%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM588+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:15:52 PM UTC 2026
% Result : Theorem 3.16s 1.30s
% Output : Refutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 30
% Syntax : Number of formulae : 202 ( 38 unt; 18 def)
% Number of atoms : 768 ( 121 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 937 ( 371 ~; 370 |; 145 &)
% ( 33 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 12 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 13 con; 0-3 aty)
% Number of variables : 230 ( 0 sgn 208 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ~ ? [X1] : aElementOf0(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(f9,axiom,
! [X0] :
( ( aSet0(X0)
& isCountable0(X0) )
=> X0 != slcrc0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin_01) ).
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aSet0(X0)
& aSet0(X1)
& aSet0(X2) )
=> ( ( aSubsetOf0(X0,X1)
& aSubsetOf0(X1,X2) )
=> aSubsetOf0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubTrans) ).
fof(f16,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aElement0(X1) )
=> ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(f23,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(f47,axiom,
! [X0] :
( ( aSubsetOf0(X0,szNzAzT0)
& X0 != slcrc0 )
=> ! [X1] :
( X1 = szmzizndt0(X0)
<=> ( aElementOf0(X1,X0)
& ! [X2] :
( aElementOf0(X2,X0)
=> sdtlseqdt0(X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMin) ).
fof(f57,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aElementOf0(X1,szNzAzT0) )
=> ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
fof(f80,axiom,
( aElementOf0(xk,szNzAzT0)
& szszuzczcdt0(xk) = xK ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3533) ).
fof(f82,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3671) ).
fof(f88,conjecture,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(X1) )
=> ! [X2] :
( ( aSet0(X2)
& aElementOf0(X2,slbdtsldtrb0(X1,xk)) )
=> aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f89,negated_conjecture,
~ ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(X1) )
=> ! [X2] :
( ( aSet0(X2)
& aElementOf0(X2,slbdtsldtrb0(X1,xk)) )
=> aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) ) ) ),
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f97,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f98,plain,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f101,plain,
! [X0] :
( X0 != slcrc0
| ~ aSet0(X0)
| ~ isCountable0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f102,plain,
! [X0] :
( X0 != slcrc0
| ~ aSet0(X0)
| ~ isCountable0(X0) ),
inference(flattening,[],[f101]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f109,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X0)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f110,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X0)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(flattening,[],[f109]) ).
fof(f113,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f114,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f113]) ).
fof(f156,plain,
! [X0] :
( ! [X1] :
( X1 = szmzizndt0(X0)
<=> ( aElementOf0(X1,X0)
& ! [X2] :
( sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,X0) ) ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(ennf_transformation,[],[f47]) ).
fof(f157,plain,
! [X0] :
( ! [X1] :
( X1 = szmzizndt0(X0)
<=> ( aElementOf0(X1,X0)
& ! [X2] :
( sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,X0) ) ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(flattening,[],[f156]) ).
fof(f171,plain,
! [X0,X1] :
( ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f172,plain,
! [X0,X1] :
( ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f171]) ).
fof(f200,plain,
! [X0] :
( ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f210,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& aSet0(X2)
& aElementOf0(X2,slbdtsldtrb0(X1,xk)) )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(X1) )
& aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f89]) ).
fof(f211,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& aSet0(X2)
& aElementOf0(X2,slbdtsldtrb0(X1,xk)) )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(X1) )
& aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f210]) ).
fof(f215,definition,
! [X2,X0,X1] :
( sP2(X2,X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f216,definition,
! [X1,X0] :
( ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> sP2(X2,X0,X1) )
| ~ sP3(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f217,plain,
! [X0,X1] :
( sP3(X1,X0)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(definition_folding,[],[f114,f216,f215]) ).
fof(f218,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(nnf_transformation,[],[f98]) ).
fof(f219,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(flattening,[],[f218]) ).
fof(f220,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(rectify,[],[f219]) ).
fof(f221,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| aElementOf0(sK4(X0),X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f220]) ).
fof(f222,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f103]) ).
fof(f223,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(flattening,[],[f222]) ).
fof(f224,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f223]) ).
fof(f225,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK5(X0,X1),X0)
& aElementOf0(sK5(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f224]) ).
fof(f232,plain,
! [X1,X0] :
( ! [X2] :
( ( X2 = sdtmndt0(X0,X1)
| ~ sP2(X2,X0,X1) )
& ( sP2(X2,X0,X1)
| sdtmndt0(X0,X1) != X2 ) )
| ~ sP3(X1,X0) ),
inference(nnf_transformation,[],[f216]) ).
fof(f233,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| ~ sP2(X2,X1,X0) )
& ( sP2(X2,X1,X0)
| sdtmndt0(X1,X0) != X2 ) )
| ~ sP3(X0,X1) ),
inference(rectify,[],[f232]) ).
fof(f234,plain,
! [X2,X0,X1] :
( ( sP2(X2,X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3
| ~ aElementOf0(X3,X2) )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3 )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| ~ aElementOf0(X3,X2) ) ) )
| ~ sP2(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f215]) ).
fof(f235,plain,
! [X2,X0,X1] :
( ( sP2(X2,X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3
| ~ aElementOf0(X3,X2) )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3 )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| ~ aElementOf0(X3,X2) ) ) )
| ~ sP2(X2,X0,X1) ) ),
inference(flattening,[],[f234]) ).
