TSTP Solution File: SYN551+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN551+1 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 : 24
% Number of leaves : 55
% Syntax : Number of formulae : 229 ( 102 unt; 0 def)
% Number of atoms : 468 ( 464 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 433 ( 194 ~; 166 |; 50 &)
% ( 1 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-1 aty)
% Number of variables : 132 ( 0 sgn 50 !; 38 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this_cute_thing,conjecture,
( ( ? [X] : X = f(g(X))
& ! [Y,Z] :
( ( Y = f(g(Y))
& Z = f(g(Z)) )
=> Y = Z ) )
<=> ( ? [X] : X = g(f(X))
& ! [Y,Z] :
( ( Y = g(f(Y))
& Z = g(f(Z)) )
=> Y = Z ) ) ) ).
fof(subgoal_0,plain,
( ( ? [X] : X = f(g(X))
& ! [Y,Z] :
( ( Y = f(g(Y))
& Z = f(g(Z)) )
=> Y = Z ) )
=> ? [X] : X = g(f(X)) ),
inference(strip,[],[prove_this_cute_thing]) ).
fof(subgoal_1,plain,
( ( ? [X] : X = f(g(X))
& ! [Y,Z] :
( ( Y = f(g(Y))
& Z = f(g(Z)) )
=> Y = Z )
& ? [X] : X = g(f(X)) )
=> ! [Y,Z] :
( ( Y = g(f(Y))
& Z = g(f(Z)) )
=> Y = Z ) ),
inference(strip,[],[prove_this_cute_thing]) ).
fof(subgoal_2,plain,
( ( ? [X] : X = g(f(X))
& ! [Y,Z] :
( ( Y = g(f(Y))
& Z = g(f(Z)) )
=> Y = Z ) )
=> ? [X] : X = f(g(X)) ),
inference(strip,[],[prove_this_cute_thing]) ).
fof(subgoal_3,plain,
( ( ? [X] : X = g(f(X))
& ! [Y,Z] :
( ( Y = g(f(Y))
& Z = g(f(Z)) )
=> Y = Z )
& ? [X] : X = f(g(X)) )
=> ! [Y,Z] :
( ( Y = f(g(Y))
& Z = f(g(Z)) )
=> Y = Z ) ),
inference(strip,[],[prove_this_cute_thing]) ).
fof(negate_0_0,plain,
~ ( ( ? [X] : X = f(g(X))
& ! [Y,Z] :
( ( Y = f(g(Y))
& Z = f(g(Z)) )
=> Y = Z ) )
=> ? [X] : X = g(f(X)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ? [X] : X = f(g(X))
& ! [X] : X != g(f(X))
& ! [Y,Z] :
( Y != f(g(Y))
| Z != f(g(Z))
| Y = Z ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [X] : X != g(f(X)),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X] : X != g(f(X)),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
? [X] : X = f(g(X)),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_4,plain,
skolemFOFtoCNF_X = f(g(skolemFOFtoCNF_X)),
inference(skolemize,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
X != g(f(X)),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
g(skolemFOFtoCNF_X) != g(f(g(skolemFOFtoCNF_X))),
inference(subst,[],[refute_0_0:[bind(X,$fot(g(skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_2,plain,
skolemFOFtoCNF_X = f(g(skolemFOFtoCNF_X)),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
X0 = X0,
introduced(tautology,[refl,[$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( $equal(f(g(skolemFOFtoCNF_X)),skolemFOFtoCNF_X) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
g(skolemFOFtoCNF_X) != g(skolemFOFtoCNF_X),
inference(resolve,[$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,
$false,
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_X),g(skolemFOFtoCNF_X)) )],[refute_0_11,refute_0_10]) ).
fof(negate_1_0,plain,
~ ( ( ? [X] : X = f(g(X))
& ! [Y,Z] :
( ( Y = f(g(Y))
& Z = f(g(Z)) )
=> Y = Z )
& ? [X] : X = g(f(X)) )
=> ! [Y,Z] :
( ( Y = g(f(Y))
& Z = g(f(Z)) )
=> Y = Z ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
( ? [X] : X = f(g(X))
& ? [X] : X = g(f(X))
& ? [Y,Z] :
( Y != Z
& Y = g(f(Y))
& Z = g(f(Z)) )
& ! [Y,Z] :
( Y != f(g(Y))
| Z != f(g(Z))
| Y = Z ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
? [Y,Z] :
( Y != Z
& Y = g(f(Y))
& Z = g(f(Z)) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
( skolemFOFtoCNF_Y != skolemFOFtoCNF_Z
& skolemFOFtoCNF_Y = g(f(skolemFOFtoCNF_Y))
& skolemFOFtoCNF_Z = g(f(skolemFOFtoCNF_Z)) ),
inference(skolemize,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
skolemFOFtoCNF_Y != skolemFOFtoCNF_Z,
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
skolemFOFtoCNF_Y = g(f(skolemFOFtoCNF_Y)),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_5,plain,
? [X] : X = g(f(X)),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_6,plain,
skolemFOFtoCNF_X_2 = g(f(skolemFOFtoCNF_X_2)),
inference(skolemize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [Y,Z] :
( Y != f(g(Y))
| Z != f(g(Z))
| Y = Z ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_8,plain,
! [Y,Z] :
( Y != f(g(Y))
| Z != f(g(Z))
| Y = Z ),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
? [X] : X = f(g(X)),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_10,plain,
skolemFOFtoCNF_X_1 = f(g(skolemFOFtoCNF_X_1)),
inference(skolemize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
skolemFOFtoCNF_Z = g(f(skolemFOFtoCNF_Z)),
inference(conjunct,[],[normalize_1_2]) ).
cnf(refute_1_0,plain,
skolemFOFtoCNF_Y != skolemFOFtoCNF_Z,
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
skolemFOFtoCNF_Y = g(f(skolemFOFtoCNF_Y)),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_2,plain,
skolemFOFtoCNF_X_2 = g(f(skolemFOFtoCNF_X_2)),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_3,plain,
( Y != f(g(Y))
| Z != f(g(Z))
| Y = Z ),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_4,plain,
( X_1 != f(g(X_1))
| skolemFOFtoCNF_X_1 != f(g(skolemFOFtoCNF_X_1))
| X_1 = skolemFOFtoCNF_X_1 ),
inference(subst,[],[refute_1_3:[bind(Y,$fot(X_1)),bind(Z,$fot(skolemFOFtoCNF_X_1))]]) ).
cnf(refute_1_5,plain,
skolemFOFtoCNF_X_1 = f(g(skolemFOFtoCNF_X_1)),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_6,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_1_7,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_1_8,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_1_6,refute_1_7]) ).
cnf(refute_1_9,plain,
( skolemFOFtoCNF_X_1 != f(g(skolemFOFtoCNF_X_1))
| f(g(skolemFOFtoCNF_X_1)) = skolemFOFtoCNF_X_1 ),
inference(subst,[],[refute_1_8:[bind(X0,$fot(skolemFOFtoCNF_X_1)),bind(Y0,$fot(f(g(skolemFOFtoCNF_X_1))))]]) ).
cnf(refute_1_10,plain,
f(g(skolemFOFtoCNF_X_1)) = skolemFOFtoCNF_X_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_1,f(g(skolemFOFtoCNF_X_1))) )],[refute_1_5,refute_1_9]) ).
cnf(refute_1_11,plain,
( f(g(skolemFOFtoCNF_X_1)) != skolemFOFtoCNF_X_1
| skolemFOFtoCNF_X_1 != skolemFOFtoCNF_X_1
| skolemFOFtoCNF_X_1 = f(g(skolemFOFtoCNF_X_1)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_X_1,f(g(skolemFOFtoCNF_X_1))) ),[1],$fot(skolemFOFtoCNF_X_1)]]) ).
