%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM629+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 12:16:03 PM UTC 2026
% Result : Theorem 0.17s 16.80s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 10 unt; 2 def)
% Number of atoms : 317 ( 32 equ)
% Maximal formula atoms : 22 ( 6 avg)
% Number of connectives : 373 ( 107 ~; 89 |; 148 &)
% ( 10 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 12 con; 0-2 aty)
% Number of variables : 86 ( 79 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
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/sandbox/benchmark/theBenchmark.p',m__3623) ).
fof(f82,axiom,
! [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)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
fof(f111,axiom,
( aElementOf0(xn,szDzozmdt0(xd))
& sdtlpdtrp0(xd,xn) = szDzizrdt0(xd)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0)
& sdtlpdtrp0(xe,xn) = xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5309) ).
fof(f113,axiom,
( ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
& aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5334) ).
fof(f114,axiom,
( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0) )
& aSet0(xD)
& ! [X0] :
( aElementOf0(X0,xD)
<=> ( aElement0(X0)
& aElementOf0(X0,sdtlpdtrp0(xN,xn))
& X0 != szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
& xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5585) ).
fof(f115,conjecture,
( ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xD) )
| aSubsetOf0(xP,xD)
| aElementOf0(xP,slbdtsldtrb0(xD,xk)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f116,negated_conjecture,
~ ( ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xD) )
| aSubsetOf0(xP,xD)
| aElementOf0(xP,slbdtsldtrb0(xD,xk)) ),
inference(negated_conjecture,[status(cth)],[f115]) ).
fof(f119,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(f132,plain,
( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0) )
& aSet0(xD)
& ! [X1] :
( aElementOf0(X1,xD)
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xn))
& szmzizndt0(sdtlpdtrp0(xN,xn)) != X1 ) )
& xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))) ),
inference(rectify,[],[f114]) ).
fof(f145,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,[],[f119]) ).
fof(f146,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,[],[f145]) ).
fof(f147,plain,
! [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,[],[f82]) ).
fof(f178,plain,
( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(X0,xP) )
& aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(ennf_transformation,[],[f113]) ).
fof(f179,plain,
( ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xn)) )
& aSet0(xD)
& ! [X1] :
( aElementOf0(X1,xD)
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xn))
& szmzizndt0(sdtlpdtrp0(xN,xn)) != X1 ) )
& xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))) ),
inference(ennf_transformation,[],[f132]) ).
fof(f180,plain,
( ? [X0] :
( ~ aElementOf0(X0,xD)
& aElementOf0(X0,xP) )
& ~ aSubsetOf0(xP,xD)
& ~ aElementOf0(xP,slbdtsldtrb0(xD,xk)) ),
inference(ennf_transformation,[],[f116]) ).
fof(f195,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f273,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 ) )
| ~ sP4(X0) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f274,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))))
& sP4(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))) )
| ~ sP5(X0) ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f275,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( sP5(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,[],[f146,f274,f273]) ).
fof(f317,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))))
& sP4(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))) )
| ~ sP5(X0) ),
inference(nnf_transformation,[],[f274]) ).
fof(f318,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))))
& sP4(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))) )
| ~ sP5(X0) ),
inference(rectify,[],[f317]) ).
fof(f322,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( sP5(X0)
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ( ~ aElementOf0(sK35(X0),szNzAzT0)
& aElementOf0(sK35(X0),sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(X1,sK35(X0))],[f275]) ).
fof(f393,plain,
( ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xn)) )
& aSet0(xD)
& ! [X1] :
( ( aElementOf0(X1,xD)
| ~ aElement0(X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xn))
| szmzizndt0(sdtlpdtrp0(xN,xn)) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xn))
& szmzizndt0(sdtlpdtrp0(xN,xn)) != X1 )
| ~ aElementOf0(X1,xD) ) )
& xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))) ),
inference(nnf_transformation,[],[f179]) ).
fof(f394,plain,
( ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xn)) )
& aSet0(xD)
& ! [X1] :
( ( aElementOf0(X1,xD)
| ~ aElement0(X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xn))
| szmzizndt0(sdtlpdtrp0(xN,xn)) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xn))
& szmzizndt0(sdtlpdtrp0(xN,xn)) != X1 )
| ~ aElementOf0(X1,xD) ) )
& xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))) ),
inference(flattening,[],[f393]) ).
fof(f395,plain,
( ~ aElementOf0(sK54,xD)
& aElementOf0(sK54,xP)
& ~ aSubsetOf0(xP,xD)
& ~ aElementOf0(xP,slbdtsldtrb0(xD,xk)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(X0,sK54)],[f180]) ).
fof(f398,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,[],[f195]) ).
fof(f399,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,[],[f398]) ).
fof(f400,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,[],[f399]) ).
fof(f401,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK56(X0,X1),X0)
& aElementOf0(sK56(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(X2,sK56(X0,X1))],[f400]) ).
fof(f497,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f508,plain,
! [X0] :
( sP5(X0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f322]) ).
fof(f514,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f515,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f723,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f111]) ).
fof(f729,plain,
! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[],[f178]) ).
fof(f730,plain,
xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),
inference(cnf_transformation,[],[f394]) ).
fof(f735,plain,
aSet0(xD),
inference(cnf_transformation,[],[f394]) ).
fof(f739,plain,
aElementOf0(sK54,xP),
inference(cnf_transformation,[],[f395]) ).
fof(f740,plain,
~ aElementOf0(sK54,xD),
inference(cnf_transformation,[],[f395]) ).
