%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM569+3 : 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 : n018.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 12:15:47 PM UTC 2026
% Result : Theorem 7.13s 7.22s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 21
% Syntax : Number of formulae : 165 ( 24 unt; 16 def)
% Number of atoms : 635 ( 51 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 746 ( 276 ~; 271 |; 151 &)
% ( 17 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 13 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 120 ( 0 sgn 108 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f27,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( X0 = sz00
| ? [X1] :
( aElementOf0(X1,szNzAzT0)
& X0 = szszuzczcdt0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtra) ).
fof(f39,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> iLess0(X0,szszuzczcdt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
fof(f75,axiom,
( aSet0(xS)
& ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(f81,axiom,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( ( ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,X0)) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X1) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,X0))
& X1 != szmzizndt0(sdtlpdtrp0(xN,X0)) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3623) ).
fof(f82,conjecture,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( iLess0(X1,X0)
=> ( aSet0(sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> aElementOf0(X2,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X1)) ) ) )
=> ( ( ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f83,negated_conjecture,
~ ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( iLess0(X1,X0)
=> ( aSet0(sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> aElementOf0(X2,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X1)) ) ) )
=> ( ( ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,X0)) ) ) ),
inference(negated_conjecture,[status(cth)],[f82]) ).
fof(f93,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( ( ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,X0)) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) ) ),
inference(rectify,[],[f81]) ).
fof(f94,plain,
~ ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( iLess0(X1,X0)
=> ( aSet0(sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> aElementOf0(X2,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X1)) ) ) )
=> ( ( ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X0))
=> aElementOf0(X3,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,X0)) ) ) ),
inference(rectify,[],[f83]) ).
fof(f127,plain,
! [X0] :
( X0 = sz00
| ? [X1] :
( aElementOf0(X1,szNzAzT0)
& X0 = szszuzczcdt0(X1) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f128,plain,
! [X0] :
( X0 = sz00
| ? [X1] :
( aElementOf0(X1,szNzAzT0)
& X0 = szszuzczcdt0(X1) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f127]) ).
fof(f142,plain,
! [X0] :
( iLess0(X0,szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f194,plain,
( aSet0(xS)
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) )
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
inference(ennf_transformation,[],[f75]) ).
fof(f199,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f93]) ).
fof(f200,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f199]) ).
fof(f201,plain,
? [X0] :
( ( ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ? [X3] :
( ~ aElementOf0(X3,szNzAzT0)
& aElementOf0(X3,sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0)) )
& ! [X1] :
( ( aSet0(sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X1)) )
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X1)) )
| ~ iLess0(X1,X0)
| ~ aElementOf0(X1,szNzAzT0) )
& aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f94]) ).
fof(f202,plain,
? [X0] :
( ( ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ? [X3] :
( ~ aElementOf0(X3,szNzAzT0)
& aElementOf0(X3,sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0)) )
& ! [X1] :
( ( aSet0(sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X1)) )
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X1)) )
| ~ iLess0(X1,X0)
| ~ aElementOf0(X1,szNzAzT0) )
& aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f201]) ).
fof(f214,definition,
! [X0] :
( ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
| ~ sP8(X0) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f215,definition,
! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sP8(X0)
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ sP9(X0) ),
introduced(definition,[new_symbols(definition,[sP9])],[predicate_definition_introduction]) ).
fof(f216,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( sP9(X0)
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(definition_folding,[],[f200,f215,f214]) ).
fof(f237,plain,
! [X0] :
( X0 = sz00
| ( aElementOf0(sK14(X0),szNzAzT0)
& szszuzczcdt0(sK14(X0)) = X0 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X1,sK14(X0))],[f128]) ).
fof(f292,plain,
! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sP8(X0)
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ sP9(X0) ),
inference(nnf_transformation,[],[f215]) ).
fof(f293,plain,
! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sP8(X0)
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ sP9(X0) ),
inference(rectify,[],[f292]) ).
fof(f294,plain,
! [X0] :
( ! [X3] :
( ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X3)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X3 )
& ( ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 )
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
| ~ sP8(X0) ),
inference(nnf_transformation,[],[f214]) ).
fof(f295,plain,
! [X0] :
( ! [X3] :
( ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X3)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X3 )
& ( ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 )
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
| ~ sP8(X0) ),
inference(flattening,[],[f294]) ).
fof(f296,plain,
! [X0] :
( ! [X1] :
( ( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X1 )
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
| ~ sP8(X0) ),
inference(rectify,[],[f295]) ).
fof(f297,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( sP9(X0)
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ( ~ aElementOf0(sK39(X0),szNzAzT0)
& aElementOf0(sK39(X0),sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(X1,sK39(X0))],[f216]) ).
fof(f298,plain,
? [X0] :
( ( ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0)) )
& ! [X2] :
( ( aSet0(sdtlpdtrp0(xN,X2))
& ! [X3] :
( aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X2)) )
& aSubsetOf0(sdtlpdtrp0(xN,X2),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X2)) )
| ~ iLess0(X2,X0)
| ~ aElementOf0(X2,szNzAzT0) )
& aElementOf0(X0,szNzAzT0) ),
inference(rectify,[],[f202]) ).