fof(f236,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ~ aSet0(X0)
| ? [X3] :
( ( ~ aElement0(X3)
| ~ aElementOf0(X3,X1)
| X2 = X3
| ~ aElementOf0(X3,X0) )
& ( ( aElement0(X3)
& aElementOf0(X3,X1)
& X2 != X3 )
| aElementOf0(X3,X0) ) ) )
& ( ( aSet0(X0)
& ! [X4] :
( ( aElementOf0(X4,X0)
| ~ aElement0(X4)
| ~ aElementOf0(X4,X1)
| X2 = X4 )
& ( ( aElement0(X4)
& aElementOf0(X4,X1)
& X2 != X4 )
| ~ aElementOf0(X4,X0) ) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f235]) ).
fof(f237,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ~ aSet0(X0)
| ( ( ~ aElement0(sK7(X0,X1,X2))
| ~ aElementOf0(sK7(X0,X1,X2),X1)
| sK7(X0,X1,X2) = X2
| ~ aElementOf0(sK7(X0,X1,X2),X0) )
& ( ( aElement0(sK7(X0,X1,X2))
& aElementOf0(sK7(X0,X1,X2),X1)
& sK7(X0,X1,X2) != X2 )
| aElementOf0(sK7(X0,X1,X2),X0) ) ) )
& ( ( aSet0(X0)
& ! [X4] :
( ( aElementOf0(X4,X0)
| ~ aElement0(X4)
| ~ aElementOf0(X4,X1)
| X2 = X4 )
& ( ( aElement0(X4)
& aElementOf0(X4,X1)
& X2 != X4 )
| ~ aElementOf0(X4,X0) ) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f236]) ).
fof(f243,plain,
! [X0] :
( ! [X1] :
( ( X1 = szmzizndt0(X0)
| ~ aElementOf0(X1,X0)
| ? [X2] :
( ~ sdtlseqdt0(X1,X2)
& aElementOf0(X2,X0) ) )
& ( ( aElementOf0(X1,X0)
& ! [X2] :
( sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,X0) ) )
| szmzizndt0(X0) != X1 ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(nnf_transformation,[],[f157]) ).
fof(f244,plain,
! [X0] :
( ! [X1] :
( ( X1 = szmzizndt0(X0)
| ~ aElementOf0(X1,X0)
| ? [X2] :
( ~ sdtlseqdt0(X1,X2)
& aElementOf0(X2,X0) ) )
& ( ( aElementOf0(X1,X0)
& ! [X2] :
( sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,X0) ) )
| szmzizndt0(X0) != X1 ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(flattening,[],[f243]) ).
fof(f245,plain,
! [X0] :
( ! [X1] :
( ( X1 = szmzizndt0(X0)
| ~ aElementOf0(X1,X0)
| ? [X2] :
( ~ sdtlseqdt0(X1,X2)
& aElementOf0(X2,X0) ) )
& ( ( aElementOf0(X1,X0)
& ! [X3] :
( sdtlseqdt0(X1,X3)
| ~ aElementOf0(X3,X0) ) )
| szmzizndt0(X0) != X1 ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(rectify,[],[f244]) ).
fof(f246,plain,
! [X0] :
( ! [X1] :
( ( X1 = szmzizndt0(X0)
| ~ aElementOf0(X1,X0)
| ( ~ sdtlseqdt0(X1,sK10(X0,X1))
& aElementOf0(sK10(X0,X1),X0) ) )
& ( ( aElementOf0(X1,X0)
& ! [X3] :
( sdtlseqdt0(X1,X3)
| ~ aElementOf0(X3,X0) ) )
| szmzizndt0(X0) != X1 ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0,X1))],[f245]) ).
fof(f259,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1 )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| ~ aElementOf0(X3,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(nnf_transformation,[],[f172]) ).
fof(f260,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1 )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| ~ aElementOf0(X3,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f259]) ).
fof(f261,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1 )
& ( ( aSubsetOf0(X4,X0)
& sbrdtbr0(X4) = X1 )
| ~ aElementOf0(X4,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(rectify,[],[f260]) ).
fof(f262,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ( ( ~ aSubsetOf0(sK14(X0,X1,X2),X0)
| sbrdtbr0(sK14(X0,X1,X2)) != X1
| ~ aElementOf0(sK14(X0,X1,X2),X2) )
& ( ( aSubsetOf0(sK14(X0,X1,X2),X0)
& sbrdtbr0(sK14(X0,X1,X2)) = X1 )
| aElementOf0(sK14(X0,X1,X2),X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1 )
& ( ( aSubsetOf0(X4,X0)
& sbrdtbr0(X4) = X1 )
| ~ aElementOf0(X4,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X3,sK14(X0,X1,X2))],[f261]) ).
fof(f278,plain,
( ~ aElementOf0(sK27,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK25),szmzizndt0(sdtlpdtrp0(xN,sK25))),xk))
& aSet0(sK27)
& aElementOf0(sK27,slbdtsldtrb0(sK26,xk))
& aSubsetOf0(sK26,sdtmndt0(sdtlpdtrp0(xN,sK25),szmzizndt0(sdtlpdtrp0(xN,sK25))))
& isCountable0(sK26)
& aElementOf0(sK25,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25,sK26,sK27]),skolemize(X0,sK25),skolemize(X1,sK26),skolemize(X2,sK27)],[f211]) ).
fof(f279,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f281,plain,
! [X0] :
( aSet0(X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f221]) ).
fof(f285,plain,
! [X0] :
( slcrc0 != X0
| ~ aSet0(X0)
| ~ isCountable0(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f287,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f225]) ).
fof(f293,plain,
! [X2,X0,X1] :
( ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| aSubsetOf0(X0,X2)
| ~ aSet0(X0)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(cnf_transformation,[],[f110]) ).