cnf(refute_1_12,plain,
( skolemFOFtoCNF_X_1 != skolemFOFtoCNF_X_1
| skolemFOFtoCNF_X_1 = f(g(skolemFOFtoCNF_X_1)) ),
inference(resolve,[$cnf( $equal(f(g(skolemFOFtoCNF_X_1)),skolemFOFtoCNF_X_1) )],[refute_1_10,refute_1_11]) ).
cnf(refute_1_13,plain,
( X_1 != f(g(X_1))
| skolemFOFtoCNF_X_1 != skolemFOFtoCNF_X_1
| X_1 = skolemFOFtoCNF_X_1 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_1,f(g(skolemFOFtoCNF_X_1))) )],[refute_1_12,refute_1_4]) ).
cnf(refute_1_14,plain,
skolemFOFtoCNF_X_1 = skolemFOFtoCNF_X_1,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_X_1)]]) ).
cnf(refute_1_15,plain,
( X_1 != f(g(X_1))
| X_1 = skolemFOFtoCNF_X_1 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_1,skolemFOFtoCNF_X_1) )],[refute_1_14,refute_1_13]) ).
cnf(refute_1_16,plain,
( f(skolemFOFtoCNF_X_2) != f(g(f(skolemFOFtoCNF_X_2)))
| f(skolemFOFtoCNF_X_2) = skolemFOFtoCNF_X_1 ),
inference(subst,[],[refute_1_15:[bind(X_1,$fot(f(skolemFOFtoCNF_X_2)))]]) ).
cnf(refute_1_17,plain,
( skolemFOFtoCNF_X_2 != g(f(skolemFOFtoCNF_X_2))
| g(f(skolemFOFtoCNF_X_2)) = skolemFOFtoCNF_X_2 ),
inference(subst,[],[refute_1_8:[bind(X0,$fot(skolemFOFtoCNF_X_2)),bind(Y0,$fot(g(f(skolemFOFtoCNF_X_2))))]]) ).
cnf(refute_1_18,plain,
g(f(skolemFOFtoCNF_X_2)) = skolemFOFtoCNF_X_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,g(f(skolemFOFtoCNF_X_2))) )],[refute_1_2,refute_1_17]) ).
cnf(refute_1_19,plain,
( f(skolemFOFtoCNF_X_2) != f(skolemFOFtoCNF_X_2)
| g(f(skolemFOFtoCNF_X_2)) != skolemFOFtoCNF_X_2
| f(skolemFOFtoCNF_X_2) = f(g(f(skolemFOFtoCNF_X_2))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(skolemFOFtoCNF_X_2),f(g(f(skolemFOFtoCNF_X_2)))) ),[1,0],$fot(skolemFOFtoCNF_X_2)]]) ).
cnf(refute_1_20,plain,
( f(skolemFOFtoCNF_X_2) != f(skolemFOFtoCNF_X_2)
| f(skolemFOFtoCNF_X_2) = f(g(f(skolemFOFtoCNF_X_2))) ),
inference(resolve,[$cnf( $equal(g(f(skolemFOFtoCNF_X_2)),skolemFOFtoCNF_X_2) )],[refute_1_18,refute_1_19]) ).
cnf(refute_1_21,plain,
( f(skolemFOFtoCNF_X_2) != f(skolemFOFtoCNF_X_2)
| f(skolemFOFtoCNF_X_2) = skolemFOFtoCNF_X_1 ),
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_X_2),f(g(f(skolemFOFtoCNF_X_2)))) )],[refute_1_20,refute_1_16]) ).
cnf(refute_1_22,plain,
f(skolemFOFtoCNF_X_2) = f(skolemFOFtoCNF_X_2),
introduced(tautology,[refl,[$fot(f(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_1_23,plain,
f(skolemFOFtoCNF_X_2) = skolemFOFtoCNF_X_1,
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_X_2),f(skolemFOFtoCNF_X_2)) )],[refute_1_22,refute_1_21]) ).
cnf(refute_1_24,plain,
g(f(skolemFOFtoCNF_X_2)) = g(f(skolemFOFtoCNF_X_2)),
introduced(tautology,[refl,[$fot(g(f(skolemFOFtoCNF_X_2)))]]) ).
cnf(refute_1_25,plain,
( f(skolemFOFtoCNF_X_2) != skolemFOFtoCNF_X_1
| g(f(skolemFOFtoCNF_X_2)) != g(f(skolemFOFtoCNF_X_2))
| g(f(skolemFOFtoCNF_X_2)) = g(skolemFOFtoCNF_X_1) ),
introduced(tautology,[equality,[$cnf( $equal(g(f(skolemFOFtoCNF_X_2)),g(f(skolemFOFtoCNF_X_2))) ),[1,0],$fot(skolemFOFtoCNF_X_1)]]) ).
cnf(refute_1_26,plain,
( f(skolemFOFtoCNF_X_2) != skolemFOFtoCNF_X_1
| g(f(skolemFOFtoCNF_X_2)) = g(skolemFOFtoCNF_X_1) ),
inference(resolve,[$cnf( $equal(g(f(skolemFOFtoCNF_X_2)),g(f(skolemFOFtoCNF_X_2))) )],[refute_1_24,refute_1_25]) ).
cnf(refute_1_27,plain,
g(f(skolemFOFtoCNF_X_2)) = g(skolemFOFtoCNF_X_1),
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_X_2),skolemFOFtoCNF_X_1) )],[refute_1_23,refute_1_26]) ).
cnf(refute_1_28,plain,
( g(f(skolemFOFtoCNF_X_2)) != g(skolemFOFtoCNF_X_1)
| skolemFOFtoCNF_X_2 != g(f(skolemFOFtoCNF_X_2))
| skolemFOFtoCNF_X_2 = g(skolemFOFtoCNF_X_1) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_X_2,g(f(skolemFOFtoCNF_X_2))) ),[1],$fot(g(skolemFOFtoCNF_X_1))]]) ).
cnf(refute_1_29,plain,
( skolemFOFtoCNF_X_2 != g(f(skolemFOFtoCNF_X_2))
| skolemFOFtoCNF_X_2 = g(skolemFOFtoCNF_X_1) ),
inference(resolve,[$cnf( $equal(g(f(skolemFOFtoCNF_X_2)),g(skolemFOFtoCNF_X_1)) )],[refute_1_27,refute_1_28]) ).
cnf(refute_1_30,plain,
skolemFOFtoCNF_X_2 = g(skolemFOFtoCNF_X_1),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,g(f(skolemFOFtoCNF_X_2))) )],[refute_1_2,refute_1_29]) ).
cnf(refute_1_31,plain,
( skolemFOFtoCNF_X_2 != g(skolemFOFtoCNF_X_1)
| g(skolemFOFtoCNF_X_1) = skolemFOFtoCNF_X_2 ),
inference(subst,[],[refute_1_8:[bind(X0,$fot(skolemFOFtoCNF_X_2)),bind(Y0,$fot(g(skolemFOFtoCNF_X_1)))]]) ).
cnf(refute_1_32,plain,
g(skolemFOFtoCNF_X_1) = skolemFOFtoCNF_X_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,g(skolemFOFtoCNF_X_1)) )],[refute_1_30,refute_1_31]) ).
cnf(refute_1_33,plain,
( f(skolemFOFtoCNF_Y) != f(g(f(skolemFOFtoCNF_Y)))
| f(skolemFOFtoCNF_Y) = skolemFOFtoCNF_X_1 ),
inference(subst,[],[refute_1_15:[bind(X_1,$fot(f(skolemFOFtoCNF_Y)))]]) ).
cnf(refute_1_34,plain,
( skolemFOFtoCNF_Y != g(f(skolemFOFtoCNF_Y))
| g(f(skolemFOFtoCNF_Y)) = skolemFOFtoCNF_Y ),
inference(subst,[],[refute_1_8:[bind(X0,$fot(skolemFOFtoCNF_Y)),bind(Y0,$fot(g(f(skolemFOFtoCNF_Y))))]]) ).