fof(f299,plain,
( ( ( ( ~ aSet0(sdtlpdtrp0(xN,sK40))
| ( ~ aElementOf0(sK41,szNzAzT0)
& aElementOf0(sK41,sdtlpdtrp0(xN,sK40)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,sK40),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,sK40)) )
& ! [X2] :
( ( aSet0(sdtlpdtrp0(xN,X2))
& ! [X3] :
( aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X2)) )
& aSubsetOf0(sdtlpdtrp0(xN,X2),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X2)) )
| ~ iLess0(X2,sK40)
| ~ aElementOf0(X2,szNzAzT0) )
& aElementOf0(sK40,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40,sK41]),skolemize(X0,sK40),skolemize(X1,sK41)],[f298]) ).
fof(f351,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| szszuzczcdt0(sK14(X0)) = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f237]) ).
fof(f352,plain,
! [X0] :
( aElementOf0(sK14(X0),szNzAzT0)
| sz00 = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f237]) ).
fof(f363,plain,
! [X0] :
( iLess0(X0,szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f446,plain,
isCountable0(xS),
inference(cnf_transformation,[],[f194]) ).
fof(f447,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f194]) ).
fof(f500,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f293]) ).
fof(f502,plain,
! [X2,X0] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f293]) ).
fof(f503,plain,
! [X0] :
( aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f293]) ).
fof(f504,plain,
! [X0] :
( sP8(X0)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f293]) ).
fof(f509,plain,
! [X0,X1] :
( ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| aElementOf0(X1,sdtlpdtrp0(xN,X0))
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f296]) ).
fof(f512,plain,
! [X0] :
( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| sP9(X0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f297]) ).
fof(f515,plain,
xS = sdtlpdtrp0(xN,sz00),
inference(cnf_transformation,[],[f297]) ).
fof(f518,plain,
aElementOf0(sK40,szNzAzT0),
inference(cnf_transformation,[],[f299]) ).
fof(f519,plain,
! [X2] :
( isCountable0(sdtlpdtrp0(xN,X2))
| ~ iLess0(X2,sK40)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(cnf_transformation,[],[f299]) ).
fof(f520,plain,
! [X2] :
( aSubsetOf0(sdtlpdtrp0(xN,X2),szNzAzT0)
| ~ iLess0(X2,sK40)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(cnf_transformation,[],[f299]) ).
fof(f521,plain,
! [X2,X3] :
( aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X2))
| ~ iLess0(X2,sK40)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(cnf_transformation,[],[f299]) ).
fof(f523,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,sK40),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,sK40)) ),
inference(cnf_transformation,[],[f299]) ).
fof(f524,plain,
( ~ aSet0(sdtlpdtrp0(xN,sK40))
| aElementOf0(sK41,sdtlpdtrp0(xN,sK40))
| ~ isCountable0(sdtlpdtrp0(xN,sK40)) ),
inference(cnf_transformation,[],[f299]) ).
fof(f525,plain,
( ~ aSet0(sdtlpdtrp0(xN,sK40))
| ~ aElementOf0(sK41,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,sK40)) ),
inference(cnf_transformation,[],[f299]) ).
fof(f569,definition,
sF42 = sdtlpdtrp0(xN,sK40),
introduced(definition,[new_symbols(definition,[sF42])],[function_definition]) ).
fof(f570,plain,
sdtlpdtrp0(xN,sK40) = sF42,
inference(reorient_equations,[],[f569]) ).
fof(f571,plain,
( ~ aSet0(sF42)
| ~ aElementOf0(sK41,szNzAzT0)
| ~ isCountable0(sF42) ),
inference(definition_folding,[],[f525,f570,f570]) ).
fof(f572,plain,
( ~ aSet0(sF42)
| aElementOf0(sK41,sF42)
| ~ isCountable0(sF42) ),
inference(definition_folding,[],[f524,f570,f570,f570]) ).
fof(f573,plain,
( ~ aSubsetOf0(sF42,szNzAzT0)
| ~ isCountable0(sF42) ),
inference(definition_folding,[],[f523,f570,f570]) ).
fof(f574,definition,
! [X2] : sF43(X2) = sdtlpdtrp0(xN,X2),
introduced(definition,[new_symbols(definition,[sF43])],[function_definition]) ).
fof(f575,plain,
! [X2] : sdtlpdtrp0(xN,X2) = sF43(X2),
inference(reorient_equations,[],[f574]) ).
fof(f577,plain,
! [X2,X3] :
( ~ aElementOf0(X3,sF43(X2))
| aElementOf0(X3,szNzAzT0)
| ~ iLess0(X2,sK40)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(definition_folding,[],[f521,f575]) ).
fof(f578,plain,
! [X2] :
( aSubsetOf0(sF43(X2),szNzAzT0)
| ~ iLess0(X2,sK40)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(definition_folding,[],[f520,f575]) ).
