TSTP Solution File: NUM565+3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM565+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 12:27:47 EDT 2022
% Result : Theorem 0.40s 0.57s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 42 ( 16 unt; 0 def)
% Number of atoms : 131 ( 65 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 140 ( 51 ~; 32 |; 45 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 20 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mCardEmpty,axiom,
! [W0] :
( aSet0(W0)
=> ( sbrdtbr0(W0) = sz00
<=> W0 = slcrc0 ) ) ).
fof(m__3476,hypothesis,
( aSet0(slcrc0)
& ~ ? [W0] : aElementOf0(W0,slcrc0)
& ! [W0] :
( aElementOf0(W0,slcrc0)
=> aElementOf0(W0,xS) )
& aSubsetOf0(slcrc0,xS)
& aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)) ) ).
fof(m__,conjecture,
! [W0] :
( ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& sbrdtbr0(W0) = sz00
& aElementOf0(W0,slbdtsldtrb0(xS,sz00)) )
=> ( ( aSet0(slcrc0)
& ~ ? [W1] : aElementOf0(W1,slcrc0) )
=> sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ) ).
fof(subgoal_0,plain,
! [W0] :
( ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& sbrdtbr0(W0) = sz00
& aElementOf0(W0,slbdtsldtrb0(xS,sz00))
& aSet0(slcrc0)
& ~ ? [W1] : aElementOf0(W1,slcrc0) )
=> sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ! [W0] :
( ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& sbrdtbr0(W0) = sz00
& aElementOf0(W0,slbdtsldtrb0(xS,sz00))
& aSet0(slcrc0)
& ~ ? [W1] : aElementOf0(W1,slcrc0) )
=> sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [W0] :
( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0)
& sbrdtbr0(W0) = sz00
& aElementOf0(W0,slbdtsldtrb0(xS,sz00))
& aSet0(W0)
& aSet0(slcrc0)
& aSubsetOf0(W0,xS)
& ! [W1] : ~ aElementOf0(W1,slcrc0)
& ! [W1] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00))
& aSet0(slcrc0)
& aSubsetOf0(slcrc0,xS)
& ! [W0] : ~ aElementOf0(W0,slcrc0)
& ! [W0] :
( ~ aElementOf0(W0,slcrc0)
| aElementOf0(W0,xS) ) ),
inference(canonicalize,[],[m__3476]) ).
fof(normalize_0_2,plain,
aSet0(slcrc0),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
? [W0] :
( sdtlpdtrp0(xc,W0) != sdtlpdtrp0(xc,slcrc0)
& sbrdtbr0(W0) = sz00
& aElementOf0(W0,slbdtsldtrb0(xS,sz00))
& aSet0(W0)
& aSubsetOf0(W0,xS)
& ! [W1] : ~ aElementOf0(W1,slcrc0)
& ! [W1] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) ) ),
inference(simplify,[],[normalize_0_0,normalize_0_2]) ).
fof(normalize_0_4,plain,
( sdtlpdtrp0(xc,skolemFOFtoCNF_W0) != sdtlpdtrp0(xc,slcrc0)
& sbrdtbr0(skolemFOFtoCNF_W0) = sz00
& aElementOf0(skolemFOFtoCNF_W0,slbdtsldtrb0(xS,sz00))
& aSet0(skolemFOFtoCNF_W0)
& aSubsetOf0(skolemFOFtoCNF_W0,xS)
& ! [W1] : ~ aElementOf0(W1,slcrc0)
& ! [W1] :
( ~ aElementOf0(W1,skolemFOFtoCNF_W0)
| aElementOf0(W1,xS) ) ),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
sdtlpdtrp0(xc,skolemFOFtoCNF_W0) != sdtlpdtrp0(xc,slcrc0),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [W0] :
( ~ aSet0(W0)
| ( W0 != slcrc0
<=> sbrdtbr0(W0) != sz00 ) ),
inference(canonicalize,[],[mCardEmpty]) ).
fof(normalize_0_7,plain,
! [W0] :
( ~ aSet0(W0)
| ( W0 != slcrc0
<=> sbrdtbr0(W0) != sz00 ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [W0] :
( ( W0 != slcrc0
| ~ aSet0(W0)
| sbrdtbr0(W0) = sz00 )
& ( sbrdtbr0(W0) != sz00
| ~ aSet0(W0)
| W0 = slcrc0 ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [W0] :
( sbrdtbr0(W0) != sz00
| ~ aSet0(W0)
| W0 = slcrc0 ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
sbrdtbr0(skolemFOFtoCNF_W0) = sz00,
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_11,plain,
aSet0(skolemFOFtoCNF_W0),
inference(conjunct,[],[normalize_0_4]) ).
cnf(refute_0_0,plain,
sdtlpdtrp0(xc,skolemFOFtoCNF_W0) != sdtlpdtrp0(xc,slcrc0),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_1,plain,
( sbrdtbr0(W0) != sz00
| ~ aSet0(W0)
| W0 = slcrc0 ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_2,plain,
( sbrdtbr0(skolemFOFtoCNF_W0) != sz00
| ~ aSet0(skolemFOFtoCNF_W0)
| skolemFOFtoCNF_W0 = slcrc0 ),
inference(subst,[],[refute_0_1:[bind(W0,$fot(skolemFOFtoCNF_W0))]]) ).
cnf(refute_0_3,plain,
sbrdtbr0(skolemFOFtoCNF_W0) = sz00,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_4,plain,
( sbrdtbr0(skolemFOFtoCNF_W0) != sz00
| sz00 != sz00
| sbrdtbr0(skolemFOFtoCNF_W0) = sz00 ),
introduced(tautology,[equality,[$cnf( ~ $equal(sbrdtbr0(skolemFOFtoCNF_W0),sz00) ),[0],$fot(sz00)]]) ).
