%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM571+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.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 : Mon Jul 18 12:27:51 EDT 2022
% Result : Theorem 0.38s 0.55s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 68 ( 26 unt; 0 def)
% Number of atoms : 249 ( 91 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 256 ( 75 ~; 79 |; 82 &)
% ( 3 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 27 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__3435,hypothesis,
( aSet0(xS)
& ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ) ).
fof(m__3623,hypothesis,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( ( ( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,W0)) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W1)
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ).
fof(m__3702_02,hypothesis,
( xi != sz00
=> ( ? [W0] :
( aElementOf0(W0,szNzAzT0)
& szszuzczcdt0(W0) = xi )
& aSet0(sdtlpdtrp0(xN,xi))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> aElementOf0(W0,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,xi)) ) ) ).
fof(m__,conjecture,
( ( ( aSet0(sdtlpdtrp0(xN,xi))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> aElementOf0(W0,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,xi)) ) ).
fof(subgoal_0,plain,
( ~ ( aSet0(sdtlpdtrp0(xN,xi))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> aElementOf0(W0,szNzAzT0) ) )
=> aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
inference(strip,[],[m__]) ).
fof(subgoal_1,plain,
( ( ( aSet0(sdtlpdtrp0(xN,xi))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> aElementOf0(W0,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) )
=> isCountable0(sdtlpdtrp0(xN,xi)) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ( ~ ( aSet0(sdtlpdtrp0(xN,xi))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> aElementOf0(W0,szNzAzT0) ) )
=> aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
& ( ~ aSet0(sdtlpdtrp0(xN,xi))
| ? [W0] :
( ~ aElementOf0(W0,szNzAzT0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi)) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN)
& ! [W0] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ? [W1] :
( ~ aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlpdtrp0(xN,W0)) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
& ! [W1] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ! [W1] :
( ~ aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ),
inference(canonicalize,[],[m__3623]) ).
fof(normalize_0_3,plain,
sdtlpdtrp0(xN,sz00) = xS,
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
( xi = sz00
| ( aSet0(sdtlpdtrp0(xN,xi))
& aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,xi))
& ? [W0] :
( szszuzczcdt0(W0) = xi
& aElementOf0(W0,szNzAzT0) )
& ! [W0] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| aElementOf0(W0,szNzAzT0) ) ) ),
inference(canonicalize,[],[m__3702_02]) ).
fof(normalize_0_5,plain,
! [W0] :
( ( szszuzczcdt0(skolemFOFtoCNF_W0) = xi
| xi = sz00 )
& ( xi = sz00
| aElementOf0(skolemFOFtoCNF_W0,szNzAzT0) )
& ( xi = sz00
| aSet0(sdtlpdtrp0(xN,xi)) )
& ( xi = sz00
| aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) )
& ( xi = sz00
| isCountable0(sdtlpdtrp0(xN,xi)) )
& ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| xi = sz00
| aElementOf0(W0,szNzAzT0) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
( xi = sz00
| aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( aSet0(xS)
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS)
& ! [W0] :
( ~ aElementOf0(W0,xS)
| aElementOf0(W0,szNzAzT0) ) ),
inference(canonicalize,[],[m__3435]) ).
fof(normalize_0_8,plain,
aSubsetOf0(xS,szNzAzT0),
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
sdtlpdtrp0(xN,sz00) = xS,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
( xi = sz00
| aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
xi = sz00,
inference(resolve,[$cnf( aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) )],[refute_0_2,refute_0_0]) ).
cnf(refute_0_4,plain,
sdtlpdtrp0(xN,xi) = sdtlpdtrp0(xN,xi),
introduced(tautology,[refl,[$fot(sdtlpdtrp0(xN,xi))]]) ).
cnf(refute_0_5,plain,
( sdtlpdtrp0(xN,xi) != sdtlpdtrp0(xN,xi)
| xi != sz00
| sdtlpdtrp0(xN,xi) = sdtlpdtrp0(xN,sz00) ),
introduced(tautology,[equality,[$cnf( $equal(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xi)) ),[1,1],$fot(sz00)]]) ).