fof(f579,plain,
! [X2] :
( ~ iLess0(X2,sK40)
| isCountable0(sF43(X2))
| ~ aElementOf0(X2,szNzAzT0) ),
inference(definition_folding,[],[f519,f575]) ).
fof(f582,definition,
( spl44_1
<=> isCountable0(sF42) ),
introduced(definition,[new_symbols(definition,[spl44_1])],[avatar_definition]) ).
fof(f584,plain,
( ~ isCountable0(sF42)
| spl44_1 ),
inference(avatar_component_clause,[],[f582]) ).
fof(f586,definition,
( spl44_2
<=> aSubsetOf0(sF42,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl44_2])],[avatar_definition]) ).
fof(f588,plain,
( ~ aSubsetOf0(sF42,szNzAzT0)
| spl44_2 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f589,plain,
( ~ spl44_1
| ~ spl44_2 ),
inference(avatar_split_clause,[],[f573,f586,f582]) ).
fof(f591,definition,
( spl44_3
<=> aElementOf0(sK41,sF42) ),
introduced(definition,[new_symbols(definition,[spl44_3])],[avatar_definition]) ).
fof(f593,plain,
( aElementOf0(sK41,sF42)
| ~ spl44_3 ),
inference(avatar_component_clause,[],[f591]) ).
fof(f595,definition,
( spl44_4
<=> aSet0(sF42) ),
introduced(definition,[new_symbols(definition,[spl44_4])],[avatar_definition]) ).
fof(f597,plain,
( ~ aSet0(sF42)
| spl44_4 ),
inference(avatar_component_clause,[],[f595]) ).
fof(f598,plain,
( ~ spl44_1
| spl44_3
| ~ spl44_4 ),
inference(avatar_split_clause,[],[f572,f595,f591,f582]) ).
fof(f600,definition,
( spl44_5
<=> aElementOf0(sK41,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl44_5])],[avatar_definition]) ).
fof(f602,plain,
( ~ aElementOf0(sK41,szNzAzT0)
| spl44_5 ),
inference(avatar_component_clause,[],[f600]) ).
fof(f603,plain,
( ~ spl44_1
| ~ spl44_5
| ~ spl44_4 ),
inference(avatar_split_clause,[],[f571,f595,f600,f582]) ).
fof(f620,plain,
sF42 = sF43(sK40),
inference(superposition,[],[f570,f575]) ).
fof(f621,plain,
! [X0] :
( isCountable0(sF43(szszuzczcdt0(X0)))
| ~ sP9(X0) ),
inference(superposition,[],[f500,f575]) ).
fof(f629,definition,
( spl44_10
<=> ! [X0] :
( ~ aElementOf0(X0,sF42)
| aElementOf0(X0,szNzAzT0) ) ),
introduced(definition,[new_symbols(definition,[spl44_10])],[avatar_definition]) ).
fof(f630,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF42)
| aElementOf0(X0,szNzAzT0) )
| ~ spl44_10 ),
inference(avatar_component_clause,[],[f629]) ).
fof(f647,plain,
xS = sF43(sz00),
inference(superposition,[],[f575,f515]) ).
fof(f659,plain,
! [X0] :
( ~ aSubsetOf0(sF43(X0),szNzAzT0)
| sP9(X0)
| ~ isCountable0(sF43(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[],[f512,f575]) ).
fof(f666,plain,
! [X0] :
( sP9(X0)
| ~ isCountable0(sF43(X0))
| ~ aElementOf0(X0,szNzAzT0)
| ~ iLess0(X0,sK40)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[],[f659,f578]) ).
fof(f668,plain,
! [X0] :
( sP9(X0)
| ~ isCountable0(sF43(X0))
| ~ aElementOf0(X0,szNzAzT0)
| ~ iLess0(X0,sK40) ),
inference(duplicate_literal_removal,[],[f666]) ).
fof(f669,plain,
! [X0] :
( ~ iLess0(X0,sK40)
| ~ aElementOf0(X0,szNzAzT0)
| sP9(X0) ),
inference(forward_subsumption_resolution,[],[f668,f579]) ).
fof(f677,plain,
! [X0,X1] :
( aElementOf0(X0,sdtlpdtrp0(xN,X1))
| ~ sP8(X1)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(X1)))
| ~ sP9(X1) ),
inference(resolution,[],[f509,f502]) ).
fof(f697,plain,
! [X0,X1] :
( aElementOf0(X0,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(X1)))
| ~ sP9(X1) ),
inference(forward_subsumption_resolution,[],[f677,f504]) ).
fof(f698,plain,
! [X0,X1] :
( aElementOf0(X0,sF43(X1))
| ~ aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(X1)))
| ~ sP9(X1) ),
inference(forward_demodulation,[],[f697,f575]) ).