fof(f306,plain,
! [X2,X0,X1] :
( sP2(X2,X1,X0)
| sdtmndt0(X1,X0) != X2
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f233]) ).
fof(f312,plain,
! [X2,X0,X1] :
( ~ sP2(X0,X1,X2)
| aSet0(X0) ),
inference(cnf_transformation,[],[f237]) ).
fof(f317,plain,
! [X0,X1] :
( sP3(X1,X0)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f217]) ).
fof(f325,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f354,plain,
! [X0,X1] :
( aElementOf0(X1,X0)
| szmzizndt0(X0) != X1
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f246]) ).
fof(f379,plain,
! [X2,X0,X1,X4] :
( sbrdtbr0(X4) = X1
| ~ aElementOf0(X4,X2)
| slbdtsldtrb0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f262]) ).
fof(f380,plain,
! [X2,X0,X1,X4] :
( aSubsetOf0(X4,X0)
| ~ aElementOf0(X4,X2)
| slbdtsldtrb0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f262]) ).
fof(f381,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1
| slbdtsldtrb0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f262]) ).
fof(f437,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f80]) ).
fof(f443,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f200]) ).
fof(f444,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f200]) ).
fof(f454,plain,
aElementOf0(sK25,szNzAzT0),
inference(cnf_transformation,[],[f278]) ).
fof(f456,plain,
aSubsetOf0(sK26,sdtmndt0(sdtlpdtrp0(xN,sK25),szmzizndt0(sdtlpdtrp0(xN,sK25)))),
inference(cnf_transformation,[],[f278]) ).
fof(f457,plain,
aElementOf0(sK27,slbdtsldtrb0(sK26,xk)),
inference(cnf_transformation,[],[f278]) ).
fof(f458,plain,
aSet0(sK27),
inference(cnf_transformation,[],[f278]) ).
fof(f459,plain,
~ aElementOf0(sK27,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK25),szmzizndt0(sdtlpdtrp0(xN,sK25))),xk)),
inference(cnf_transformation,[],[f278]) ).
fof(f460,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f281]) ).
fof(f462,plain,
( ~ aSet0(slcrc0)
| ~ isCountable0(slcrc0) ),
inference(equality_resolution,[],[f285]) ).
fof(f465,plain,
! [X0,X1] :
( sP2(sdtmndt0(X1,X0),X1,X0)
| ~ sP3(X0,X1) ),
inference(equality_resolution,[],[f306]) ).
fof(f468,plain,
! [X0] :
( aElementOf0(szmzizndt0(X0),X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(equality_resolution,[],[f354]) ).
fof(f478,plain,
! [X2,X0,X4] :
( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| slbdtsldtrb0(X0,sbrdtbr0(X4)) != X2
| ~ aSet0(X0)
| ~ aElementOf0(sbrdtbr0(X4),szNzAzT0) ),
inference(equality_resolution,[],[f381]) ).
fof(f479,plain,
! [X0,X4] :
( aElementOf0(X4,slbdtsldtrb0(X0,sbrdtbr0(X4)))
| ~ aSubsetOf0(X4,X0)
| ~ aSet0(X0)
| ~ aElementOf0(sbrdtbr0(X4),szNzAzT0) ),
inference(equality_resolution,[],[f478]) ).
fof(f480,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
| aSubsetOf0(X4,X0)
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(equality_resolution,[],[f380]) ).
fof(f481,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
| sbrdtbr0(X4) = X1
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(equality_resolution,[],[f379]) ).
fof(f497,definition,
sF28 = sdtlpdtrp0(xN,sK25),
introduced(definition,[new_symbols(definition,[sF28])],[function_definition]) ).
fof(f498,plain,
sdtlpdtrp0(xN,sK25) = sF28,
inference(reorient_equations,[],[f497]) ).
fof(f499,definition,
sF29 = szmzizndt0(sF28),
introduced(definition,[new_symbols(definition,[sF29])],[function_definition]) ).
fof(f500,plain,
szmzizndt0(sF28) = sF29,
inference(reorient_equations,[],[f499]) ).
fof(f501,definition,
sF30 = sdtmndt0(sF28,sF29),
introduced(definition,[new_symbols(definition,[sF30])],[function_definition]) ).
fof(f502,plain,
sdtmndt0(sF28,sF29) = sF30,
inference(reorient_equations,[],[f501]) ).
fof(f503,definition,
sF31 = slbdtsldtrb0(sF30,xk),
introduced(definition,[new_symbols(definition,[sF31])],[function_definition]) ).
fof(f504,plain,
slbdtsldtrb0(sF30,xk) = sF31,
inference(reorient_equations,[],[f503]) ).
fof(f505,plain,
~ aElementOf0(sK27,sF31),
inference(definition_folding,[],[f459,f504,f502,f500,f498,f498]) ).
fof(f506,definition,
sF32 = slbdtsldtrb0(sK26,xk),
introduced(definition,[new_symbols(definition,[sF32])],[function_definition]) ).
fof(f507,plain,
slbdtsldtrb0(sK26,xk) = sF32,
inference(reorient_equations,[],[f506]) ).
fof(f508,plain,
aElementOf0(sK27,sF32),
inference(definition_folding,[],[f457,f507]) ).
fof(f509,plain,
aSubsetOf0(sK26,sF30),
inference(definition_folding,[],[f456,f502,f500,f498,f498]) ).
fof(f514,definition,
( spl33_1
<=> aSet0(slcrc0) ),
introduced(definition,[new_symbols(definition,[spl33_1])],[avatar_definition]) ).