cnf(refute_1_35,plain,
g(f(skolemFOFtoCNF_Y)) = skolemFOFtoCNF_Y,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y,g(f(skolemFOFtoCNF_Y))) )],[refute_1_1,refute_1_34]) ).
cnf(refute_1_36,plain,
( f(skolemFOFtoCNF_Y) != f(skolemFOFtoCNF_Y)
| g(f(skolemFOFtoCNF_Y)) != skolemFOFtoCNF_Y
| f(skolemFOFtoCNF_Y) = f(g(f(skolemFOFtoCNF_Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(skolemFOFtoCNF_Y),f(g(f(skolemFOFtoCNF_Y)))) ),[1,0],$fot(skolemFOFtoCNF_Y)]]) ).
cnf(refute_1_37,plain,
( f(skolemFOFtoCNF_Y) != f(skolemFOFtoCNF_Y)
| f(skolemFOFtoCNF_Y) = f(g(f(skolemFOFtoCNF_Y))) ),
inference(resolve,[$cnf( $equal(g(f(skolemFOFtoCNF_Y)),skolemFOFtoCNF_Y) )],[refute_1_35,refute_1_36]) ).
cnf(refute_1_38,plain,
( f(skolemFOFtoCNF_Y) != f(skolemFOFtoCNF_Y)
| f(skolemFOFtoCNF_Y) = skolemFOFtoCNF_X_1 ),
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_Y),f(g(f(skolemFOFtoCNF_Y)))) )],[refute_1_37,refute_1_33]) ).
cnf(refute_1_39,plain,
f(skolemFOFtoCNF_Y) = f(skolemFOFtoCNF_Y),
introduced(tautology,[refl,[$fot(f(skolemFOFtoCNF_Y))]]) ).
cnf(refute_1_40,plain,
f(skolemFOFtoCNF_Y) = skolemFOFtoCNF_X_1,
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_Y),f(skolemFOFtoCNF_Y)) )],[refute_1_39,refute_1_38]) ).
cnf(refute_1_41,plain,
g(f(skolemFOFtoCNF_Y)) = g(f(skolemFOFtoCNF_Y)),
introduced(tautology,[refl,[$fot(g(f(skolemFOFtoCNF_Y)))]]) ).
cnf(refute_1_42,plain,
( f(skolemFOFtoCNF_Y) != skolemFOFtoCNF_X_1
| g(f(skolemFOFtoCNF_Y)) != g(f(skolemFOFtoCNF_Y))
| g(f(skolemFOFtoCNF_Y)) = g(skolemFOFtoCNF_X_1) ),
introduced(tautology,[equality,[$cnf( $equal(g(f(skolemFOFtoCNF_Y)),g(f(skolemFOFtoCNF_Y))) ),[1,0],$fot(skolemFOFtoCNF_X_1)]]) ).
cnf(refute_1_43,plain,
( f(skolemFOFtoCNF_Y) != skolemFOFtoCNF_X_1
| g(f(skolemFOFtoCNF_Y)) = g(skolemFOFtoCNF_X_1) ),
inference(resolve,[$cnf( $equal(g(f(skolemFOFtoCNF_Y)),g(f(skolemFOFtoCNF_Y))) )],[refute_1_41,refute_1_42]) ).
cnf(refute_1_44,plain,
g(f(skolemFOFtoCNF_Y)) = g(skolemFOFtoCNF_X_1),
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_Y),skolemFOFtoCNF_X_1) )],[refute_1_40,refute_1_43]) ).
cnf(refute_1_45,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_1_46,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_1_8,refute_1_45]) ).
cnf(refute_1_47,plain,
( g(f(skolemFOFtoCNF_Y)) != g(skolemFOFtoCNF_X_1)
| g(skolemFOFtoCNF_X_1) != skolemFOFtoCNF_X_2
| g(f(skolemFOFtoCNF_Y)) = skolemFOFtoCNF_X_2 ),
inference(subst,[],[refute_1_46:[bind(X0,$fot(g(f(skolemFOFtoCNF_Y)))),bind(Y0,$fot(g(skolemFOFtoCNF_X_1))),bind(Z0,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_1_48,plain,
( g(skolemFOFtoCNF_X_1) != skolemFOFtoCNF_X_2
| g(f(skolemFOFtoCNF_Y)) = skolemFOFtoCNF_X_2 ),
inference(resolve,[$cnf( $equal(g(f(skolemFOFtoCNF_Y)),g(skolemFOFtoCNF_X_1)) )],[refute_1_44,refute_1_47]) ).
cnf(refute_1_49,plain,
g(f(skolemFOFtoCNF_Y)) = skolemFOFtoCNF_X_2,
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_X_1),skolemFOFtoCNF_X_2) )],[refute_1_32,refute_1_48]) ).
cnf(refute_1_50,plain,
( g(f(skolemFOFtoCNF_Y)) != skolemFOFtoCNF_X_2
| skolemFOFtoCNF_Y != g(f(skolemFOFtoCNF_Y))
| skolemFOFtoCNF_Y = skolemFOFtoCNF_X_2 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y,g(f(skolemFOFtoCNF_Y))) ),[1],$fot(skolemFOFtoCNF_X_2)]]) ).
cnf(refute_1_51,plain,
( skolemFOFtoCNF_Y != g(f(skolemFOFtoCNF_Y))
| skolemFOFtoCNF_Y = skolemFOFtoCNF_X_2 ),
inference(resolve,[$cnf( $equal(g(f(skolemFOFtoCNF_Y)),skolemFOFtoCNF_X_2) )],[refute_1_49,refute_1_50]) ).
cnf(refute_1_52,plain,
skolemFOFtoCNF_Y = skolemFOFtoCNF_X_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y,g(f(skolemFOFtoCNF_Y))) )],[refute_1_1,refute_1_51]) ).
cnf(refute_1_53,plain,
( skolemFOFtoCNF_X_2 != skolemFOFtoCNF_Z
| skolemFOFtoCNF_Y != skolemFOFtoCNF_X_2
| skolemFOFtoCNF_Y = skolemFOFtoCNF_Z ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y,skolemFOFtoCNF_X_2) ),[1],$fot(skolemFOFtoCNF_Z)]]) ).
cnf(refute_1_54,plain,
( skolemFOFtoCNF_X_2 != skolemFOFtoCNF_Z
| skolemFOFtoCNF_Y = skolemFOFtoCNF_Z ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y,skolemFOFtoCNF_X_2) )],[refute_1_52,refute_1_53]) ).
cnf(refute_1_55,plain,
skolemFOFtoCNF_Z = g(f(skolemFOFtoCNF_Z)),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_56,plain,
( f(skolemFOFtoCNF_Z) != f(g(f(skolemFOFtoCNF_Z)))
| f(skolemFOFtoCNF_Z) = skolemFOFtoCNF_X_1 ),
inference(subst,[],[refute_1_15:[bind(X_1,$fot(f(skolemFOFtoCNF_Z)))]]) ).
cnf(refute_1_57,plain,
( skolemFOFtoCNF_Z != g(f(skolemFOFtoCNF_Z))
| g(f(skolemFOFtoCNF_Z)) = skolemFOFtoCNF_Z ),
inference(subst,[],[refute_1_8:[bind(X0,$fot(skolemFOFtoCNF_Z)),bind(Y0,$fot(g(f(skolemFOFtoCNF_Z))))]]) ).
cnf(refute_1_58,plain,
g(f(skolemFOFtoCNF_Z)) = skolemFOFtoCNF_Z,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z,g(f(skolemFOFtoCNF_Z))) )],[refute_1_55,refute_1_57]) ).
cnf(refute_1_59,plain,
( f(skolemFOFtoCNF_Z) != f(skolemFOFtoCNF_Z)
| g(f(skolemFOFtoCNF_Z)) != skolemFOFtoCNF_Z
| f(skolemFOFtoCNF_Z) = f(g(f(skolemFOFtoCNF_Z))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(skolemFOFtoCNF_Z),f(g(f(skolemFOFtoCNF_Z)))) ),[1,0],$fot(skolemFOFtoCNF_Z)]]) ).