fof(f699,plain,
! [X0,X1] :
( ~ aElementOf0(X0,sF43(szszuzczcdt0(X1)))
| aElementOf0(X0,sF43(X1))
| ~ sP9(X1) ),
inference(forward_demodulation,[],[f698,f575]) ).
fof(f708,plain,
( sK40 = szszuzczcdt0(sK14(sK40))
| sz00 = sK40 ),
inference(resolution,[],[f351,f518]) ).
fof(f710,definition,
( spl44_19
<=> sz00 = sK40 ),
introduced(definition,[new_symbols(definition,[spl44_19])],[avatar_definition]) ).
fof(f711,plain,
( sz00 != sK40
| spl44_19 ),
inference(avatar_component_clause,[],[f710]) ).
fof(f712,plain,
( sz00 = sK40
| ~ spl44_19 ),
inference(avatar_component_clause,[],[f710]) ).
fof(f714,definition,
( spl44_20
<=> sK40 = szszuzczcdt0(sK14(sK40)) ),
introduced(definition,[new_symbols(definition,[spl44_20])],[avatar_definition]) ).
fof(f716,plain,
( sK40 = szszuzczcdt0(sK14(sK40))
| ~ spl44_20 ),
inference(avatar_component_clause,[],[f714]) ).
fof(f717,plain,
( spl44_19
| spl44_20 ),
inference(avatar_split_clause,[],[f708,f714,f710]) ).
fof(f732,plain,
( sF42 = sF43(sz00)
| ~ spl44_19 ),
inference(superposition,[],[f620,f712]) ).
fof(f738,plain,
( xS = sF42
| ~ spl44_19 ),
inference(forward_demodulation,[],[f732,f647]) ).
fof(f743,plain,
( ~ isCountable0(xS)
| spl44_1
| ~ spl44_19 ),
inference(superposition,[],[f584,f738]) ).
fof(f744,plain,
( $false
| spl44_1
| ~ spl44_19 ),
inference(forward_subsumption_resolution,[],[f743,f446]) ).
fof(f745,plain,
( spl44_1
| ~ spl44_19 ),
inference(avatar_contradiction_clause,[],[f744]) ).
fof(f747,plain,
( ~ aSubsetOf0(xS,szNzAzT0)
| spl44_2
| ~ spl44_19 ),
inference(forward_demodulation,[],[f588,f738]) ).
fof(f751,plain,
( $false
| spl44_2
| ~ spl44_19 ),
inference(forward_subsumption_resolution,[],[f747,f447]) ).
fof(f752,plain,
( spl44_2
| ~ spl44_19 ),
inference(avatar_contradiction_clause,[],[f751]) ).
fof(f761,plain,
( isCountable0(sF43(sK40))
| ~ sP9(sK14(sK40))
| ~ spl44_20 ),
inference(superposition,[],[f621,f716]) ).
fof(f762,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF43(sK40))
| aElementOf0(X0,sF43(sK14(sK40)))
| ~ sP9(sK14(sK40)) )
| ~ spl44_20 ),
inference(superposition,[],[f699,f716]) ).
fof(f763,plain,
( aSet0(sdtlpdtrp0(xN,sK40))
| ~ sP9(sK14(sK40))
| ~ spl44_20 ),
inference(superposition,[],[f503,f716]) ).
fof(f765,plain,
( iLess0(sK14(sK40),sK40)
| ~ aElementOf0(sK14(sK40),szNzAzT0)
| ~ spl44_20 ),
inference(superposition,[],[f363,f716]) ).
fof(f767,definition,
( spl44_23
<=> aElementOf0(sK14(sK40),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl44_23])],[avatar_definition]) ).
fof(f768,plain,
( aElementOf0(sK14(sK40),szNzAzT0)
| ~ spl44_23 ),
inference(avatar_component_clause,[],[f767]) ).
fof(f769,plain,
( ~ aElementOf0(sK14(sK40),szNzAzT0)
| spl44_23 ),
inference(avatar_component_clause,[],[f767]) ).
fof(f771,definition,
( spl44_24
<=> iLess0(sK14(sK40),sK40) ),
introduced(definition,[new_symbols(definition,[spl44_24])],[avatar_definition]) ).
fof(f773,plain,
( iLess0(sK14(sK40),sK40)
| ~ spl44_24 ),
inference(avatar_component_clause,[],[f771]) ).
fof(f774,plain,
( ~ spl44_23
| spl44_24
| ~ spl44_20 ),
inference(avatar_split_clause,[],[f765,f714,f771,f767]) ).
fof(f776,plain,
( aSet0(sF42)
| ~ sP9(sK14(sK40))
| ~ spl44_20 ),
inference(forward_demodulation,[],[f763,f570]) ).
fof(f777,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF42)
| aElementOf0(X0,sF43(sK14(sK40)))
| ~ sP9(sK14(sK40)) )
| ~ spl44_20 ),
inference(forward_demodulation,[],[f762,f620]) ).
fof(f778,plain,
( isCountable0(sF42)
| ~ sP9(sK14(sK40))
| ~ spl44_20 ),
inference(forward_demodulation,[],[f761,f620]) ).