fof(f523,definition,
( spl33_3
<=> isCountable0(slcrc0) ),
introduced(definition,[new_symbols(definition,[spl33_3])],[avatar_definition]) ).
fof(f525,plain,
( ~ isCountable0(slcrc0)
| spl33_3 ),
inference(avatar_component_clause,[],[f523]) ).
fof(f526,plain,
( ~ spl33_3
| ~ spl33_1 ),
inference(avatar_split_clause,[],[f462,f514,f523]) ).
fof(f527,plain,
spl33_1,
inference(avatar_split_clause,[],[f460,f514]) ).
fof(f530,plain,
( isCountable0(sF28)
| ~ aElementOf0(sK25,szNzAzT0) ),
inference(superposition,[],[f443,f498]) ).
fof(f531,plain,
isCountable0(sF28),
inference(forward_subsumption_resolution,[],[f530,f454]) ).
fof(f532,plain,
( aElementOf0(sF29,sF28)
| ~ aSubsetOf0(sF28,szNzAzT0)
| slcrc0 = sF28 ),
inference(superposition,[],[f468,f500]) ).
fof(f534,definition,
( spl33_4
<=> slcrc0 = sF28 ),
introduced(definition,[new_symbols(definition,[spl33_4])],[avatar_definition]) ).
fof(f536,plain,
( slcrc0 = sF28
| ~ spl33_4 ),
inference(avatar_component_clause,[],[f534]) ).
fof(f538,definition,
( spl33_5
<=> aSubsetOf0(sF28,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl33_5])],[avatar_definition]) ).
fof(f540,plain,
( ~ aSubsetOf0(sF28,szNzAzT0)
| spl33_5 ),
inference(avatar_component_clause,[],[f538]) ).
fof(f542,definition,
( spl33_6
<=> aElementOf0(sF29,sF28) ),
introduced(definition,[new_symbols(definition,[spl33_6])],[avatar_definition]) ).
fof(f544,plain,
( aElementOf0(sF29,sF28)
| ~ spl33_6 ),
inference(avatar_component_clause,[],[f542]) ).
fof(f545,plain,
( spl33_4
| ~ spl33_5
| spl33_6 ),
inference(avatar_split_clause,[],[f532,f542,f538,f534]) ).
fof(f548,plain,
! [X0] :
( ~ aElementOf0(X0,sF32)
| sbrdtbr0(X0) = xk
| ~ aSet0(sK26)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(superposition,[],[f481,f507]) ).
fof(f549,plain,
! [X0] :
( ~ aElementOf0(X0,sF32)
| sbrdtbr0(X0) = xk
| ~ aSet0(sK26) ),
inference(forward_subsumption_resolution,[],[f548,f437]) ).
fof(f552,definition,
( spl33_7
<=> aSet0(sK26) ),
introduced(definition,[new_symbols(definition,[spl33_7])],[avatar_definition]) ).
fof(f553,plain,
( aSet0(sK26)
| ~ spl33_7 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f554,plain,
( ~ aSet0(sK26)
| spl33_7 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f556,definition,
( spl33_8
<=> ! [X0] :
( ~ aElementOf0(X0,sF32)
| sbrdtbr0(X0) = xk ) ),
introduced(definition,[new_symbols(definition,[spl33_8])],[avatar_definition]) ).
fof(f557,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF32)
| sbrdtbr0(X0) = xk )
| ~ spl33_8 ),
inference(avatar_component_clause,[],[f556]) ).
fof(f558,plain,
( ~ spl33_7
| spl33_8 ),
inference(avatar_split_clause,[],[f549,f556,f552]) ).
fof(f560,definition,
( spl33_9
<=> aSet0(sF30) ),
introduced(definition,[new_symbols(definition,[spl33_9])],[avatar_definition]) ).
fof(f561,plain,
( aSet0(sF30)
| ~ spl33_9 ),
inference(avatar_component_clause,[],[f560]) ).
fof(f562,plain,
( ~ aSet0(sF30)
| spl33_9 ),
inference(avatar_component_clause,[],[f560]) ).
fof(f569,plain,
! [X0] :
( ~ aElementOf0(X0,sF32)
| aSubsetOf0(X0,sK26)
| ~ aSet0(sK26)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(superposition,[],[f480,f507]) ).
fof(f598,definition,
( spl33_11
<=> sP3(sF29,sF28) ),
introduced(definition,[new_symbols(definition,[spl33_11])],[avatar_definition]) ).
fof(f599,plain,
( sP3(sF29,sF28)
| ~ spl33_11 ),
inference(avatar_component_clause,[],[f598]) ).
fof(f600,plain,
( ~ sP3(sF29,sF28)
| spl33_11 ),
inference(avatar_component_clause,[],[f598]) ).
fof(f615,definition,
( spl33_14
<=> aSet0(sF28) ),
introduced(definition,[new_symbols(definition,[spl33_14])],[avatar_definition]) ).
fof(f616,plain,
( aSet0(sF28)
| ~ spl33_14 ),
inference(avatar_component_clause,[],[f615]) ).
fof(f617,plain,
( ~ aSet0(sF28)
| spl33_14 ),
inference(avatar_component_clause,[],[f615]) ).
fof(f620,plain,
( aSet0(sK26)
| ~ aSet0(sF30) ),
inference(resolution,[],[f287,f509]) ).
fof(f626,definition,
( spl33_15
<=> aElement0(sF29) ),
introduced(definition,[new_symbols(definition,[spl33_15])],[avatar_definition]) ).
fof(f627,plain,
( aElement0(sF29)
| ~ spl33_15 ),
inference(avatar_component_clause,[],[f626]) ).