cnf(refute_1_60,plain,
( f(skolemFOFtoCNF_Z) != f(skolemFOFtoCNF_Z)
| f(skolemFOFtoCNF_Z) = f(g(f(skolemFOFtoCNF_Z))) ),
inference(resolve,[$cnf( $equal(g(f(skolemFOFtoCNF_Z)),skolemFOFtoCNF_Z) )],[refute_1_58,refute_1_59]) ).
cnf(refute_1_61,plain,
( f(skolemFOFtoCNF_Z) != f(skolemFOFtoCNF_Z)
| f(skolemFOFtoCNF_Z) = skolemFOFtoCNF_X_1 ),
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_Z),f(g(f(skolemFOFtoCNF_Z)))) )],[refute_1_60,refute_1_56]) ).
cnf(refute_1_62,plain,
f(skolemFOFtoCNF_Z) = f(skolemFOFtoCNF_Z),
introduced(tautology,[refl,[$fot(f(skolemFOFtoCNF_Z))]]) ).
cnf(refute_1_63,plain,
f(skolemFOFtoCNF_Z) = skolemFOFtoCNF_X_1,
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_Z),f(skolemFOFtoCNF_Z)) )],[refute_1_62,refute_1_61]) ).
cnf(refute_1_64,plain,
g(f(skolemFOFtoCNF_Z)) = g(f(skolemFOFtoCNF_Z)),
introduced(tautology,[refl,[$fot(g(f(skolemFOFtoCNF_Z)))]]) ).
cnf(refute_1_65,plain,
( f(skolemFOFtoCNF_Z) != skolemFOFtoCNF_X_1
| g(f(skolemFOFtoCNF_Z)) != g(f(skolemFOFtoCNF_Z))
| g(f(skolemFOFtoCNF_Z)) = g(skolemFOFtoCNF_X_1) ),
introduced(tautology,[equality,[$cnf( $equal(g(f(skolemFOFtoCNF_Z)),g(f(skolemFOFtoCNF_Z))) ),[1,0],$fot(skolemFOFtoCNF_X_1)]]) ).
cnf(refute_1_66,plain,
( f(skolemFOFtoCNF_Z) != skolemFOFtoCNF_X_1
| g(f(skolemFOFtoCNF_Z)) = g(skolemFOFtoCNF_X_1) ),
inference(resolve,[$cnf( $equal(g(f(skolemFOFtoCNF_Z)),g(f(skolemFOFtoCNF_Z))) )],[refute_1_64,refute_1_65]) ).
cnf(refute_1_67,plain,
g(f(skolemFOFtoCNF_Z)) = g(skolemFOFtoCNF_X_1),
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_Z),skolemFOFtoCNF_X_1) )],[refute_1_63,refute_1_66]) ).
cnf(refute_1_68,plain,
( g(f(skolemFOFtoCNF_Z)) != g(skolemFOFtoCNF_X_1)
| g(skolemFOFtoCNF_X_1) != skolemFOFtoCNF_X_2
| g(f(skolemFOFtoCNF_Z)) = skolemFOFtoCNF_X_2 ),
inference(subst,[],[refute_1_46:[bind(X0,$fot(g(f(skolemFOFtoCNF_Z)))),bind(Y0,$fot(g(skolemFOFtoCNF_X_1))),bind(Z0,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_1_69,plain,
( g(skolemFOFtoCNF_X_1) != skolemFOFtoCNF_X_2
| g(f(skolemFOFtoCNF_Z)) = skolemFOFtoCNF_X_2 ),
inference(resolve,[$cnf( $equal(g(f(skolemFOFtoCNF_Z)),g(skolemFOFtoCNF_X_1)) )],[refute_1_67,refute_1_68]) ).
cnf(refute_1_70,plain,
g(f(skolemFOFtoCNF_Z)) = skolemFOFtoCNF_X_2,
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_X_1),skolemFOFtoCNF_X_2) )],[refute_1_32,refute_1_69]) ).
cnf(refute_1_71,plain,
( g(f(skolemFOFtoCNF_Z)) != skolemFOFtoCNF_X_2
| skolemFOFtoCNF_Z != g(f(skolemFOFtoCNF_Z))
| skolemFOFtoCNF_Z = skolemFOFtoCNF_X_2 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Z,g(f(skolemFOFtoCNF_Z))) ),[1],$fot(skolemFOFtoCNF_X_2)]]) ).
cnf(refute_1_72,plain,
( skolemFOFtoCNF_Z != g(f(skolemFOFtoCNF_Z))
| skolemFOFtoCNF_Z = skolemFOFtoCNF_X_2 ),
inference(resolve,[$cnf( $equal(g(f(skolemFOFtoCNF_Z)),skolemFOFtoCNF_X_2) )],[refute_1_70,refute_1_71]) ).
cnf(refute_1_73,plain,
skolemFOFtoCNF_Z = skolemFOFtoCNF_X_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z,g(f(skolemFOFtoCNF_Z))) )],[refute_1_55,refute_1_72]) ).
cnf(refute_1_74,plain,
( skolemFOFtoCNF_X_2 != skolemFOFtoCNF_X_2
| skolemFOFtoCNF_Z != skolemFOFtoCNF_X_2
| skolemFOFtoCNF_X_2 = skolemFOFtoCNF_Z ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Z) ),[1],$fot(skolemFOFtoCNF_X_2)]]) ).
cnf(refute_1_75,plain,
( skolemFOFtoCNF_X_2 != skolemFOFtoCNF_X_2
| skolemFOFtoCNF_X_2 = skolemFOFtoCNF_Z ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z,skolemFOFtoCNF_X_2) )],[refute_1_73,refute_1_74]) ).
cnf(refute_1_76,plain,
( skolemFOFtoCNF_X_2 != skolemFOFtoCNF_X_2
| skolemFOFtoCNF_Y = skolemFOFtoCNF_Z ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Z) )],[refute_1_75,refute_1_54]) ).
cnf(refute_1_77,plain,
skolemFOFtoCNF_X_2 != skolemFOFtoCNF_X_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_1_76,refute_1_0]) ).
cnf(refute_1_78,plain,
skolemFOFtoCNF_X_2 = skolemFOFtoCNF_X_2,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_X_2)]]) ).
cnf(refute_1_79,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) )],[refute_1_78,refute_1_77]) ).
fof(negate_2_0,plain,
~ ( ( ? [X] : X = g(f(X))
& ! [Y,Z] :
( ( Y = g(f(Y))
& Z = g(f(Z)) )
=> Y = Z ) )
=> ? [X] : X = f(g(X)) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
( ? [X] : X = g(f(X))
& ! [X] : X != f(g(X))
& ! [Y,Z] :
( Y != g(f(Y))
| Z != g(f(Z))
| Y = Z ) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,plain,
! [X] : X != f(g(X)),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
! [X] : X != f(g(X)),
inference(specialize,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
? [X] : X = g(f(X)),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_4,plain,
skolemFOFtoCNF_X_3 = g(f(skolemFOFtoCNF_X_3)),
inference(skolemize,[],[normalize_2_3]) ).
cnf(refute_2_0,plain,
X != f(g(X)),
inference(canonicalize,[],[normalize_2_2]) ).
cnf(refute_2_1,plain,
f(skolemFOFtoCNF_X_3) != f(g(f(skolemFOFtoCNF_X_3))),
inference(subst,[],[refute_2_0:[bind(X,$fot(f(skolemFOFtoCNF_X_3)))]]) ).
cnf(refute_2_2,plain,
skolemFOFtoCNF_X_3 = g(f(skolemFOFtoCNF_X_3)),
inference(canonicalize,[],[normalize_2_4]) ).
cnf(refute_2_3,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_2_4,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_2_5,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_2_3,refute_2_4]) ).