fof(f779,plain,
( ~ sP9(sK14(sK40))
| spl44_4
| ~ spl44_20 ),
inference(forward_subsumption_resolution,[],[f776,f597]) ).
fof(f781,definition,
( spl44_25
<=> sP9(sK14(sK40)) ),
introduced(definition,[new_symbols(definition,[spl44_25])],[avatar_definition]) ).
fof(f782,plain,
( sP9(sK14(sK40))
| ~ spl44_25 ),
inference(avatar_component_clause,[],[f781]) ).
fof(f783,plain,
( ~ sP9(sK14(sK40))
| spl44_25 ),
inference(avatar_component_clause,[],[f781]) ).
fof(f785,definition,
( spl44_26
<=> ! [X0] :
( ~ aElementOf0(X0,sF42)
| aElementOf0(X0,sF43(sK14(sK40))) ) ),
introduced(definition,[new_symbols(definition,[spl44_26])],[avatar_definition]) ).
fof(f786,plain,
( ! [X0] :
( aElementOf0(X0,sF43(sK14(sK40)))
| ~ aElementOf0(X0,sF42) )
| ~ spl44_26 ),
inference(avatar_component_clause,[],[f785]) ).
fof(f787,plain,
( ~ spl44_25
| spl44_26
| ~ spl44_20 ),
inference(avatar_split_clause,[],[f777,f714,f785,f781]) ).
fof(f788,plain,
( ~ spl44_25
| spl44_4
| ~ spl44_20 ),
inference(avatar_split_clause,[],[f779,f714,f595,f781]) ).
fof(f789,plain,
( sz00 = sK40
| ~ aElementOf0(sK40,szNzAzT0)
| spl44_23 ),
inference(resolution,[],[f769,f352]) ).
fof(f790,plain,
( ~ aElementOf0(sK40,szNzAzT0)
| spl44_19
| spl44_23 ),
inference(forward_subsumption_resolution,[],[f789,f711]) ).
fof(f791,plain,
( $false
| spl44_19
| spl44_23 ),
inference(forward_subsumption_resolution,[],[f790,f518]) ).
fof(f792,plain,
( spl44_19
| spl44_23 ),
inference(avatar_contradiction_clause,[],[f791]) ).
fof(f793,plain,
( ~ aElementOf0(sK14(sK40),szNzAzT0)
| sP9(sK14(sK40))
| ~ spl44_24 ),
inference(resolution,[],[f773,f669]) ).
fof(f798,plain,
( sP9(sK14(sK40))
| ~ spl44_23
| ~ spl44_24 ),
inference(forward_subsumption_resolution,[],[f793,f768]) ).
fof(f799,plain,
( $false
| ~ spl44_23
| ~ spl44_24
| spl44_25 ),
inference(forward_subsumption_resolution,[],[f798,f783]) ).
fof(f800,plain,
( ~ spl44_23
| ~ spl44_24
| spl44_25 ),
inference(avatar_contradiction_clause,[],[f799]) ).
fof(f801,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF42)
| aElementOf0(X0,szNzAzT0)
| ~ iLess0(sK14(sK40),sK40)
| ~ aElementOf0(sK14(sK40),szNzAzT0) )
| ~ spl44_26 ),
inference(resolution,[],[f786,f577]) ).
fof(f802,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF42)
| aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sK14(sK40),szNzAzT0) )
| ~ spl44_24
| ~ spl44_26 ),
inference(forward_subsumption_resolution,[],[f801,f773]) ).
fof(f803,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF42)
| aElementOf0(X0,szNzAzT0) )
| ~ spl44_23
| ~ spl44_24
| ~ spl44_26 ),
inference(forward_subsumption_resolution,[],[f802,f768]) ).
fof(f804,plain,
( spl44_10
| ~ spl44_23
| ~ spl44_24
| ~ spl44_26 ),
inference(avatar_split_clause,[],[f803,f785,f771,f767,f629]) ).
fof(f805,plain,
( aElementOf0(sK41,szNzAzT0)
| ~ spl44_3
| ~ spl44_10 ),
inference(resolution,[],[f630,f593]) ).
fof(f806,plain,
( $false
| ~ spl44_3
| spl44_5
| ~ spl44_10 ),
inference(forward_subsumption_resolution,[],[f805,f602]) ).
fof(f807,plain,
( ~ spl44_3
| spl44_5
| ~ spl44_10 ),
inference(avatar_contradiction_clause,[],[f806]) ).
fof(f809,plain,
( ~ sP9(sK14(sK40))
| spl44_1
| ~ spl44_20 ),
inference(forward_subsumption_resolution,[],[f778,f584]) ).
fof(f812,plain,
( $false
| spl44_1
| ~ spl44_20
| ~ spl44_25 ),
inference(forward_subsumption_resolution,[],[f809,f782]) ).
fof(f813,plain,
( spl44_1
| ~ spl44_20
| ~ spl44_25 ),
inference(avatar_contradiction_clause,[],[f812]) ).