cnf(refute_0_6,plain,
( xi != sz00
| sdtlpdtrp0(xN,xi) = sdtlpdtrp0(xN,sz00) ),
inference(resolve,[$cnf( $equal(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xi)) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
sdtlpdtrp0(xN,xi) = sdtlpdtrp0(xN,sz00),
inference(resolve,[$cnf( $equal(xi,sz00) )],[refute_0_3,refute_0_6]) ).
cnf(refute_0_8,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_9,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_10,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_12,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( sdtlpdtrp0(xN,sz00) != xS
| sdtlpdtrp0(xN,xi) != sdtlpdtrp0(xN,sz00)
| sdtlpdtrp0(xN,xi) = xS ),
inference(subst,[],[refute_0_12:[bind(X,$fot(sdtlpdtrp0(xN,xi))),bind(Y,$fot(sdtlpdtrp0(xN,sz00))),bind(Z,$fot(xS))]]) ).
cnf(refute_0_14,plain,
( sdtlpdtrp0(xN,sz00) != xS
| sdtlpdtrp0(xN,xi) = xS ),
inference(resolve,[$cnf( $equal(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00)) )],[refute_0_7,refute_0_13]) ).
cnf(refute_0_15,plain,
sdtlpdtrp0(xN,xi) = xS,
inference(resolve,[$cnf( $equal(sdtlpdtrp0(xN,sz00),xS) )],[refute_0_1,refute_0_14]) ).
cnf(refute_0_16,plain,
( sdtlpdtrp0(xN,xi) != xS
| ~ aSubsetOf0(xS,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
introduced(tautology,[equality,[$cnf( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),[0],$fot(xS)]]) ).
cnf(refute_0_17,plain,
( ~ aSubsetOf0(xS,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
inference(resolve,[$cnf( $equal(sdtlpdtrp0(xN,xi),xS) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
~ aSubsetOf0(xS,szNzAzT0),
inference(resolve,[$cnf( aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) )],[refute_0_17,refute_0_0]) ).
cnf(refute_0_19,plain,
aSubsetOf0(xS,szNzAzT0),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_20,plain,
$false,
inference(resolve,[$cnf( aSubsetOf0(xS,szNzAzT0) )],[refute_0_19,refute_0_18]) ).
fof(negate_1_0,plain,
~ ( ( ( aSet0(sdtlpdtrp0(xN,xi))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> aElementOf0(W0,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) )
=> isCountable0(sdtlpdtrp0(xN,xi)) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
( ~ isCountable0(sdtlpdtrp0(xN,xi))
& ( aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,xi))
& ! [W0] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| aElementOf0(W0,szNzAzT0) ) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
~ isCountable0(sdtlpdtrp0(xN,xi)),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
( sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN)
& ! [W0] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& ( ~ aSet0(sdtlpdtrp0(xN,W0))
| ? [W1] :
( ~ aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlpdtrp0(xN,W0)) ) ) )
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
& ! [W1] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ! [W1] :
( ~ aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( ~ aElement0(W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ),
inference(canonicalize,[],[m__3623]) ).
fof(normalize_1_3,plain,
sdtlpdtrp0(xN,sz00) = xS,
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
( xi = sz00
| ( aSet0(sdtlpdtrp0(xN,xi))
& aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,xi))
& ? [W0] :
( szszuzczcdt0(W0) = xi
& aElementOf0(W0,szNzAzT0) )
& ! [W0] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| aElementOf0(W0,szNzAzT0) ) ) ),
inference(canonicalize,[],[m__3702_02]) ).
fof(normalize_1_5,plain,
! [W0] :
( ( szszuzczcdt0(skolemFOFtoCNF_W0) = xi
| xi = sz00 )
& ( xi = sz00
| aElementOf0(skolemFOFtoCNF_W0,szNzAzT0) )
& ( xi = sz00
| aSet0(sdtlpdtrp0(xN,xi)) )
& ( xi = sz00
| aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) )
& ( xi = sz00
| isCountable0(sdtlpdtrp0(xN,xi)) )
& ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| xi = sz00
| aElementOf0(W0,szNzAzT0) ) ),
inference(clausify,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
( xi = sz00
| isCountable0(sdtlpdtrp0(xN,xi)) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
( aSet0(xS)
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS)
& ! [W0] :
( ~ aElementOf0(W0,xS)
| aElementOf0(W0,szNzAzT0) ) ),
inference(canonicalize,[],[m__3435]) ).