fof(f628,plain,
( ~ aElement0(sF29)
| spl33_15 ),
inference(avatar_component_clause,[],[f626]) ).
fof(f634,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X0))
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f444,f287]) ).
fof(f636,plain,
( aSubsetOf0(sF28,szNzAzT0)
| ~ aElementOf0(sK25,szNzAzT0) ),
inference(superposition,[],[f444,f498]) ).
fof(f637,plain,
( ~ aElementOf0(sK25,szNzAzT0)
| spl33_5 ),
inference(forward_subsumption_resolution,[],[f636,f540]) ).
fof(f639,plain,
! [X0] :
( aSet0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f634,f325]) ).
fof(f640,plain,
( $false
| spl33_5 ),
inference(forward_subsumption_resolution,[],[f637,f454]) ).
fof(f641,plain,
spl33_5,
inference(avatar_contradiction_clause,[],[f640]) ).
fof(f647,plain,
( aSet0(sF28)
| ~ aElementOf0(sK25,szNzAzT0) ),
inference(superposition,[],[f639,f498]) ).
fof(f648,plain,
( ~ aElementOf0(sK25,szNzAzT0)
| spl33_14 ),
inference(forward_subsumption_resolution,[],[f647,f617]) ).
fof(f649,plain,
( $false
| spl33_14 ),
inference(forward_subsumption_resolution,[],[f648,f454]) ).
fof(f650,plain,
spl33_14,
inference(avatar_contradiction_clause,[],[f649]) ).
fof(f655,plain,
( isCountable0(slcrc0)
| ~ spl33_4 ),
inference(superposition,[],[f531,f536]) ).
fof(f658,plain,
( $false
| spl33_3
| ~ spl33_4 ),
inference(forward_subsumption_resolution,[],[f655,f525]) ).
fof(f659,plain,
( spl33_3
| ~ spl33_4 ),
inference(avatar_contradiction_clause,[],[f658]) ).
fof(f708,plain,
! [X0,X1] :
( aSet0(sdtmndt0(X0,X1))
| ~ sP3(X1,X0) ),
inference(resolution,[],[f312,f465]) ).
fof(f709,plain,
( aSet0(sF30)
| ~ sP3(sF29,sF28) ),
inference(superposition,[],[f708,f502]) ).
fof(f715,plain,
( aElement0(sF29)
| ~ aSet0(sF28)
| ~ spl33_6 ),
inference(resolution,[],[f279,f544]) ).
fof(f716,plain,
( ~ aSet0(sF28)
| ~ spl33_6
| spl33_15 ),
inference(forward_subsumption_resolution,[],[f715,f628]) ).
fof(f729,plain,
( $false
| ~ spl33_6
| ~ spl33_14
| spl33_15 ),
inference(forward_subsumption_resolution,[],[f716,f616]) ).
fof(f730,plain,
( ~ spl33_6
| ~ spl33_14
| spl33_15 ),
inference(avatar_contradiction_clause,[],[f729]) ).
fof(f821,plain,
( ~ aSet0(sF28)
| ~ aElement0(sF29)
| spl33_11 ),
inference(resolution,[],[f317,f600]) ).
fof(f822,plain,
( ~ aElement0(sF29)
| spl33_11
| ~ spl33_14 ),
inference(forward_subsumption_resolution,[],[f821,f616]) ).
fof(f823,plain,
( $false
| spl33_11
| ~ spl33_14
| ~ spl33_15 ),
inference(forward_subsumption_resolution,[],[f822,f627]) ).
fof(f824,plain,
( spl33_11
| ~ spl33_14
| ~ spl33_15 ),
inference(avatar_contradiction_clause,[],[f823]) ).
fof(f827,plain,
( ~ sP3(sF29,sF28)
| spl33_9 ),
inference(forward_subsumption_resolution,[],[f709,f562]) ).
fof(f850,plain,
( $false
| spl33_9
| ~ spl33_11 ),
inference(forward_subsumption_resolution,[],[f827,f599]) ).
fof(f851,plain,
( spl33_9
| ~ spl33_11 ),
inference(avatar_contradiction_clause,[],[f850]) ).
fof(f856,plain,
( ~ aSet0(sF30)
| spl33_7 ),
inference(forward_subsumption_resolution,[],[f620,f554]) ).
fof(f862,plain,
( $false
| spl33_7
| ~ spl33_9 ),
inference(forward_subsumption_resolution,[],[f856,f561]) ).
fof(f863,plain,
( spl33_7
| ~ spl33_9 ),
inference(avatar_contradiction_clause,[],[f862]) ).
fof(f881,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF32)
| aSubsetOf0(X0,sK26)
| ~ aElementOf0(xk,szNzAzT0) )
| ~ spl33_7 ),
inference(forward_subsumption_resolution,[],[f569,f553]) ).
fof(f885,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF32)
| aSubsetOf0(X0,sK26) )
| ~ spl33_7 ),
inference(forward_subsumption_resolution,[],[f881,f437]) ).
fof(f915,plain,
( aSubsetOf0(sK27,sK26)
| ~ spl33_7 ),
inference(resolution,[],[f885,f508]) ).
fof(f1299,plain,
! [X0] :
( ~ aSubsetOf0(X0,sK26)
| aSubsetOf0(X0,sF30)
| ~ aSet0(X0)
| ~ aSet0(sK26)
| ~ aSet0(sF30) ),
inference(resolution,[],[f293,f509]) ).