cnf(refute_2_6,plain,
( skolemFOFtoCNF_X_3 != g(f(skolemFOFtoCNF_X_3))
| g(f(skolemFOFtoCNF_X_3)) = skolemFOFtoCNF_X_3 ),
inference(subst,[],[refute_2_5:[bind(X0,$fot(skolemFOFtoCNF_X_3)),bind(Y0,$fot(g(f(skolemFOFtoCNF_X_3))))]]) ).
cnf(refute_2_7,plain,
g(f(skolemFOFtoCNF_X_3)) = skolemFOFtoCNF_X_3,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_3,g(f(skolemFOFtoCNF_X_3))) )],[refute_2_2,refute_2_6]) ).
cnf(refute_2_8,plain,
( f(skolemFOFtoCNF_X_3) != f(skolemFOFtoCNF_X_3)
| g(f(skolemFOFtoCNF_X_3)) != skolemFOFtoCNF_X_3
| f(skolemFOFtoCNF_X_3) = f(g(f(skolemFOFtoCNF_X_3))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(skolemFOFtoCNF_X_3),f(g(f(skolemFOFtoCNF_X_3)))) ),[1,0],$fot(skolemFOFtoCNF_X_3)]]) ).
cnf(refute_2_9,plain,
( f(skolemFOFtoCNF_X_3) != f(skolemFOFtoCNF_X_3)
| f(skolemFOFtoCNF_X_3) = f(g(f(skolemFOFtoCNF_X_3))) ),
inference(resolve,[$cnf( $equal(g(f(skolemFOFtoCNF_X_3)),skolemFOFtoCNF_X_3) )],[refute_2_7,refute_2_8]) ).
cnf(refute_2_10,plain,
f(skolemFOFtoCNF_X_3) != f(skolemFOFtoCNF_X_3),
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_X_3),f(g(f(skolemFOFtoCNF_X_3)))) )],[refute_2_9,refute_2_1]) ).
cnf(refute_2_11,plain,
f(skolemFOFtoCNF_X_3) = f(skolemFOFtoCNF_X_3),
introduced(tautology,[refl,[$fot(f(skolemFOFtoCNF_X_3))]]) ).
cnf(refute_2_12,plain,
$false,
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_X_3),f(skolemFOFtoCNF_X_3)) )],[refute_2_11,refute_2_10]) ).
fof(negate_3_0,plain,
~ ( ( ? [X] : X = g(f(X))
& ! [Y,Z] :
( ( Y = g(f(Y))
& Z = g(f(Z)) )
=> Y = Z )
& ? [X] : X = f(g(X)) )
=> ! [Y,Z] :
( ( Y = f(g(Y))
& Z = f(g(Z)) )
=> Y = Z ) ),
inference(negate,[],[subgoal_3]) ).
fof(normalize_3_0,plain,
( ? [X] : X = f(g(X))
& ? [X] : X = g(f(X))
& ? [Y,Z] :
( Y != Z
& Y = f(g(Y))
& Z = f(g(Z)) )
& ! [Y,Z] :
( Y != g(f(Y))
| Z != g(f(Z))
| Y = Z ) ),
inference(canonicalize,[],[negate_3_0]) ).
fof(normalize_3_1,plain,
? [Y,Z] :
( Y != Z
& Y = f(g(Y))
& Z = f(g(Z)) ),
inference(conjunct,[],[normalize_3_0]) ).
fof(normalize_3_2,plain,
( skolemFOFtoCNF_Y_1 != skolemFOFtoCNF_Z_1
& skolemFOFtoCNF_Y_1 = f(g(skolemFOFtoCNF_Y_1))
& skolemFOFtoCNF_Z_1 = f(g(skolemFOFtoCNF_Z_1)) ),
inference(skolemize,[],[normalize_3_1]) ).
fof(normalize_3_3,plain,
skolemFOFtoCNF_Y_1 != skolemFOFtoCNF_Z_1,
inference(conjunct,[],[normalize_3_2]) ).
fof(normalize_3_4,plain,
skolemFOFtoCNF_Y_1 = f(g(skolemFOFtoCNF_Y_1)),
inference(conjunct,[],[normalize_3_2]) ).
fof(normalize_3_5,plain,
? [X] : X = f(g(X)),
inference(conjunct,[],[normalize_3_0]) ).
fof(normalize_3_6,plain,
skolemFOFtoCNF_X_4 = f(g(skolemFOFtoCNF_X_4)),
inference(skolemize,[],[normalize_3_5]) ).
fof(normalize_3_7,plain,
! [Y,Z] :
( Y != g(f(Y))
| Z != g(f(Z))
| Y = Z ),
inference(conjunct,[],[normalize_3_0]) ).
fof(normalize_3_8,plain,
! [Y,Z] :
( Y != g(f(Y))
| Z != g(f(Z))
| Y = Z ),
inference(specialize,[],[normalize_3_7]) ).
fof(normalize_3_9,plain,
? [X] : X = g(f(X)),
inference(conjunct,[],[normalize_3_0]) ).
fof(normalize_3_10,plain,
skolemFOFtoCNF_X_5 = g(f(skolemFOFtoCNF_X_5)),
inference(skolemize,[],[normalize_3_9]) ).
fof(normalize_3_11,plain,
skolemFOFtoCNF_Z_1 = f(g(skolemFOFtoCNF_Z_1)),
inference(conjunct,[],[normalize_3_2]) ).
cnf(refute_3_0,plain,
skolemFOFtoCNF_Y_1 != skolemFOFtoCNF_Z_1,
inference(canonicalize,[],[normalize_3_3]) ).
cnf(refute_3_1,plain,
skolemFOFtoCNF_Y_1 = f(g(skolemFOFtoCNF_Y_1)),
inference(canonicalize,[],[normalize_3_4]) ).
cnf(refute_3_2,plain,
skolemFOFtoCNF_X_4 = f(g(skolemFOFtoCNF_X_4)),
inference(canonicalize,[],[normalize_3_6]) ).
cnf(refute_3_3,plain,
( Y != g(f(Y))
| Z != g(f(Z))
| Y = Z ),
inference(canonicalize,[],[normalize_3_8]) ).
cnf(refute_3_4,plain,
( X_5 != g(f(X_5))
| skolemFOFtoCNF_X_5 != g(f(skolemFOFtoCNF_X_5))
| X_5 = skolemFOFtoCNF_X_5 ),
inference(subst,[],[refute_3_3:[bind(Y,$fot(X_5)),bind(Z,$fot(skolemFOFtoCNF_X_5))]]) ).
cnf(refute_3_5,plain,
skolemFOFtoCNF_X_5 = g(f(skolemFOFtoCNF_X_5)),
inference(canonicalize,[],[normalize_3_10]) ).
cnf(refute_3_6,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_3_7,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_3_8,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_3_6,refute_3_7]) ).
cnf(refute_3_9,plain,
( skolemFOFtoCNF_X_5 != g(f(skolemFOFtoCNF_X_5))
| g(f(skolemFOFtoCNF_X_5)) = skolemFOFtoCNF_X_5 ),
inference(subst,[],[refute_3_8:[bind(X0,$fot(skolemFOFtoCNF_X_5)),bind(Y0,$fot(g(f(skolemFOFtoCNF_X_5))))]]) ).
cnf(refute_3_10,plain,
g(f(skolemFOFtoCNF_X_5)) = skolemFOFtoCNF_X_5,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_5,g(f(skolemFOFtoCNF_X_5))) )],[refute_3_5,refute_3_9]) ).
cnf(refute_3_11,plain,
( g(f(skolemFOFtoCNF_X_5)) != skolemFOFtoCNF_X_5
| skolemFOFtoCNF_X_5 != skolemFOFtoCNF_X_5
| skolemFOFtoCNF_X_5 = g(f(skolemFOFtoCNF_X_5)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_X_5,g(f(skolemFOFtoCNF_X_5))) ),[1],$fot(skolemFOFtoCNF_X_5)]]) ).
