) != X )
& ( X != f(g(X))
| skolemFOFtoCNF_Y_1(X) = f(g(skolemFOFtoCNF_Y_1(X))) ) ),
inference(clausify,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [X] :
( X != f(g(X))
| skolemFOFtoCNF_Y_1(X) = f(g(skolemFOFtoCNF_Y_1(X))) ),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
? [X] :
( X = g(f(X))
& ! [Y] :
( Y != g(f(Y))
| Y = X ) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_6,plain,
( skolemFOFtoCNF_X_1 = g(f(skolemFOFtoCNF_X_1))
& ! [Y] :
( Y != g(f(Y))
| Y = skolemFOFtoCNF_X_1 ) ),
inference(skolemize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
skolemFOFtoCNF_X_1 = g(f(skolemFOFtoCNF_X_1)),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [Y] :
( Y != g(f(Y))
| Y = skolemFOFtoCNF_X_1 ),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_9,plain,
! [Y] :
( Y != g(f(Y))
| Y = skolemFOFtoCNF_X_1 ),
inference(specialize,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [X] :
( X != f(g(X))
| skolemFOFtoCNF_Y_1(X) != X ),
inference(conjunct,[],[normalize_1_3]) ).
cnf(refute_1_0,plain,
( X != f(g(X))
| skolemFOFtoCNF_Y_1(X) = f(g(skolemFOFtoCNF_Y_1(X))) ),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_1,plain,
( f(skolemFOFtoCNF_X_1) != f(g(f(skolemFOFtoCNF_X_1)))
| skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)) = f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))) ),
inference(subst,[],[refute_1_0:[bind(X,$fot(f(skolemFOFtoCNF_X_1)))]]) ).
cnf(refute_1_2,plain,
skolemFOFtoCNF_X_1 = g(f(skolemFOFtoCNF_X_1)),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_3,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_1_4,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_1_5,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_1_3,refute_1_4]) ).
cnf(refute_1_6,plain,
( skolemFOFtoCNF_X_1 != g(f(skolemFOFtoCNF_X_1))
| g(f(skolemFOFtoCNF_X_1)) = skolemFOFtoCNF_X_1 ),
inference(subst,[],[refute_1_5:[bind(X0,$fot(skolemFOFtoCNF_X_1)),bind(Y0,$fot(g(f(skolemFOFtoCNF_X_1))))]]) ).
cnf(refute_1_7,plain,
g(f(skolemFOFtoCNF_X_1)) = skolemFOFtoCNF_X_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_1,g(f(skolemFOFtoCNF_X_1))) )],[refute_1_2,refute_1_6]) ).
cnf(refute_1_8,plain,
( f(skolemFOFtoCNF_X_1) != f(skolemFOFtoCNF_X_1)
| g(f(skolemFOFtoCNF_X_1)) != skolemFOFtoCNF_X_1
| f(skolemFOFtoCNF_X_1) = f(g(f(skolemFOFtoCNF_X_1))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(skolemFOFtoCNF_X_1),f(g(f(skolemFOFtoCNF_X_1)))) ),[1,0],$fot(skolemFOFtoCNF_X_1)]]) ).
cnf(refute_1_9,plain,
( f(skolemFOFtoCNF_X_1) != f(skolemFOFtoCNF_X_1)
| f(skolemFOFtoCNF_X_1) = f(g(f(skolemFOFtoCNF_X_1))) ),
inference(resolve,[$cnf( $equal(g(f(skolemFOFtoCNF_X_1)),skolemFOFtoCNF_X_1) )],[refute_1_7,refute_1_8]) ).
cnf(refute_1_10,plain,
( f(skolemFOFtoCNF_X_1) != f(skolemFOFtoCNF_X_1)
| skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)) = f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))) ),
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_X_1),f(g(f(skolemFOFtoCNF_X_1)))) )],[refute_1_9,refute_1_1]) ).
cnf(refute_1_11,plain,
f(skolemFOFtoCNF_X_1) = f(skolemFOFtoCNF_X_1),
introduced(tautology,[refl,[$fot(f(skolemFOFtoCNF_X_1))]]) ).
cnf(refute_1_12,plain,
skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)) = f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))),
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_X_1),f(skolemFOFtoCNF_X_1)) )],[refute_1_11,refute_1_10]) ).
cnf(refute_1_13,plain,
( Y != g(f(Y))
| Y = skolemFOFtoCNF_X_1 ),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_14,plain,
( g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))) != g(f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))))
| g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))) = skolemFOFtoCNF_X_1 ),
inference(subst,[],[refute_1_13:[bind(Y,$fot(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))))]]) ).