cnf(s1,plain,
( ~ spl44_1
| ~ spl44_2 ),
inference(sat_conversion,[],[f589]) ).
cnf(s2,plain,
( ~ spl44_1
| spl44_3
| ~ spl44_4 ),
inference(sat_conversion,[],[f598]) ).
cnf(s3,plain,
( ~ spl44_1
| ~ spl44_4
| ~ spl44_5 ),
inference(sat_conversion,[],[f603]) ).
cnf(s13,plain,
( spl44_19
| spl44_20 ),
inference(sat_conversion,[],[f717]) ).
cnf(s16,plain,
( spl44_1
| ~ spl44_19 ),
inference(sat_conversion,[],[f745]) ).
cnf(s17,plain,
( spl44_2
| ~ spl44_19 ),
inference(sat_conversion,[],[f752]) ).
cnf(s19,plain,
( ~ spl44_20
| ~ spl44_23
| spl44_24 ),
inference(sat_conversion,[],[f774]) ).
cnf(s20,plain,
( ~ spl44_20
| ~ spl44_25
| spl44_26 ),
inference(sat_conversion,[],[f787]) ).
cnf(s21,plain,
( spl44_4
| ~ spl44_20
| ~ spl44_25 ),
inference(sat_conversion,[],[f788]) ).
cnf(s22,plain,
( spl44_19
| spl44_23 ),
inference(sat_conversion,[],[f792]) ).
cnf(s23,plain,
( ~ spl44_23
| ~ spl44_24
| spl44_25 ),
inference(sat_conversion,[],[f800]) ).
cnf(s24,plain,
( spl44_10
| ~ spl44_23
| ~ spl44_24
| ~ spl44_26 ),
inference(sat_conversion,[],[f804]) ).
cnf(s25,plain,
( ~ spl44_3
| spl44_5
| ~ spl44_10 ),
inference(sat_conversion,[],[f807]) ).
cnf(s27,plain,
( spl44_1
| ~ spl44_20
| ~ spl44_25 ),
inference(sat_conversion,[],[f813]) ).
cnf(s31,plain,
spl44_1,
inference(rat,[],[s23,s19,s27,s13,s22,s16]) ).
cnf(s32,plain,
~ spl44_2,
inference(rat,[],[s1,s31]) ).
cnf(s33,plain,
~ spl44_19,
inference(rat,[],[s17,s32]) ).
cnf(s34,plain,
spl44_23,
inference(rat,[],[s22,s33]) ).
cnf(s35,plain,
spl44_20,
inference(rat,[],[s13,s33]) ).
cnf(s36,plain,
spl44_24,
inference(rat,[],[s19,s34,s35]) ).
cnf(s37,plain,
spl44_25,
inference(rat,[],[s23,s34,s36]) ).
cnf(s38,plain,
spl44_26,
inference(rat,[],[s20,s35,s37]) ).
cnf(s39,plain,
spl44_4,
inference(rat,[],[s21,s35,s37]) ).
cnf(s40,plain,
spl44_10,
inference(rat,[],[s24,s36,s34,s38]) ).
cnf(s41,plain,
~ spl44_5,
inference(rat,[],[s3,s31,s39]) ).
cnf(s42,plain,
spl44_3,
inference(rat,[],[s2,s31,s39]) ).
cnf(s43,plain,
$false,
inference(rat,[],[s25,s40,s41,s42]) ).
fof(f814,plain,
$false,
inference(avatar_sat_refutation,[],[s43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM569+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/5.59 % Computer : n018.cluster.edu
% 0.11/5.59 % Model : x86_64 x86_64
% 0.11/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.59 % Memory : 8046.5625MB
% 0.11/5.59 % OS : Linux 6.8.0-71-generic
% 0.11/5.59 % CPULimit : 300
% 0.11/5.59 % WCLimit : 300
% 0.11/5.59 % DateTime : Sun Sep 27 20:35:16 UTC 2026
% 0.11/5.59 % CPUTime :
% 0.11/5.59 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/5.63 Running first-order theorem proving
% 0.14/5.63 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
% 7.13/7.22 % (2701679)Detected formulas, will run a generic FOF schedule.
% 7.13/7.22 % (2701688)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=908567200:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 7.13/7.22 % (2701687)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3272645282:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 7.13/7.22 % (2701686)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=241243739:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 7.13/7.22 % (2701684)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=2578133259:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 7.13/7.22 % (2701685)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=1175705534:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 7.13/7.22 % (2701688)Instruction limit reached!
% 7.13/7.22 % (2701688)------------------------------
% 7.13/7.22 % (2701688)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.13/7.22 % (2701688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.13/7.22 % (2701688)CaDiCaL version: 2.1.3
% 7.13/7.22 % (2701688)Termination reason: Instruction limit
% 7.13/7.22 % (2701688)Termination phase: Saturation
% 7.13/7.22 % (2701688)Time elapsed: 0.042 s
% 7.13/7.22 % (2701688)Peak memory usage: 89 MB
% 7.13/7.22 % (2701688)Instructions burned: 121 (million)
% 7.13/7.22 % (2701689)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2375078780:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 7.13/7.22 % (2701690)dis-21_1_sil=8000:lcm=predicate:random_seed=3244546792: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)
% 7.13/7.22 % (2701687)Instruction limit reached!