cnf(refute_3_12,plain,
( skolemFOFtoCNF_X_5 != skolemFOFtoCNF_X_5
| skolemFOFtoCNF_X_5 = g(f(skolemFOFtoCNF_X_5)) ),
inference(resolve,[$cnf( $equal(g(f(skolemFOFtoCNF_X_5)),skolemFOFtoCNF_X_5) )],[refute_3_10,refute_3_11]) ).
cnf(refute_3_13,plain,
( X_5 != g(f(X_5))
| skolemFOFtoCNF_X_5 != skolemFOFtoCNF_X_5
| X_5 = skolemFOFtoCNF_X_5 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_5,g(f(skolemFOFtoCNF_X_5))) )],[refute_3_12,refute_3_4]) ).
cnf(refute_3_14,plain,
skolemFOFtoCNF_X_5 = skolemFOFtoCNF_X_5,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_X_5)]]) ).
cnf(refute_3_15,plain,
( X_5 != g(f(X_5))
| X_5 = skolemFOFtoCNF_X_5 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_5,skolemFOFtoCNF_X_5) )],[refute_3_14,refute_3_13]) ).
cnf(refute_3_16,plain,
( g(skolemFOFtoCNF_X_4) != g(f(g(skolemFOFtoCNF_X_4)))
| g(skolemFOFtoCNF_X_4) = skolemFOFtoCNF_X_5 ),
inference(subst,[],[refute_3_15:[bind(X_5,$fot(g(skolemFOFtoCNF_X_4)))]]) ).
cnf(refute_3_17,plain,
( skolemFOFtoCNF_X_4 != f(g(skolemFOFtoCNF_X_4))
| f(g(skolemFOFtoCNF_X_4)) = skolemFOFtoCNF_X_4 ),
inference(subst,[],[refute_3_8:[bind(X0,$fot(skolemFOFtoCNF_X_4)),bind(Y0,$fot(f(g(skolemFOFtoCNF_X_4))))]]) ).
cnf(refute_3_18,plain,
f(g(skolemFOFtoCNF_X_4)) = skolemFOFtoCNF_X_4,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_4,f(g(skolemFOFtoCNF_X_4))) )],[refute_3_2,refute_3_17]) ).
cnf(refute_3_19,plain,
( f(g(skolemFOFtoCNF_X_4)) != skolemFOFtoCNF_X_4
| g(skolemFOFtoCNF_X_4) != g(skolemFOFtoCNF_X_4)
| g(skolemFOFtoCNF_X_4) = g(f(g(skolemFOFtoCNF_X_4))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(g(skolemFOFtoCNF_X_4),g(f(g(skolemFOFtoCNF_X_4)))) ),[1,0],$fot(skolemFOFtoCNF_X_4)]]) ).
cnf(refute_3_20,plain,
( g(skolemFOFtoCNF_X_4) != g(skolemFOFtoCNF_X_4)
| g(skolemFOFtoCNF_X_4) = g(f(g(skolemFOFtoCNF_X_4))) ),
inference(resolve,[$cnf( $equal(f(g(skolemFOFtoCNF_X_4)),skolemFOFtoCNF_X_4) )],[refute_3_18,refute_3_19]) ).
cnf(refute_3_21,plain,
( g(skolemFOFtoCNF_X_4) != g(skolemFOFtoCNF_X_4)
| g(skolemFOFtoCNF_X_4) = skolemFOFtoCNF_X_5 ),
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_X_4),g(f(g(skolemFOFtoCNF_X_4)))) )],[refute_3_20,refute_3_16]) ).
cnf(refute_3_22,plain,
g(skolemFOFtoCNF_X_4) = g(skolemFOFtoCNF_X_4),
introduced(tautology,[refl,[$fot(g(skolemFOFtoCNF_X_4))]]) ).
cnf(refute_3_23,plain,
g(skolemFOFtoCNF_X_4) = skolemFOFtoCNF_X_5,
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_X_4),g(skolemFOFtoCNF_X_4)) )],[refute_3_22,refute_3_21]) ).
cnf(refute_3_24,plain,
f(g(skolemFOFtoCNF_X_4)) = f(g(skolemFOFtoCNF_X_4)),
introduced(tautology,[refl,[$fot(f(g(skolemFOFtoCNF_X_4)))]]) ).
cnf(refute_3_25,plain,
( f(g(skolemFOFtoCNF_X_4)) != f(g(skolemFOFtoCNF_X_4))
| g(skolemFOFtoCNF_X_4) != skolemFOFtoCNF_X_5
| f(g(skolemFOFtoCNF_X_4)) = f(skolemFOFtoCNF_X_5) ),
introduced(tautology,[equality,[$cnf( $equal(f(g(skolemFOFtoCNF_X_4)),f(g(skolemFOFtoCNF_X_4))) ),[1,0],$fot(skolemFOFtoCNF_X_5)]]) ).
cnf(refute_3_26,plain,
( g(skolemFOFtoCNF_X_4) != skolemFOFtoCNF_X_5
| f(g(skolemFOFtoCNF_X_4)) = f(skolemFOFtoCNF_X_5) ),
inference(resolve,[$cnf( $equal(f(g(skolemFOFtoCNF_X_4)),f(g(skolemFOFtoCNF_X_4))) )],[refute_3_24,refute_3_25]) ).
cnf(refute_3_27,plain,
f(g(skolemFOFtoCNF_X_4)) = f(skolemFOFtoCNF_X_5),
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_X_4),skolemFOFtoCNF_X_5) )],[refute_3_23,refute_3_26]) ).
cnf(refute_3_28,plain,
( f(g(skolemFOFtoCNF_X_4)) != f(skolemFOFtoCNF_X_5)
| skolemFOFtoCNF_X_4 != f(g(skolemFOFtoCNF_X_4))
| skolemFOFtoCNF_X_4 = f(skolemFOFtoCNF_X_5) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_X_4,f(g(skolemFOFtoCNF_X_4))) ),[1],$fot(f(skolemFOFtoCNF_X_5))]]) ).
cnf(refute_3_29,plain,
( skolemFOFtoCNF_X_4 != f(g(skolemFOFtoCNF_X_4))
| skolemFOFtoCNF_X_4 = f(skolemFOFtoCNF_X_5) ),
inference(resolve,[$cnf( $equal(f(g(skolemFOFtoCNF_X_4)),f(skolemFOFtoCNF_X_5)) )],[refute_3_27,refute_3_28]) ).
cnf(refute_3_30,plain,
skolemFOFtoCNF_X_4 = f(skolemFOFtoCNF_X_5),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_4,f(g(skolemFOFtoCNF_X_4))) )],[refute_3_2,refute_3_29]) ).
cnf(refute_3_31,plain,
( skolemFOFtoCNF_X_4 != f(skolemFOFtoCNF_X_5)
| f(skolemFOFtoCNF_X_5) = skolemFOFtoCNF_X_4 ),
inference(subst,[],[refute_3_8:[bind(X0,$fot(skolemFOFtoCNF_X_4)),bind(Y0,$fot(f(skolemFOFtoCNF_X_5)))]]) ).
cnf(refute_3_32,plain,
f(skolemFOFtoCNF_X_5) = skolemFOFtoCNF_X_4,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_4,f(skolemFOFtoCNF_X_5)) )],[refute_3_30,refute_3_31]) ).
cnf(refute_3_33,plain,
( g(skolemFOFtoCNF_Y_1) != g(f(g(skolemFOFtoCNF_Y_1)))
| g(skolemFOFtoCNF_Y_1) = skolemFOFtoCNF_X_5 ),
inference(subst,[],[refute_3_15:[bind(X_5,$fot(g(skolemFOFtoCNF_Y_1)))]]) ).