fof(normalize_1_8,plain,
isCountable0(xS),
inference(conjunct,[],[normalize_1_7]) ).
cnf(refute_1_0,plain,
~ isCountable0(sdtlpdtrp0(xN,xi)),
inference(canonicalize,[],[normalize_1_1]) ).
cnf(refute_1_1,plain,
sdtlpdtrp0(xN,sz00) = xS,
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_2,plain,
( xi = sz00
| isCountable0(sdtlpdtrp0(xN,xi)) ),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_3,plain,
xi = sz00,
inference(resolve,[$cnf( isCountable0(sdtlpdtrp0(xN,xi)) )],[refute_1_2,refute_1_0]) ).
cnf(refute_1_4,plain,
sdtlpdtrp0(xN,xi) = sdtlpdtrp0(xN,xi),
introduced(tautology,[refl,[$fot(sdtlpdtrp0(xN,xi))]]) ).
cnf(refute_1_5,plain,
( sdtlpdtrp0(xN,xi) != sdtlpdtrp0(xN,xi)
| xi != sz00
| sdtlpdtrp0(xN,xi) = sdtlpdtrp0(xN,sz00) ),
introduced(tautology,[equality,[$cnf( $equal(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xi)) ),[1,1],$fot(sz00)]]) ).
cnf(refute_1_6,plain,
( xi != sz00
| sdtlpdtrp0(xN,xi) = sdtlpdtrp0(xN,sz00) ),
inference(resolve,[$cnf( $equal(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xi)) )],[refute_1_4,refute_1_5]) ).
cnf(refute_1_7,plain,
sdtlpdtrp0(xN,xi) = sdtlpdtrp0(xN,sz00),
inference(resolve,[$cnf( $equal(xi,sz00) )],[refute_1_3,refute_1_6]) ).
cnf(refute_1_8,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_9,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_10,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_8,refute_1_9]) ).
cnf(refute_1_11,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_1_12,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_1_10,refute_1_11]) ).
cnf(refute_1_13,plain,
( sdtlpdtrp0(xN,sz00) != xS
| sdtlpdtrp0(xN,xi) != sdtlpdtrp0(xN,sz00)
| sdtlpdtrp0(xN,xi) = xS ),
inference(subst,[],[refute_1_12:[bind(X,$fot(sdtlpdtrp0(xN,xi))),bind(Y,$fot(sdtlpdtrp0(xN,sz00))),bind(Z,$fot(xS))]]) ).
cnf(refute_1_14,plain,
( sdtlpdtrp0(xN,sz00) != xS
| sdtlpdtrp0(xN,xi) = xS ),
inference(resolve,[$cnf( $equal(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00)) )],[refute_1_7,refute_1_13]) ).
cnf(refute_1_15,plain,
sdtlpdtrp0(xN,xi) = xS,
inference(resolve,[$cnf( $equal(sdtlpdtrp0(xN,sz00),xS) )],[refute_1_1,refute_1_14]) ).
cnf(refute_1_16,plain,
( sdtlpdtrp0(xN,xi) != xS
| ~ isCountable0(xS)
| isCountable0(sdtlpdtrp0(xN,xi)) ),
introduced(tautology,[equality,[$cnf( ~ isCountable0(sdtlpdtrp0(xN,xi)) ),[0],$fot(xS)]]) ).
cnf(refute_1_17,plain,
( ~ isCountable0(xS)
| isCountable0(sdtlpdtrp0(xN,xi)) ),
inference(resolve,[$cnf( $equal(sdtlpdtrp0(xN,xi),xS) )],[refute_1_15,refute_1_16]) ).
cnf(refute_1_18,plain,
~ isCountable0(xS),
inference(resolve,[$cnf( isCountable0(sdtlpdtrp0(xN,xi)) )],[refute_1_17,refute_1_0]) ).
cnf(refute_1_19,plain,
isCountable0(xS),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_20,plain,
$false,
inference(resolve,[$cnf( isCountable0(xS) )],[refute_1_19,refute_1_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : NUM571+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.11 % Command : metis --show proof --show saturation %s
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Wed Jul 6 06:16:22 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.38/0.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.38/0.55
% 0.38/0.55 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.38/0.55
%------------------------------------------------------------------------------