% 7.13/7.22 % (2701687)------------------------------
% 7.13/7.22 % (2701687)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.13/7.22 % (2701687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.13/7.22 % (2701687)CaDiCaL version: 2.1.3
% 7.13/7.22 % (2701687)Termination reason: Instruction limit
% 7.13/7.22 % (2701687)Termination phase: Saturation
% 7.13/7.22 % (2701687)Time elapsed: 0.072 s
% 7.13/7.22 % (2701687)Peak memory usage: 89 MB
% 7.13/7.22 % (2701687)Instructions burned: 110 (million)
% 7.13/7.22 % (2701697)lrs+10_1_sil=8000:sp=occurrence:random_seed=4040906911:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 7.13/7.22 % (2701690)Instruction limit reached!
% 7.13/7.22 % (2701690)------------------------------
% 7.13/7.22 % (2701690)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.13/7.22 % (2701690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.13/7.22 % (2701690)CaDiCaL version: 2.1.3
% 7.13/7.22 % (2701690)Termination reason: Instruction limit
% 7.13/7.22 % (2701690)Termination phase: Saturation
% 7.13/7.22 % (2701690)Time elapsed: 0.080 s
% 7.13/7.22 % (2701690)Peak memory usage: 90 MB
% 7.13/7.22 % (2701690)Instructions burned: 133 (million)
% 7.13/7.22 % (2701689)Instruction limit reached!
% 7.13/7.22 % (2701689)------------------------------
% 7.13/7.22 % (2701689)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.13/7.22 % (2701689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.13/7.22 % (2701689)CaDiCaL version: 2.1.3
% 7.13/7.22 % (2701689)Termination reason: Instruction limit
% 7.13/7.22 % (2701689)Termination phase: Saturation
% 7.13/7.22 % (2701689)Time elapsed: 0.107 s
% 7.13/7.22 % (2701689)Peak memory usage: 90 MB
% 7.13/7.22 % (2701689)Instructions burned: 139 (million)
% 7.13/7.22 % (2701697)Instruction limit reached!
% 7.13/7.22 % (2701697)------------------------------
% 7.13/7.22 % (2701697)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.13/7.22 % (2701697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.13/7.22 % (2701697)CaDiCaL version: 2.1.3
% 7.13/7.22 % (2701697)Termination reason: Instruction limit
% 7.13/7.22 % (2701697)Termination phase: Saturation
% 7.13/7.22 % (2701697)Time elapsed: 0.101 s
% 7.13/7.22 % (2701697)Peak memory usage: 92 MB
% 7.13/7.22 % (2701697)Instructions burned: 288 (million)
% 7.13/7.22 % (2701699)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3499952984:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 7.13/7.22 % (2701699)Refutation not found, incomplete strategy
% 7.13/7.22 % (2701699)------------------------------
% 7.13/7.22 % (2701699)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.13/7.22 % (2701699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.13/7.22 % (2701699)CaDiCaL version: 2.1.3
% 7.13/7.22 % (2701699)Termination reason: Refutation not found, incomplete strategy
% 7.13/7.22 % (2701699)Time elapsed: 0.007 s
% 7.13/7.22 % (2701699)Peak memory usage: 89 MB
% 7.13/7.22 % (2701699)Instructions burned: 9 (million)
% 7.13/7.22 % (2701701)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2592717372:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 7.13/7.22 % (2701702)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=1160248453:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 7.13/7.22 % (2701703)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1749124795:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 7.13/7.22 % (2701702)Instruction limit reached!
% 7.13/7.22 % (2701702)------------------------------
% 7.13/7.22 % (2701702)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.13/7.22 % (2701702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.13/7.22 % (2701702)CaDiCaL version: 2.1.3
% 7.13/7.22 % (2701702)Termination reason: Instruction limit
% 7.13/7.22 % (2701702)Termination phase: Saturation
% 7.13/7.22 % (2701702)Time elapsed: 0.148 s
% 7.13/7.22 % (2701702)Peak memory usage: 92 MB
% 7.13/7.22 % (2701702)Instructions burned: 249 (million)
% 7.13/7.22 % (2701703)Instruction limit reached!
% 7.13/7.22 % (2701703)------------------------------
% 7.13/7.22 % (2701703)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.13/7.22 % (2701703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.13/7.22 % (2701703)CaDiCaL version: 2.1.3
% 7.13/7.22 % (2701703)Termination reason: Instruction limit
% 7.13/7.22 % (2701703)Termination phase: Saturation
% 7.13/7.22 % (2701703)Time elapsed: 0.099 s
% 7.13/7.22 % (2701703)Peak memory usage: 90 MB
% 7.13/7.22 % (2701703)Instructions burned: 297 (million)
% 7.13/7.22 % (2701699)------------------------------
% 7.13/7.22 % (2701699)------------------------------
% 7.13/7.22 % (2701701)Instruction limit reached!