fof(f1309,plain,
( ! [X0] :
( ~ aSubsetOf0(X0,sK26)
| aSubsetOf0(X0,sF30)
| ~ aSet0(X0)
| ~ aSet0(sF30) )
| ~ spl33_7 ),
inference(forward_subsumption_resolution,[],[f1299,f553]) ).
fof(f1320,plain,
( ! [X0] :
( ~ aSubsetOf0(X0,sK26)
| aSubsetOf0(X0,sF30)
| ~ aSet0(X0) )
| ~ spl33_7
| ~ spl33_9 ),
inference(forward_subsumption_resolution,[],[f1309,f561]) ).
fof(f2019,plain,
( xk = sbrdtbr0(sK27)
| ~ spl33_8 ),
inference(resolution,[],[f557,f508]) ).
fof(f2022,plain,
( ! [X0] :
( aElementOf0(sK27,slbdtsldtrb0(X0,xk))
| ~ aSubsetOf0(sK27,X0)
| ~ aSet0(X0)
| ~ aElementOf0(xk,szNzAzT0) )
| ~ spl33_8 ),
inference(superposition,[],[f479,f2019]) ).
fof(f2023,plain,
( ! [X0] :
( aElementOf0(sK27,slbdtsldtrb0(X0,xk))
| ~ aSubsetOf0(sK27,X0)
| ~ aSet0(X0) )
| ~ spl33_8 ),
inference(forward_subsumption_resolution,[],[f2022,f437]) ).
fof(f2031,plain,
( aElementOf0(sK27,sF31)
| ~ aSubsetOf0(sK27,sF30)
| ~ aSet0(sF30)
| ~ spl33_8 ),
inference(superposition,[],[f2023,f504]) ).
fof(f2036,plain,
( ~ aSubsetOf0(sK27,sF30)
| ~ aSet0(sF30)
| ~ spl33_8 ),
inference(forward_subsumption_resolution,[],[f2031,f505]) ).
fof(f2038,plain,
( ~ aSubsetOf0(sK27,sF30)
| ~ spl33_8
| ~ spl33_9 ),
inference(forward_subsumption_resolution,[],[f2036,f561]) ).
fof(f2155,plain,
( aSubsetOf0(sK27,sF30)
| ~ aSet0(sK27)
| ~ spl33_7
| ~ spl33_9 ),
inference(resolution,[],[f1320,f915]) ).
fof(f2157,plain,
( ~ aSet0(sK27)
| ~ spl33_7
| ~ spl33_8
| ~ spl33_9 ),
inference(forward_subsumption_resolution,[],[f2155,f2038]) ).
fof(f2159,plain,
( $false
| ~ spl33_7
| ~ spl33_8
| ~ spl33_9 ),
inference(forward_subsumption_resolution,[],[f2157,f458]) ).
fof(f2160,plain,
( ~ spl33_7
| ~ spl33_8
| ~ spl33_9 ),
inference(avatar_contradiction_clause,[],[f2159]) ).
cnf(s2,plain,
( ~ spl33_1
| ~ spl33_3 ),
inference(sat_conversion,[],[f526]) ).
cnf(s3,plain,
spl33_1,
inference(sat_conversion,[],[f527]) ).
cnf(s4,plain,
( spl33_4
| ~ spl33_5
| spl33_6 ),
inference(sat_conversion,[],[f545]) ).
cnf(s5,plain,
( ~ spl33_7
| spl33_8 ),
inference(sat_conversion,[],[f558]) ).
cnf(s10,plain,
spl33_5,
inference(sat_conversion,[],[f641]) ).
cnf(s12,plain,
spl33_14,
inference(sat_conversion,[],[f650]) ).
cnf(s13,plain,
( spl33_3
| ~ spl33_4 ),
inference(sat_conversion,[],[f659]) ).
cnf(s19,plain,
( ~ spl33_6
| ~ spl33_14
| spl33_15 ),
inference(sat_conversion,[],[f730]) ).
cnf(s25,plain,
( spl33_11
| ~ spl33_14
| ~ spl33_15 ),
inference(sat_conversion,[],[f824]) ).
cnf(s33,plain,
( spl33_9
| ~ spl33_11 ),
inference(sat_conversion,[],[f851]) ).
cnf(s34,plain,
( spl33_7
| ~ spl33_9 ),
inference(sat_conversion,[],[f863]) ).
cnf(s94,plain,
( ~ spl33_7
| ~ spl33_8
| ~ spl33_9 ),
inference(sat_conversion,[],[f2160]) ).
cnf(s98,plain,
( spl33_4
| spl33_6 ),
inference(rat,[],[s4,s10]) ).
cnf(s99,plain,
~ spl33_3,
inference(rat,[],[s2,s3]) ).
cnf(s100,plain,
~ spl33_4,
inference(rat,[],[s13,s99]) ).
cnf(s102,plain,
spl33_6,
inference(rat,[],[s98,s100]) ).
cnf(s103,plain,
spl33_15,
inference(rat,[],[s19,s12,s102]) ).
cnf(s104,plain,
spl33_11,
inference(rat,[],[s25,s12,s103]) ).
cnf(s106,plain,
spl33_9,
inference(rat,[],[s33,s104]) ).
cnf(s109,plain,
spl33_7,
inference(rat,[],[s34,s106]) ).
cnf(s112,plain,
~ spl33_8,
inference(rat,[],[s94,s106,s109]) ).
cnf(s115,plain,
$false,
inference(rat,[],[s5,s112,s109]) ).
fof(f2162,plain,
$false,
inference(avatar_sat_refutation,[],[s115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM588+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.33 % Computer : n012.cluster.edu
% 0.03/0.33 % Model : x86_64 x86_64
% 0.03/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.33 % Memory : 8046.5625MB
% 0.03/0.33 % OS : Linux 6.8.0-71-generic
% 0.03/0.33 % CPULimit : 300
% 0.03/0.33 % WCLimit : 300
% 0.03/0.33 % DateTime : Sun Sep 27 20:37:50 UTC 2026
% 0.03/0.33 % CPUTime :
% 0.03/0.33 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.35 Running first-order theorem proving
% 0.03/0.35 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.16/1.30 % (2715852)Detected formulas, will run a generic FOF schedule.