cnf(refute_3_34,plain,
( skolemFOFtoCNF_Y_1 != f(g(skolemFOFtoCNF_Y_1))
| f(g(skolemFOFtoCNF_Y_1)) = skolemFOFtoCNF_Y_1 ),
inference(subst,[],[refute_3_8:[bind(X0,$fot(skolemFOFtoCNF_Y_1)),bind(Y0,$fot(f(g(skolemFOFtoCNF_Y_1))))]]) ).
cnf(refute_3_35,plain,
f(g(skolemFOFtoCNF_Y_1)) = skolemFOFtoCNF_Y_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1,f(g(skolemFOFtoCNF_Y_1))) )],[refute_3_1,refute_3_34]) ).
cnf(refute_3_36,plain,
( f(g(skolemFOFtoCNF_Y_1)) != skolemFOFtoCNF_Y_1
| g(skolemFOFtoCNF_Y_1) != g(skolemFOFtoCNF_Y_1)
| g(skolemFOFtoCNF_Y_1) = g(f(g(skolemFOFtoCNF_Y_1))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(g(skolemFOFtoCNF_Y_1),g(f(g(skolemFOFtoCNF_Y_1)))) ),[1,0],$fot(skolemFOFtoCNF_Y_1)]]) ).
cnf(refute_3_37,plain,
( g(skolemFOFtoCNF_Y_1) != g(skolemFOFtoCNF_Y_1)
| g(skolemFOFtoCNF_Y_1) = g(f(g(skolemFOFtoCNF_Y_1))) ),
inference(resolve,[$cnf( $equal(f(g(skolemFOFtoCNF_Y_1)),skolemFOFtoCNF_Y_1) )],[refute_3_35,refute_3_36]) ).
cnf(refute_3_38,plain,
( g(skolemFOFtoCNF_Y_1) != g(skolemFOFtoCNF_Y_1)
| g(skolemFOFtoCNF_Y_1) = skolemFOFtoCNF_X_5 ),
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_Y_1),g(f(g(skolemFOFtoCNF_Y_1)))) )],[refute_3_37,refute_3_33]) ).
cnf(refute_3_39,plain,
g(skolemFOFtoCNF_Y_1) = g(skolemFOFtoCNF_Y_1),
introduced(tautology,[refl,[$fot(g(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_3_40,plain,
g(skolemFOFtoCNF_Y_1) = skolemFOFtoCNF_X_5,
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_Y_1),g(skolemFOFtoCNF_Y_1)) )],[refute_3_39,refute_3_38]) ).
cnf(refute_3_41,plain,
f(g(skolemFOFtoCNF_Y_1)) = f(g(skolemFOFtoCNF_Y_1)),
introduced(tautology,[refl,[$fot(f(g(skolemFOFtoCNF_Y_1)))]]) ).
cnf(refute_3_42,plain,
( f(g(skolemFOFtoCNF_Y_1)) != f(g(skolemFOFtoCNF_Y_1))
| g(skolemFOFtoCNF_Y_1) != skolemFOFtoCNF_X_5
| f(g(skolemFOFtoCNF_Y_1)) = f(skolemFOFtoCNF_X_5) ),
introduced(tautology,[equality,[$cnf( $equal(f(g(skolemFOFtoCNF_Y_1)),f(g(skolemFOFtoCNF_Y_1))) ),[1,0],$fot(skolemFOFtoCNF_X_5)]]) ).
cnf(refute_3_43,plain,
( g(skolemFOFtoCNF_Y_1) != skolemFOFtoCNF_X_5
| f(g(skolemFOFtoCNF_Y_1)) = f(skolemFOFtoCNF_X_5) ),
inference(resolve,[$cnf( $equal(f(g(skolemFOFtoCNF_Y_1)),f(g(skolemFOFtoCNF_Y_1))) )],[refute_3_41,refute_3_42]) ).
cnf(refute_3_44,plain,
f(g(skolemFOFtoCNF_Y_1)) = f(skolemFOFtoCNF_X_5),
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_Y_1),skolemFOFtoCNF_X_5) )],[refute_3_40,refute_3_43]) ).
cnf(refute_3_45,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_3_46,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_3_8,refute_3_45]) ).
cnf(refute_3_47,plain,
( f(g(skolemFOFtoCNF_Y_1)) != f(skolemFOFtoCNF_X_5)
| f(skolemFOFtoCNF_X_5) != skolemFOFtoCNF_X_4
| f(g(skolemFOFtoCNF_Y_1)) = skolemFOFtoCNF_X_4 ),
inference(subst,[],[refute_3_46:[bind(X0,$fot(f(g(skolemFOFtoCNF_Y_1)))),bind(Y0,$fot(f(skolemFOFtoCNF_X_5))),bind(Z0,$fot(skolemFOFtoCNF_X_4))]]) ).
cnf(refute_3_48,plain,
( f(skolemFOFtoCNF_X_5) != skolemFOFtoCNF_X_4
| f(g(skolemFOFtoCNF_Y_1)) = skolemFOFtoCNF_X_4 ),
inference(resolve,[$cnf( $equal(f(g(skolemFOFtoCNF_Y_1)),f(skolemFOFtoCNF_X_5)) )],[refute_3_44,refute_3_47]) ).
cnf(refute_3_49,plain,
f(g(skolemFOFtoCNF_Y_1)) = skolemFOFtoCNF_X_4,
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_X_5),skolemFOFtoCNF_X_4) )],[refute_3_32,refute_3_48]) ).
cnf(refute_3_50,plain,
( f(g(skolemFOFtoCNF_Y_1)) != skolemFOFtoCNF_X_4
| skolemFOFtoCNF_Y_1 != f(g(skolemFOFtoCNF_Y_1))
| skolemFOFtoCNF_Y_1 = skolemFOFtoCNF_X_4 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y_1,f(g(skolemFOFtoCNF_Y_1))) ),[1],$fot(skolemFOFtoCNF_X_4)]]) ).
cnf(refute_3_51,plain,
( skolemFOFtoCNF_Y_1 != f(g(skolemFOFtoCNF_Y_1))
| skolemFOFtoCNF_Y_1 = skolemFOFtoCNF_X_4 ),
inference(resolve,[$cnf( $equal(f(g(skolemFOFtoCNF_Y_1)),skolemFOFtoCNF_X_4) )],[refute_3_49,refute_3_50]) ).
cnf(refute_3_52,plain,
skolemFOFtoCNF_Y_1 = skolemFOFtoCNF_X_4,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1,f(g(skolemFOFtoCNF_Y_1))) )],[refute_3_1,refute_3_51]) ).
cnf(refute_3_53,plain,
( skolemFOFtoCNF_X_4 != skolemFOFtoCNF_Z_1
| skolemFOFtoCNF_Y_1 != skolemFOFtoCNF_X_4
| skolemFOFtoCNF_Y_1 = skolemFOFtoCNF_Z_1 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_4) ),[1],$fot(skolemFOFtoCNF_Z_1)]]) ).
cnf(refute_3_54,plain,
( skolemFOFtoCNF_X_4 != skolemFOFtoCNF_Z_1
| skolemFOFtoCNF_Y_1 = skolemFOFtoCNF_Z_1 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_4) )],[refute_3_52,refute_3_53]) ).
cnf(refute_3_55,plain,
skolemFOFtoCNF_Z_1 = f(g(skolemFOFtoCNF_Z_1)),
inference(canonicalize,[],[normalize_3_11]) ).
cnf(refute_3_56,plain,
( g(skolemFOFtoCNF_Z_1) != g(f(g(skolemFOFtoCNF_Z_1)))
| g(skolemFOFtoCNF_Z_1) = skolemFOFtoCNF_X_5 ),
inference(subst,[],[refute_3_15:[bind(X_5,$fot(g(skolemFOFtoCNF_Z_1)))]]) ).
cnf(refute_3_57,plain,
( skolemFOFtoCNF_Z_1 != f(g(skolemFOFtoCNF_Z_1))
| f(g(skolemFOFtoCNF_Z_1)) = skolemFOFtoCNF_Z_1 ),
inference(subst,[],[refute_3_8:[bind(X0,$fot(skolemFOFtoCNF_Z_1)),bind(Y0,$fot(f(g(skolemFOFtoCNF_Z_1))))]]) ).