% 7.13/7.22 % (2701701)------------------------------
% 7.13/7.22 % (2701701)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.13/7.22 % (2701701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.13/7.22 % (2701701)CaDiCaL version: 2.1.3
% 7.13/7.22 % (2701701)Termination reason: Instruction limit
% 7.13/7.22 % (2701701)Termination phase: Saturation
% 7.13/7.22 % (2701701)Time elapsed: 0.231 s
% 7.13/7.22 % (2701701)Peak memory usage: 92 MB
% 7.13/7.22 % (2701701)Instructions burned: 326 (million)
% 7.13/7.22 % (2701709)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2836217165:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 7.13/7.22 % (2701708)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1345462539:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 7.13/7.22 % (2701709)Instruction limit reached!
% 7.13/7.22 % (2701709)------------------------------
% 7.13/7.22 % (2701709)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.13/7.22 % (2701709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.13/7.22 % (2701709)CaDiCaL version: 2.1.3
% 7.13/7.22 % (2701709)Termination reason: Instruction limit
% 7.13/7.22 % (2701709)Termination phase: Saturation
% 7.13/7.22 % (2701709)Time elapsed: 0.042 s
% 7.13/7.22 % (2701709)Peak memory usage: 91 MB
% 7.13/7.22 % (2701709)Instructions burned: 115 (million)
% 7.13/7.22 % (2701710)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1578117891:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 7.13/7.22 % (2701711)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2595294265:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 7.13/7.22 % (2701710)Instruction limit reached!
% 7.13/7.22 % (2701710)------------------------------
% 7.13/7.22 % (2701710)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.13/7.22 % (2701710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.13/7.22 % (2701710)CaDiCaL version: 2.1.3
% 7.13/7.22 % (2701710)Termination reason: Instruction limit
% 7.13/7.22 % (2701710)Termination phase: Saturation
% 7.13/7.22 % (2701710)Time elapsed: 0.071 s
% 7.13/7.22 % (2701710)Peak memory usage: 89 MB
% 7.13/7.22 % (2701710)Instructions burned: 129 (million)
% 7.13/7.22 % (2701714)lrs+10_1_sil=8000:sp=occurrence:random_seed=3699858641:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 7.13/7.22 % (2701684)First to succeed.
% 7.13/7.22 % (2701684)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2701679"
% 7.13/7.22 % (2701711)Instruction limit reached!
% 7.13/7.22 % (2701711)------------------------------
% 7.13/7.22 % (2701711)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.13/7.22 % (2701711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.13/7.22 % (2701711)CaDiCaL version: 2.1.3
% 7.13/7.22 % (2701711)Termination reason: Instruction limit
% 7.13/7.22 % (2701711)Termination phase: Property scanning
% 7.13/7.22 % (2701711)Time elapsed: 0.043 s
% 7.13/7.22 % (2701711)Peak memory usage: 86 MB
% 7.13/7.22 % (2701711)Instructions burned: 116 (million)
% 7.13/7.22 % (2701685)Also succeeded, but the first one will report.
% 7.13/7.22 % (2701717)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=35040091:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 7.13/7.22 % (2701719)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1558378878:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 7.13/7.22 % (2701714)Instruction limit reached!
% 7.13/7.22 % (2701714)------------------------------
% 7.13/7.22 % (2701714)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.13/7.22 % (2701714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.13/7.22 % (2701714)CaDiCaL version: 2.1.3
% 7.13/7.22 % (2701714)Termination reason: Instruction limit
% 7.13/7.22 % (2701714)Termination phase: Saturation
% 7.13/7.22 % (2701714)Time elapsed: 0.305 s
% 7.13/7.22 % (2701714)Peak memory usage: 98 MB
% 7.13/7.22 % (2701714)Instructions burned: 908 (million)
% 7.13/7.22 % (2701684)Refutation found. Thanks to Tanya!
% 7.13/7.22 % SZS status Theorem for theBenchmark
% 7.13/7.22 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/7.41 % (2701684)------------------------------
% 0.15/7.41 % (2701684)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/7.41 % (2701684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/7.41 % (2701684)CaDiCaL version: 2.1.3
% 0.15/7.41 % (2701684)Termination reason: Refutation
% 0.15/7.41 % (2701684)Time elapsed: 0.680 s
% 0.15/7.41 % (2701684)Peak memory usage: 130 MB
% 0.15/7.41 % (2701684)Instructions burned: 1012 (million)
% 0.15/7.41 % (2701684)------------------------------
% 0.15/7.41 % (2701684)------------------------------
% 0.15/7.41 % (2701679)Success in time 1.151 s
% 0.15/7.41 % Vampire exiting
%------------------------------------------------------------------------------