% 3.16/1.30 % (2715858)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=566576611:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.16/1.30 % (2715859)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1837589028:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.16/1.30 % (2715863)dis-21_1_sil=8000:lcm=predicate:random_seed=1636900647:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.16/1.30 % (2715862)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3125530100:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.16/1.30 % (2715860)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1718478027:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.16/1.30 % (2715861)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4278988713:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.16/1.30 % (2715857)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3722583179:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.16/1.30 % (2715863)Instruction limit reached!
% 3.16/1.30 % (2715863)------------------------------
% 3.16/1.30 % (2715863)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.16/1.30 % (2715863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/1.30 % (2715863)CaDiCaL version: 2.1.3
% 3.16/1.30 % (2715863)Termination reason: Instruction limit
% 3.16/1.30 % (2715863)Termination phase: Saturation
% 3.16/1.30 % (2715863)Time elapsed: 0.035 s
% 3.16/1.30 % (2715863)Peak memory usage: 88 MB
% 3.16/1.30 % (2715863)Instructions burned: 133 (million)
% 3.16/1.30 % (2715860)Instruction limit reached!
% 3.16/1.30 % (2715860)------------------------------
% 3.16/1.30 % (2715860)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.16/1.30 % (2715860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/1.30 % (2715860)CaDiCaL version: 2.1.3
% 3.16/1.30 % (2715860)Termination reason: Instruction limit
% 3.16/1.30 % (2715860)Termination phase: Saturation
% 3.16/1.30 % (2715860)Time elapsed: 0.036 s
% 3.16/1.30 % (2715860)Peak memory usage: 89 MB
% 3.16/1.30 % (2715860)Instructions burned: 112 (million)
% 3.16/1.30 % (2715861)Instruction limit reached!
% 3.16/1.30 % (2715861)------------------------------
% 3.16/1.30 % (2715861)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.16/1.30 % (2715861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/1.30 % (2715861)CaDiCaL version: 2.1.3
% 3.16/1.30 % (2715861)Termination reason: Instruction limit
% 3.16/1.30 % (2715861)Termination phase: Saturation
% 3.16/1.30 % (2715861)Time elapsed: 0.039 s
% 3.16/1.30 % (2715861)Peak memory usage: 88 MB
% 3.16/1.30 % (2715861)Instructions burned: 119 (million)
% 3.16/1.30 % (2715862)Instruction limit reached!
% 3.16/1.30 % (2715862)------------------------------
% 3.16/1.30 % (2715862)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.16/1.30 % (2715862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/1.30 % (2715862)CaDiCaL version: 2.1.3
% 3.16/1.30 % (2715862)Termination reason: Instruction limit
% 3.16/1.30 % (2715862)Termination phase: Saturation
% 3.16/1.30 % (2715862)Time elapsed: 0.056 s
% 3.16/1.30 % (2715862)Peak memory usage: 90 MB
% 3.16/1.30 % (2715862)Instructions burned: 141 (million)
% 3.16/1.30 % (2715873)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2281061609:i=325:sd=1:ss=axioms:sgt=32_2998 on theBenchmark for (2998ds/325Mi)
% 3.16/1.30 % (2715871)lrs+10_1_sil=8000:sp=occurrence:random_seed=3770048949:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.16/1.30 % (2715872)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3488666932:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 3.16/1.30 % (2715874)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1412778244:s2a=on:i=248:s2at=1.23:gtg=position_2998 on theBenchmark for (2998ds/248Mi)
% 3.16/1.30 % (2715872)Instruction limit reached!
% 3.16/1.30 % (2715872)------------------------------
% 3.16/1.30 % (2715872)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.16/1.30 % (2715872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/1.30 % (2715872)CaDiCaL version: 2.1.3
% 3.16/1.30 % (2715872)Termination reason: Instruction limit
% 3.16/1.30 % (2715872)Termination phase: Saturation
% 3.16/1.30 % (2715872)Time elapsed: 0.048 s
% 3.16/1.30 % (2715872)Peak memory usage: 89 MB
% 3.16/1.30 % (2715872)Instructions burned: 158 (million)
% 3.16/1.30 % (2715871)Instruction limit reached!
% 3.16/1.30 % (2715871)------------------------------
% 3.16/1.30 % (2715871)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.16/1.30 % (2715871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/1.30 % (2715871)CaDiCaL version: 2.1.3
% 3.16/1.30 % (2715871)Termination reason: Instruction limit
% 3.16/1.30 % (2715871)Termination phase: Saturation
% 3.16/1.30 % (2715871)Time elapsed: 0.100 s
% 3.16/1.30 % (2715871)Peak memory usage: 92 MB
% 3.16/1.30 % (2715871)Instructions burned: 288 (million)
% 3.16/1.30 % (2715874)Instruction limit reached!