cnf(refute_3_58,plain,
f(g(skolemFOFtoCNF_Z_1)) = skolemFOFtoCNF_Z_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z_1,f(g(skolemFOFtoCNF_Z_1))) )],[refute_3_55,refute_3_57]) ).
cnf(refute_3_59,plain,
( f(g(skolemFOFtoCNF_Z_1)) != skolemFOFtoCNF_Z_1
| g(skolemFOFtoCNF_Z_1) != g(skolemFOFtoCNF_Z_1)
| g(skolemFOFtoCNF_Z_1) = g(f(g(skolemFOFtoCNF_Z_1))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(g(skolemFOFtoCNF_Z_1),g(f(g(skolemFOFtoCNF_Z_1)))) ),[1,0],$fot(skolemFOFtoCNF_Z_1)]]) ).
cnf(refute_3_60,plain,
( g(skolemFOFtoCNF_Z_1) != g(skolemFOFtoCNF_Z_1)
| g(skolemFOFtoCNF_Z_1) = g(f(g(skolemFOFtoCNF_Z_1))) ),
inference(resolve,[$cnf( $equal(f(g(skolemFOFtoCNF_Z_1)),skolemFOFtoCNF_Z_1) )],[refute_3_58,refute_3_59]) ).
cnf(refute_3_61,plain,
( g(skolemFOFtoCNF_Z_1) != g(skolemFOFtoCNF_Z_1)
| g(skolemFOFtoCNF_Z_1) = skolemFOFtoCNF_X_5 ),
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_Z_1),g(f(g(skolemFOFtoCNF_Z_1)))) )],[refute_3_60,refute_3_56]) ).
cnf(refute_3_62,plain,
g(skolemFOFtoCNF_Z_1) = g(skolemFOFtoCNF_Z_1),
introduced(tautology,[refl,[$fot(g(skolemFOFtoCNF_Z_1))]]) ).
cnf(refute_3_63,plain,
g(skolemFOFtoCNF_Z_1) = skolemFOFtoCNF_X_5,
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_Z_1),g(skolemFOFtoCNF_Z_1)) )],[refute_3_62,refute_3_61]) ).
cnf(refute_3_64,plain,
f(g(skolemFOFtoCNF_Z_1)) = f(g(skolemFOFtoCNF_Z_1)),
introduced(tautology,[refl,[$fot(f(g(skolemFOFtoCNF_Z_1)))]]) ).
cnf(refute_3_65,plain,
( f(g(skolemFOFtoCNF_Z_1)) != f(g(skolemFOFtoCNF_Z_1))
| g(skolemFOFtoCNF_Z_1) != skolemFOFtoCNF_X_5
| f(g(skolemFOFtoCNF_Z_1)) = f(skolemFOFtoCNF_X_5) ),
introduced(tautology,[equality,[$cnf( $equal(f(g(skolemFOFtoCNF_Z_1)),f(g(skolemFOFtoCNF_Z_1))) ),[1,0],$fot(skolemFOFtoCNF_X_5)]]) ).
cnf(refute_3_66,plain,
( g(skolemFOFtoCNF_Z_1) != skolemFOFtoCNF_X_5
| f(g(skolemFOFtoCNF_Z_1)) = f(skolemFOFtoCNF_X_5) ),
inference(resolve,[$cnf( $equal(f(g(skolemFOFtoCNF_Z_1)),f(g(skolemFOFtoCNF_Z_1))) )],[refute_3_64,refute_3_65]) ).
cnf(refute_3_67,plain,
f(g(skolemFOFtoCNF_Z_1)) = f(skolemFOFtoCNF_X_5),
inference(resolve,[$cnf( $equal(g(skolemFOFtoCNF_Z_1),skolemFOFtoCNF_X_5) )],[refute_3_63,refute_3_66]) ).
cnf(refute_3_68,plain,
( f(g(skolemFOFtoCNF_Z_1)) != f(skolemFOFtoCNF_X_5)
| f(skolemFOFtoCNF_X_5) != skolemFOFtoCNF_X_4
| f(g(skolemFOFtoCNF_Z_1)) = skolemFOFtoCNF_X_4 ),
inference(subst,[],[refute_3_46:[bind(X0,$fot(f(g(skolemFOFtoCNF_Z_1)))),bind(Y0,$fot(f(skolemFOFtoCNF_X_5))),bind(Z0,$fot(skolemFOFtoCNF_X_4))]]) ).
cnf(refute_3_69,plain,
( f(skolemFOFtoCNF_X_5) != skolemFOFtoCNF_X_4
| f(g(skolemFOFtoCNF_Z_1)) = skolemFOFtoCNF_X_4 ),
inference(resolve,[$cnf( $equal(f(g(skolemFOFtoCNF_Z_1)),f(skolemFOFtoCNF_X_5)) )],[refute_3_67,refute_3_68]) ).
cnf(refute_3_70,plain,
f(g(skolemFOFtoCNF_Z_1)) = skolemFOFtoCNF_X_4,
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_X_5),skolemFOFtoCNF_X_4) )],[refute_3_32,refute_3_69]) ).
cnf(refute_3_71,plain,
( f(g(skolemFOFtoCNF_Z_1)) != skolemFOFtoCNF_X_4
| skolemFOFtoCNF_Z_1 != f(g(skolemFOFtoCNF_Z_1))
| skolemFOFtoCNF_Z_1 = skolemFOFtoCNF_X_4 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Z_1,f(g(skolemFOFtoCNF_Z_1))) ),[1],$fot(skolemFOFtoCNF_X_4)]]) ).
cnf(refute_3_72,plain,
( skolemFOFtoCNF_Z_1 != f(g(skolemFOFtoCNF_Z_1))
| skolemFOFtoCNF_Z_1 = skolemFOFtoCNF_X_4 ),
inference(resolve,[$cnf( $equal(f(g(skolemFOFtoCNF_Z_1)),skolemFOFtoCNF_X_4) )],[refute_3_70,refute_3_71]) ).
cnf(refute_3_73,plain,
skolemFOFtoCNF_Z_1 = skolemFOFtoCNF_X_4,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z_1,f(g(skolemFOFtoCNF_Z_1))) )],[refute_3_55,refute_3_72]) ).
cnf(refute_3_74,plain,
( skolemFOFtoCNF_X_4 != skolemFOFtoCNF_X_4
| skolemFOFtoCNF_Z_1 != skolemFOFtoCNF_X_4
| skolemFOFtoCNF_X_4 = skolemFOFtoCNF_Z_1 ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_X_4,skolemFOFtoCNF_Z_1) ),[1],$fot(skolemFOFtoCNF_X_4)]]) ).
cnf(refute_3_75,plain,
( skolemFOFtoCNF_X_4 != skolemFOFtoCNF_X_4
| skolemFOFtoCNF_X_4 = skolemFOFtoCNF_Z_1 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_X_4) )],[refute_3_73,refute_3_74]) ).
cnf(refute_3_76,plain,
( skolemFOFtoCNF_X_4 != skolemFOFtoCNF_X_4
| skolemFOFtoCNF_Y_1 = skolemFOFtoCNF_Z_1 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_4,skolemFOFtoCNF_Z_1) )],[refute_3_75,refute_3_54]) ).
cnf(refute_3_77,plain,
skolemFOFtoCNF_X_4 != skolemFOFtoCNF_X_4,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1) )],[refute_3_76,refute_3_0]) ).
cnf(refute_3_78,plain,
skolemFOFtoCNF_X_4 = skolemFOFtoCNF_X_4,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_X_4)]]) ).
cnf(refute_3_79,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_4,skolemFOFtoCNF_X_4) )],[refute_3_78,refute_3_77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN551+1 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n018.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 23:04:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.38
%------------------------------------------------------------------------------