fof(f753,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f401]) ).
fof(f1653,plain,
! [X0] :
( ~ aElementOf0(sK54,X0)
| ~ aSubsetOf0(X0,xD)
| ~ aSet0(xD) ),
inference(resolution,[],[f753,f740]) ).
fof(f1655,plain,
! [X0] :
( ~ aSubsetOf0(X0,xD)
| ~ aElementOf0(sK54,X0) ),
inference(forward_subsumption_resolution,[],[f1653,f735]) ).
fof(f2243,plain,
! [X0] :
( sP5(X0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f508,f515]) ).
fof(f2244,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sP5(X0) ),
inference(forward_subsumption_resolution,[],[f2243,f514]) ).
fof(f2256,plain,
sP5(xn),
inference(resolution,[],[f2244,f723]) ).
fof(f2771,plain,
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xD)
| ~ sP5(xn) ),
inference(superposition,[],[f497,f730]) ).
fof(f2773,plain,
aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xD),
inference(forward_subsumption_resolution,[],[f2771,f2256]) ).
fof(f2781,plain,
~ aElementOf0(sK54,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(resolution,[],[f2773,f1655]) ).
fof(f2787,plain,
~ aElementOf0(sK54,xP),
inference(resolution,[],[f2781,f729]) ).
fof(f2789,plain,
$false,
inference(forward_subsumption_resolution,[],[f2787,f739]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM629+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/16.01 % Computer : n004.cluster.edu
% 0.13/16.01 % Model : x86_64 x86_64
% 0.13/16.01 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/16.01 % Memory : 8046.5625MB
% 0.13/16.01 % OS : Linux 6.8.0-71-generic
% 0.13/16.01 % CPULimit : 300
% 0.13/16.01 % WCLimit : 300
% 0.13/16.01 % DateTime : Sun Sep 27 20:50:53 UTC 2026
% 0.13/16.02 % CPUTime :
% 0.13/16.02 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/16.05 Running first-order theorem proving
% 0.17/16.05 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/16.80 % (3866363)Detected formulas, will run a generic FOF schedule.
% 0.17/16.80 % (3866440)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=219740282:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.17/16.80 % (3866440)First to succeed.
% 0.17/16.80 % (3866440)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3866363"
% 0.17/16.80 % (3866436)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=2368894829:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.17/16.80 % (3866438)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=2597797376:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.17/16.80 % (3866437)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=4186671871:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.17/16.80 % (3866439)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2752032506:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.17/16.80 % (3866441)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3443289799:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.17/16.80 % (3866442)dis-21_1_sil=8000:lcm=predicate:random_seed=2636162785: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)
% 0.17/16.80 % (3866439)Instruction limit reached!
% 0.17/16.80 % (3866439)------------------------------
% 0.17/16.80 % (3866439)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/16.80 % (3866439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/16.80 % (3866439)CaDiCaL version: 2.1.3
% 0.17/16.80 % (3866439)Termination reason: Instruction limit
% 0.17/16.80 % (3866439)Termination phase: Saturation
% 0.17/16.80 % (3866439)Time elapsed: 0.064 s
% 0.17/16.80 % (3866439)Peak memory usage: 90 MB
% 0.17/16.80 % (3866439)Instructions burned: 110 (million)
% 0.17/16.80 % (3866442)Instruction limit reached!
% 0.17/16.80 % (3866442)------------------------------
% 0.17/16.80 % (3866442)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/16.80 % (3866442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/16.80 % (3866442)CaDiCaL version: 2.1.3
% 0.17/16.80 % (3866442)Termination reason: Instruction limit
% 0.17/16.80 % (3866442)Termination phase: Saturation
% 0.17/16.80 % (3866442)Time elapsed: 0.067 s
% 0.17/16.80 % (3866442)Peak memory usage: 90 MB
% 0.17/16.80 % (3866442)Instructions burned: 130 (million)
% 0.17/16.80 % (3866441)Instruction limit reached!
% 0.17/16.80 % (3866441)------------------------------
% 0.17/16.80 % (3866441)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/16.80 % (3866441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/16.80 % (3866441)CaDiCaL version: 2.1.3
% 0.17/16.80 % (3866441)Termination reason: Instruction limit
% 0.17/16.80 % (3866441)Termination phase: Saturation
% 0.17/16.80 % (3866441)Time elapsed: 0.094 s
% 0.17/16.80 % (3866441)Peak memory usage: 90 MB
% 0.17/16.80 % (3866441)Instructions burned: 140 (million)
% 0.17/16.80 % (3866440)Refutation found. Thanks to Tanya!
% 0.17/16.80 % SZS status Theorem for theBenchmark
% 0.17/16.80 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/17.00 % (3866440)------------------------------
% 0.17/17.00 % (3866440)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/17.00 % (3866440)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/17.00 % (3866440)CaDiCaL version: 2.1.3
% 0.17/17.00 % (3866440)Termination reason: Refutation
% 0.17/17.00 % (3866440)Time elapsed: 0.031 s
% 0.17/17.00 % (3866440)Peak memory usage: 90 MB
% 0.17/17.00 % (3866440)Instructions burned: 87 (million)
% 0.17/17.00 % (3866440)------------------------------
% 0.17/17.00 % (3866440)------------------------------
% 0.17/17.00 % (3866363)Success in time 0.304 s
% 0.17/17.00 % Vampire exiting
%------------------------------------------------------------------------------