% 3.16/1.30 % (2715874)------------------------------
% 3.16/1.30 % (2715874)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.16/1.30 % (2715874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/1.30 % (2715874)CaDiCaL version: 2.1.3
% 3.16/1.30 % (2715874)Termination reason: Instruction limit
% 3.16/1.30 % (2715874)Termination phase: Saturation
% 3.16/1.30 % (2715874)Time elapsed: 0.081 s
% 3.16/1.30 % (2715874)Peak memory usage: 92 MB
% 3.16/1.30 % (2715874)Instructions burned: 251 (million)
% 3.16/1.30 % (2715873)Instruction limit reached!
% 3.16/1.30 % (2715873)------------------------------
% 3.16/1.30 % (2715873)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.16/1.30 % (2715873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/1.30 % (2715873)CaDiCaL version: 2.1.3
% 3.16/1.30 % (2715873)Termination reason: Instruction limit
% 3.16/1.30 % (2715873)Termination phase: Saturation
% 3.16/1.30 % (2715873)Time elapsed: 0.123 s
% 3.16/1.30 % (2715873)Peak memory usage: 92 MB
% 3.16/1.30 % (2715873)Instructions burned: 327 (million)
% 3.16/1.30 % (2715879)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2888364756:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 3.16/1.30 % (2715880)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2244237647:i=2350_2996 on theBenchmark for (2996ds/2350Mi)
% 3.16/1.30 % (2715881)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2442595893:cts=off:i=113:fsr=off:ss=included:sgt=4_2996 on theBenchmark for (2996ds/113Mi)
% 3.16/1.30 % (2715882)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1632726174:i=127:av=off:fsr=off:sup=off_2995 on theBenchmark for (2995ds/127Mi)
% 3.16/1.30 % (2715881)Instruction limit reached!
% 3.16/1.30 % (2715881)------------------------------
% 3.16/1.30 % (2715881)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.16/1.30 % (2715881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/1.30 % (2715881)CaDiCaL version: 2.1.3
% 3.16/1.30 % (2715881)Termination reason: Instruction limit
% 3.16/1.30 % (2715881)Termination phase: Saturation
% 3.16/1.30 % (2715881)Time elapsed: 0.041 s
% 3.16/1.30 % (2715881)Peak memory usage: 90 MB
% 3.16/1.30 % (2715881)Instructions burned: 114 (million)
% 3.16/1.30 % (2715879)Instruction limit reached!
% 3.16/1.30 % (2715879)------------------------------
% 3.16/1.30 % (2715879)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.16/1.30 % (2715879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/1.30 % (2715879)CaDiCaL version: 2.1.3
% 3.16/1.30 % (2715879)Termination reason: Instruction limit
% 3.16/1.30 % (2715879)Termination phase: Saturation
% 3.16/1.30 % (2715879)Time elapsed: 0.099 s
% 3.16/1.30 % (2715879)Peak memory usage: 90 MB
% 3.16/1.30 % (2715879)Instructions burned: 296 (million)
% 3.16/1.30 % (2715882)Instruction limit reached!
% 3.16/1.30 % (2715882)------------------------------
% 3.16/1.30 % (2715882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.16/1.30 % (2715882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/1.30 % (2715882)CaDiCaL version: 2.1.3
% 3.16/1.30 % (2715882)Termination reason: Instruction limit
% 3.16/1.30 % (2715882)Termination phase: Saturation
% 3.16/1.30 % (2715882)Time elapsed: 0.037 s
% 3.16/1.30 % (2715882)Peak memory usage: 89 MB
% 3.16/1.30 % (2715882)Instructions burned: 129 (million)
% 3.16/1.30 % (2715857)First to succeed.
% 3.16/1.30 % (2715857)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2715852"
% 3.16/1.30 % (2715887)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3039445676:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 3.16/1.30 % (2715888)lrs+10_1_sil=8000:sp=occurrence:random_seed=614155864:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2994 on theBenchmark for (2994ds/907Mi)
% 3.16/1.30 % (2715889)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2604796751:i=437:sd=1:aac=none:ss=included_2994 on theBenchmark for (2994ds/437Mi)
% 3.16/1.30 % (2715887)Instruction limit reached!
% 3.16/1.30 % (2715887)------------------------------
% 3.16/1.30 % (2715887)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.16/1.30 % (2715887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/1.30 % (2715887)CaDiCaL version: 2.1.3
% 3.16/1.30 % (2715887)Termination reason: Instruction limit
% 3.16/1.30 % (2715887)Termination phase: Saturation
% 3.16/1.30 % (2715887)Time elapsed: 0.038 s
% 3.16/1.30 % (2715887)Peak memory usage: 89 MB
% 3.16/1.30 % (2715887)Instructions burned: 115 (million)
% 3.16/1.30 % (2715889)Also succeeded, but the first one will report.
% 3.16/1.30 % (2715857)Refutation found. Thanks to Tanya!
% 3.16/1.30 % SZS status Theorem for theBenchmark
% 3.16/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.16/1.40 % (2715857)------------------------------
% 3.16/1.40 % (2715857)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.16/1.40 % (2715857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/1.40 % (2715857)CaDiCaL version: 2.1.3
% 3.16/1.40 % (2715857)Termination reason: Refutation
% 3.16/1.40 % (2715857)Time elapsed: 0.447 s
% 3.16/1.40 % (2715857)Peak memory usage: 130 MB
% 3.16/1.40 % (2715857)Instructions burned: 1194 (million)
% 3.16/1.40 % (2715857)------------------------------
% 3.16/1.40 % (2715857)------------------------------
% 3.16/1.40 % (2715852)Success in time 0.75 s
% 3.16/1.40 % Vampire exiting
%------------------------------------------------------------------------------