cnf(refute_0_5,plain,
( sz00 != sz00
| sbrdtbr0(skolemFOFtoCNF_W0) = sz00 ),
inference(resolve,[$cnf( $equal(sbrdtbr0(skolemFOFtoCNF_W0),sz00) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( sz00 != sz00
| ~ aSet0(skolemFOFtoCNF_W0)
| skolemFOFtoCNF_W0 = slcrc0 ),
inference(resolve,[$cnf( $equal(sbrdtbr0(skolemFOFtoCNF_W0),sz00) )],[refute_0_5,refute_0_2]) ).
cnf(refute_0_7,plain,
sz00 = sz00,
introduced(tautology,[refl,[$fot(sz00)]]) ).
cnf(refute_0_8,plain,
( ~ aSet0(skolemFOFtoCNF_W0)
| skolemFOFtoCNF_W0 = slcrc0 ),
inference(resolve,[$cnf( $equal(sz00,sz00) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
aSet0(skolemFOFtoCNF_W0),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_10,plain,
skolemFOFtoCNF_W0 = slcrc0,
inference(resolve,[$cnf( aSet0(skolemFOFtoCNF_W0) )],[refute_0_9,refute_0_8]) ).
cnf(refute_0_11,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_12,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_13,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( skolemFOFtoCNF_W0 != slcrc0
| slcrc0 = skolemFOFtoCNF_W0 ),
inference(subst,[],[refute_0_13:[bind(X,$fot(skolemFOFtoCNF_W0)),bind(Y,$fot(slcrc0))]]) ).
cnf(refute_0_15,plain,
slcrc0 = skolemFOFtoCNF_W0,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W0,slcrc0) )],[refute_0_10,refute_0_14]) ).
cnf(refute_0_16,plain,
sdtlpdtrp0(xc,slcrc0) = sdtlpdtrp0(xc,slcrc0),
introduced(tautology,[refl,[$fot(sdtlpdtrp0(xc,slcrc0))]]) ).
cnf(refute_0_17,plain,
( sdtlpdtrp0(xc,slcrc0) != sdtlpdtrp0(xc,slcrc0)
| slcrc0 != skolemFOFtoCNF_W0
| sdtlpdtrp0(xc,slcrc0) = sdtlpdtrp0(xc,skolemFOFtoCNF_W0) ),
introduced(tautology,[equality,[$cnf( $equal(sdtlpdtrp0(xc,slcrc0),sdtlpdtrp0(xc,slcrc0)) ),[1,1],$fot(skolemFOFtoCNF_W0)]]) ).
cnf(refute_0_18,plain,
( slcrc0 != skolemFOFtoCNF_W0
| sdtlpdtrp0(xc,slcrc0) = sdtlpdtrp0(xc,skolemFOFtoCNF_W0) ),
inference(resolve,[$cnf( $equal(sdtlpdtrp0(xc,slcrc0),sdtlpdtrp0(xc,slcrc0)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
sdtlpdtrp0(xc,slcrc0) = sdtlpdtrp0(xc,skolemFOFtoCNF_W0),
inference(resolve,[$cnf( $equal(slcrc0,skolemFOFtoCNF_W0) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
( sdtlpdtrp0(xc,skolemFOFtoCNF_W0) != sdtlpdtrp0(xc,skolemFOFtoCNF_W0)
| sdtlpdtrp0(xc,slcrc0) != sdtlpdtrp0(xc,skolemFOFtoCNF_W0)
| sdtlpdtrp0(xc,skolemFOFtoCNF_W0) = sdtlpdtrp0(xc,slcrc0) ),
introduced(tautology,[equality,[$cnf( ~ $equal(sdtlpdtrp0(xc,skolemFOFtoCNF_W0),sdtlpdtrp0(xc,slcrc0)) ),[1],$fot(sdtlpdtrp0(xc,skolemFOFtoCNF_W0))]]) ).
cnf(refute_0_21,plain,
( sdtlpdtrp0(xc,skolemFOFtoCNF_W0) != sdtlpdtrp0(xc,skolemFOFtoCNF_W0)
| sdtlpdtrp0(xc,skolemFOFtoCNF_W0) = sdtlpdtrp0(xc,slcrc0) ),
inference(resolve,[$cnf( $equal(sdtlpdtrp0(xc,slcrc0),sdtlpdtrp0(xc,skolemFOFtoCNF_W0)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
sdtlpdtrp0(xc,skolemFOFtoCNF_W0) != sdtlpdtrp0(xc,skolemFOFtoCNF_W0),
inference(resolve,[$cnf( $equal(sdtlpdtrp0(xc,skolemFOFtoCNF_W0),sdtlpdtrp0(xc,slcrc0)) )],[refute_0_21,refute_0_0]) ).
cnf(refute_0_23,plain,
sdtlpdtrp0(xc,skolemFOFtoCNF_W0) = sdtlpdtrp0(xc,skolemFOFtoCNF_W0),
introduced(tautology,[refl,[$fot(sdtlpdtrp0(xc,skolemFOFtoCNF_W0))]]) ).
cnf(refute_0_24,plain,
$false,
inference(resolve,[$cnf( $equal(sdtlpdtrp0(xc,skolemFOFtoCNF_W0),sdtlpdtrp0(xc,skolemFOFtoCNF_W0)) )],[refute_0_23,refute_0_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM565+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 02:12:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.40/0.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.40/0.57
% 0.40/0.57 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.40/0.57
%------------------------------------------------------------------------------