cnf(refute_1_15,plain,
( skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)) != f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))))
| f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))) = skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)) ),
inference(subst,[],[refute_1_5:[bind(X0,$fot(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))),bind(Y0,$fot(f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))))))]]) ).
cnf(refute_1_16,plain,
f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))) = skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)),f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))))) )],[refute_1_12,refute_1_15]) ).
cnf(refute_1_17,plain,
( f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))) != skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))
| g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))) != g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))
| g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))) = g(f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))),g(f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))))) ),[1,0],$fot(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))]]) ).
cnf(refute_1_18,plain,
( g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))) != g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))
| g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))) = g(f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))))) ),
inference(resolve,[$cnf( $equal(f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))),skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))) )],[refute_1_16,refute_1_17]) ).
cnf(refute_1_19,plain,
( g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))) != g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))
| g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))) = skolemFOFtoCNF_X_1 ),
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))),g(f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))))) )],[refute_1_18,refute_1_14]) ).
cnf(refute_1_20,plain,
g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))) = g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))),
introduced(tautology,[refl,[$fot(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))))]]) ).
cnf(refute_1_21,plain,
g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))) = skolemFOFtoCNF_X_1,
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))),g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))) )],[refute_1_20,refute_1_19]) ).
cnf(refute_1_22,plain,
f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))) = f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))),
introduced(tautology,[refl,[$fot(f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))))]]) ).
cnf(refute_1_23,plain,
( f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))) != f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))))
| g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))) != skolemFOFtoCNF_X_1
| f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))) = f(skolemFOFtoCNF_X_1) ),
introduced(tautology,[equality,[$cnf( $equal(f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))),f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))))) ),[1,0],$fot(skolemFOFtoCNF_X_1)]]) ).
cnf(refute_1_24,plain,
( g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))) != skolemFOFtoCNF_X_1
| f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))) = f(skolemFOFtoCNF_X_1) ),
inference(resolve,[$cnf( $equal(f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))),f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))))) )],[refute_1_22,refute_1_23]) ).
cnf(refute_1_25,plain,
f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))) = f(skolemFOFtoCNF_X_1),
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))),skolemFOFtoCNF_X_1) )],[refute_1_21,refute_1_24]) ).
cnf(refute_1_26,plain,
( f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))) != f(skolemFOFtoCNF_X_1)
| skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)) != f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))))
| skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)) = f(skolemFOFtoCNF_X_1) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)),f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))))) ),[1],$fot(f(skolemFOFtoCNF_X_1))]]) ).
cnf(refute_1_27,plain,
( skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)) != f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))))
| skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)) = f(skolemFOFtoCNF_X_1) ),
inference(resolve,[$cnf( $equal(f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)))),f(skolemFOFtoCNF_X_1)) )],[refute_1_25,refute_1_26]) ).
cnf(refute_1_28,plain,
skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)) = f(skolemFOFtoCNF_X_1),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)),f(g(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1))))) )],[refute_1_12,refute_1_27]) ).
cnf(refute_1_29,plain,
( X != f(g(X))
| skolemFOFtoCNF_Y_1(X) != X ),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_30,plain,
( f(skolemFOFtoCNF_X_1) != f(g(f(skolemFOFtoCNF_X_1)))
| skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)) != f(skolemFOFtoCNF_X_1) ),
inference(subst,[],[refute_1_29:[bind(X,$fot(f(skolemFOFtoCNF_X_1)))]]) ).
cnf(refute_1_31,plain,
( f(skolemFOFtoCNF_X_1) != f(skolemFOFtoCNF_X_1)
| skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)) != f(skolemFOFtoCNF_X_1) ),
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_X_1),f(g(f(skolemFOFtoCNF_X_1)))) )],[refute_1_9,refute_1_30]) ).
cnf(refute_1_32,plain,
skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)) != f(skolemFOFtoCNF_X_1),
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_X_1),f(skolemFOFtoCNF_X_1)) )],[refute_1_11,refute_1_31]) ).
cnf(refute_1_33,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1(f(skolemFOFtoCNF_X_1)),f(skolemFOFtoCNF_X_1)) )],[refute_1_28,refute_1_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN551+3 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n016.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 : Tue Jul 12 07:46:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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
% 0.13/0.36
%------------------------------------------------------------------------------